APPENDIX
APPENDIX WORK IN PROGRESS A complementary fatigue test with "frame half" specimens B3 and B4, indicated in figure 2, is in progress as this paper is being prepared. These specimens also have forgings of 7079 (overaged). They are, relative to B1 and B2, constructed with better stabilization of the frame parts by two ordinary bulkheads, with reinforcement of the inner skin, and smaller openings for the linkage system. They are also polished in critical forging areas.
The test load spectrum has been slightly changed according to new conditions. Fur- ther, critical stresses are lowered 5 to 10 percent by a more favorable stress distribu- tion in the modified specimen and 12 percent by a decrease of the jack load over the entire spectrum. Consequently, the total lowering is =20 percent. All these changes have been made in order to get a better load distribution with more correct stress levels for the proper simulation of aircraft structural fatigue conditions.
ACKNOWLEDGMENTS The author is indebted to Saab-Scania Aktiebolag for permission to prepare and publish this paper. Many persons involved in the reported investigations have kindly assisted with basic data for this paper. Invaluable assistance with the preparation of the manuscript has been given by Mr. E. Persson, senior stress engineer, fatigue branch, Saab-Scania.
REFERENCES 1. Larsson, S. E.: The Development of a Calculation Method for the Fatigue Strength of Lugs and a Study of Test Results for Lugs of Aluminium. Fatigue Design Proce- dures, E. Gassner and W. Schutz, eds., Pergamon Press, Inc., c.1969, pp. 309-342.
2. Forsyth, P. J. E.: The Physical Basis of Metal Fatigue. Blackie & Son, Ltd. (London), 1969.
3. Schijve, J.; and De Rijk, P.: The Crack Propagation in Two Aluminium Alloys in an Indoor and an Outdoor Environment Under Random and Programmed Load Sequences.
NLR-TR M.2156, Nat. Lucht- Ruimtevaartlab. (Amsterdam), Nov. 1965.
--- ---------- --- - - - - - TABLE 1.- SUMMARY OF TEST RESULTS FROM SPECIMENS A (THE WING BEAM) (a) Strain-gage results Stress at limit load, 2, u, MN/m for specimen - Strain-gage no. Strain-gage location (shown in fig. 10) Al A2 A3 341 308 300 01 Beam at notch, 7 mm from edge, outer side 298 298 292 02 Beam at hole 1, 6 mm from step, mean value 269 286 271 03 Flange between holes 1 and 2, outer side (b) History of cracks Equivalent flying hours for specimen - Figure no. Crack no.
Comments Al A2 A3 9 11 (3400) Geometry and surface finish not representative. Cracks occurred at flange (principal notch radius r = 10 mm). Cracks were removed and shape of specimen was modified.
10 and 11 21 8400 Modified shape and pOlishing. l::::: 1 mm.
Small crack found, 15 200 Crack increased to l = t = 12 mm, o = 6.0 to 11.5 mm.
12 and 13 31 l::::: 5 mm.
7 700 Modified shape and polishing. Small crack found, 10 500 Several cracks joined in one, l = t = 12 mm, 0=3 to 4 mm.
11 600 Crack propagated to ~ 50 , l = t , o = 14 to 16 mm.
9 ~1 000 Crack in flange in edge of bolt hole 1, 0=2 mm max., fretting.
10 22 15 200 Two cracks ±45° in flange at bolt hole 1, l ::::: 2 mm ::::: 0.5t.
12 and 13 32 10 500 Crack out from flange at bolt hole 1, ::::: 10 mm visible.
11 100 Propagated ::::::3.5 mm, then nonpropagating.
10 and 11 23 15 200 Crack through in flange at bolt hole 2; crack through ::::: O. 5t in t flange at bolt hole 9.
--------- --- 24 100 15 200 11 700 Testing ended. No failure or secondary-type failure.
TABLE II.- SUMMARY OF TEST RESULTS FROM SPECIMEN B (THE FUSELAGE FRAME) (a) Strain-gage results Stress at limit load, (J, MN/ m , Strain-gage Strain-gage location (shown in fig. 17) for specimen - no.
B1 B2 - -- *286 F-01 Sheet} Section through upper wing-joint hole of forward frame 323 299 F-02 Boom *312 R-01 --- Sheet} Section through upper wing-joint hole of rear frame 308 323 R-02 Boom 277 R-03
---
Priricipal stress on rear side "'13 mm from corner with
web~}
radius of 15 mm R-04 255 webG) --- * Mean value over sheet thickness.
(b) History of cracks Equivalent flying hours Figure Crack for specimen - Comments no. no.
Bl B2 visible.
18 S-l1 4300 Inner sheet of frame assembly; cracks from two screws , l = 3 to 5 mm l = 4 to 10 mm, stopped at two.
4800 Cracks at thr ee holes, Inner sheet of frame assembly; cracks from one screw , l = 1 to 3 mm visible.
18 8-21 4300 visible .
4800 Cracks from three screws , l = 2 to 5 mm Forward forging, web 0; corner crack from milling step mark , l '" 30 mm.
14 F-12 5300 Forward forging , web CD; corner crack from milling step mark , l '" 15 mm.
17 F-22 5300 17 F-23 5300 Forward forging , web~); corner c' rack from milling step mark , l '" 10 mm .
Rear forging , web CD; failure due to crack, -l '" 30 mm, in corner.
14 to 16 R- 13 5300 14 R-14 5300 Rear forging , web 0; corner crack from milling step mark, l" 19 mm.
Figur e 1. - Location of wing beam and fuselage frame in the Viggen aircraft.
- -@
I-I Figure 2. - Rear view of wing beam and fuselage frame assembly .
+
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.
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Figure 3.- Test specimen A with forces indicated by arrows.
T d O^ 4.
Limit 10C load 8( 6G —20 Figure 5.- The load spectrum used in testing.
Limit load —20 Flight no.
Figure 6.- Example of load sequences in the randomized flight-by-flight program.
Punched tape Programmer Double-acting Relay plate cylinders Amplifier Summing amplifier + Swashplate- type Amplifier hydraulic - pump EI -hydr.
servo Pressure valve gauge Constant Reli e f hydraulic valve pressure Figure 7.- Diagram of the test equipment system.
Figure 8.- Arrangement of test specimens.
a m N Fatigue cracks Hole no.
Figure 10.- Test specimen Ap with cracks found.
raugue cracks of type no. 23 Figure 11.- Details of the cracked specimen Ap.
Figure 12.- Test specimen A3 with cracks found.
Figure 13.- Details of the cracked specimen A3.
U a c a^ c U a^ L a c Y U A U QJ J m L m c a> E ^u a^ a m v a^ m W Hole Figure 15.- Fractured area of specimen B1.
LracK no. K — I Length l rp=5mm r=15mm
'\^ I
Web
Crack de pth 3
Milling step marks
I -I
Figure 16.- The surface shape in a cracked area of specimen 81.
Q, c OC w C
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+
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LL M O Edge no. 1 1*::1 ..[ = 12 1* = 1 + dl + d2 L- -I"'-'I.Lf- -;::-----.,.
Edge no. 2 Short crack crack Mean curve ~O~ -----r-----.------.-----.------.-- ~~ ,---~,-----~ A3 A2 30 ;-----~-- ---- ~----~ ------4_---- ~~~ --4_--+__4--~~ Edge no. 1 and 2 Total crack length (separate small cracks (visible at 1.0 /0 limit load), in edge no. 1 earlier) 1* 20 ~-----+------+----- -r----~~~--~ ~---+~--~ ~~~
, . d..t*
11-=- dT mm ~l = 2,5 10 - m m/h 10 -t- -----j--------j------_t_-----t-----::l~_+__=.,c:....:.--t___F_--_t_----_; V"2 = 8,0. 10-3 - .. - V: = 20 0 10- -11-
t
no.1 0;---r--+ --~-- +- ~--_r~ ~~~~ -- ~ _.,__+--,_ --~~ --4_-- --~
o 2 6 7 8 10 12 11. 16 x 10
Flying hou rs ,. T, h Fi gure 20 .- Crack pr opagation at fl ange notch in specimens A2 and A3.
Nominal stress at limit load, C^ MN/m2 Figure 21.- Results of a cumulative damage calculation for specimen A material, AZ 74.
Figure 22.- Examples of interacting stress concentrations.
THE BOEING 747 FATIGUE INTEGRITY PROGRAM By Max M. Spencer The Boeing Company Everett, Washington, U.S.A.
Cq INTRODUCTION The Boeing 747 is designed and certified as a fail-safe airplane. (See ref. 1.)
The fatigue integrity program was established to insure economic operations and to provide foundation data for inspection and maintenance. Significant features of the 747 fatigue integrity program are 1. Fatigue analyses which are continually updated to reflect design changes, fatigue test results, and static and flight load survey measurements 2. Material selection and detail design by using initial fatigue analyses, ser- vice experience, and testing 3. Fatigue testing to check detail design quality and to verify the analyses, culminated by the test of a structurally complete airframe These three features are interrelated during all program phases of conception, design, design check, production, and operation.
Desired fatigue reliability levels are established by using data from statistical studies on military as well as commercial fleets. Appropriate fatigue reliability fac- tors (scatter factors) are considered in the fatigue life evaluations. Essential fatigue analysis factors are fatigue loading environment, load-stress relationships, fatigue performance data (S-N curves), and cumulative damage theory.
The 747 fatigue loading environments were established by using NASA, military, and Boeing data, in conjunction with aircraft aerodynamics and loads data, customer route structure analyses, and flight load surveys. Because of the airplane size and the complex landing-gear system, the 747 ground-handling and landing load spectra received special attention.
Fatigue stress analyses were performed with the aid of experimental as well as analytical procedures. Extensive application was made of the stress severity factor, developed at Boeing, for evaluating peak stresses in complex joints.
A frame of reference was established by families of structural fatigue perfor- mance curves (S-N curves) encompassing the range of materials and fatigue qualities anticipated for the 747 airplane design. Modifications to the endurance limit and the low-stress region of the curves were made by using service experience and structural component and full-scale fatigue tests. These modifications were necessary to account for the inherent shortcoming of Miner's method for predicting fatigue life for spectrum- loaded structures by using constant-amplitude generated S-N curves.
Each family of fatigue performance curves was assigned a fatigue quality identified by a fatigue performance index (FPI). The FPI of structural details was estimated by a semiempirical relationship.
The most significant factors in attaining satisfactory fatigue quality are detail design and material selection. From previous airplane experience and initial fatigue analyses, material was selected which satisfied the static, fatigue, and fail-safe requirements.
Careful consideration to detail design with respect to fatigue and fail safety was given to all primary structural components.
All major details on the airplane were analyzed by using the technique outlined above. These analyses were verified by extensive full-scale and component tests.
Fatigue developmental and verification tests conducted specifically for the 747 airplane included Quonset-hut tests Wing, body, and nose landing-gear testz Outboard-flap functional and fatigue tests Full-scale horizontal-tail tests Fuselage crown stringer splice tests Side-of-body rib-component tests Numerous small-scale specimen tests concerning – Shot peening Fastener development Cold working Wing—side-of-body joint configuration Window forging configurations In addition, a full-scale airplane fatigue test is in progress. This test utilizes a flight-by-flight load spectrum including pressure cycles applied in a manner to represent the fatigue loading during a typical flight. The test objectives are to 1. Locate any fatigue-critical areas early in production 2. Provide test data for analytical service-life prediction 3. Help develop inspection and maintenance procedures 4. Evaluate fail-safe characteristics of major structural components and assemblies The 747 fatigue integrity program provides a high degree of confidence in the ability of the structure to withstand service loads. Safe and economic operation is insured by the continual updating of analyses to reflect design changes and fatigue test results.
SYMBOLS D drag load d diameter, inches FMEAN mean stress g acceleration due to gravity stress concentration factor Kt Kt,b bearing stress concentration factor gross-area stress concentration factor Kt I g OP load transferred P - OP bypass load S side load T torque t thickness, inches V vertical load w width, inches C1 hole condition factor 0 hole filling factor semispan station measured from root (see fig. 6) bearing distribution factor stress a ABBREVIATIONS AIRP, A/P airplane body station BS t center line dynamic magnification factor DMF FLT f light fatigue performance index FPI FRF fatigue reliability factor FWD forward ground air ground GAG GRND ground IHL intermittent high loads inboard INBD LE leading edge MED medium ML marker loads OUTBD outboard SL sea level SSF stress severity factor trailing edge TE W/O without forward spar FS STA station UNSYM unsymmetrical APPROACH The service-life objective of current Boeing commercial airplanes is 20 years. In pursuing this objective on the 747, a program consisting of analysis, material selection and detail design, and testing has been followed. There is an obvious overlap and inter- dependence of these elements in design, development, and maintenance of aircraft. Delin- eation of specific subelements, such as analysis or testing, is done simply to affirm that many techniques may be used in designing for fatigue and to emphasize that several tech- niques have been applied in parallel as a check-and-balance approach on the 747.
Analysis Essential fatigue analysis factors include fatigue loading environment, load-stress relationships, fatigue performance data (S-N curves), and a cumulative damage theory.
In defining expected aircraft fatigue loading, both usage (flight profiles) and environment (gust, maneuver, etc.) are required (table 1). Fatigue loadings were established by using military, NASA, and Boeing data for taxi, gust, maneuver, landing, and ground-handling environments. A peak-to-peak definition of the ground-air-ground cycle was used.
Extensive route structure analysis of expected 747-100 operation resulted in the flight length distribution illustrated in figure 1 and a 20-year usage goal of 60 000 hours for each airplane. To encompass the wide range of flight lengths from this study, the flight profiles shown in figure 2 were developed. The average flight length of the three simulated commercial flights is 3 hours, the average expected over a 20-year service life. Four percent of the total 60 000 hours usage is expected to be consumed in training and is represented for analysis by 600 4-hour, zero-payload flights, also shown in figure 2.
Fuel consumption data are applied to all flight profiles to determine gross-weight variation within each flight. Each flight is subsequently divided into appropriate segments as shown in figure 3. Climb and descent portions of the flight are actually covered by numerous altitude segments to account for the very large variation in gust environment statistics with altitude. Flight mean loads, dynamic response to gust, and response to maneuver are determined from aeroelastic analysis for each flight segment.
Analytical techniques include engineering theory and finite-element methods; exper- imental techniques include photostress and strain gages. These analytical and experi- mental techniques are used to convert external airplane loads into the stresses required for fatigue analysis: 1g stress, stress response to gust, and stress response to maneu- ver. In addition to conventional stress analysis, the stress-severity-factor technique is used (ref. 2). This technique was developed primarily to evaluate load and stress distri- butions in multifastened joints. It is also used to locate fatigue-critical locations, estab- lish fatigue performance estimates, and evaluate possible design improvements. The stress severity factor includes the effects of geometric stress concentration factor Kt, fastener load distribution, type of fastener, bearing stress distribution, hole surface con- dition, and residual stresses. The equation for the stress severity factor is 'peak SSF = 'ref 1 R 'ref [load transfer + cbypass]01 P - OP a _ 1 P t g]a Kt,bB + tw K ^td 'ref Because of its ease of application and relatively good agreement in analyzing air- plane structure (ref. 3), Miner's theory of cumulative damage is used. Two shortcom- ings of Miner's method have been observed in laboratory testing. One is the inability to account for damage from stress amplitudes below the constant-amplitude endurance limit: the other is the so-called sequence effect where in block-type loading, a substantial dif- ference in life has been observed in some tests in which the order of application of high and low load blocks has been varied. The second shortcoming is somewhat academic for evaluating flight structure since relatively few parts, if any, are subjected to two-step high-low or low-high block loads in service. The sequence effect is of course very real in simulated flight testing and is the primary reason that flight-by-flight testing is preferred.
To correct Miner's method to account for damage below the constant-amplitude endurance limit, two techniques are available. One is simply to translate (reduce) the S-N curve linearly on life at each alternating stress level (ref. 4). The other is to reshape (change the slope of) the S-N curve. The latter course has been followed in this work and is illustrated in figure 4. The level to which the S-N curves have been reduced at infinite life is the nonpropagating crack threshold stress. The shape and location of the upper portion of the S-N curve are essentially unaltered, which retains the advantage of fatigue quality determination from constant-amplitude testing. The resulting curves, which are then termed fatigue performance curves, are mathematically defined with a Stuessi type equation (ref. 5) and verified with fleet analysis and flight-by- flight spectrum tests.
In the early stages of airplane configuration development (prior to built-up struc- ture tests), the fatigue quality of a given design may not be known with high confidence.
To preclude having to rerun fatigue analysis whenever a slight change in detail geometry is made, as well as to provide a frame of reference for fleet analysis, a family of fatigue performance curves was developed for each of the materials used on the 747. The ref- erence curve for each was that for basic structure (which is defined as skin-stringer construction having no significant load transfer between skin and stringer). The basic- structure curve was based on built-up structure fatigue performance data which were available for the material and type of construction in question. It should be noted that simple coupon (Kt) data are not used to estimate life of aircraft structure directly (refs. 6 to 9). With the basic-structure curve as a reference, the remainder of the family of fatigue performance curves for each material was developed by using the variation of life with quality from past tests (refs. 10, 11, and 12).
The term used to identify fatigue quality is the fatigue performance index (FPI), and each of the many curves is identified with a fraction corresponding to the familiar 1/Kt form. (Basic structure, for example, was initially identified as FPI = 1/2.5.) An exam- ple of curves used for analysis of a given detail is shown in figure 5. Fatigue analyses conducted in this manner are essentially parametric studies of life as a function of qual- ity. A sufficient number of analyses are conducted to bracket the expected fatigue quality.
Curves developed in this way, for fatigue performance indices of 0 to 1, and for each material, were mathematically defined and programed for computerized fatigue analysis.
Techniques for estimating fatigue quality involved stress-severity-factor analysis, previous airplane tests, or fleet data. The factors accounted for in the estimating tech- nique are geometric stress concentration, load transfer, type of fastener (interference, design, and modulus of elasticity), bearing stress distribution, hole surface condition, residual stresses, and material. Constants were determined which provided the best fit of estimated life versus test- or fleet-demonstrated life from approximately 2000 assess- ments. The sequence of analysis, test, and fatigue performance estimation is discussed in the section entitled "Typical Results."
Figure 6 illustrates the scope of the fatigue analyses conducted on basic structures, and figure 7 illustrates typical details selected for analysis.
Fatigue reliability factors (scatter factors) accounting for fatigue performance variability, possible load environment variability, and the number of tests conducted on representative built-up structures are included in each basic structure or detail fatigue analysis. The magnitudes of the fatigue reliability factors varied from 2 to 4, with 4 being used in preliminary analysis when the least built-up structure data were available, and 2 being used when large numbers of representative built-up structure tests were completed.
Materials Selection and Detail Design This facet of the 747 fatigue integrity program is intended to cover fatigue improve- ment activities which parallel the basic analysis. Fleet experience, for example, can play a major role in complementing preliminary fatigue analysis, that is, as a check and balance. Fleet experience with similar parts can augment conventional fatigue analysis, provide positive assessment of detail design quality, even derive new model fatigue per- formance providing usage, stress, and detail design are not substantially different.
During the design stage, guides for satisfactory fatigue design (or at least guides for identification of possible problems such as given in ref. 13) are of value. The best experience of course is fleet experience, and listings of previous industry airplane prob- lems (cause and effect) were used as design background on the 747. These types of activ- ities, together with preliminary fatigue analysis, resulted in numerous design improve- ments, a few of which are shown in figures 8, 9, and 10, and in the following materials section: Wing lower surface — 2024 skin and stiffeners Wing upper surface — 7075 skin and stiffeners Body skin — primarily 2024 Body frames and stiffeners — 7075 Empennage — 7075 Landing gear — primarily 4340 steel heat-treated to yield an ultimate strength varying from 270 to 300 ksi Forgings — 7075-T73 (stress corrosion is a prime consideration) Testing Analysis and past experience are very important in establishing preliminary design geometries, materials, and allowable stress levels. The proof of fatigue quality, however, must come from test or flight experience. Since the objective of the fatigue integrity program is to minimize early flight fatigue experience (i.e., cracks), early testing is a key element (refs. 14 and 15). An extensive verification test program was conducted on representative sections of the entire airplane (figs. 11 to 17) . All these test structures were constructed with the same finishes, fasteners, and geometries as were planned for production airplanes. Both constant-amplitude and flight-by-flight spectrum tests were run. In addition to the panel and pressurized fuselage test program summarized in fig- ures 11 to 17, numerous small-scale development-type tests were conducted. Major- component tests, including landing gears, trailing-edge flaps, and horizontal stabilizer, are discussed in the section entitled "Tests of Major Components." The culmination of the 747 fatigue test program is the full-scale fatigue test, which is discussed subsequently.
TYPICAL RESULTS Typical of the analyses conducted on the airplane is that shown in figure 18. This particular analysis was conducted for three fatigue qualities and included a fatigue relia- bility factor (FRF) of 4.0. The analysis illustrates variation of life with spanwise and chordwise location as well as the approximate quality required to achieve the fatigue life goal of 60 000 hours.
Typical test quality determination is illustrated in figure 19, where fatigue quality is plotted against cycles to first crack. The quality associated with the number of cycles endured at the listed stress state is 0.361, or in 1/Kt form, FPI = 1/2.77. This qual- ity, incidentally, is very near the initial quality estimated for basic structure FPI = 0.4 or 1/2.5 and is near the upper end of the qualities for which the analysis in figure 17 was conducted.
Application of test-determined quality and a revised fatigue reliability factor FRF = 2.95 (which is appropriate after additional testing) results in the estimated fleet fatigue performance of stringer runouts shown in figure 20.
Additional examples of the type of data available from fatigue analyses are shown in figures 21, 22, and 23. Since several flights were included in the basic definition of usage, parametric-type analyses illustrating the influence of flight length on fatigue life are available. These particular analyses have been useful in assessing fatigue life of 747 derivatives for different kinds of usage, especially short-range operation. Zones of life deficiencies and stress reductions or quality improvements required to achieve appropriate life goals for 1-hour average flight operation, for instance, are also fallouts of basic airplane analysis.
TESTS OF MAJOR COMPONENTS Major-component tests include: nose, wing, and body landing gears, horizontal stabilizer, and outboard trailing-edge flap. Photographs and descriptions of landing-gear test specimens are given in figure 24. In order to represent flight airplane structure, test specimens are production parts and jig structure is designed to simulate the flexi- bility of airplane support structure. These specimens are subjected to block-type loadings shown in figures 25, 26, and 27. Each block consists of loadings equivalent to 1000 flights, 5 percent of the one lifetime goal of 20 000 flights. The numerous environmental condi- tions included in analysis and test of each gear are also listed on the respective figures.
The outboard-flap test is illustrated in figure 28. The test consisted of stress surveys, functional testing in which the flap was raised and lowered 5000 times, and fatigue testing the outboard flap in the fully extended position. The inboard flap and leading-edge flaps are tested in the fatigue test on the full-scale airplane.
The horizontal stabilizer is tested separately from the full-scale airplane fatigue test primarily to avoid the complication of meshing with fin load systems (fig. 29). Since the stabilizer is mounted in a determinate manner on two hinges and a jackscrew, a fully representative load spectrum can be applied in both the full-scale test, through dummy stabilizer structure, and the separate test. An added advantage is that the stabilizer test can then be conducted at a faster rate. To allow for the fin-empennage airload interaction with the stabilizer, the vertical gust loads are applied in both separate and full-scale tests with a ±20-percent asymmetry. Derived spectrum loads are applied to the inboard and outboard elevators on the left side and through dummy elevators on the right side. Addi- tional elevator loads representing take-off rotation and climb rotation are applied in the take-off phase, and loads representing spoiler trim and landing flare are applied in the landing phase.
FATIGUE TEST OF FULL-SCALE AIRPLANE General Description of Specimen and Test Rig The culmination of the test phase of the fatigue integrity program is the fatigue test of the full-scale airplane (fig. 30). The test specimen is a structurally complete airframe of typical production configuration. Omitted are main and nose landing gears, trailing- edge flaps except left-hand inboard, leading-edge flaps except left-hand flap numbers 3, 7, and 12, ailerons, spoilers, engine pod, and the horizontal stabilizer, which is tested separately. Loads are applied through representative dummy structures for the major components omitted from the test.
Loads are applied to the airplane by using 86 hydraulic actuators, which are con- trolled by an automatic closed-loop electro-hydraulic servo system. The command or program signal is supplied to the servo systems by a digital programer. This programer and the data acquisition functions for the test are controlled by a Digital Equipment Cor- poration PDP-8 computer. The computer is also used to automate many of the operating functions of the test.
To prevent the test specimen from being loaded to levels that are outside defined tolerances, a lockup manifold is installed on each hydraulic actuator. When the lockup system is actuated, the actuator holds the load at the limit of present tolerances until problem correction. Stainless-steel safety links are included in all load systems attached to the airplane. These are designed to yield before local airplane structure is damaged by inadvertent overloading. There is also a two-way relief valve installed in each load system to limit actuator pressure and thereby prevent an overload.
Load Spectrum Derivation The main purpose of the airplane fatigue test is to better determine the true struc- tural fatigue performance by eliminating most of the assumptions which are necessary in the analysis. The specific objectives of the test are to locate as quickly as possible any fatigue-critical areas with a program accurately representing typical service loads, to provide test data for analytical service life predictions, to help develop inspection and maintenance procedures for the airlines, and to evaluate fail-safe characteristics of major structural parts. Criteria considered in developing the load spectrum are Flight-by-flight testing Average of mixture of flights used as base Match upper surface ground-air-ground stresses Match upper surface taxi damage Match lower surface flight segment damage distribution Match lg stresses in 3-hour flight Equivalent gust and maneuver cycles One lateral cycle for one vertical cycle in flight segments Lateral-load cycles quarter of a cycle out of phase with vertical-load cycles Representative cabin pressurization and depressurization Average flap utilization Mean engine thrust in each flight segment Equivalent landing-gear loads in ground-handling phase Intermittent high loads and marker loads To give the correct combination of spectrum loads, cabin pressure, and ground-air- ground cycle loads, the test is conducted on a flight-by-flight basis. An average flight based on the mixture of four analysis flights is used for deriving the test program. For convenience, damage in the average flight is factored by 19 800/20 000 = 0.99 to give 20 000 average flights in 60 000 hours of service. Therefore, each test spectrum repre- sents 3 hours of flying in the mixture of flights.
From the derived gust, maneuver, and taxi damage in each flight segment, the required test cycles are found by using the appropriate stresses from the 3-hour flight (fig. 2).
Incremental stresses due to gust or maneuver and the relationship between gust speed and airplane acceleration differ for each component. Therefore, the damage due to gust and maneuvers is considered independently and is applied to each component with representative loads. Equivalent gust loads are factored by appropriate dynamic mag- nification factors.
On the basis of aircraft industry experience, both wing upper and wing lower sur- faces are of fatigue concern. Therefore, a load program is derived which is representa- tive for both surfaces. The wing upper surface GAG cycle (which is given by the cycle from the maximum once-per-flight tension stress on the ground, to the maximum once- per-flight compression stress in the air, to the maximum once-per-flight tension stress on the ground) damage is matched by a slightly modified GAG cycle for the 3-hour flight.
This modification limits the maximum allowable tension stress in the taxi segment. To reduce the number of cycles, the mean stress in the taxi is reduced below the 1g level allowing a higher alternating stress. With this additional variable the required number of cycles, which was fixed at five, can be matched. Having fixed the upper surface GAG cycle stresses and matched the taxi damage, 97 percent of the total upper surface damage is matched.
, For the wing lower surface, the GAG cycle gives approximately 30 percent of the total damage. The lower surface taxi damage corresponds to the cycles already deter- mined for the upper surface. The small difference between the analysis and test taxi damage is corrected in the GAG cycle damage to give the correct total damage. The lower surface GAG stresses are determined by the same method used for the upper sur- face. With a representative Ig stress in each flight segment, the maximum allowable alternating stress, and hence the maximum equivalent alternating cycle, is limited by the GAG cycle stresses. To achieve the best damage match at other locations, the maximum GAG stresses are fixed in the same flight segments as the analysis. Maximum upper sur- face tension and lower surface compression stresses occur in the taxi segments. The maximum upper surface compression stress occurs in the hold segment, and the maxi- mum lower surface tension stress occurs during flaps-down climb. Gust and maneuver damage is matched in each segment by finding the minimum number of cycles based on the 1g and GAG stress limitations.
Figure 31 illustrates the vertical-load program derived for the wing. Fuselage vertical loads correspond to the gust, maneuver, and taxi loads derived similarly to those for the wing. Since it is impractical to load all the passenger and cargo floor, represen- tative loads are applied in fore, mid, and aft body locations. The numerous other load spectra and the approximate phasing with vertical loads are shown in figure 32. For ref- erence purposes, the average 3-hour flight is subdivided into eleven phases, shown by Roman numerals.
For the lateral-load program, the load magnitude is found by matching the damage in each segment with the same number of cycles as the vertical-load program. In the segments with an even number of cycles, half the cycles are applied with a gust load dis- tribution and half with maneuver load distribution. The cycles in the other segments are arranged so that the total flight damage is half gust and half maneuver.
Additional discrete rudder loads which occur during take-off, flap extension, approach, and landing roll-out are applied during phase I for convenience. It is con- sidered unlikely that the maximum lateral loads generally occur at the same time as the maximum vertical loads. Therefore, the lateral-load cycles are applied one-quarter of a cycle out of phase with the vertical-load cycles. This means the peak lateral load occurs with 1g vertical load and the maximum and minimum vertical loads occur with zero lateral load.
Cabin pressure differential varies from zero to 0.6 psi in phase IV, from 0.6 lin- early to 9.0 psi in phase V, is constant at 9.0 psi in phases VI and VII, varies from 9.0 linearly to 0.6 psi in phase VIII, is constant at 0.6 psi in phase IX, and varies from 0.6 psi to zero in phase X.
Loads representing an average utilization are applied to the leading-edge (LE) and trailing-edge (TE) flaps. On the leading edge the loads are applied to flaps 3, 7, and 12 on the left-hand side. The remaining flap loads are applied through dummy flaps with representative loads on the support structure. Loads on trailing-edge flaps are applied to the inboard flap on the left side with the remaining loads applied to the tracks through dummy flaps. Most of the damage to TE flaps occurs during approach with the flaps fully extended. Therefore, the test loads are applied with the flaps in the extended position.
An equivalent load cycle is applied in phase III to represent the damage in the most criti- cal track and carriage sections during take-off with flaps at 15 0 . In the analysis of the primary structure on the LE flaps, most of the damage occurs during take-off. The max- imum flap load during take-off occurs with the flaps extended at the end of the take-off rotation. Therefore, the test loads are applied with the flaps in the extended position.
An equivalent cycle is applied during the approach in phase X. When the LE flaps are retracted, the uplock load exceeds all the 1g, gust, and maneuver airloads. Therefore no loads are applied on the leading-edge flaps during the remaining flight stages. To represent the uplock stress which occurs during flight and the two cycles during ground handling, three equivalent load cycles are applied in phase I.
Mean fore and aft nacelle loads in the 3-hour flight are applied in each phase. Max- imum gross thrust during take-off and reverse thrust during landing are applied in phases III and IX, respectively.
Landing-gear loads in an average flight are applied through dummy gears to the landing-gear support structure. The dummy gear has a representative relative stiffness to give a true load distribution. In phase I ground handling the vertical, fore and aft, and side loads are based on the same criteria used to derive the separate landing-gear test program. The main difference between the two tests is the block loading in the gear test, which has 1000 flights in each test spectrum and flight-by-flight loading in the airplane fatigue test. Vertical loads in phase H taxi correspond to the loads derived for the wing.
Average spinup and springback loads are applied in phase XI landing.
The spectrum applied on the airplane fatigue test represents typical loads which occur in an average flight. In addition to these loads, the airframe is subjected to infre- quent high loads during the 60 000-hour life of the airplane. These loads have a negligi- ble effect on the cumulative fatigue damage but affect the damage rate and crack initiation and propagation. Therefore, to include this effect in the program, the loads which occur three times in 60 000 hours flying are applied. These loads are termed intermittent high loads (IHL).
Since any cabin pressure differential higher than the normal 9.0 psi is unlikely to occur, no intermittent high cabin pressure is applied.
In previous fatigue tests it has been difficult to establish crack initiation times, crack propagation rates, and crack life prior to rapid fracture in inaccessible areas, and for cracks which were not found until the test was completed. To help in establishing crack data, unique loads, termed marker loads (ML), are applied during the test. These marker loads are arranged in sequence with the intermittent high loads so that a definite test time can be determined from the striations (table 2).
In the test spectrum the cabin pressure is cycled from zero to 9.0 psi to zero once per flight. This gives a representative cycle for a typical flight. In the training flight the airplane climbs to a varying altitude three times. To represent these pressure cycles and concurrently provide a ML pattern for pressure-critical components, those additional pressure cycles from the training flights are applied.
The present status of the major-component and full-scale airplane fatigue tests is given in table 3. The differing test goals specified in this table are an outgrowth of the fatigue reliability factor criteria discussed in the section entitled "Approach." In gen- eral, critical details in landing-gear structure are single-detail-type items, for example, a fillet radius. For these types of tests, a larger statistical factor is required to achieve desired reliability levels in service.
In built-up structure tests such as the outboard flap, horizontal stabilizer, and full- scale airplane, several points usually are identically stressed and therefore constitute a larger sample and require lower statistical factors. All major components have been subjected to loads exceeding the planned requirements for the basic passenger airplane.
Many of the tests have been continued beyond the original test goals in order to substan- tiate derivative airplane requirements. Pending identification of requirements more severe than those currently estimated, some tests have been suspended.
CONCLUDING REMARKS The Boeing 747 fatigue integrity program provides a high degree of confidence in the ability of the structure to withstand service loads. Safe and economic operation is insured through fail-safe design augmented with a continually updated program reflecting past experience, analysis, and test-demonstrated fatigue performance.
REFERENCES 1. Anon.: Airworthiness Standards: Transport Category Airplane. Federal Aviation Regulations — Part 25, Federal Aviation Agency, Nov. 1968.
2. Jarfall, L. E.: Optimum Design of Joints: The Severity Factor Concept. The Aero Research Institute of Sweden, May 1967.
3. Chrichlow, W. J.; Young, Louis; McCulloch, A. J.; and Melcon, M. A.: An Engineer- ing Evaluation of Methods for the Prediction of Fatigue Life in Airframe Struc- tures. Technical Report ASD-TR-61-434, Mar. 1962.
4. Smith, James M.: Extended Service Life Wing Design F-8 Crusader. Aerospace Structures Design Conference, Seattle, Washington, Aug. 1969.
5. Stuessi, F.: Theory and Test Results on the Fatigue of Metals. ASCE Proceedings, Vol. 85 (Jrle, Structural Div. #ST8), Paper #2222, pp. 65-90, Oct. 1959.
6. Hyler, W. S.; et al.: Fatigue Behavior of Aircraft Structural Beams. NACA TN 4137, Jan. 1958, p. 59.
7. Sines, G.; and Waisman, J. L., eds.: Metal Fatigue. McGraw-Hill, New York, 1959, pp. 319-320.
8. Harris, W. J.: Metallic Fatigue. Pergamon Press, 1961, p. 166.
9. Barrois, W.; and Ripley, E. L.: Symposium on Fatigue of Aircraft Structures, Pergamon Press, 1963, p. 88.
10. Grover, H. J.; Bishop, S. M.; and Jackson, L. R.: Fatigue Strength of Aircraft Materials-Axial-Load Fatigue Tests on Unnotched Sheet Specimens of 24S-T3 and 75S-T6 Aluminum Alloys and of SAE 4130 Steel. NACA T N 2324, Mar. 1951.
11. Grover, H. J.; Bishop, S. M.; and Jackson, L. R.: Fatigue Strengths of Aircraft Materials-Axial-Load Fatigue Tests on Notched Sheet Specimens of 24S-T3 and 75S-T6 Aluminum Alloys and of SAE 4130 Steel With Stress-Concentration Factors of 2.0 and 4.0. NACA TN 2389, June 1951.
12. Grover, H. J.; Bishop, S. M.; and Jackson, L. R.: Fatigue Strengths of Aircraft Materials-Axial-Load Fatigue Tests on Notched Sheet Specimens of 24S-T3 and 75S-T6 Aluminum Alloys and SAE 4130 Steel With Stress-Concentration Factor of 5.0. NACA TN 2390, June 1951.
13. Smith, C. R.: Tips on Fatigue. Navweps 00-25-559, 1963.
14. Illg, W.: Factors in Evaluating Fatigue Life of Structural Parts. NASA TN D-725, Apr. 1961.
15. Schijve, J.: Cumulative Damage Problems in Aircraft Structures and Materials.
The Aeronautical Journal of the Royal Aeronautical Society, vol. 74, no. 714, June 1970.
.......
~ ~ TABLE 1. - FAT I GUE ANALY SI S DETAIL S • ENVI RONMENT • Gust • G round Handling Loads • Landing Loads • Mi sc ellaneous • FLIGHT PROFILES • FLIGHT SEGMENTATION • STRESS DETERMINATION • FATIGUE PERFORMANCE DATA • Built- Up Structure Panel Tests • Full-Scale Cyclic Tests • Fleet Service • APPLY PRINCI PLES OF MINER'S METHOD TO PRODUCE CALCULATED FATIGUE PERFORMANCE TABL E 2. - LOAD SEQUENCE OF MAR K ER LO A DS AND I NTERM ITT EN T HI GH L OADS PROGRAM EQUIVALENT TOTAL!
NUMBER OF NUMBER OF NUMBER FLYING TIME ML CYCLES IHL CYCLES CYCLES ~ 6,66 7 20,000 HR 2 1 3 13,333 40 , 000 HR 3 1 ~ 20,000 60,000 H R ~ 5 26,66 7 80 , 000 HR 1 6 33,333 100 , 000 HR 3 1 ~ 40 OOO 120 000 HR 2 1 3 L -- One Marker Load Is As Follows: 1 X TYPE B MARKER LOAD 5 X TYPE A MARKER LOADS • FOR EACH MARKER LOAD CYCLE APPLY FIVE TYPE "A" ML CYCLES FOLLOWED BY ONE TYPE "B" ML CYCLE.
NOTE: • MINIMUM LOAD IS ZERO UNLESS OTHERWISE STATED.
• THE ML'S AND IHL'S ARE TO BE APPLIED CONSECUTIVELY WITH THE TOTAL NUMBER OF ML'S APPLIED FIRST .
• THE ML AND IHL GUST CYCLES MUST INCLUDE THE APPROPRIATE DYNAMIC MAGNIFICATION FACTORS .
......
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~ ~ a:> TABLE 3. - FAT I GUE T EST STATUS BASIC AfsP aJRRENT TEST GOAL LlFETIM S ITEM TESTED STATUS (LiFETIMES)<D COMPLETED I • LANDING GEAR .( 4.6 SUSPENDED • NOSE 5.5 SUSPENDED • WING 4 5.1 SUSPENDED • BODY 2 5.8 TEST IN PROGRESS • HORIZONTAL STABILIZER 2 2.2 SUSPENDED • OUTBOARD FLAP 2 0.64 STOPPED FOR INSPECTION • AIRFRAME CYCliNG
1ST MAJOR INSPECTION l
(18,000 Simulated FIt Houn) r CYCLING RES;j-RTED nd
START CYClING--, r 2 MAJOR INSPECTION 2 LIFETIME
r-CYCLING RESTART COMPLETED 1-7 6-23 10-10 2-16 5-22 6-1-n
.. y! Z V <:>
II ....... IIIIIIIIIIIIII .. IIIIIIIIII .. IIIIIIIIIIII]I!~IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII1II11 (38.(265 Simulated Flight Houn Completed) <D 1 LIFETIME = 20 YEARS OF EXPECTED SERVICf (APPROX 2° 000 FLIGHTS)" I
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NOTE~ IN 60,000 HOURS OF SERVICE OPERATION , THE FOLLOWING DISTRIBUTI ON OF FLIGHTS IS USED : -9600 - ONE HOUR -4800 - THREE HOUR -4800 - SEVEN HOUR _ 600 - TRAINING Figure 2 .- Fl i ght prof il es. Operating empty weig h t, 360 000 lb.
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CLIMB ROTATION SPEED BRAKE \ HOLD APPLICA TION PREFLIGHT CHECK DYNAMIC . TAKE-OFF LANDING ROTATION FLAPS DOW N APPROACH __________________ •• ~LANDING FLARE -~ ~ ...
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CYCLES TO FIRST CRACK Figure 4 .- Modified Miner's me t hod.
fATIGUE PERFORMANCE INDEX (FPII DETERMINED BY ONE OF THE FOLLOWING: .fPC - 1.01 k SSF .FLEET DATA .TEST OF ACTUAL STRUCTURE EXAMPLE FOR GIVEN MEAN STRESS - 1.011.87 FPI - 1.0/2.5 ALTERNATING - 1.013.5 STRESS- 30 KSI FPI - 1.014.5 FPI - 1.018.0
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CYCLES TO FIRST CRACK Figure 5. - Fatigue performance curves .
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AND FUSELAGE LANDING GEARS Figure 7.- Typi ca l detai I analysis locations .
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SKIN CRACK IN SKIN NO RIVETED DOUILERS USED IN WING lOX INTEGRALLY MACHINED REINFORCEMENTS
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SPAR WEB FWD CHORD SPLICE • SKIN CRACKS AT UPPER REAR SPAR CHORD SPLICE WING SKIN DESIGN "7- SPAR CHORD UP • NO CHORD SPLICES EXCEPT WHERE SKIN IS SPLICED • CONTINUOUS SKIN PAD AT SPAR CHORD- ---- SPAR WEB NO STEPS IN SKIN OR CHORD Figure 9.- Tension- critica l design .
.....
Cl1 Cl1 I-' C]1 m COMMON DESIGN CRACK FRAME DESIGN CHANNEL CLIP SKIN Figure 10 .- Attachm en t of fuselage stiffener to fram e.
TEST NO. OF 'AHEL DESCRII'TION .. ANE STRESSES 10.±. 9 KSI [j> ACCESS HOLE ANO SPANWISE SPLICE • SPECTRUM 10 t. 9 ICSI 2 [P REAR SPA" STRINGER "UNOUT ANO GEAR afAM ATTACH AREA [}> NACELLE ATTACH AREA AT F I 10~' KIf Z 10 t. 9 KSI 2 ~ Mlo.A" "UNCUT AND NACELLE DRAG FITTING 10 t.e KSI 2 ~ JOINT AT SIDE OF 800Y [J> FLN DETAIL (FIBERGLASS) VC FLAI' - FLEXURE CYCLING [t> FLN DETAIL (AL HONEYCOMB) fLN FAIRING SEGMENT - SONIC [t:> TRAILING-EDGE STRUCTURE AILERON SEGMENT - SONIC (f> FUNCTIONAL FATIGUE AND FAIL.aAFE COM'LETE LE VARIABLE CAMBER flAl' .-tCTRUM I AHO COMPLETE OUTBOARD TE fLAP Figure 11. - Testing of wing lower surface .
.....
C}l -J "S o c ;: NO. OF TEST STRESSES I PANELS I PANEL DESCRIPTION [:> BASIC SKIN-STRINGER (OUTBD)} I -5 ±. 18.5 KSI
B:>- BASIC SKIN-STRINGER (INBD)
§::> JOINT AT SIDE OF BODY \ -5.5±. 14.5
P BASIC SKIN-STRINGER (CENTER) -5.5 ±. 14.5
Figure 13.- Upper surface fatigue test panels.
,....
CJ1 to ~ CT.> o SKIN AND STIFFENER SPLICES.· STIFFENER ONLY SPLICE A· SKIN ONLY SPLICE. • STATION STATION 1350 941 LAP SPLICES 2ANDJROW CONFIGURA nONS WITH AND W/O BONO .063 THRU .160 SKIN -TEST PLAN - 3 PANELS, STRESS 7 ±. 6 KSI Figure 14. - Fu se la ge testing.
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ECTION 41 UPPER • STRESS SURVEY • PRESSURE FATIGUE SECTION ~2 UPPER TEST • FAil-SAFE TEST flOOR LINE DIVIDES SECTIONS 42 UPPER AND 41 UPPER FROM SECTIONS 46 LOWER AND 46 UPPER SECTION 46 UPPER SECTION 46 LOWER Figure 17.- Pressu r ized fuse l age tes t.
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eMATERIAL - 2024-T3 eTEST DATA TEST APPLICABLE STRESS TEST CYCLES REFERENCES KSI EWA 21·110012, PANEL NO.2 10±9 327,200 e DEMONSTRATED FPI - .361 = 1/2.77 e FATIGUE PERFORMANCE RELIABILITY FACTOR (FRF) TEST DEMONSTRATED F.P.I.
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f-4 O'l CJ1 ~ m m ., SIDE OF IODY ~i\; NOTES: (1) 2024-- T3 MATERIAL (2) FRF - 2.95 (3) FPI - 1/2. n FOR TYPICAL (4) FPI • 1/3.14 FOR SKIN SPLICE (6) -INDICATES SKIN SPLICE RUNOUT (6) BASED ON 3-HOUR FLIGHT ----FRONTSP~R
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LIFE - HOURS 50 , 000 .......... -- - -~::~ - - - - - - - - ........ _-- --, MIXTURE;:' L, HOUR FLIGHT FLIGHTS .8 .6 .7 .8 o . Hili .2 .3 .4 .6 'T1 STATION Figure 21.- Fatigue performance of wing lower surface on 747 basic passenger airplane .
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~ ..;] o DESCRt PTION 1. TEST SPECIMEN IS A PRODUCTION GEAR, EXCLUDING WHEELS, TIRES AND THREE BRAKES 2. JIG SIMULATES THE AIRPLANE SUPPORT STRUCTURE.
3. LOADS ARE APPLIED IN A MANNER TO SIMULATE ACTUAL GROUND LOAD ING.
4. TEST SCHEDULED FOR EQUIVALENT OF 4x60000 ,.. 240000 HOURS IN MIXTURE OF FLIGHTS.
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'- • • BODY GEAR NOSE GEAR WING GEAR Figure 24.- Landing -ge ar fatigue test.
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VERTICAL
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SIDE LOAD SIDE LOAD IN KIPS S (KIPS) 0 I k AT GfK)UM) AIIIO "AIIlAllll - JO --- ----- - -- - - -l- - - - -- - - - - - - J - - - - - - ~ ~~ ~~: .I. - - - - - j - - - - - - J - - - - -~ J- - - - - J - - - - -y-~ ~ - - --
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. I I DRAG Jt Iii , LOAD I ! DRAG LOAD IN KIPS D (KIPS) • AT TOW LUG ~ .. STATtC ANO ULl ro ......
P'fM'fNOtCUlA" TO A..Xl( .zo I I ...
0( I 0 +50 o CYCLESI 198 "95 """" -J Fi gure 25.- 747 nos e gear fat i gue t es t. Loadin g block .
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>' I I I I 1 I I I _________________________ __ ------ ~ -1- ------- ~ ------ -} -------- ~ ------- -1- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- ~ 50 :Jo£ ~ 20 :Jo£ . I , ~ k « Y ~ I '" ~> • ~ O I ~ , , r .....
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:x: -200 V -400 ~ -600 1-' LEFT BODY GEAR:
* rOIlQUE APl'tIED BY A SIDE LOAD COUPLE
LOADS & TORQUE POSITIVE AS SHOWN Figure 26.- 747 body gear fatigue test. Loading block.
-28 V't !!: ~ SIDE LOAD AT GlOUNO V't LEFT WING GEAR *TOIQUE APPLIED IV MEANS OF SIDE LOAD COUPlf LOADS & TOIQUE POSITIVE AS SHOWN ......
..J W Figure 27 .- 747 wing gear fatigue t est. Loading block.
......
-;J "'" • TEST SPECIMEN CONSISTS OF COMPLETE PRODUCTION FLAP AND DRIVE SYSTEM • TESTING INCLUDES STRESS SURVEY, SYSTEM CYCLIC TESTING, STRUCTU RAL FAT IGUE TESTING AND FAILSAFE TESTING • SIMULATED AIRLOADS ARE APPLIED DIRECTLY TO THE FLAP SURFACES • TEST IS SCHEDU LED FOR EQU IVALENT OF 2 X 60,000 (120,000) HOURS IN MIXTURE OF FLIGHTS OUTBOARD FLAP SYSTEM Figure 28 .- Tests of trailing-edge flap and flap d rive system.
PHASE VI .... % %11> i'", «'AI ~~ ~'1' ~~ M G I M I G I M G M IG GIMIG I G 1 M BEAM SHEAR (KIPS) AT 01 l .... 1 II I A ~ xl I I l~tAl-tJ\ I I I I SIDE OF BODY ELEVATOR LOADS (KIPS) II\J I I'll STAB III ZER TEST SET -U P NOTE: • M = tv'IANEUVER CYCLES • G = GUST CYCLES • TEST IS SCHEDULED FOR EQUIVALENT OF 2 X 120,000 ~40,OOO) HOURS IN MIXTURE OF FLIGHTS Figure 29.- Fatigue test of hori zonta l stabi li zer.
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-J O'l CONTROL ROOM TEST SET-U P NOTE: TEST IS SCHEDULED FOR 2 X 60,000 (120,000) HOURS IN MIXTU RE OF FLIGHTS.
HYDRAULI CS ROOM Figure 30.- Airplane fatigue test.
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FATIGUE AND FAIL-SAFE DESIGN FEATURES OF THE DC-10 AIRPLANE By M. Stone Douglas Aircraft Company McDonnell Douglas Corporation
Long Beach, California, U.S.A. a . a_( <399
SUMMARY The philosophy and methods used in the design of the DC-10 aircraft to assure structural reliability against cracks under repeated service loads are described in detail. The approach consists of three complementary parts: (1) the structure is designed to be fatigue resistant for a crack-free life of 60 000 flight hours; (2) inas- much as small undetected cracks could develop from other sources, such as material flaws and manufacturing preloads, the structure also is designed to arrest and control cracks within a reasonable service-inspection interval; and (3) a meaningful service- inspection program has been defined on the basis of analysis and test experience from the design development program. This service-inspection program "closes the loop" to assure the structural integrity of the DC-10 airframe. Selected materials, fasten- ers, and structural arrangements are used to achieve these design features with min- imum structural weight and with economy in manufacturing and maintenance. Exten- sive analyses and testing were performed to develop and verify the design.
The basic design considerations for fatigue-resistant structure are illustrated in terms of material selection, design loads spectra, methods for accurate stress and fatigue damage analysis, and proven concepts for efficient detail design. Special emphasis is given to the DC-10 development test program. The initial stage of this program was a series of screening tests of candidate materials, types of fasteners, stress coining, surface treatments, manufacturing processes, and so forth.
INTRODUCTION The structural design goals for the DC-10, shown in figure 1, were to produce an airplane that is superior to the DC-8 and DC-9 and that will be operated safely and economically for at least 20 years. Three complementary criteria were established to assure this goal: (1) The structure has a crack-free life of 60 000 flight hours on the basis of design, analysis, and tests in excess of 120 000 flight hours.
(2) The structure is damage tolerant. Adequate residual strength is available after a crack has propagated, and the basic structural configuration provides for slow crack growth and arrestment before reaching critical lengths.
(3) An inspection program has been established on the basis of a fail-safe structure with adequate external detectability, as verified by component tests. In addition, the start of inspection and sampling intervals were based on fatigue, corrosion, and crack- propagation resistance of the structure.
STRUCTURAL RELIABILITY A distribution is shown in figure 2 to indicate the overwhelming influence of devel- opment testing and detail design on the structural reliability of the DC-10. These two items were accomplished during initial design stage; they allow true optimization of the DC-10 airframe by "placing the structural material where it is most effective" and thereby provide maximum-fatigue-life assurance. In any event, it is necessary to estab- lish fatigue criteria, identify sensitive areas, establish fastener policies, and plan an early development testing program. Without these procedures, the structural design cannot be successful.
A new computer analysis system was used with a high degree of accuracy in pre- dicting the actual working stress levels and deflections in the structural elements. Full- scale fatigue tests were used to reveal weak links and verify that proper analysis and detail testing were accomplished during the aircraft design.
FATIGUE-SENSITIVE AREAS Once the fatigue-sensitive areas are recognized, proper emphasis can be given to these problem areas to assure fatigue reliability. In the design of the DC-10 aircraft, these areas, as shown in figures 3 and 4, were given special attention during design, analysis, and testing.
The fatigue reliability of the wing box and fuselage pressure shell, splices, joints, and other discontinuities has been made equal to or better than that of the basic struc- tural items 4, 9, and 10 of figure 3.
ANALYSIS Evolution of FORMAT In order to assure design static and fatigue strength, actual working stresses and deflections were predicted with the use of the FORTRAN Matrix Abstraction Technique (FORMAT) developed by Douglas Aircraft Company over a period of 20 years (ref. 1).
Improved computer methods and techniques, such as FORMAT, gave increased analysis capability and visibility over the original DC-8 airframe, as shown in figure 5.
The FORMAT system is fully automatic so, even during preliminary design, struc- tural weight is minimized and fatigue characteristics are improved by placing the mate- rial where it is most effective (ref. 2).
Deflections Figure 6 shows the excellent correlation of deflections from FORMAT analysis with test results. The comparison shows deflections for limit-positive-load conditions for the wing, fuselage, and horizontal stabilizer. The test results were obtained from a success- ful static-load test completed on the second production aircraft in August 1970. The air- craft was fully instrumented with strain gages and deflection transducers by using a sophisticated 1000-channel data system.
Stress Analysis Figure 7 shows the stresses in the complicated root section of the wing subjected to limit positive-maneuver loads (from the front spar (F.S.) to the rear spar (R.S.)) and the equally sensitive fuselage section above the wing subjected to limit down-bending loads. The circles represent static test measurements, and the solid line indicates the stresses computed by FORMAT analysis. The dashed lines indicate the stresses com- puted by elementary beam theory which underestimates the stresses at the sensitive structural areas. The excellent accuracy of the detail stress analysis allows the calcu- lation of reliable local stress levels and assures the fatigue quality of the DC-10 structure.
Working Stresses The working stress levels for the DC-10 wing have been carefully established on the basis of the working stresses used on earlier airplanes which, since, have had proven longevity (fig. 8). The working stress levels for the fuselage shell have increased mainly because of the wide-body cross section. This increase in stress has been accomplished with no loss in fatigue strength through improvement in detail design.
Fatigue Quality Structure The increase in working stress levels and the additional requirement for dependable long-life aircraft make it mandatory to increase the fatigue quality of all structural ele- ments. The results of several thousand constant-amplitude component fatigue tests of structural elements of various configurations are summarized in figure 9. (R is the maximum stress in any cycle divided by the minimum stress in the cycle.) It is note- worthy that the basic structure has considerable longevity as attested by the DC-3, DC-6, DC-7, and DC-8 airframe structure. As shown, the DC-6 and DC-7 joints were critical; the DC-8 joints were practically equivalent to the basic structure, and the DC-10 joints are equal to or better than the basic structure. The DC-10 structure incorporated the best structural details gained from knowledge of DC-8 structure and DC-10 development testing.
DEVELOPMENT TESTS The results of over 2000 fatigue development tests conducted on the DC-8 and DC-9 have been used in conjunction with an additional 1700 fatigue development DC-10 tests to substantiate crack-free, long-life structures. The fatigue development test program has been completed in time to permit the designer to incorporate the test findings into the design. The DC-10 program was planned to utilize small inexpensive specimens as well as large aircraft components.
Specimen Development Testing Double bow-tie wing specimens have been used to obtain reliable fatigue data in minimum time and at minimum expense. Results from specimens of this type have been found to correlate closely with results from more complex and expensive specimens com- posed of skin and stringers. These tests permit rapid evaluation of various attachment types, hole sizes, hole-preparation methods, material-thickness effects, claddings, and so forth, on the fatigue life of the basic structure. Bow-tie wing specimens cannot be used for all configurations; therefore, more typical simple wing slices were also used to eval- uate fasteners. Over 300 specimens of these types were tested. The test results are shown in figure 10.
The simple longitudinal and transverse skin splices and the longeron-to -frame - connection fuselage fatigue development tests were separately conducted to evaluate and screen materials, fastener selection, surface treatment, and so forth. The results of the longitudinal and transverse tests are shown in figure 10.
Component Development Testing Structural-wing-component fatigue development tests were conducted on actual parts that are used in the final aircraft design. All the knowledge gained through the bow-tie and other specimen testing was incorporated in the structural components. Approximately 140 tests were conducted. These aircraft components (fig. 3) were tested and improved until at least 150 000 to 350 000 flight hours were attained. The results are shown in figure 11 for constant-amplitude tests. After the final configurations were selected, flight-by-flight spectrum tests were conducted on major components to verify the mini- mum of 150 000 flight hours.
Six curved stiffened 168- by 104-inch panels, representing various areas of the fuselage, were tested under combined biaxial loads, pressure, and inertia loads. The design features gained on the previously described specimen development tests were incorporated into the design of these panels. The panels consisted of eight frames, 11 longerons, four-way splice (longitudinal and transverse) basic structure, and longeron- to-frame connections. Fatigue tests were performed on the curved panels. Both pres- sure and axial loads were cycled at constant load levels to simulate stresses higher than those which would produce fatigue damage equivalent to the full spectrum of loads expe- rienced by the aircraft in flight (fig. 11). Additional fatigue tests were conducted on window-belt panels and pressure-bulkhead panels.
These specimens were tested in 1.5-million-pound fatigue test machines at the lab- oratory test facility. Four of these machines could each hold and test two specimens simultaneously. In this way, the tests were finished quickly so that the findings could be incorporated into the drawings early in the design.
DETAIL DESIGN The basic design considerations for fatigue-resistant structure have been estab- lished for the DC-10 by paying strict attention to proven detail design concepts. Before fabrication, wooden models of all important structural fittings were made to review for notch concentrations and unexpected machine mismatch areas. Photo stress tests were also conducted on main fittings to determine the stress distributions and peak stress magnitudes in areas where stresses are difficult to predict. On the basis of DC-8 and DC-9 experience, coupled with the extensive DC-10 development test program, many fatigue design features were established, as shown in figures 12, 13, and 14.
The fatigue life of the DC-10 inboard sweep break skin-stringer joint (fig. 12) became greater than that of the adjoining basic structure after the components were prop- erly tapered and material was added locally at the discontinuities. Interference-fit attachments were also used to increase fatigue life.
To attain maximum fatigue-resistant structure of basic leading-edge skin to spar- cap structure, a sacrificial doubler has been used to attach the interchangeable leading- edge section to the front-spar (F.S.) cap as shown in figure 13. This design allows the use of interference attachments in the heavier spar-cap flanges.
Figure 14 shows the fuselage detail design features. The use of properly stepped doublers around the fuselage door corners reduces stress concentrations. Adding a local channel pad to the longeron reduces local bending between the longeron and frame connec- tion. The scalloped longeron splice fitting and fingered doublers assure uniform load transfer and reduce the first attachment load.
QUALIFICATION TESTING The DC-10 is undergoing a flight-by-flight production-airplane fatigue test to 120 000 flight hours and 84 000 flights. The fourth production airplane is divided into three major sections, as shown in figure 15. The shaded test structures shown at the ends of each section represent steel drums that are a minimum of one fuselage diameter in length to assure that load is properly introduced into the aircraft structure. Special design aluminum transition sections modulate interaction effects between the steel drums and aircraft structure to preclude fatigue failures in that region. The division into three sections was based on the following factors: (1) There are fewer compromises in the load spectrum.
(2) Noncritical loads can be eliminated and other critical loads added for each undi- vided section.
(3) Sections can continue cycling while one section is down for inspection or repair.
The cycles are being applied to each individual section as shown in the following table: Number of cycles applied to — Type of load Forward Wing-fuselage Aft section section section Ground loads . . . . . . . . . . . . . . 252 000 389 840 168 000 Flight loads . . . . . . . . . . . . . . 383 040 913 332 753 648 Landing impact . 37 800 36 540 . . . . . . . . . . . . 37 800 Ground-Air -Ground (G-A-G) * . . . . . 84 000 84 000 84 000 Fuselage pressurizations . . . . . . . 84 000 84 000 84 000 Total: 840 840 1 507 712 1 127 448 *Inherently obtained because the load spectrum is applied on a flight-by- flight basis.
Testing experience has shown that proper loads can be applied more accurately to smaller components subjected to large concentrated loads. The main and nose landing gears and adjacent support structure, therefore, are tested separately so that every detailed area is subjected to the millions of cycles that occur in service (ref. 3).
DAMAGE-TOLERANT STRUCTURE The DC-10 primary structure is designed to be fail-safe, with the exception of the landing gear for which fail-safe design is not practical. The fail-safe criterion used in the DC-10 is more stringent than specification requirements; that is, the structure must support the fail-safe load soon after several components have failed.
Identification of Sensitive Areas (Fuselage) The radial loading due to cabin internal pressure can start a longitudinal skin crack in two locations: (1) At the skin line where the fingered doubler is attached to the skin of the longitu- dinal skin splice, shown in figure 16(a) (This type of fatigue crack results in a one-bay longitudinal skin crack.)
(2) At the first attachment of shear clip frame to skin, shown in figure 16(b) (The fatigue crack of this type can propagate into a two-bay longitudinal crack.)
The combined pressure and axial loads can start a transverse skin crack where the longeron is attached to the frame. After failure of the longeron a skin crack can form which may propagate into two adjacent skin bays, shown in figure 16(c). Recognition of these facts led to the following damage-tolerant conditions selected for the fuselage shell structure shown in figure 16(d): (1) Two-bay longitudinal crack with center crack stoppers failed (2) Two-bay transverse crack with center longeron failed The design selected contains titanium crack stoppers at each frame capable of arresting a two-bay longitudinal crack. The hat section longerons act as natural transverse crack stoppers.
Stress Analysis (Fuselage Panels) The equation for the fracture strength of stiffened thin panels containing a crack is KcRct Q
VW
R tan (&) where gross residual stress, psi QR Kc plane stress fracture toughness, psi in.
Crack-tip stress of unstiffened panel Rct Crack-tip stress of stiffened panel panel width, inches W a half crack length, inches as stiffener stress, psi a gross applied stress, psi Toughness Kc is determined from tests on stiffened panels as shown in figure 17(a).
The ratio Rct is determined from analysis of unstiffened and stiffened panels having the same grid size by taking a ratio between the crack-tip stresses (ref. 4). The idealized structure and analysis are based on the FORTRAN Matrix Abstraction Technique (FORMAT) shown in figure 17(b).
Skin Fracture Criterion (Fuselage Panels) Results of fuselage panel residual strength tests are shown that verify test and theory correlation. The shape of the curve is determined by analysis and the height by critical fracture toughness Kc . (Note the point of fast fracture.) The curve plotted in figure 17(c) shows correlation with the analysis at critical crack length, crack arrest, and final failure.
The maximum allowable principal stress for a two-bay longitudinal crack is above the maximum operating principal stress for the DC-10 and provides an adequate margin of safety.
Stiffener Criteria (Fuselage Panels) Stiffener strength must be adequate. In order to maintain the skin fracture strength, the stiffener must not fail. An example of frame (aluminum) stress and outer-crack- stopper (titanium) stress correlation is shown in figure 17(d).
Fail-Safe Testing (Fuselage Panels) Extensive fail-safe testing has been completed. A comprehensive test program was initiated early in the DC-10 design to verify analytical methods and to evaluate various stiffener configurations and materials. Figure 18 illustrates some of the fail-safe devel- opment test specimens. Finally, six 118.5-inch-radius curved panels were tested to determine the residual strength. These tests showed that the fuselage shell structure provides more than adequate fail-safe capability for the conservative two-bay selected damage-tolerance criteria.
Stress Analysis and Testing (Wing Panels) An important design consideration of the DC-10 wing structure is to sustain an ini- tial failure of a member but allow for extension of the failure over a reasonable number of additional flight hours. This approach assures that an initial crack will not grow to critical proportion before it is detected during routine inspection intervals.
The damage-tolerance criterion, a two-bay crack with center stringer failed, has been incorporated into the design of the DC-10 wing box structure shown in figure 19. In addition, four separate skin panels are used on the wing lower surface to arrest further any crack propagation.
Figure 20 shows FORMAT analysis correlation with experimental results obtained from tests of large skin-stringer panels representing typical wing box construction.
Stresses at adjacent stringers have been calculated as functions of crack length. The results have been verified by strain-gage test results.
STRUCTURAL INSPECTION AND MAINTENANCE PROGRAM The purpose of the structural inspection and maintenance program is to detect structural problems on aircraft before airworthiness is affected or expensive repairs become necessary. The importance of the structural inspection and maintenance program was recognized during initial DC-10 design stages. Goals were established to provide required structural airworthiness levels at minimum inspection and maintenance costs.
The main approach is to give full assurance that the aircraft structure will be rela- tively crack free for its intended service life of 60 000 flight hours and 42 000 flights.
This high degree of structural reliability was achieved by designing, analyzing, and testing to (1) a fatigue life in excess of 120 000 flight hours and 84 000 flights to crack initiation and (2) a fail-safe life based on a two-bay crack length requirement.
Fatigue Life Item (1) — that is, a fatigue life in excess of 120 000 flight hours and 84 000 flights to crack initiation — incorporates various design features.
Working stress levels. - Accurate stress levels were predicted for structural sizing using FORMAT analysis. Stress levels are equivalent to those of the DC-8 and DC-9, which have excellent service experience.
Detail design. - Stress concentrations were minimized in joints, splices, and basic structure by the use of proper tapering and scalloping, stress coining, and interference- fit attachments (ref. 5). Preload stresses were minimized by providing flexible structure in design, shop fabrication assembly, and installation tolerance control. Detail design quality of the structure is equivalent to, or better than, DC-8 and DC-9 quality, as verified through component fatigue test results.
Corrosion and stress corrosion. - Corrosion was prevented through faying-surface sealing, priming, top coating epoxy paints, draining, using clad aluminum materials, and using high-strength fasteners installed wet with sealant or primer. Stress corrosion resistance was maximized by utilizing 7075-T73 material, which has a high corrosion threshold.
Fail-Safe Life Item (2) — a fail-safe life based on a two-bay crack length requirement — involves two main design considerations. The use of FORMAT analysis, verified by large panel component tests, enabled the structure to be designed for slow crack growth and crack arrestment.
Crack growth. - Slow crack growth is attained through the selection of 2024 alumi- num with its high fracture toughness properties (low notch sensitivity) and by the use of low working stress levels (ref. 6).
Crack arrestment. - Cracks are arrested by the use of titanium straps at fuselage frames, additional spanwise splices, separately attached but closely spaced wing stringers, and stiffeners attached to the fuselage shell and bulkheads.
Significant Structural Items Because of the high probability of a long fatigue life, the inspection program will be started rather late in the service life. Also, because the structure is fail-safe, the inspections can be spaced somewhat farther apart than those on older types of aircraft (ref. 7).
The selection of the significant structural items to be inspected is based on the knowledge and experience with past programs and the manufacturer's assessment of the most fatigue- and corrosion-sensitive structure. It is necessary, therefore, to define the following two steps: (1) External structural members are designed to crack before complex or hidden joints, doublers, frames, and so forth. This "controlled failure" approach was developed and confirmed by many component tests. For example, over 300 fuselage skin splice specimens were tested to assure skin external crack failures (fig. 21).
(2) Internal members, if cracked, are designed to eventually propagate the crack through to the external members so that the crack becomes externally detectable. The slow crack growth provides sufficient time to inspect and detect cracks before failure, and crack arrestment and the two-bay-crack residual strength of the design provide ade- quate fail-safe strength.
Initial Inspection and Intervals The inspection plan has been designed to detect crack initiation, early signs of cor- rosion, and manufacturing variabilities (preload). The statistical approach was used to obtain a feel for the effect of fatigue variability (ref. 8) and fracture roughness charac- teristics. The variabilities required the use of knowledge gained from the DC-8 and DC-9 successful service experience.
The plan of inspection for structural fatigue critical items is listed below: (1) External items receive 100-percent inspection at periodic intervals.
(2) Internal items, with external detectability, receive 100-percent inspection exter- nally at periodic intervals.
(3) Major load-carrying internal items, without external detectability, are inspected as frequently as the external items.
(4) Other load-carrying internal items, without external detectability, receive only sampling inspection.
The inspection and maintenance program for the DC-10 is designed to assure max- imum vehicle airworthiness at minimum cost.
CONCLUSIONS To date, both the DC-8 and DC-9 fleets have been flown with only a few isolated fatigue failures in the primary structure; this fact is significant because high-time DC-81s have accumulated about 48 000 flight hours and 28 000 landings, and DC-9's have recorded 32 000 landings.
The DC-10 is a third-generation jetliner and, therefore, is expected to be superior to its predecessors because of the following factors: (1) Crack-free life of 60 000 flight hours (2) Slow crack growth and arrestment (3) External detectability in main load-carrying structure (4) Completed development testing during initial design (5) Detail design and fatigue procedures based on past experience (6) Working stress levels and deflections based on accurate design (7) Fatigue critical areas recognized in planning stage (8) Full-scale tests reveal weak links and check performance.
REFERENCES 1. Picard, J.; and Morris, R. C.: FORMAT II — Second Version of Fortran Matrix Abstraction Technique. AFFDL-TR-66-207, Vols. I and III.
2. Warren, D. S.: Applications Experience With the FORMAT Computer Program.
Douglas Paper 5095, presented to the Second Air Force Conference on Matrix Methods, Wright-Patterson Air Force Base, Ohio, Oct. 15-17, 1968.
3. Stone, M.: Fatigue and Fail-Safe Design of a New Jet Transport Airplane. Douglas Paper 3342, presented to the International Committee on Aeronautical Fatigue (ICAF) Symposium, Munich, Germany, June 16-18, 1965.
4. Swift, T.; and Wang, D. Y.: Damage Tolerant Design-Analysis Methods and Test Ver- ification of Fuselage Structure. Presented to the Air Force Conference on Fatigue and Fracture of Aircraft Structures and Materials, Miami, Florida, Dec. 15-18, 1969.
5. Speakman, E. R.: Fatigue Life Improvement Through Stress Coining Methods. Douglas Paper 5516, presented at AIAA Meeting in Los Angeles, California, July 14-16, 1969.
6. Schijve, J.: National Aerospace Laboratory NLR, Amsterdam, Fatigue of Aircraft Structures, presented at the Twelfth Israel Annual Conference on Aviation and Aeronautics, Mar. 1970.
7. Eggwertz, S.; and Lindsjo, G.: Study of Inspection Intervals for Fail-Safe Structures.
Report 120, Aeronautical Research Institute of Sweden, Stockholm, 1970.
8. Abelkis, P. R.: Fatigue Life Scatter Factors for Design and Analysis of Aircraft Structures. Douglas Paper 4807, 1968.
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PRECEDING PAGE BLANK NOT THE PRACTICAL IMPLEMENTATION OF FATIGUE REQUIREMENTS TO MILITARY AIRCRAFT AND HELICOPTERS IN THE UNITED KINGDOM By R. D. J. Maxwell Royal Aircraft Establishment, Farnborough, Hampshire, United Kingdom SUMMARY The paper describes the methods adopted in the United Kingdom to ensure the structural integrity of military aeroplanes and helicopters from the fatigue point of view. It describes the procedure adopted from the writing of the specification to the monitoring of fatigue life in service, and outlines the requirements to be met and the way in which they are satisfied. It also indicates some of the outstanding problems that remain to be solved.
INTRODUCTION The formal airworthiness requirements for the design of military aircraft and helicopter structures against fatigue are contained in the Ministry of Aviation Supply's publication AvP 970. This document lists a number of mandatory requirements together with advisory leaflets as to how these requirements may be satisfied. Although the mandatory parts, which are written in fairly general terms, are still valid, the advisory leaflets, written mainly in 1958-1959, are now a little out of date and do not always agree with current practice. The object of this paper is to describe the existing process of ensuring an acceptable fatigue performance including both the satisfaction of the mandatory requirements and the subsequent monitoring of that performance in service.
However, before starting the main part of the paper it is worth indicating how the Structures Department of the Royal Aircraft Establishment, which is part of the Ministry of Aviation Supply, is involved in the various phases of an aircraft's develop- ment and operational use. Its activities can be summarized as follows: (a) Making critical comments on the initial specification from the Ministry of Defence, who is the customer, and the early brochures from the manufacturers. These comments are made through the Project team in the Ministry of Aviation Supply, which is the procurement authority.
(b) Interpreting the aircraft usage in terms of load spectra by discussions with the Ministry of Defence and the manufacturers.
(c) Agreeing with the manufacturers, as required by AvP 970, on the extent of fatigue testing to be done.
(d) Agreeing with the manufacturers after completion of fatigue testing on the ser- vice life to be promulgated to the Ministry of Defence through the Project team.
(e) Acting as technical adviser to the Project team in discussions on fatigue arising in service.
It is clear therefore that Structures Department has a hand in every phase of the air- craft's life.
THE GENERAL PROBLEM Throughout the sequence of operations, the general fatigue problem will be con- sidered under three basic headings: (a) The determination of the loads/stress spectra experienced by various parts of the structure (b) The determination of the fatigue performance of various parts of the structure (c) The estimation and monitoring of the service life In general, the procedure will be considered in two phases: (a) The design-development phase, that is, up to the aircraft's entrance into service (b) The production and service phase Firstly, fixed-wing aircraft designed on safe-life principles will be considered; secondly, fixed-wing aircraft that are essentially fail-safe; thirdly, helicopters which are invari- ably designed safe-life; and lastly, fail-safe helicopters.
WRITING THE AIRCRAFT SPECIFICATION When the fatigue life specification is written, two important aspects need to be covered. Firstly, the role or combination of roles for which the specified life is required must be described in sufficient detail to enable load spectrum estimates to be made.
This description is extremely important, as contractual compliance with the fatigue life requirements will be determined by tests under these load spectra. Thus, the require- ment should indicate (a) The types of role in which the aircraft will be operated (that is, route flying, ground-attack, marine reconnaissance, etc.) and the proportion of time spent in each role (b) Flight profiles anticipated (heights, speeds) (c) Operating weights and stores to be carried (d) Numbers of landings (e) Numbers of pressurizations Secondly, it must be made clear whether the required life is the minimum to be achieved in the stated mixture of roles or whether it is the average life to be achieved.
This definition of the life determines whether the life is to be achieved under the most severe spectrum or under an average spectrum, estimated from the stated usage.
DETERMINATION OF LOAD SPECTRA At the beginning of the design-development phase, the load spectra for the aircraft are estimated for the specified utilisation. The estimates are obtained mainly from data collected from previous aircraft. Toward the end of this phase, the estimates may be modified by loads measured on prototype aircraft. The loads to be considered include those discussed in the following paragraphs.
Gust Loads The gust loads are estimated from the flight profiles quoted in the aircraft speci- fication by using mainly discrete gust data with rigid-body response giving centre-of- gravity accelerations. For larger aircraft some allowance is made for flexibility. The use of power spectral methods to estimate gust loads in terms of centre-of-gravity accelerations is under consideration. The same discrete gust data are used to estimate tailplane and fin loads. Fin load frequencies are arbitrarily multiplied by 3 to allow for Dutch roll type of response and to allow for some manoeuvre content.
Manoeuvre Loads Manoeuvre loads again are obtained in the form of centre-of-gravity accelerations.
They are compiled mainly from the load spectra collected from fatigue (load) meters (counting accelerometers) on previous aircraft flying similar roles with some allowance where necessary for different design limit values of centre-of-gravity acceleration. If new types of role are envisaged, manoeuvre loads must be estimated by consultation with the operators. Manoeuvre loads are mainly of significance for the wing and fuse- lage but may also be important for the tailplane. Attempts have been made on some aircraft to calculate the tailplane loads required to initiate the centre-of-gravity accel- erations of the manoeuvre spectra. In general, such calculations suggest that peak loads of about twice the magnitude of the tail balancing loads for the manoeuvre under consid- eration are obtained.
Ground-Air Cycle Until recently this ground-air cycle, a once per flight cycle, which is mainly of importance for the wings has been considered to range from a lower limit given by the down load generated by a 1.2g acceleration while taxying under maximum take-off load to an upper limit occurring in the Ig level flight condition. It is now considered that a more realistic allowance for the ground-air cycle is obtained for transport and heavy bomber aircraft if the upper limit of the cycle is taken as the Ig condition plus the posi- tive load occurring once per flight. In addition, it recognised that the once per flight down load for this class of aircraft is likely to be between 1.3g and 1.4g rather than 1.2g.
The ground-air cycle is normally considered to be unimportant for fighter-attack air- craft where negative manoeuvres in flight give greater down loads than those experienced on the ground.
Ground Loads Estimates of ground loads are, of course, of primary importance for the fatigue- life assessment of the undercarriage, but the loads transmitted to the rest of the struc- ture can also be important for the top surfaces of wings and fuselages of large aircraft.
Many modern transports and heavy bombers have undercarriages on or near the fuselage.
Consequently, the top surfaces of the large-span, fuel-filled wings are in tension on the ground. The alternating stresses generated by ground loads can therefore cause fatigue problems in the top wing surfaces. Similarly, bending loads in the long fuselages can produce fatigue-prone regions. In general, little data analogous to the gust and manoeuvre data exist. At present, methods of measurement and analysis of such loads on development aircraft are difficult and no operational recorders are available.
Although power spectral methods of analysis are giving some indication of the vertical loads likely to be experienced, little has been done to calculate side loads, which may be extremely important for the undercarriage.
Local and Acoustic Loads Local loads include such loads as those due to flap and airbrake operations. Esti- mates of sound pressure levels for acoustic loads can be made once the engine type and configuration are known.
CONVERSION OF LOAD SPECTRA TO STRESS SPECTRA The structure is examined in detail and at all stations considered to contain possible fatigue problems, the local stresses corresponding to the various parts of the load spec- trum are calculated. In general, rigid body conditions are used, but some allowance for dynamic effects is made if it is thought that the stress levels will be significantly affected. In the later stages of the design-development phase, the stress calculations are supplemented by flight measurements on prototype aircraft. The importance of knowing the utilisation pattern in some detail again becomes apparent since the centre- of-gravity accelerations of the load spectrum must be associated with the correct weight and flight conditions to obtain the corresponding stresses. Hence, an estimate must be made of where in the flight the accelerations are most likely to occur.
ASSESSMENT OF FATIGUE PERFORMANCE The initial assessment of fatigue performance is by a calculation using Miner's hypothesis to evaluate the lives of those components for which the stress spectra have been determined together with S-N curves appropriate to the type of component and material considered. In general, manufacturers use their own S-N data based on tests on previous aircraft with components similar to those proposed for the new model.
Where such curves are not available, either the basic material curves are used with some allowance for stress concentrations and other effects or some typical curve such as those in the Royal Aeronautical Society/Engineering Sciences Data Unit Data Sheets.
In particular, the Heywood joint curve A, Data Sheet E.05.01 is regarded as a good starting point for calculations on aluminium alloy structures. Parts shown by the initial calculations to have marginally acceptable lives are tested under realistic load sequences of the required stress spectrum.
ASSIGNMENT OF PROVISIONAL SERVICE LIFE At this stage, the end of the design-development phase, there will be a number of prototype aircraft flying and production will be about to start. In order to provide some safeguard for early flying until the major fatigue test is completed, provisional fatigue lives are assessed on the basis of the calculations and test results available at this time.
The life of the aircraft as a whole will be determined by the life of the most critical irreplaceable component. Within that life, other components may need replacing. In all cases lives will be calculated by using the average spectrum for the sortie, or mixture of sorties, required and either the standard S-N curves or the later component tests.
These lives will then be the lives one would expect for average components, and must be divided by the following factors: (1) By 2 to account for inaccuracies in calculation and component tests compared with full-scale (major) tests. This factor is based on a paper presented by Raithby to the I.C.A.F. in 1961 (ref. 1) which showed that lives based on component tests and calcu- lations usually overestimated the lives subsequently achieved on the full-scale test.
(2) By a factor varying from 3 3 to 5 depending upon the number of specimens tested. This factor is essentially to allow for scatter. In this context, since the standard S-N curves are usually based on a large number of results a scatter factor of 33 is used.
The greater uncertainty compared with results based on the component tests is usually allowed for by using what are thought to be conservative S-N data.
(3) By a factor of 1.5 to allow for variations in load spectrum from aircraft to air- craft flying the same role, when it is assumed that the calculated life is based on an average spectrum. This factor is not required if the provisional life is to be monitored for individual aircraft by the fatigue meter or some other method of recording individual variations of load spectrum. If it is decided to use the fatigue meter to monitor the pro- visional life, a formula will be derived as described subsequently, but unless the major fatigue test is likely to be delayed or the particular aircraft are going to fly consistently in a severe role, it is normal to wait for the results of the major fatigue test before developing the fatigue meter formula.
THE MAJOR OR FULL-SCALE TEST It is now recognised that lives based on calculations or component tests are likely to be inaccurate. This condition exists partly because the loads on the particular com- ponents considered are difficult to assess accurately owing to the complex nature of the structure and partly because of the difficulty of pred'cting which are in fact the critical components. It has therefore become a matter of policy to carry out tests either on the complete structure or on the major components (complete wing, fuselage, fin, etc.). In the latter case, all parts of the structure must be covered.
The test specimen is normally an early production airframe to ensure that detail design and manufacturing standards are comparable with those of service aircraft. The load spectrum is again derived from the utilisation pattern in the specification. However, by this time some flight load measurements should have taken place on prototype aircraft so that more knowledge should be available, for example, on the dynamic response of the aircraft, and should lead to more realistic relationships between local stresses and centre-of-gravity accelerations.
Usually the loads are applied in realistic sequences by using many load levels.
For transports and heavy hombers this procedure results in flight-by-flight loading so that ground-air cycles are interspersed with flight loads and in most cases, a ground load spectrum also is applied. In addition, on some of these aircraft, the manoeuvres and gust loads have been applied in a random order between the ground-air cycles.
These realistic sequences are intended to ensure that the changing residual stress patterns around the stress concentrations which are known to affect fatigue life, but which at this time are not taken into account in theoretical assessments, are reasonably accounted for on test. The random load sequence of gusts has another advantage over the more common block programme in that it is easier to use a large number of load levels because there is no fixed pattern for each flight and hence no need to choose intervals of load that result in finite numbers of each level per flight. This procedure enables a better representation of a continuous stress spectrum to be made than can be achieved with the usual block programme. The flight-by-flight representation is not always used on fighter-attack aircraft if the negative flight manoeuvres impose bigger down loads than those on the ground.
The test is normally carried on to the "factored" required life unless prior cata- strophic failure occurs. If no such failure has taken place, a review is made and fre- quently the test is continued for another factored life or to failure to allow for any extension of life in service beyond that anticipated at the design stage.
INTERPRETATION OF MAJOR FATIGUE TEST The failure or failures that have occurred under the known loading on test have to be related to the load spectra experienced in the various roles in service and safety factors applied to allow for scatter. For each failure, the following procedure is adopted: (1) The S-N curve used to estimate the life of the failed item in the design- development phase is adjusted by factoring the stress scale until the calculation using the stress spectrum applied on the test gives the test life to failure.
(2) This adjusted S-N curve is then used to calculate the lives to be expected in the various service roles, using Miner's hypothesis and the anticipated spectra. The same curve is used to derive the coefficients of the fatigue meter formulae which are obtained by the method described by Phillips. (See ref. 2.) The use of these formulae is described subsequently.
(3) The lives for each role and the coefficients of the fatigue meter formulae are then divided by the factor to allow for scatter in performance. In general, only one specimen will have been tested so that according to the recommended factors in AvP 970 a value of 5 should be used, but in practice, a factor of 3 3 has been used for all lives based on major tests. Although this procedure is difficult to justify theoretically, it was considered reasonable in view of the greater certainty obtained from this type of test. As there has been no regular shortfall in achieved service life that could be attributed to this cause, the practice has been allowed to stand. It should nevertheless be recognised that it is extremely difficult to obtain feedback of service data on which to base a reliable correlation analysis.
(4) The lives for each role are divided by a further factor of 1.5 to allow for vari- ations of load spectrum experienced by individual aircraft flying the same role. This factor is not applied to the fatigue meter coefficients as the meter registers the indi- vidual variations.
It should be emphasized that the utilisation pattern originally laid down should represent as nearly as possible the anticipated usage in service because the fatigue test is based on this pattern and although estimates can be made for other patterns, as shown above, the accuracy of prediction is likely to fall when the new patterns deviate markedly from that used on test.
FAIL-SAFE STRUCTURES The procedure described is aimed primarily at preserving the safety of safe-life type structures which can fail without prior warning. A similar procedure is also nec- essary for fail-safe structures, which are defined as those in which fatigue cracks or component failures can be found before the strength falls to an unacceptable level. As the whole concept of fail-safe stands or falls by the ability to detect cracks early, the importance of ensuring that all cracks can be found cannot be overstressed. Hence, it is essential to obtain as much information as possible from the full-scale test on the probable location of cracks. Thus, the full-scale test is as important for fail-safe structures as for the safe-life type although the emphasis is different.
The test should first demonstrate that the structure really is fail-safe, that is, that at no time during the service life is there likely to be an undetectable major failure.
The main dangers are design errors leading to an early unexpected catastrophic failure or the accumulation of many small failures late in the life which are insignificant and difficult to detect individually but which may suddenly join to give a catastrophic failure.
The long riveted joints of pressure cabins are particularly vulnerable to this latter type of failure as the skin experiences similar stress cycles at all rivet locations. Hence, small cracks, which will almost certainly escape detection, are likely to form at about the same time along the rivet line, and these may suddenly join into one long, possibly catastrophic crack.
The second purpose of the test is to show which are the likely areas of cracking, when the cracks are likely to occur and how fast they will propagate. This information will enable inspections to be started early enough and to take place frequently enough to ensure safety. In addition, the actual inspection techniques can be developed on the complete built-up structure.
In order to show that no catastrophic failures will occur during the required life, a fail-safe structure is required to be tested to the same factors on life as a safe-life structure. In order to demonstrate that cracks are fail-safe, a crack must be allowed to propagate on test for three inspection periods after it has reached the shortest length that can be found with certainty under the inspection method to be used. At the end of that time it must sustain 80 percent of the ultimate load.
The demonstration of the residual strength characteristics poses a practical prob- lem. The 80 percent ultimate load cannot be applied at the end of the crack propagation phase if the test has not reached the factored required life because if it does not survive the application of the load, the specimen is lost or severely damaged and if it does sur- vive, the rest of the test will be invalidated because of the unrepresentative residual stress pattern generated by this exceptionally high load. The usual technique is to run the crack for three inspection periods or until the crack is considered long enough just to sustain the test load. (In this case a shorter inspection period will be imposed in service.) The crack is then repaired with a patch and the test continued. At the conclu- sion of the test the patches are removed one at a time and the 80 percent ultimate load applied. This is clearly not entirely satisfactory but no completely satisfactory solu- tion has been found. In some cases it may be possible to simulate the relevant cracks on the static test specimen if this is still available and apply the test load to that, but care must be exercised to ensure a crack tip that is typical of fatigue.
These requirements ensure safety but it is also necessary to ensure a reasonably economic aircraft. It is therefore a requirement that the first crack shall not appear on the weakest aircraft from a fatigue point of view before half the specified life has been achieved and that the amount of repair work shall not become uneconomic on the weakest aircraft before the whole specified life is achieved.
Hence it can be seen that the test requirements are similar for both fail-safe and safe-life aircraft. Therefore, although the designer is encouraged to design fail-safe (if he believes his design to be fail-safe he is at liberty to use lower factors in the design to allow for scatter than he would for safe-life design), the structure is judged on its performance in the test, such failures that occur being judged on their merits. Failures which can be considered fail-safe will require inspection in service starting at the fac- tored life, followed by repair or replacement only if they occur, whereas safe-life fail- ures require either modification of the failed item or retirement of the whole structure at the factored life.
MONITORING IN SERVICE The object of monitoring in service is to relate the load spectra experienced by individual aircraft to the failures that occur on the fatigue test. In order to assess the service load spectra, each aircraft is equipped with a fatigue (load) meter, which is a counting accelerometer recording the number of times each of eight levels of centre-of- gravity acceleration is exceeded. The actual levels recorded depend upon the type of aircraft, there being a number of standard instruments, but usually there are five levels above Ig and three below. These instruments are read after every flight and the counts recorded together with information on the type of sortie, take-off and landing weight, stores carried, number of pressurizations and any other details considered relevant to the consumption of fatigue life.
There are then three main methods of using this information: the fatigue meter formula, role lives, and total number of occurrences of a particular event, each of which tells the operator to initiate some action. Each method relates a failure under the known test loading to the loads experienced in service with the appropriate factors. If the fail- ure on test is safe-life, reaching the factored life means either that the item must be replaced or that the complete structure must be retired. If the failure is fail-safe, reaching the factored life means that inspection must start. These inspections continue at a frequency determined by the same methods; that is, the individual load spectra are related to the test loadings during the crack-propagation phase so that inspection periods may fluctuate in time depending upon usage. In practice, inspections are called for either at fixed time intervals to coincide with normal scheduled maintenance or when the moni- toring system indicates an inspection to be due; it is usually possible to ensure that most inspections occur at scheduled maintenance periods.
Of the three methods of assessing the fatigue life, the fatigue meter formula is considered to be the most accurate and is used when the stress levels at the monitored stations can be related to centre-of-gravity accelerations. This usage usually covers wing stations and fuselage stations affected by longitudinal bending. The operator is supplied with a formula consisting of coefficients by which to multiply the counts recorded on each flight at each level of g, together with overall factors depending upon type of sortie, take-off and landing weight, stores carried, etc. He thus calculates flight by flight a steadily increasing number which is a measure of fatigue damage. When the number reaches a certain value, he initiates the appropriate action, either retirement or start of inspection. In the early days of fatigue meter formulae, one simple set of coef- ficients was used to monitor the one safe-life failure that determined the ultimate life of the structure. Today, with fail-safe structures it may be necessary to monitor a series of possible failures, inspections for which will start at different times. In addi- tion, with the large variety and weight of stores that can be carried, it has become nec- essary to allow for relatively large variations in the relationship between stress at the station to be monitored and the centre-of-gravity acceleration recorded. Hence it is sometimes necessary to have a series of formulae and correction factors for one aircraft.
The second method of monitoring, role lives, is used to cover periods of flying in which the fatigue meter is unserviceable or to monitor parts for which the fatigue meter counts have no relevance but for which it is known that the load spectrum varies with the type of sortie, or role flown. In this method, the load spectra are first estimated for each type of flight (in the case of flying with an unserviceable meter these are obtained by analysis of other aircraft records on similar sorties). The factored lives are then calculated by using Miner's hypothesis and the adjusted S-N curve derived from the test.
It should be noted that if average load spectra are used, the factor of 1.5 for variation within the same sortie must be included. Each hour's flying is then divided by the factored life in the role to give the fraction of damage done. When these fractions add up to 1, the appropriate action is taken. When used to cover periods of meter unservice- ability, the operator is given a coefficient based on this fraction by which to multiply the number of hours flown in each role and this number can be added to the number obtained from the fatigue meter formulae.
The third method of monitoring is the simplest and can be used when the fatigue damage in a part is due entirely to one operation, say pressurization, when the life to "action" is given in terms of the numbers of occurrences of that operation. Again the time to action by the operator is based on the number of such cycles to failure in the fatigue test with the appropriate factor. In the case of pressurization, if the test is car- ried out by using maximum pressure differentials for every cycle and all pressurizations recorded in service are assumed to be to maximum differential, the factor used is 31 One byproduct of the recording of fatigue meter readings after every flight together with the type of sortie flown is that the load spectra are analysed on a sortie basis and used in estimating load spectra for future aircraft.
In general, it is felt that although the fatigue meter has provided and is still pro- viding an extremely valuable method of monitoring fatigue life in service, more elaborate methods are required to cope with the changes in the stress and centre-of-gravity accel- eration relationship that now occur on most aircraft. Moreover, some monitoring sys- tem must be developed for areas such as the tailplane, fin and undercarriage for which methods of monitoring are still in the exploratory stage and for which there is little or no operational data on load spectra.
THE GENERAL PROBLEM OF THE HELICOPTER In general, the approach to the fatigue problem in the helicopter is based on the same concepts as those used for fixed-wing aircraft; that is, the load spectrum and fatigue performance for each component must be determined and its life estimated and monitored in service. In the helicopter, however, most of the critical items are contained in the rotating parts and their controls and these parts are subjected to fluc- tuating loads even under steady flight conditions. Therefore, large numbers of cycles are accumulated in a short time, and there is a consequent shift of emphasis to the fatigue behaviour at the low stress end of the S-N curve. This shift of emphasis results in one of the main differences between fixed-wing aircraft and helicopter requirements; all the factors are on stress instead of on life as factors on life become meaningless when the S-N curve is nearly horizontal. The fact that stress cycles are generated even during steady flight has its impact on the estimation of load spectra. It is clear that in order to have any reasonable life at all, stress cycles in steady-flight conditions must be below the fatigue limit. Therefore, the life is determined principally by occasional excursions of the stress-cycle magnitude above the fatigue limit which are usually found to occur during a few transistory manoeuvres and short periods in a few flight conditions such as at high speed. Determination of load spectra becomes a process of defining these manoeuvres and flight conditions, estimating the frequency with which they will occur, and estimating the magnitudes and numbers of cycles occurring in each of the manoeuvres or flight conditions specified.
THE DESIGN-DEVELOPMENT PHASE FOR THE HELICOPTER Essentially, the same information needs to be written into the customer's spec- ification for the helicopter as for the fixed-wing aircraft, that is, life required, types of sortie to be flown, operating weights, and stores to be carried. However, the estima- tion of load spectra from this requirement is in terms of frequencies of occurrence of the various critical manoeuvres and flight conditions. Owing to the lack of measured operational data, these values have to be estimated from a consideration of how the helicopter is going to be used. However, with the present state of knowledge it is vir- tually impossible to calculate the stresses arising in the many components associated with the rotating parts and their controls during these critical manoeuvres and flight conditions. Consequently, at the design stage, the stresses calculated for steady cruise condition are multiplied by 1.5 and maintained below the fatigue limit of the factored S-N curve. Past experience has shown that this method provides a reasonable design starting point. The S-N curve used is either a relevant one from tests on similar com- ponents from a previous helicopter or a material curve with allowance for stress con- centrations, etc. The factor at this stage is 2 on stress.
During development, the loads and stress spectra are steadily acquired by pro- gressive flight measurement on an extensively strain gaged prototype helicopter. Sim- ple manoeuvres are flown, and stresses are measured, related to the appropriate S-N data, and assessed for safety. The helicopter is then cleared for the next more complex manoeuvre. At the same time S-N data are built up by constant-amplitude tests on the more critical items.
HELICOPTER FATIGUE SUBSTANTIATION The final life substantiation is based on flight measurements of stress, S-N curves obtained either by constant-amplitude tests or programme-load tests factored to allow for scatter, and calculations using Miner's hypothesis.
In order to obtain the stress spectrum for each component, each of the manoeuvres or flight conditions considered likely to produce fatigue damaging cycles is flown at least three times. In those conditions where the three flights give widely different results, more measurements are made. In the first analysis only the maximum stress cycle is associated with each manoeuvre or flight condition and it is conservatively assumed that this cycle occurs at the typical frequency of the stress cycle in that com- ponent for as long as the manoeuvre exists. For those components and flight conditions where the subsequent fatigue analysis shows this analysis to give unacceptably low lives, a more elaborate analysis takes place which provides a spectrum of stress amplitudes to be associated with that flight condition. The total stress spectrum can then be obtained for each component by using the frequencies of occurrence of each manoeuvre or times spent in each flight condition estimated from the specification together with the measured stress amplitudes for these manoeuvres and conditions. To allow for varia- tions in stress from helicopter to helicopter when flying the same manoeuvres, the mea- sured stresses are usually multiplied by a factor of 1.2.
The S-N curve for each component is obtained in most cases by testing at least six specimens under constant-amplitude loading; normally three specimens are tested at each of two stress amplitudes. A curve of predetermined shape based on past exper- ience is then drawn through the mean values of life obtained in each of the two groups and this curve is factored on stress values to allow for scatter. When six or more specimens have been tested, a factor of 1.6 is used for light-alloy components, and 1.4 steel and titanium. (The figure for titanium is provisional, being based on limited data.) Where less specimens have been tested, higher factors are used. It is consid- ered that gear boxes show less scatter than other components; therefore, a factor of 1.4 is used if one gear box is tested and 1.3 if four or more specimens are tested. These factors are appreciably bigger than those quoted in AvP 970, but are based on the latest information on scatter and current practice.
The fatigue life is then determined by using Miner's hypothesis except that a value
for I N
of 0.75 is used. When the maximum stress amplitude in the whole stress spectrum is below the fatigue limit of the factored S-N curve for that component, the item is considered to have a virtually infinite life. The fatigue limit for light-alloy specimens is taken as that stress amplitude giving a life of 10 9 cycles and for low and medium strength steels, that giving 5 x 10 6 cycles. Where testing of light-alloy components has only been taken to 5 x 10 6 cycles, a factor of 1.35 on stress is used to estimate the fatigue limit.
For components experiencing a complex load history, it is considered advisable to test under a mixed load level to simulate more nearly the actual conditions, although the loads will be increased to allow for scatter and to obtain failures in a reasonable time.
(This procedure is in contrast to fixed-wing practice where tests are conducted under real loads for factored times.) The results are used to locate the mean S-N curve for the component in the same way as for fixed-wing aircraft; that is, a predetermined shape of S-N curve is factored in the stress direction until the cumulative damage calculation gives the mean life achieved on test under the known loads.
MONITORING HELICOPTER LIFE At present there are no monitoring instruments for the helicopter analogous to the fatigue meter for the fixed-wing aircraft. Therefore, all components are assigned safe lives in flying hours. Although the helicopter is used in many roles, there has been no attempt as yet to define different lives for each role or record times spent in each role.
Consequently, lives have been assessed in whichever role is considered to be most severe for the component under consideration and those lives considered to be the retirement lives irrespective of the subsequent usage.
FAIL-SAFE FOR THE HELICOPTER It is clear from the previous two sections that in many ways there are greater dif- ficulties in estimating safe lives for helicopters than for fixed-wing aircraft. The lives are very dependent upon a few transistory loads occurring during certain flight conditions and manoeuvres. The flight conditions themselves are not easy to define accurately and the magnitudes of the loads within those conditions are likely to vary considerably depending upon pilot technique and state of maintenance of the helicopter. Moreover, helicopters of the same type are used for a wide variety of jobs; hence, variations in life of similar components are liable to be very large. In addition, minor damage such as a small score can result in a drastic reduction in life as the large number of cycles of stress otherwise below the fatigue limit are thus raised to a level where they add to the damage. In the circumstances, designs to fail-safe principles are highly desirable from a safety point of view.
It is often thought that this concept with its implication of redundancy can only be obtained at the cost of extra weight. It has been found in fixed-wing aircraft that this is not necessarily the case and, in fact, once the principles of design detail have been mastered, there may actually be a saving of weight in those areas of the structure designed by fatigue because lower factors to allow for scatter can be used in the design of fail-safe parts than could be used if those parts were safe-life. This condition occurs because it becomes no longer necessary to ensure that fatigue initiation probability approaches zero, the only criterion on frequency of fatigue failure being the economic ones of maintenance and repair costs. The fact that so many of the helicopter rotating parts are fatigue designed and the variations of loading from aircraft to aircraft are so great and yet there are so few fatigue failures in service suggests that there may be appreciable overdesign and therefore significant weight saving to be gained by fail-safe design as well as the added safety.
At present, there are no requirements for fail-safe for helicopters in AvP 970, but there should be no basic problem in writing such requirements in general terms.
Indeed, the approach would be identical to that used for fixed-wing aircraft; namely, that any failure shall be found before the residual strength falls below an acceptable value.
However, the real problem, once the principles of fail-safe as defined by the require- ments are fully understood, is one of detail design and it is here that the main attack must be made if the advantages of fail-safe design are to be realised. In addition, since the early detection of failures or cracks is vital to fail-safe, it would be worth putting more effort into the development of inspection techniques. This effort may involve special systems for particular parts, such as the blade inspection method developed by Sikorsky in which the blade is inflated and cracks detected by loss of pressure. However, it must be remembered that helicopters frequently operate in relatively primitive conditions so that simple techniques are required.
FUTURE WORK The procedure described in this paper for coping with the problems of fatigue in aircraft structures which has evolved over the years has maintained an acceptable stand- ard of safety. Nevertheless, every step in that process contains problems that could lead to inaccuracies. As the customer demands longer lives for his expensive aircraft, the need for better life estimation is of paramount importance, both for the safety of safe- life aircraft and the economy of fail-safe aircraft.
The areas in which effort is still needed can be considered in two main groups: those associated with defining the load-stress spectra and those concerned with the determination of fatigue performance. If the load-spectrum problems are considered first, wing loads and fuselage bending loads are reasonably served by the fatigue meter; this meter monitors loads on individual aircraft and provides operational data. However, with the wide variation in the stress and centre-of-gravity acceleration relationship possible in modern aircraft because of the high rates of fuel usage, and the large range of stores carried, some more direct method of obtaining stress spectra is required. If such methods should be developed for operational use, they would be invaluable in moni- toring fatigue life consumption of fins, tailplanes, undercarriages, and possibly even helicopter components, although in the latter case there is an additional practical problem of recording outputs through rotating machinery. In the event of monitoring by direct stress measurement being developed, it may be found that the process of feeding back to the design stage will be more difficult than that for current monitoring methods using counting accelerometers, bearing in mind that for both systems allowance must be made for the response characteristics of the aircraft on which the measurements were made before these measurements can be applied to the new aircraft. This procedure is already used to a large extent for response to turbulence, and the power spectral approach used in this connection is being applied to estimating undercarriage loads. However, more work needs to be done in relating the theoretical work in this field to measure- ments in flight and during ground operations.
The problems associated with fatigue performance will now be considered. The outstanding need is for a new cumulative damage hypothesis that takes sequence effects and fretting into account. With the greater understanding of the effects of residual stresses around stress concentrations, it is hoped that methods of accounting reliably for the former will not be too long delayed. In view of the increasing tendency to design fail-safe, there is a need for more work on methods of predicting crack propagation rates in complex structures under variable loading and the residual strengths of the cracked structures.
It is unlikely that even improved methods of estimating initiation time, crack prop- agation rates, and residual strengths will enable us to dispense with the major fatigue test. However, such improvements may help in the simplification and interpretation of this test. There are a number of questions in this connection that still require further attention. Firstly, to what extent can the time-consuming low-level stresses be omitted?
Secondly, what should be the magnitude of the biggest load applied in test? What pre- cisely is the effect of a load equal to or greater than proof load on the subsequent behaviour and can this effect be counteracted in any way ? This consideration is impor- tant in solving the problem of proving the residual strength of a cracked structure.
To summarize, it is considered that work will be required in the following areas: (1) Theoretical work on dynamic response giving load and stress distributions (2) Development of flight measurement and analysis techniques to check and modify the theoretical assessments (3) The development of operational monitoring devices measuring stress directly.
These devices may be expensive and consequently limited to use on a few aircraft.
(4) The development of monitoring devices that can be used on every aircraft to measure parameters that can be related to the stresses measured on the more elaborate instruments. It is considered essential on military aircraft that some monitoring device is used on every aircraft as the variations in load spectra on aircraft in the same role can be very large.
(5) Development of new cumulative damage theories to account for sequence effects and fretting (6) Development of methods of predicting crack-propagation rates in complex structures under variable loading (7) Development of methods of predicting residual strengths of cracked structures (8) Assessment of what stress levels should be included in fatigue tests under realistic loads (9) The development of aircraft capable of sustained supersonic flight means that more work will be needed in the fields of estimating, measuring, and monitoring stresses due to thermal effects, and interpreting their influence on the fatigue problem.
REFERENCES 1. Raithby, K. D.: A Comparison of Predicted and Achieved Lives of Aircraft Structures.
Tech. Note No. Struct. 301, Brit. R.A.E., 1961. (Paper presented at I.C.A.F.
Symposium on Fatigue (Paris), May 1961.)
2. Phillips, d.: Formulae for Use With the Fatigue Load Meter in the Assessment of Wing Fatigue Life. Tech. Note No. Struct. 279, Brit. R.A.E., 1960.
PRECEDING PAGE BLANK NOT FILMEdM9^2_ ?9901 A PROPOSED USAF FATIGUE EVALUATION PROGRAM BASED UPON RECENT SYSTEMS' EXPERIENCE By G. P. Haviland and G. F. Purkey Aeronautical Systems Division, U.S. Air Force United States SUMMARY The United States Air Force has published a document entitled, "Aircraft Struc- tural Integrity Program" (ASIP). One phase of the program is concerned with the fatigue life certification of all types of military aircraft. The document describes the criteria, analyses, and tests that are necessary in order to satisfy the USAF fatigue life requirement. The authors have noted that some recent and valid criticism has been directed toward the document, particularly the fatigue-life requirements contained in it. This paper proposes some changes based on surveys conducted in the United States and abroad as well as some recent systems' experience. The surveys covered both military and civilian organizations. The paper contains the fatigue certification case histories of selected military and commercial aircraft. The design development element tests, preproduction design verification tests, and full-scale fatigue tests of each are described. The paper concludes with a brief status report on the revisions to the MIL-A-008860 series specifications.
INTRODUCTION In 1965, Miller and Lowndes presented a paper before this group entitled "The U.S. Air Force Weapon Systems Fatigue Certification Program." (See ref. 1.) Their paper described the evolution of the USAF fatigue life requirements up to that time.
One section of the paper listed the aircraft which were considered to be the first line systems of the USAF in 1965. These aircraft are as follows: Fighters Bombers Trainers Transport F-89 B-47 T-37 C-130 F-100 B-52 T-38 C-133 F-101 B-66 KC-135 F-102 F-104 F-105 F-106 Of these only the following aircraft were committed to a fatigue evaluation program: Fighters Bombers Trainers Transport F-101 B-47 T-37 C-130 F-104 B-52 T-38 C-133 KC-135 F-105 F-106 Five years later, the first line systems of the USAF are as follows: Fighters Bombers Trainers Transport F-100 B-52 T-37 C-130 F-105 FB-111 T-38 KC-135 C-5 F-106 F-4 F-5 F-111 A-37 Of these currently operational systems, every one except the F-4 has undergone the U.S. Air Force fatigue evaluation program. The F-4 was procured by the U.S. Navy and has not been required to conform to Air Force Aircraft Structural Integrity Program (ASIP). It is also acknowledged that the F-100 although not originally designed or tested under any formal program has required several life extensions. Each one has been approved after additional fatigue testing. It is interesting to note that all aircraft now in our inventory have undergone a fatigue evaluation program of some kind. This statement was not true 5 years ago. With this as an introduction, we wish to expand on the USAF's fatigue evaluation program and how it has changed over the last 5 years.
HISTORY OF STRUCTURAL EVALUATION PROGRAM 1965 to 1968 Period Figure 1 shows a typical structural evaluation program of the 1965 to 1968 time period. (Also see refs. 2 and 3.) At that time, ASIP required element and component tests, but the number and specimen sizes were left to the contractor's discretion. The static test, flight loads survey, and the first fatigue test were run concurrently. After initial operational capability (IOC) the program called for service-loads determination fol- lowed by a second fatigue specimen to be tested to the service-loads spectrum. At that time, it appeared to be a good plan and the requirements formalizing the program were written as an ASD Technical Report 66-57 "Air Force Structural Integrity Program Requirements," dated January 1968 (ref. 4) and into various specifications and contracts.
For those of you who are satisfied with your program now, please note that in 1968 we believed that this program was the best in the world. Events proved us to be wrong.
1968 to Early 1970 Period In September 1968 the Assistant Secretary of the Air Force for Research and Development, Dr, Flax, requested that a study be performed addressing problems asso- ciated with structural test program planning and with scheduling practices. (This study is referred to as the Flax study.) Briefly restated, the action items were (a) Examine current Air Force structural test procedures and policies for aircraft in development.
(b) Assess structural test program scheduling problems.
(c) Assess past and present structural testing to determine problems or deficiencies in established policies and procedures.
(d) Provide recommendations to revise present Air Force structural test verifica- tion practices and policies, considering proper balance between program risks and costs.
The approach used in the Flax study was to prepare case histories of the then cur- rent systems and a number of typical earlier systems on which information was available.
Included in the study were such data as original test schedules, the details of static and fatigue tests, actual start and completion of the tests, and the production rates. The case histories were carefully studied to establish trends and to identify problem areas. With these thoughts in mind, let us consider the actual structural program schedules of some of the Air Force aircraft that were used in the study.
The first aircraft is a large transport, the C-141. Figure 2 shows the schedule.
The C-141 comes as close as any airplane to fulfilling the total ASIP requirements. It has a static test, structural flight tests, full-scale fatigue tests of two articles, and a life- history recorder program, the data from which are being used for the second fatigue test.
Figure 2 refers to fatigue test articles A, B, C, D, and E which are shown pictorially in figure 3.
There were a large number of engineering changes generated by the C-141 fatigue test program. Most of them were incorporated in production but very late in time. You can see that there were essentially no component tests. We did a static test and a flight loads survey almost concurrently as called for by the 1968 ASIP schedule shown earlier, but the fatigue test was very late in starting. We had aircraft out in the operational fleet before we had one lifetime on the fatigue test specimen.
Using hindsight, if we had started the first fatigue test earlier, we would have been able to incorporate the changes into earlier production airframes. Instead, we were unable to get changes into production earlier than the 200th airframe and we only had 285 airframes in the production contract. The fatigue test article had been identified early enough (it was the seventh airframe), but the actual start of the testing slipped because of management considerations. The lesson learned here was an important one.
If you have a production airframe, get started on the fatigue test as early as possible.
In order to understand more about how the commercial manufacturers design and build airframes, we will deviate from the Flax study and show you a comparison we made between the C-141 and, with the assistance of the Boeing Company, the Boeing 727. We found that Boeing uses a modified form of ASIP. Boeing does everything that ASIP requires, but not in as much depth or detail as we in the Air Force do. For example, a flight loads survey was conducted on the 727 because the FAA was interested in the T-tail.
Otherwise, the survey would not have been flown. Our load survey on the C-141 was very comprehensive.
Let us consider the fatigue tests of the two aircraft. The preparation of the fatigue spectra for the C-141 was complicated by the large number of missions assigned to the aircraft. Low level penetration, air delivery of cargo and wartime training missions had to be included in the spectrum. Therefore, the C-141 required about twice the fatigue test segments needed for the 727. The Boeing 727 has essentially a single logistic mis- sion at altitude.
The way we did our tests compared with the way Boeing performed their fatigue tests is also very interesting. A list of the fatigue test articles for the 727 and the 747 follow: 727 and 747 nose landing gear Main landing gear Airframe Wing Fuselage Vertical tail Horizontal tail Control surfaces The horizontal tail was a separate test specimen for the 747. You have already seen those for the C-141 fatigue test specimen in figure 3. We chose to break the airframe up into components so that a failure on one specimen will not cause an interruption to the others. This method is more expensive than the method used by Boeing but it is less risky.
Figure 4 is a direct comparison between the test schedules of the C-141 and the 727. The differences in magnitude of the scope of the tests are significant. Our static test took longer because of down time and a need to retest the wing after uncovering a different load distribution than expected during the flight loads survey. Our fatigue test also took longer because of the multimission requirement of the C-141. The major dif- ferences between Boeing tests and the USAF tests are as follows: 13 missions C-141 1 mission Boeing tests whole structure USAF test major components Boeing performs modest flight loads survey USAF performs full flight loads survey Now let us consider another Air Force aircraft test program, that for the F-5 (fig. 5). This program was successful for two reasons: First, the F-5 airframe was essentially the same as that of the T-38 and the Norair N-156 which had undergone an extensive structural evaluation program. Secondly, the items that were changed on the F-5 from the T-38 were tested as components during the design development testing phase of the program. The primary difference between the T-38 and the F-5 was, of course, that the T-38 was a trainer type aircraft designed for the training environment, whereas the F-5 was a fighter type with external stores and tip tanks, leading-edge flaps, and drag chute; the F-5 was also designed for the close ground support fighter environment. This type of redesign readily lends itself to verification of structural adequacy by utilizing small components or element testing. In the development of the F-5, it it had not had the T-38 as a predecessor, the component tests would have been required.
It should be noted that the service-loads—life-history phase was limited on the F-5 evaluation. It started late and was stopped much too early. If a continuous program had been accomplished, the loss of an F-5 at Williams Air Force Base in early 1970 might have been averted. At Williams AFB, training is conducted for Military Assistance Program (MAP) pilots. During this training a large number of 2g to 3g maneuvers are accomplished. The fatigue damage accumulated from this training is much greater than the average damage accumulation and a fatigue crack developed in the center wing lower skin that caused the loss of pilot and aircraft. This fatigue critical area had been detected in the full-scale fatigue test. Had an adequate service-loads or life-history program been in being, the damage accumulation should have been detected and an adequate inspection program could have anticipated the need for repair.
The timing of the full-scale fatigue test also could stand some improvement in that it could have started sooner. Again, the previous T-38 tests along with the F-5 develop- ment tests minimized the impact of the later start and did allow the use of a truly produc- tion configuration for the full-scale fatigue test.
Out of the Flax study came some very significant recommendations: (a) Continue early static and fatigue tests (b) Emphasize component tests (c) Establish firm policy on structural integrity program (d) Perform cost effectiveness studies during contract definition phase between developmental and production testing and between production build-up and structural retrofit. These recommendations were acicepted and we revised our ASIP requirements document ASD TR 66-57 (ref. 5). It was published in May 1970 and many of you are famil- iar with it.
Now we want to discuss the present ASIP schedule, the one called for by the 1970 version of ASD TR 66-57. Before doing that, let us agree on some definitions of element tests, design-development tests, preproduction design verification tests, and full-scale tests. Element tests involve relatively small parts of the structure, joints, small panels, or stringer to frame splices. These are very small pieces but, as you know, extremely important to the structure. Design development and preproduction design verification tests consist of those tests of materials, structural elements, and structural components performed early in the design phase to provide a realistic basis for the design analysis r and major structural ground tests. The design development tests are the most basic and earliest tests and are conducted to establish basic design concepts and configurations such as choice of materials, panel sizes, splices, fittings, etc. Preproduction design verification (PDV) tests are conducted after the design development tests, but prior to the full-scale static and fatigue tests. These tests of full-scale components (wing carry through, wing pivots, horizontal-tail support, etc.) are conducted to provide early design information wherever analytical methods may be inadequate to achieve a high degree of confidence in the strength and fatigue properties of the design. These tests are intended to reveal design "glitches" prior to the full-scale ground tests.
With these thoughts as background, let us consider our present ASIP schedule. It is representative of the program now being used on the F-15 and provided the original scheme for the B-1 (fig. 6). It requires that the contractor conduct early preproduction design verification component tests of major assemblies. It also requires two full-scale fatigue tests, the first as early as possible and concurrent with the static test and the flight loads survey. After IOC it requires a service-loads program to obtain the spectrum for the second fatigue test.
1970 to Present Thus far we have traced the changes to the ASIP fatigue evaluation program from 1965 to 1970. Then we had some structural problems which focused national attention on the structural integrity of some of our systems, notably the F-111 and the C-5.
At the direction of Secretary of the Air Force, Seamans, a group of experts was formed to look into the problems we were having or might have in the future. There fol- lowed a year and a half of study, reappraisal, reviews, audits, and an overall reevalua- tion of ASIP and its requirements.
One phase of the structural integrity review involved a trip to Europe. The authors had an opportunity to visit some of you in your home countries of France, Holland, and England. We learned quite a bit from our discussions with you and have since been involved in various meetings and conferences on ASIP.
We had thought of ASIP as a logical, step-by-step program, which, if followed, would insure a structurally sound airplane. But we were mistaken, those of you in Europe seem to be able to design and build sound airframes without a formal structural integrity program such as ASIP. Moreover, we found that ASIP as applied to programs here in the U.S. sometimes worked and sometimes it did not. The primary variable seemed to be the contractor or perhaps the type of contract and not ASIP itself. Thus, our experience has shown that the structural quality of an airplane is a function of who designs it and how he designs and builds it. It has had little to do with the ASIP docu- mentation. This may be an oversimplification of the situation we face in the Air Force today. We realize that our treatment so far has not addressed the basic question of "Do we really need an ASIP at all?" Even so, permit me to pursue a line of reasoning based on the following premises: (a) ASIP should be effective regardless of the contractor or the contract selected.
(b) It is not.
(c) Therefore, ASIP should be changed.
As a result of recent systems' experience, structural development cost restraints, and a review of international structural test practices, the Air Force is proposing a structural development test program that is different from that used before. The signifi- cant change is in the method of fatigue evaluation, as you will notice (fig. 7). The pre- production tests of major assemblies and the early fatigue tests now required seem to be duplicative efforts rather than what is desired. The preproduction tests should identify deficiencies that can be corrected in time for validation on the early full-scale fatigue test.
In the proposed program, design development and preproduction design verification (PDV) tests that are more extensive than those originally identified by the USAF in 1970 are envisioned. The very early component tests must now provide for complete struc- tural evaluation (strength, fatigue, fracture) of the major critical areas of the primary structure. This is necessary (mandatory, even) inasmuch as these component tests are to be the main basis for determining adequacy of the design, proof of compliance, and even early life flight safety since the full-scale fatigue test will be delayed under this proposal. The PDV tests must be comprehensive. Note that this requirement is an intrinsic part of the proposed program.
The important scheduling of the full-scale static test and the flight loads measure- ment program retain their original timing. These tests are to coincide with the delivery of the first flight article and are to receive equal priority with other subsystem evaluation requirements.
The major change that we are proposing focuses on the full-scale fatigue test.
Until now we have identified, in the initial system plans, a requirement for two full-scale fatigue tests, one strictly an early design evaluation test and the other a delayed test (approximately two or more years after initial operational capability) that utilized the results of the earlier design evaluation tests (static test, fatigue test, and flight loads survey). This late fatigue test was also intended to be delayed until completion of the service-loads recording program so that accurate service environment data would be available. However, even when faced with the real-world past experience that all first line military aircraft systems (especially fighters) eventually undergo more than one full-scale fatigue test, USAF management was unwilling to identify funds for two full- scale fatigue tests during initial program definition.
Recognizing this situation and the increased emphasis that we are placing on early component PDV testing and the desire to make the PDV tests effectively impact the design phase as well as the full-scale testing, we are proposing to identify a single fatigue test which will be conducted later than the first test and earlier than the second test previously required. This revised scheduling of the single full-scale fatigue test is necessary so that it will incorporate the findings of the PDV tests, static test, and the flight loads survey.
In all probability, it will not be delayed a sufficient amount of time to use the results of the service-loads recording program.
Finally, we recognize, and everyone else should also, that additional laboratory tests (even flight tests) may be required as extensive service experience is accumulated.
However, no attempt will be made to identify any additional test requirements in the orig- inal development process.
There are definite critical control points in our proposed program that must con- stantly be reviewed as new systems are developed. There are also some important questions that must be answered: (1) Can the structures discipline effectively divert major airframe components from the ever present push to get a flight article as early as possible? Our proposed fatigue evaluation program has as its very foundation a comprehensive PDV test pro- gram that will require major structural components early enough to complete the tests before flight articles are produced. Can we win out against the competition and acquire these early components in time for the structural evaluation?
(2) The full-scale fatigue test can no longer be used as contractual proof that the design fatigue life requirements have been met. The test will now be based on results of earlier design and test information that cannot be accurately foreseen. Demonstration of structural fatigue quality assurance requirements must utilize the PDV tests.
(3) USAF management must be aware that major changes in the aircraft structure or mission may require further validation. Also, further validation may be required if the single fatigue test did not contain inputs that are representative of the service envi- ronment for the original design missions.
We have outlined the proposed changes that the U.S. Air Force is planning in the fatigue evaluation program for future systems. These changes are planned to be incor- porated into a revision of both the technical report ASD TR 66-57, dated May 1970, and the appropriate Structures Military Specifications, commonly referred to as the 8860 series specifications.
UPDATING OF SPECIFICATIONS MIL-A-8860 Specifications To conclude our treatment of the proposed fatigue evaluation program, it may be useful to review our recent progress in updating the MIL-A-8860 specifications. As a result of the Seamans' study, it was suggested that our organization (Aeronautical Systems Division) have the prime responsibility for the documents. Previously, the responsibility rested with the Flight Dynamics Laboratory. We propose to cover some of the significant changes we are making in three selected specifications as well as in the ASD TR 66-57.
The revision of the technical report ASD TR 66-57 will convert the format of the report from an ASD TR to a MIL-STD-(USAF). In addition to the fatigue evaluation changes just discussed, it is planned to include in the revised MIL-STD new or increased emphasis on materials selection, fracture mechanics requirements, and damage tolerance design.
The addition of the requirements for materials selection are presently being written.
The area of fracture mechanics principles is, of course, directly related to materials selection and some of the research work being accomplished in this area is the subject of a paper by Howard A. Wood, of the Air Force Flight Dynamics Laboratory (paper no. 14 of this compilation).
In the area of damage tolerance design requirements, we have made some progress in updating our requirements. Since the new MIL-STD will only summarize the damage tolerance requirements that are contained in the MIL-A-8860 series specifications, our initial effort has been concentrated on revising these specifications. In an attempt to expedite the revision, the Air Force elected to revise and publish "USAF only" revisions.
These limited coordinated (USAF only) military specifications have been prepared by using currently available technical information, but they have not been approved for promulga- tion as a fully coordinated (USAF, Navy, and Army) revision of military specifications.
They are subject to modification. Pending their promulgation as fully coordinated mili- tary specifications, they may be used in procurement (USAF). The damage tolerance design requirements contained in these revised specifications are covered in the following sections.
Damage Tolerance Requirements for Inclusion in MIL-A-008860A (USAF) The primary structure shall incorporate materials, stress levels, and structural configurations which will minimize the probability of loss of the aircraft due to propaga- tion of undetected flaws, cracks, or other damage. Slow crack growth, alternate load- paths and systems, and other available principles shall be employed to achieve this cap- ability. For this damage tolerance requirement, the primary structure is defined as including all structural elements the failure of which will (a) Cause uncontrollable motions of the aircraft within the speed limits for its structural design (b) Prevent an aircraft from achieving speeds sufficiently low to effect a safe landing (c) Reduce the ultimate factor of safety for flight design conditions from 1.5 to a value less than 1.0.
Damage Tolerance Requirements for Inclusion in MIL-A-008866A (USAF) General requirements.- Safe-life design shall be employed as the primary means of satisfying the specified service life requirement established in appropriate contractual documents for each USAF aircraft system. In addition, damage tolerance concepts shall be applied as a design requirement for primary structure vital to the integrity of the vehicle or the safety of personnel. This latter requirement stems from the recognition that, despite concerted safe-life-insurance efforts through design, analyses, and tests, undetected flaws or damage can exist in critical structural components at some time dur- ing the life of the aircraft with attendant, serious consequences.
Safe life.- The fatigue critical areas of the airframe shall be identified through analyses and tests (developmental, preproduction component, and full-scale article). The structure shall be shown to withstand, without structural failure, the design repeated loads spectrum equal to the design fatigue-scatter factor times the service-loads spectrum.
A service-loads spectrum is defined for one lifetime only and does not include a design fatigue-scatter factor. Modifications found necessary to satisfy this requirement shall be incorporated prior to aircraft delivery or by retrofit in fleet aircraft as agreed to by the procuring agency.
Design fatigue-scatter factor.- The design fatigue-scatter factor is a factor to pro- vide protection against fatigue failure of those fleet airplanes that experience a service- loads spectrum more severe than the design service-loads spectrum and have fatigue-life capabilities less than those of laboratory test articles. The design fatigue-scatter factor shall be a minimum of 4.0 or as otherwise approved by the procuring activity.
Service-loads spectrum.- The service-loads spectrum is derived from a collection of loads spectra. Each loads spectrum in this collection shall define the expected (aver- age) number of load cycles according to load magnitude for a given source of repeated loads. The loads spectrum for each significant source of repeated loads shall be based on a realistic interpretation of the design usage. The contractor shall include all signifi- cant sources of repeated loads. The sources of repeated loads may include, but not be limited to, ground handling and taxiing operations, landing operations, flight maneuvers, atmospheric turbulence, inflight refueling, autopilot, inputs, cabin pressurization, buffet- ing, terrain-following maneuvers, and the ground-air-ground cycle.
Damage tolerance.- The primary structure vital to the integrity of the vehicle or to the safety of personnel shall incorporate materials, stress levels, and structural configu- rations which minimize the probability of structural failure due to the propagation of undetected flaws, cracks, or other damage. The choice of damage-tolerant design con- cepts (fail safe, safe crack growth, or combinations thereof) for the design of specific critical structural components shall be as agreed between the procuring agency and the contractor. Analysis and supporting tests shall be conducted to evaluate the flaw growth and residual strength characteristics of the critical structural components.
Fail safe.- Primary structure that is designed fail safe shall be readily inspectable and meet the following requirements after failure of a principal structural element: (1) the remaining structure shall sustain without failure the maximum expected load or limit load, whichever is greater, (2) the airplane shall be controllable within the design speed limits, and (3) catastrophic failure of the remaining structure will not occur under repeated load conditions during the period to the next opportunity to detect the failure.
Verification of the ability of the remaining structure to withstand the repeated loads shall be accomplished by determining the crack growth period from an initial flaw to failure of a principal element, and then ensuring that the life (including the factor of four) of the remaining structure will equal or exceed the time interval established for the next inspec- tion. Inspection intervals shall be as agreed to by the procuring agency, but, in general, these intervals shall be of reasonable duration commensurate with total system require- ments. Readily inspectable structure is defined as that which can be inspected after removal of access panels, doors, etc. Removal of permanent type skins and fasteners is not included. The details of inspection shall be agreed upon by the procuring agency and the contractor.
Safe crack growth.- Critical primary structure that is not fail safe shall be designed so that initial flaws will not propagate to the critical crack length during the specified ser- vice life of the airplane. Through fracture data tests and analysis, the characteristics and dimensions of the smallest initial defect that could grow to critical size during the specified service life shall be determined. Once these initial flaw sizes have been identi- fied, quality control procedures shall be developed so that parts containing initial flaws of these dimensions will not be accepted. In the event that the identified initial flaw sizes are smaller than the quality control detection capability, changes shall be made in the materials and/or stress levels so that larger initial flaws (compatible with quality control capability) can be tolerated.
Damage-Tolerance Test Requirements for Inclusion in MIL-A-008867A (USAF) Fracture data tests.- Fracture data shall be generated during the design develop- ment test phase on all candidate materials for which no valid data base exists to support the analysis requirements. These tests shall include plane strain and plane stress tests to determine fracture toughness values as well as crack propagation tests to determine incremental crack extension rates. These data shall be used for comparative evaluation of proposed materials and designs. Fracture toughness values shall be determined in accordance with the procedures set forth in the current standards. Specifications shall be prepared to ensure that materials having minimum guaranteed fracture-toughness param- eter values are used in manufacture where test specimens having dimensions that (K,C) satisfy ASTM requirements can be obtained. Continued sampling of final manufactured parts shall be accomplished throughout the production life to ensure consistency with the required strength and toughness levels.
Crack propagation tests shall be conducted on element specimens to determine the conventional cyclic crack growth rate and sustained load growth rate data. These tests shall include the evaluation of the effects of various atmospheric environments (such as temperature, humidity, fuel, salt, etc.). Spectrum tests of flawed specimens shall also be conducted when insufficient data exists or when proven analytical capability to predict spectrum effects is lacking.
Crack growth tests.- Crack growth tests of preproduction components shall be con- ducted as required to verify that the damage tolerance criteria have been met. These tests shall be accomplished by applying a spectrum of loads and environment that simu- lates operational usage which will determine the time to crack initiation and the time to failure of a single principal element. These tests shall utilize, wherever possible, the existing component structures fabricated for evaluation of the strength and fatigue proper- ties as an "add-on" test effort. When necessary, additional component structures shall be fabricated.
The revised structural specifications are as follows: Specification number Short title MIL-A-008860A (USAF) General MIL-A-008861A (USAF) Flight loads MIL-A-008862A (USAF) Ground loads MIL-A-008865A (USAF) Miscellaneous loads MIL-A-008866A (USAF) Fatigue MIL-A-008867A (USAF) Ground tests MIL-A-008869A (USAF) Nuclear MIL-A-008870A (USAF) Flutter MIL-A-8871A (USAF) Flight test MIL-A-8892A (USAF) Vibration MIL-A-8893A (USAF) Sonic fatigue These specifications listed are dated 31 March 1971 and are presently in printing; the estimated distribution date is July 1971. The MIL-A-008860A, 61A, 62A, 65A, 67A, 69A, and 70A are former ASG (joint) specifications which have been revised as USAF only specifications. MIL-A-008871A has always been a USAF only specification. MIL-A-8892 and MIL-A-8893 are new specifications which apply to USAF only.
The next two major efforts that are presently being accomplished are, revision of ASD TR 66-57 into a MIL-STD, and full coordination on the revised specification will result in ASG type specifications.
CONCLUDING REMARKS We are proposing the elimination of one full-scale fatigue test article and replacing it with early full-scale component tests. The full-scale fatigue test is performed later than present requirements state but earlier than the previously required second fatigue test. To formalize this change in the fatigue evaluation program, we are revising the 8860 series of specifications and writing the USAF ASIP into a separate Military Standard.
The authors wish to express their appreciation to Mr. Troy King for his assistance in preparing this paper.
REFERENCES 1. Miller, W. B.; and Lowndes, H. B.: The U.S. Air Force Weapon Systems Fatigue Certification Program. Technical Paper, ASD, U.S. Air Force, June 1965.
2. Anon.: Detailed Requirements for Structural Fatigue Certification Programs. Tech.
Memo. WCLS-TM-58-4, U.S. Air Force, June 27, 1968.
3. Anon.: Detailed Requirements and Status Air Force Structural Integrity Program.
ASD TN 61-141, U.S. Air Force, Sept. 1961.
4. Anon.: Air Force Structural Integrity Program Requirements. ASD Tech. Rep. 66-57, U.S. Air Force, Jan. 1968.
5. Anon.: Air Force Aircraft Structural Integrity Program: Airplane Requirements.
ASD Tech. Rep. 66-57, U.S. Air Force, May 1970.
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kK ^, NOT FILMED 4AEVAK PRECED&6 FATIGUE TESTS WITH RANDOM FLIGHT-SIMULATION LOADING By J. Schijve National Aerospace Laboratory, Amsterdam, The Netherlands SUMMARY Crack propagation was studied in a full-scale wing structure under different sim- ulated flight conditions. Omission of low-amplitude gust cycles had a small effect on the crack rate. Truncation of the infrequently occurring high-amplitude gust cycles to a lower level had a noticeably accelerating effect on crack growth. The application of fail-safe load (100 percent limit load) effectively stopped subsequent crack growth under resumed flight-simulation loading.
In another flight-simulation test series on sheet specimens, the variables studied are the design stress level and the cyclic frequency of the random gust loading. In- flight mean stresses vary from .5.5 to 10.0 kg/mm 2 . The effect of the stress level is larger for the 2024 alloy than for the 7075 alloy. Three frequencies were employed: namely, 10 cps, 1 cps, and 0.1 cps. The frequency effect was small.
The advantages and limitations of flight-simulation tests are compared with those of alternative test procedures such as constant-amplitude tests, program tests, and random-load tests. Various testing purposes are considered. The variables of flight- simulation tests are listed and their effects are discussed.
A proposal is made for performing systematic flight-simulation tests in such a way that the compiled data may be used as a source of reference. The data could be used for estimating fatigue properties in the design stage of an aircraft and serve other purposes as well.
INTRODUCTION The fatigue loads in a flight-simulation test are supposed to be a valid represen- tation of the loading conditions in service. In the present paper, an attempt is made to analyze the merits and the limitations of flight-simulation fatigue tests.
Recently at the National Aerospace Laboratory, extensive studies have been made regarding fatigue crack propagation under random flight-simulation loading in 2024-T3 and 7075-T6 aluminum alloys (refs. 1 to 3). Tests on crack propagation in a full-scale wing structure have just been completed and the results are summarized herein.
Another program on the frequency effect under flight-simulation loading is halfway finished. It also includes the effect of the design stress level. Preliminary data are given in a subsequent section.
A comparison is made between flight-simulation testing and alternative test proce- dures. The objectives of testing are obviously important for such a comparison. The variables of flight-simulation testing are listed and data on the significance of the vari- ables are reviewed. The information is fairly limited as yet. Finally, a proposal is made for performing systematic flight-simulation tests in order to compile data that may be used as a source of reference.
TWO RECENT NATIONAL AEROSPACE LABORATORY TEST PROGRAMS Crack Propagation in a Full-Scale Wing Structure Under Random Flight-Simulation Loading The fatigue test and the fail-safe tests on the wing of the F-28 aircraft were suc- cessfully completed in April 1970. It was then decided to employ the test setup and the wing for a general crack propagation investigation. The aim of the investigation was to study the effects of (1) omitting low-amplitude gust cycles (2) truncating very-high-amplitude gust cycles to a lower level (3) increasing the stress level by 25 percent (4) preceding limit loads delaying subsequent crack growth.
The wing loads applied by 12 hydraulic cylinders included gust loads, ground-to-air cycles, flap loads, and undercarriage loads. The load sequence was a random flight simulation similar to the sequences applied in the certification tests on the wing and in tests on sheet specimens (refs. 1 to 3). A sample of a load record is given in figure 1, and the test setup is shown in figure 2. The gust load spectrum was approximated by a stepped function. (See fig. 3.)
Three test series (A, B, C) were carried out and data from the certification tests (series R) were also used for comparison. In the certification tests the low-amplitude cycles were not omitted. The omission of these cycles in test series A reduced testing time from 116 seconds to 46 seconds per flight; this implies a considerable time saving.
The certification tests were completed by three fail-safe tests up to limit load, and this allowed observations on the effect of limit load application on subsequent crack growth during test series A, B, and C.
The numbers of simulated flights are indicated in figure 3. In each test series (A, B, C), groups of 2 to 4 artificial cracks were applied in the following elements: skin between stringers, skin and stringer flange, stringer head (Z -stringer), and spar web.
The cracks were applied at similar locations with approximately the same stress level in all test series. In the certification tests (series R), a large number of cracks were tested; however, for comparison with the present test series only a few cracks could be used in view of the similarity of location and stress level.
The complete results as given in reference 4 showed low scatter in each group of 2 to 4 similar cracks. A summary of the average results is presented herein. As an illustration, figure 4 shows average crack propagation curves for the skin when the stringer flange is also cracked. From similar curves, average crack rates were drawn and comparisons are made in this study.
Effect of omitting low-amplitude gust cycles.- The effect of omitting low-amplitude gust cycles from flight-simulation loading (comparison of results of test series A and R) is presented in the following table: Average effect Cracked component Material on crack rate Skin between stringers 2024-T3 Slightly slower Skin at stringer 2024-T3 About equal Stringer flange 7075-T6 1.5 times slower Head of stringer 7075-T6 2 times faster Spar web 7075-T6 1.5 times slower The fourth result in the table (Head of stringer) is believed to be an erratic one which can- not be explained as yet. If this result is ignored, the table indicates a slightly slower or equal crack rate in the 2024-T3 skin material and a 1.5 times slower rate in the 7075-T6 material. These trends are in good agreement with previous tests employing similar load sequences (refs. 1 and 3) on 2024-T3 and 7075-T6 sheet specimens. In those tests, omitting gust cycles with the lowest amplitude implied that the average crack rates were about 1.2 times and 1.4 times slower for the 2024-T3 and 7075-T6 aluminum alloys, respectively.
Effect of truncating high-amplitude cycles.- The effect of truncating high-amplitude cycles is presented in figure 3 where it is seen that the three highest amplitudes were reduced to the next highest one. A summary of the results of truncating high-amplitude gust cycles of flight-simulation loading (comparison of results of test series B and A) is given in the following table: Average effect Cracked component Material on crack rate Skin between stringers 2024-T3 2.5 times faster Skin at stringer 2024-T3 2 times faster Stringer flange 7075-T6 2 times faster Stringer head 2024-T3 4 times faster Stringer head 7075-T6 2 times faster Spar web 7075-T6 1.5 times faster The last column of the table shows that truncation of the high-amplitude gust cycles to a lower level in all cases accelerated the crack growth. On the average the crack rate was about 2.3 times faster in test series B than in test series A. In reference 2 with flight- simulation tests on sheet specimens carried out at similar stress levels, the same truncation caused a 3 times faster crack rate. Although the factor is somewhat higher, it is still thought to be a fair agreement.
Effect of increasing the design stress level. - In test series C all loads applied were 25 percent higher than those in test series A. Obviously higher crack rates should then be expected which was confirmed by test series C. Unfortunately there was a fairly large variation between the accelerating effect of the various components. On the average the crack rate was 2.5 times faster in test series C. Sheet specimen data from reference 2 predicted a somewhat higher crack rate, whereas results in the following section of this paper predicted a lower crack rate.
Effect of fail-safe loads on subsequent crack propagation.- Several investigations (refs. 5 to 8) employing constant-amplitude loading have shown very long crack-growth delays if the test was interrupted for a high load. The wing test offered an opportunity to observe the effect of a high load on crack propagation under flight-simulation loading.
Test series R was completed by applying limit load three times. Some 10 cracks that had shown a reasonable amount of crack growth during test series R were left unrepaired.
Without exceptions, the limit load applications had a large delaying effect on the growth of these cracks. Some examples are shown in figure 5. The vertical bar in the graphs indicates the stable crack growth during the three fail-safe tests up to limit load. Several cracks came to a complete standstill with a tendency to resume crack growth during test series C (25 percent higher loads).
It was suggested now and then to apply periodically fail-safe loads in a full-scale test. The argument was that hidden cracks would then readily show up. Unfortunately, this might well be the best method to hide these cracks completely, since further growth will be drastically delayed.
Effects of Frequency and Design Stress Level on Crack Propagation Under Random Flight-Simulation Loading The test program is still in progress and preliminary results can be presented only.
Tests are being carried out on 2024-T3 Alclad and 7075-T6 Alclad specimens. Specimen width is 160 mm and the thickness is 2 mm. The cracks are starting from a central saw- cut notch. Some specimens were precracked by constant-amplitude fatigue testing to a semicrack length 1 of 10 mm or of 20 mm. Others were given a saw cut to a semicrack length 1 of 8 mm and were tested without additional precracking.
The load sequences applied are the same as those applied to the wing, with one addi- tional feature. In each flight each positive gust load was followed by a negative one and vice versa. However, the amplitude for each half-cycle was selected at random from the amplitudes to be applied in that flight.a Truncation of the gust spectrum occurred at the same level as shown in figure 3 for test series B, whereas the low-amplitude cycles were not omitted. The first tests were started with the following values for the stress levels: Mean stress in flight Sill = 7.0 kg/mm2 Gust amplitudes Sa = 1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7 kg/mm2 Minimum stress in GTAC Smin = -3.4 kg/mm2 Hence, the truncation level is Sa = 7.7 kg/mm 2 . The same values were applied in ref- erences 1 and 3.
Changing the design stress level implies that all stress levels should be multiplied by the same factor. With the mean stress in flight as the characteristic stress level, tests are carried out at S m = 10.0, 8.5, 7.0, 5.5 kg/mm 2 . The gust amplitude and the minimum stress in the ground-to-air cycles are amplified accordingly. Test results are available for a loading frequency of 10 cps. (See fig. 6. b) It turns out that the effect of the stress level is different for the two alloys. At Sm = 5.5 kg/mm 2 , the 2024 alloy is still far superior to the 7075 alloy. At higher S m values the difference is negligible.
It is thought that this relatively good behavior of the 7075 alloy should be attributed to the fact that favorable residual stresses are better maintained in this alloy. It is noteworthy a In the terminology of Naumann (ref. 9) the wing loading employed "random cycles" and the specimens were loaded by "random half-cycles, restrained."
b Since the stress histories were the same in all tests, except for the intensity of the stress, it was hoped to correlate the data for different stress levels by employing the stress intensity factor K. The results were disappointing and apparently similar K values do not imply similar crack rates in this case. This is attributed to different K-histories in the crack tip area and predominant interaction effects of stress cycles with different amplitudes. This issue will be discussed in more detail in the final report of this investigation.
that a trend such as that illustrated by figure 6 cannot be predicted from constant- amplitude data.
The effect of the load cycling frequency is studied by carrying out tests at 10 cps, 1 cps, and 0.1 cps. Available data have been compiled in the following table: 7075-T6 2024-T3 aluminum alloy aluminum alloy 24 to 60 Crack growth 21, mm . . . 24 to 60 40 to 60 40 to 60 . . . . . . . 10 8.5 10 8.5 Sm, kg/mm 2 .
Life in flights at — 1105 1235 1382 1520 10 cps . . . . . . . . . .
1 cps . . . . . . . . . . 1262 1116 1265 1360 1234 1350 0.1 cps . . . . . . . . . 1200 As the table shows, the effect is not fully systematic but it is small, as might have been expected from constant-amplitude data (refs. 10 and 11). Of course one should be careful about generalizing the present data, especially if corrosive environments are present.
-SIMULATION TESTING FLIGHT In this section of the paper, various aspects of flight-simulation testing are dis- cussed and a proposal is made for a systematic compilation of flight-simulation fatigue test data.
Development of Several Fatigue Testing Procedures In the past attempts were made to predict fatigue strength and fatigue life from simple fatigue data. Several complicating factors were early recognized and extensively studied. Examples are the presence of a mean stress as opposed to zero mean stress, the presence of notches as opposed to unnotched material, and the existence of large com- ponents as opposed to small laboratory specimens. Other factors, such as the effect of surface finish and fretting corrosion, led to an overwhelming number of empirical investi- gations. Qualitatively, understanding of all these influencing factors has highly increased.
Nevertheless, it is still generally believed necessary to perform fatigue tests on the real components and preferably on a full-scale structure. For full-scale testing there are additional arguments, such as a realistic representation of eccentricities and load trans- mission in the structure and the indication of accidentally poor design features.
Testing a component or a full-scale structure implies that one wants to simulate the structural configuration as realistically as possible. In great contrast with these efforts, an unrealistic simulation of service load history was usually adopted in fatigue tests.
Since the accidents with the Comets in the early fifties, several new designs were sub- jected to a full-scale fatigue test. Usually this was a flight-simulation test, that is, with a flight-by-flight loading. However, the gust loading was highly simplified in many cases.
A simulation of a complex load time history was obviously impossible in the early days. In 1939 Gassner (ref. 12) published his first paper on program loading. He pre- sented program loading as an improved method for estimating fatigue life although at that time Gassner had already realized that program loading was still afflicted with important deviations from load sequences in service. However, available testing equipment at that time could not do a better job.
Around 1960 random load fatigue tests started to draw much attention, partly because it became possible to carry out this type of testing. On the other hand, several types of fatigue loads in service had a random character. Moreover an elegant mathe- matical framework was available for dealing with random variables. Kirkby and Edwards (ref. 13) proposed to adopt narrow-band random loading in a way similar to that proposed by Gassner for program loading. This type of loading could still be applied in a resonance-type fatigue machine.
A real breakthrough was the introduction of the closed-loop electrohydraulic system with servovalves for monitoring the hydraulic load. An arbitrary load time history can be obtained from a similar electric signal. This system is now being used for relatively slow full-scale testing as well as fast testing of components or small specimens. The system has been developed to a high degree of reliability. Actually the impossibility of simulating a complex load time history has been eliminated. In other words, realistic load sequences can now be simulated in fatigue testing. It appears rather natural that a realistic simulation of a component or a structure should then be combined with a realistic simulation of service loading.
Purpose of Fatigue Testing For a discussion on testing methods it is useful to keep in mind the variety of test purposes and test articles. A broad summary is given in the following table: Test article I Testing method Test purpose Laboratory specimen Constant-amplitude test + (a) Basic data for fatigue life estimates Component I Program test I (b) Comparative design studies Full-scale structure I Random-load test I (c) Direct life estimates Flight-simulation test I (d) Indication of fatigue critical ele- ments, crack rates, and inspection methods It is thought that testing purposes (c) and (d) require a realistic simulation of both the test article and the service load time history. Consequently, some type of flight- simulation loading is necessary. With respect to test purposes (a) and (b) different opinions may be held.
The utilization of constant-amplitude test data from laboratory specimens as basic data for life estimates is a complex problem. A cumulative damage rule has to be adopted — for instance, the Palmgren-Miner rule. Then, the differences between labora- tory specimens and the actual structure have to be considered. The conclusion has to be that only very rough life estimates can be made in this way.
Gassner and Schutz (ref. 14) have proposed to use data from program tests as basic data for making life estimates. A similar proposal was made by Kirkby and Edwards (ref. 13) for random loading. There are some indications that life estimates may be improved in this way. However, discrepancies between the fatigue lives obtained in ran- dom tests and equivalent program tests (refs. 15 to 19) are not encouraging in this respect. Moreover, uncertainties about the damage rule and the relevance of the speci- mens remain. Actually flight-simulation fatigue test data could well be used for this purpose.
Test purpose (b) in the foregoing table is concerned with the comparison between different components, materials, and surface treatments for the same application in an aircraft structure. Many people still feel that constant-amplitude tests are a good means for this purpose. However, the possibility of intersecting (or nonparallel) S-N curves is making this doubtful. In figure 7, test results at stress level Saj would indicate design A to be superior to design B. However, at stress level Sa , 2 design B appears to be superior.
As an illustration of different answers to the same question, a recent investigation with constant-amplitude loading (ref. 3) indicated that the crack propagation in 7075-T6 was 4 times faster than the crack propagation in 2024-T3. However, under flight- simulation loading it was only twice as fast. The data of figure 6 are also illustrative in this respect.
The numerous test series with program loading carried out by Gassner and his coworkers (ref. 20) indicate that the risk of a misjudgment would be much smaller if pro- gram loading were adopted for comparative testing. This applies also to random loading (ref. 21). Nevertheless, if flight-simulation loading can be adopted, it apparently is the most preferable solution. Real problems should be tackled with realistic testing methods if possible. Recently Branger and Ronay (ref. 22) adopted random flight-simulation loading for exploring the fatigue behavior of a high-strength steel. Imig and Illg (ref. 23) adopted this method for studying the effect of temperature on the endurance of notched titanium-alloy specimens. At the National Aerospace Laboratory (NLR) as part of an ad-hoc problem random flight-simulation loading was used to compare two alternative types of joints.
Variables of Flight-Simulation Testing A constant-amplitude loading is easily defined by its mean, amplitude, and cyclic frequency. For program loading, additional variables are (1) load spectrum, (2) ampli- tude sequence (the programing), and (3) the maximum and the minimum amplitude to be included in the test. For random tests, similar variables can be indicated. The sequence, however, has some random character rather than being programed.
For a flight-simulation test, the situation is still more complex because different types of flight loads have to be simulated, such as gusts, maneuver loads, and ground-to- air cycles.
The main variables of flight-simulation loading, with some comments on their significance, are as follows: (1) Load spectrum Obviously the fatigue life depends on the type of load spectrum. For instance, there are large differences between the load spectra for civil and for military aircraft. Usu- ally gusts are important for civil aircraft, whereas maneuver loads are less important.
For military aircraft, the reverse is true. A realistic flight-simulation test requires the adoption of an appropriate load spectrum.
(2) Load sequence If a flight-by-flight simulation is adopted, the fatigue loads superimposed on the ground-air-ground transitions can still be applied in various sequences. The effect of sequence was studied by several authors (refs. 1, 3, 9, 19, 23, and 24) and the general impression is that in a flight-by-flight loading the sequence of the loads in each flight is of secondary importance. Although this is a convenient observation, it still appears to be advisable to adopt a realistic sequence, which generally implies a random sequence.
(3) Design stress level It is clear that an increase of the design stress level reduces fatigue life. This is illustrated for crack propagation by the curves in figure 6. Similar data were found by Branger (ref. 25) with a hole notched specimen of 7075 aluminum alloy and maneuver spectrum, by Branger and Ronay (ref. 22) with a hole notched specimen of chromium- nickel steel and maneuver spectrum, and by Imig and Illg (ref. 23) with an elliptical hole specimen of titanium alloy and supersonic transport load spectrum.
Curves giving the fatigue life as a function of the stress level applied in flight- simulation tests easily indicate the gain or loss of fatigue life if the design stress level is readjusted. Actually such curves have some similarity with Gassner's "endurance curves" (Betriebsfestigkeitskurven) and the curves of Kirkby and Edwards, who plotted the random-load fatigue life as a function of the root-mean-square stress level. How- ever, curves pertaining to flight-simulation data give more relevant information.
(4) Maximum load allowed in the test (truncation level) The wing test results presented in a previous section have confirmed earlier NLR data, which indicates that the truncation level has a predominant effect on crack propaga- tion. It is expected that this effect is more applicable to a gust spectrum than to a maneuver spectrum in view of the different shapes of the spectra. Nevertheless, the assessment of the maximum load allowed in the test is a delicate issue. This problem was discussed in reference 26; these results led to the recommendation to truncate load amplitudes expected less than 10 times in the target life of the aircraft. This proposal was made in view of the favorable effect of higher loads and the uncertainty that all air- craft of a fleet will meet those loads.
At the same time, it would also be unrealistic to truncate at a much lower level since that may also lead to unrepresentative life indications. As a consequence, a real- istic simulation is not compatible with a single loading pattern applied in all flights.
Obviously different flights should be simulated. (See fig. 1, for an example.)
(5) Minimum amplitudes to be simulated The results presented earlier for test series A have indicated that low-amplitude gust cycles may be slightly damaging in a flight simulation test. A similar indication was obtained by Naumann (ref. 9) when testing edge-notched 7075-T6 specimens. Remarkably enough Branger (ref. 25) found a small life reduction when omitting low-amplitude cycles from flight-simulation tests on 7075-T6 notched specimens (maneuver spectrum). Any- how, if accurate data are required, low-amplitude cycles have to be included.
The situation is different for low-amplitude taxiing load cycles. If the mean stress during taxiing is in compression, it was found in NLR tests (refs. 1 and 3) and by Gassner and Jacoby (ref. 24) and Imig and Illg (ref. 23) that omitting the taxiing loads did not have a noticeable effect on the fatigue life. It is expected that this trend is applicable only if the mean stress of the taxiing loads is either small or negative.
(6) Loading frequency Preliminary results presented in a previous section indicated a very small fre- quency effect if any. More data from flight-simulation tests were not available in the literature. It is expected that the frequency effect will be small for those materials that show a small frequency effect under constant-amplitude loading.
Advantages and Limitations of Flight-Simulation Tests The advantages of flight-simulation tests are clearly associated with the fact that the loading is a realistic simulation of the service load time history. For obtaining valid information on fatigue lives and crack propagation from testing components or a full-scale structure, a realistic flight-simulation test is a necessary condition.
For comparative fatigue tests on competing designs or materials, constant- amplitude tests, program tests, or random-load tests may be adopted. As explained previously, it is not certain whether the comparative result will also be valid under ser- vice loading. This uncertainty is eliminated by realistic flight-simulation loading.
With respect to estimating fatigue lives in the design stage, one could start from constant-amplitude data and calculate the fatigue life by employing a damage rule (Palmgren-Miner, for instance). This procedure implies a very large extrapolation with a doubtful extrapolation rule. By starting from relevant flight-simulation data, the extent of extrapolation and thus the uncertainty will be highly reduced. In the following section a proposal is made for compiling flight-simulation fatigue test data for this purpose.
A disadvantage is that flight-simulation testing requires a more expensive fatigue machine with more complex electrohydraulic systems. Actually the technical problems of this type of machine appear to be solved and the number of available machines is rapidly increasing. The closed-loop systems indeed allow a wide variation of testing procedures and it is sometimes surprising to see the limited utilization of the potentials of the machine in fatigue tests.
Another limitation which appears to be more serious is that the load spectrum in service will never be the same as the spectrum applied in the test. Although this is true, it is not a fair objection. If there are differences between assumed and actual load spec- tra, one might account for them by calculations or by testing. Unfortunately the Palmgren- Miner rule is unreliable for this purpose (ref. 3). It may even predict the wrong sign of life corrections. The only realistic approach is to rely on empirical trends as obtained in flight-simulation tests. The test program proposed in the following section may also be useful in this respect. For a particular aircraft, another solution is to conduct some comparative flight-simulation tests with the initial load spectrum and the actual service load spectrum. This could be done on components or relevant specimens. In this respect it was stimulating to see a good agreement between the crack propagation results of the wing and those of simple sheet specimens.
A Proposal for Systematic Flight-Simulation Tests In the foregoing sections, flight-simulation testing was recommended as being a more realistic approach to the problem of estimating fatigue properties. It was also pointed out that a compilation of systematic data from such tests would be helpful. A proposal for a compilation was made in reference 27. A test program for this purpose should include flight-simulation tests with the following variables: (1) Type of specimen Representative riveted and bolted joints should be tested.
(2) Shape of load spectrum Some typical shapes should be adopted, for instance, representing gust and maneu- ver spectra. If the effect of the load spectrum is known, one might interpolate for intermediate spectrum shapes.
(3) Design stress level Some values should be adopted in order to study the effect of the stress level in a way similar to that of Gassner for program tests.
(4) Ground-to-air cycles The number and the magnitude of ground-to-air cycles may be varied.
Such a program, which could well be extended, may be considered as an exploration of the effect of several variables on the life under flight-simulation loading. On the other hand, it may serve some practical purposes. Firstly, the data could indeed be used in the design stage for making life estimates. Secondly, this type of information could also be useful for correcting data from full-scale tests if the service load spectrum deviates from the test load spectrum. Thirdly, without actually having to design a standardized test one could use the data as a standard for comparison when checking the fatigue quality of new components. A handbook with results from systematic flight-simulation tests could be updated from time to time.
In fact, tests according to the foregoing program could be considered as collecting service experience in the laboratory. In general, the experience from fatigue failures in service does not become available in a suitable form because of insufficient data on load spectra, stress level, and structural configuration in most of the failures.
SUMMARY OF RESULTS Flight-simulation tests were made with a full-scale wing structure to study crack propagation under different loading conditions. The results are summarized as follows: 1. Omitting low-amplitude gust cycles from the flight-simulation test implied a con- siderable timesaving. However, it had a small but systematic effect on the crack propa- gation rate. The propagation rate was somewhat slower.
2. Truncation of infrequently occurring high-amplitude gust cycles to a lower level considerably accelerated crack growth.
3. Increasing the design stress level increased the crack propagation rate.
4. The application of fail-safe loads (100 percent limit load) caused a drastic delay of subsequent crack growth. Such loads increase the fatigue life.
5. Good agreement was found between wing test results and results from tests with simple sheet specimens. This illustrates that tests on laboratory specimens may indicate the effect of modifications of the load spectrum.
Flight-simulation tests were also made with 2024-T3 and 7075-T6 sheet specimens at loading frequencies of 0.1, 1, and 10 cps and at four design stress levels. Preliminary results are as follows: 6. The frequency effect was small and nonsystematic.
7. The design stress level had a considerable effect on the crack propagation rate which was different for the two alloys. The difference could not be predicted from constant-amplitude data.
A discussion was presented concerning the meaning of flight-simulation testing for various testing purposes. The variables of flight-simulation testing and their effects on the test results were discussed. The merits and the limitations of flight-simulation tests are summarized as follows: 8. As compared with constant-amplitude tests, program tests, and random-load tests, a flight-simulation test is a more realistic representation of service loading and gives more relevant information. For a full-scale test or a component test, a realistic flight-simulation loading is an essential requirement for estimating fatigue lives and crack propagation rates.
9. For comparison between competing designs, materials, or surface treatments, flight-simulation tests give more relevant indications than alternative testing methods.
10. If life estimates made in the design stage of an aircraft are based on flight- simulation . test data, the extrapolation of the test results is smaller and, hence, more reliable than for alternative procedures employing data from constant-amplitude tests, program tests, or random load tests.
11. Since sufficient data from flight-simulation tests are not available as yet, a pro- posal has been made for a systematic compilation of such data. A handbook with this type of data would also be useful as a standard for comparison. Moreover, the data could be used for evaluating the significance of differences between the load spectrum of a test and the load spectrum in service. For this purpose, the Palmgren-Miner rule is unreliable.
REFERENCES 1. Schijve, J.; Jacobs, F. A.; and Tromp, P. J.: Crack Propagation in Aluminium Alloy Sheet Materials Under Flight Simulation Loading. NLR TR 68117, 1968.
2. Schijve, J.; Jacobs, F. A.; and Tromp, P. J.: Crack Propagation in 2024-T3 Alclad Under Flight Simulation Loading. Effect of Truncating High Gust Loads. NLR TR 69050, June 1969.
3. Schijve, J.: Cumulative Damage Problems in Aircraft Structures and Materials.
Aeronaut. J., vol. 74, 1970, p. 517. (Also published as NLR MP 69005 and pre- sented as 2nd Plantema Memorial Lecture, ICAF Symp. (Stockholm), 1969.)
4. Schijve, J.; and de Rijk, P.: Crack Propagation in a Full-Scale Wing Structure Under Random Flight-Simulation Loading. Prospective NLR TR.
5. Schijve, J.: Fatigue Crack Propagation in Light Alloy Sheet Material and Structures.
Advances in Aeronautical Sciences, Vol. 3, Pergamon Press, 1961, p. 387. (Also published as NLR MP 195.)
6. Hudson, C. M.; and Hardrath, H. F.: Investigation of the Effects of Variable-Amplitude Loadings on Fatigue Crack Propagation Patterns. NASA TN D-1803, 1963.
7. Hudson, C. M.; and Raju, K. N.: Investigation of Fatigue-Crack Growth Under Simple Variable-Amplitude Loading. NASA TN D-5702, 1970.
8. McMillan, J. C.; and Hartzberg, R. W.: The Application of Electron Fractography to Fatigue Studies. Electron Fractography, Spec. Tech. Publ. 436, Amer. Soc. Testing Mater., 1968, p. 89.
9. Naumann, E. C.: Evaluation of the Influence of Load Randomization and of Ground-to- Air Cycles on Fatigue Life. NASA TN D-1584, 1964.
10. Schijve, J.: Significance of Fatigue Cracks in Micro-Range and Macro-Range. Fatigue Crack Propagation, Spec. Tech. Publ. 415, Amer. Soc. Testing Mater., 1967, p. 415.
(Also published as NLR MP 243.)
11. Bradshaw, F. J.; and Wheeler, C.: The Effect of Environment on Fatigue Crack Propa- gation. Measurement on Aluminium Alloys at Different Frequencies. Tech. Rep.
No. 68041, Brit. R.A.E., Feb. 1968.
12. Gassner, E.: Festigkeits-Versuche mit wiederholter Beanspruchung im Flugzeugbau.
Luftwissen, Bd. 6, 1939, p. 61.
13. Kirkby, W. T.; and Edwards, P. R.: Variable Amplitude Loading Approach to Material Evaluation and Component Testing and Its Application to the Design Procedures.
Fatigue Design Procedures, 4th ICAF Symposium, E. Gassner and W. Schutz, eds., Pergamon Press, 1969, p. 253.
14. Gassner, E.; and Schutz, W.: Assessment of Allowable Design Stresses and the Corresponding Fatigue Life. Fatigue Design Procedures, 4th ICAF Symposium, E. Gassner and W. Schutz, eds., Pergamon Press, 1969, p. 291.
15. Jacoby, G.: Comparison of Fatigue Lives Under Conventional Program Loading and Digital Random Loading. Effects of Environment and Complex Load History on Fatigue Life, Spec. Tech. Publ. 462, Amer. Soc. Testing Mater., 1970, p. 184.
16. Jacoby, G.: Beitrag zum Vergleich der Aussagefahigkeit von Programm — and Random-Versuchen. Z. Flugwiss., Jahrg. 18, 1970, p. 253.
17. Lipp, W.: Unterschiede in der Lebensdauerangabe nach Betriebsfestigkeitsversuchen gegenuber den Ergebnissen aus Fahrversuchen. LBF Ber. Nr. TB-80, 1968, p. 67.
18. Gassner, E.: Betriebsfestigkeit gekerbter Stahl- and Aluminiumstabe unter betriebsahnlichen and betriebsgleichen Belastungsfolgen. Materialprufung, Vol. 11, 1969, p. 373.
19. Schijve, J.; Jacobs, F. A.; and Tromp, P. J.: The Effect of Load Sequence on Fatigue Crack Propagation Under Random Loading and Program Loading. NLR TR 71014, Jan. 1971.
20. Schutz, W.: Uber eine Beziehung zwischen der Lebensdauer bei konstanter and bei veranderlicher Beanspruchungsamplitude and ihre Anwendbarkeit auf die Bemessung von Flugzeugbauteilen. Z. Flugwiss., Jahrg. 15, 1967, p. 407.
21. Kirkby, W. T.; and Edwards, P. R.: Cumulative Fatigue Damage Studies of Pinned- Lug and Clamped-Lug Structural Elements in Aluminium Alloy. Tech. Rep.
No. 69182, Brit. R.A.E., 1969.
22. Branger, J.; and Ronay, M.: Investigation of High Strength Steels Under History Program Fatigue. TR No. 56, Inst. for Study of Fatigue and Reliability, Columbia Univ., 1968.
23. Imig, L. A.; and Illg, W.: Fatigue of Notched Ti-8A1-IMO-1V Titanium Alloy at Room Temperature and 550 0 F (560 0 K) With Flight-by-Flight Loading Representative of a Supersonic Transport. NASA TN D-5294, 1969.
24. Gassner, E.; and Jacoby, G.: Experimentelle and Rechnerische Lebensdauerbeur- teilung von Bauteilen mit Start -Lande -Last -wechsel. Luftfahrttechnik- Raumfahrttechnik, Vol. 11, 1965, p. 138.
25. Branger, J.: A Review of Swiss Investigations on Aeronautical Fatigue During the Period June 1965 to July 1967. Minutes 10th Conf. ICAF, Melbourne.
26. Schijve, J.; Broek, D.; de Rijk, P.; Nederveen, A.; and Sevenhuysen, P. J.: Fatigue Tests With Random and Programmed Load Sequences With and Without Ground-to- Air Cycles. A Comparative Study on Full-Scale Wing Center Sections. NLR Rep. 5.613, Dec. 1965. (Also published as AFFDL-TR-66-143, U.S. Air Force, Oct. 1966.)
27. Schijve, J.: Load Sequences for Fatigue Testing of Components and Full-Scale Air- craft Structures. Paper presented at Seventh Congress of the International ished as I 1 ( !
i ll ' ^ ^ ^} I E .^ Figure l.- Sample of a load record, illustrating the load sequence applied in the wing fatigue test. Ten different types of weather conditions are simulated; flight type E corresponds to fairly severe storm, whereas flight type K is good weather.
AV J^^n .la_ _ ^ I I 1, •^ ^^ t w- s- Figure 2.- Test setup with right wing and whiffle tree loading systems.
AMPLITUDE OF WING BENDING MOMENT, % M ult TEST SERIES R LOW—AMPLITUDE GUST CYCLES INCLUDED 47000 FLIGHTS A A LOW—AMPLITUDE GUST CYCLES OMITTED; OMITTED 24000 FLIGHTS 1 102 104 105 106 10 103 NUMBER OF EXCEEDINGS IN 5000 FLIGHTS TRUNCATED B B HIGH—AMPLITUDE GUST CYCLES TRUNCATED; 16000 FLIGHTS ' C SIMILAR TO A, BUT ALL LOAD LEVELS INCREASED 1 10 102 103 104 105 106 25 %; 15000 FLIGHTS Figure 3.- Gust load spectra in test series A, B, and C.
CRACK LENGTH!, mm 50~ ------~------~------~--------~------+-------~------~--------r,~----+-------- 40~------+-~~--+-~~--+-------4-----~~ ~ ~--~-------+-------+-------+------~ 3 0~~ ~~~~~--~-------+--------~------+-------~---- ---+- 20L- ______ ~ ____ ~~ ____ ~ ______ ~ ______ ~ ______ ~ ______ ~ ______ ~ ______ ~ ______ ~ o 5 10 15 20 25 30 35 40 45 50 x 10 - NUMBER OF FLIGHTS Figure 4. - Example of propagation curves for cracks in the skin . Comparison between t he r esults of test series R, A, B, and C.
~ CRACK LENGTH, mm -::J STRINGER ~ SKIN L.L.
.L.
•
R A B C R A B C 20 (j) 100 120 140 160 180 200 100 120 140 160 180 200 SPAR WEB DOOR COAMING / / I I 1/ L.t.
./ 60 30 ~ .L.
_ B R A B C R A • C 40 @ 180 2 00 100 120 140 160 180 200 100 120 140 160 LI FE ( 1000 FLI G HTS ) Figure 5. - The effect of limit load (l.U on cr ack propagat i on under flight-s imu l at i on loading.
MEAN STRESS IN FLIGHT, kg / mm2 O 2024 — T 3 • 7075 — T6, 00 10 10 000 Figure 6.- Flight-simulation life for crack growth S Figure 7.- Two intersecting S-N curve I'ILA ING PAGE Ili-ANii 110
N 9 o?
pRECI RELIABILITY ANALYSIS APPLIED TO STRUCTURAL TESTS By Patricia Diamond and A. O. Payne Aeronautical Research Laboratories Department of Supply Commonwealth of Australia SUMMARY Although full-scale fatigue testing is now widely adopted in modern aircraft design practice, the current fatigue-life assessment procedures do not utilise all of the test data that is obtained, and they only partly take account of the probability of failure of the structure during the period in which it is being progressively weakened by the fatigue crack.
The present paper is concerned with the application of reliability theory to pre- dict, from structural fatigue test data, the risk of failure of a structure under service conditions because its load-carrying capability is progressively reduced by the exten- sion of a fatigue crack.
The procedure is applicable to both safe-life and fail-safe structures and, for a prescribed safety level, it will enable an inspection procedure to be planned or, if inspection is not feasible, it will evaluate the life to replacement.
The theory has been further developed to cope with the case of structures with initial cracks, such as can occur in modern high-strength materials which are suscep- tible to the formation of small flaws during the production process.
The method has been applied to a structure of high-strength steel and the results are compared with those obtained by the current life estimation procedures. This has shown that the conventional methods can be unconservative in certain cases, depending on the characteristics of the structure and the design operating conditions.
The suitability of the probabilistic approach to the interpretation of the results from full-scale fatigue testing of aircraft structures is discussed and the assumptions involved are examined.
INTRODUCTION In recent years the development of high-performance aircraft using new high- strength materials and more refined methods of stress analysis to satisfy the ultimate strength requirement has led to the fatigue performance of aircraft structures becoming a progressively more important factor.
Basic studies of the fatigue behaviour of complete structures, such as those described in references 1 and 2, have shown that a full-scale fatigue test of the structure under representative loading conditions is essential to identify the fatigue critical areas and accurately represent the complex stress conditions under fatigue loading.
Although full-scale fatigue testing is now widely adopted in aircraft design practice, this usually consists of applying to a single test specimen a loading sequence representing the service load history.
Complete failure under the test load sequence or the appearance of a crack of a particular length is defined as failure and the results are applied to determine a life under the service loading conditions.
However, such an arbitrary criterion of failure does not consider the increasing risk of static failure to which the structure is subjected as it is progressively weakened by the growing fatigue crack. The actual risk of failure could therefore differ consider- ably from that obtained by the currently used methods of life estimation.
Furthermore the difficulty of detecting very small cracks with current techniques, together with the susceptibility of the modern high-strength materials to the formation of flaws in production, may result in some probability of cracks existing in airframes prior to entering service.
This paper is concerned with applying reliability analysis to calculate the probability of survival as a function of life from the results of the full-scale fatigue test, including the case of structures which may be initially cracked.
NOMENCLATURE Footnotes for the nomenclature are found at the end of the list.
a crack length (this may refer to crack length at surface, crack depth, or some other specified dimension of crack front) crack length for complete collapse under mean load (or crack length at aF which slope of crack propagation curve becomes infinite) ao length of the largest crack that will not be detected during production process aD length of largest crack that will not be detected during in-service inspections ac length of initial crack in any structure which is cracked at beginning of its service life ^ Ft (t l) probability of variate t exceeding some particular value tl hi period of operation (or service life) to extend a crack to length Z in structure which contained initial crack of length lc, hl = nl - nc Z relative crack length aja F (Z is dimensionless and has same value whether "a" refers to crack length at surface or to crack depth) relative crack lengths corresponding to ao, aD, ac , respectively 61D,lc ZN,Zn median values of distributions of l at life N and relative life n probability of survival to life n (also called the survivorship function) L(n) LF(n),Ls(n), survivorship functions at relative life n, corresponding to risk func- tions, r F(n), rs(n), rl(n), rl *(n), rsL(n), and rs'μ(n), LI(n),LI*(n), LsOn),L s'μ (n) respectively survivorship function at relative service life h corresponding to risk Ls(h) function rs(h) for structures with initial crack life of structure expressed as number of load applications or hours of N operation Ni life to first formation of fatigue crack (also called life to inital failure) H service life of structure which was initially cracked expressed as num- ber of load applications or hours of operation relative service life of structure which was initially cracked, H/Ni h N life to produce crack length Z in any structure i Ni median of the distribution of Ni n relative life, N/Ni nl relative life to crack length 1 for any structure life of structure which has life z times median life at same crack nl z length l n F relative life to complete collapse of structure under mean load relative lives to produce crack lengths of l o, no ,nD,nc 1D , and l c , respectively nl,nF,no,nD,nc medians of distributions of nl, n F, no , nD, and nc, respectively ns relative life corresponding to particular life Ns NL estimated mean fatigue life obtained from structural fatigue test relative lives to 1st, 2d, and mth inspections carried out to detect nI(1)"I(2)'nI(m) fatigue cracks probability density function of residual strength R with mean pR'p'R value μR px(x1) probability density function of variate x at particular value x1 ^Px (x1) probability distribution of variate x at particular value x1, Px(xl) = Pr lx < x1^ P(N) probability of failure up to life N R(Z) static strength of structure containing fatigue crack of relative length 1 r(N) probability of failure in remaining fleet at Nth load application or risk of failure at life N r(n) risk of failure at relative life n for unit change in z r(h) risk of failure after period of operation h in population of structures which contain initial cracks for unit change in z r(hs risk of failure after a period of operation hs in population of struc- I lo) tures all of which contain initial crack of length to r(hs , p(lc)) risk of failure after period of operation h s in population of structures all of which contain initial cracks with probability distribution of initial crack lengths given by p(lc) r s(ns) risk of static fracture due to fatigue at particular life ns, defined as failure at life ns from fatigue crack in structure which is still able to sustain applied service load exceeding mean load rs ,4 (ns) risk of static fracture due to fatigue at life ns, assuming no variability in residual static strength of structures all containing cracks of given length r F(ns) risk of fatigue fracture at life ns, defined as failure at life ns due to fatigue crack reaching such extent that structure is unable to sustain mean load r FT (ns) the total risk of fatigue failure at life ns, r FT(ns) = rs(ns) + rF(ns) r sL (n) risk of failure at life n as calculated by conventional safe-life procedure frl (ns;l D,ni) risk of fatigue failure at life n s in population of structures which have all been previously inspected at life n l with inspection procedure which detects crack lengths greater than 1D *(ns ;1D,nl) risk of fatigue failure at life ns when cracks of length exceeding lD rl are detected by inspection at nl and are then repaired and structures returned to service * s ;lD,ns) risk of fatigue failure at life n s with continuous inspection procedure frl (n by which cracks with length exceeding 1 D are detected and are then repaired and structures returned to service risk of fatigue failure after period of operation hs in rl *(hs I p(lc);l D,hs) population of structures all initially cracked with dis- tribution of initial crack lengths given by p(lc) and continuously inspected to detect crack lengths exceeding I D; after cracks are detected they are repaired and structures returned to service risk of fatigue failure at life ns with inspection proce- rI * (ns;lD,rmax) dure detecting crack lengths greater than 1D at inspection intervals designed to limit risk below some specified value rmax; after cracks are detected they are repaired and structures returned to service risk of fatigue failure after period of operation hs in rI*(hs I p(lc);lD,rmax) population of structures all initially cracked with dis- tribution of initial crack lengths given by p(lc) and inspected to detect crack lengths exceeding 1D at inspection intervals designed to limit risk below some specified value r max ; after cracks are detected they are repaired and structures returned to service probability of detecting cracks by inspection at life rD*(nI(m);1D,nI(m-1)) nI(m) in population of structures previously inspected at with an inspection procedure nI(m-1) detecting crack lengths exceeding 1D; after cracks are detected they are repaired and structures returned to service probability of detecting cracks by inspection after period rD *(hI(m) I p(lc);lD,hl(m-1)) of operation in population of structures all hI(m) initially cracked with distribution of initial crack lengths given by p(lc) and previously inspected at hI(m-1) to detect crack lengths exceeding 1D; after cracks are detected they are repaired and structures returned to service S applied service load ultimate design load Stilt Sm mean load on structure U gust velocity Y relative service load, S/SUlt 4, 02 general symbols for mean and variance of population; used with suffix to denote variate μo mean strength (failing load) of uncracked structures A R (Z) mean strength of structures containing cracks of length Z in median crack propagation curve for population of structures, in = g(k) μR(1) mean residual strength expressed nondimensionally as function of crack μ o Z μR length Z, ^ _ 0(Z) X(i) relative strength of any structure containing crack length 1, x(Z) μR(Z) z comparative life or life factor of structure with life to crack length Z Nl,z n1,z of z times median life to same crack length, z = or nl NZ tWhere no confusion can arise subscript for variate may be omitted.
Actual dimension of detectable crack aD may be specified instead of relative crack length 1D- INTERPRETATION OF FATIGUE TEST RESULTS With the present practice of fatigue certification by full-scale testing, the data pro- vided by the test specimen representing the median structure of the population includes (1) Location of the fatigue critical areas (2) The median crack propagation curve (3) The life to final failure under the test load sequence (4) Residual strength data from static failure of the cracked specimen under the test load sequence, which include the failing load and the extent of fatigue cracking CURRENT APPROACHES TO SAFETY IN FATIGUE The current practice is to obtain from these results a mean fatigue life NL, corresponding to failure at some arbitrarily selected point on the crack propagation curve.
For a safe-life structure, N L may be the life at which the specimen broke in the fatigue test or the life at which it would be estimated to fail under some specified load such as limit load. For a fail-safe structure, N L is often taken to be the test life at which the fatigue failure became readily detectable by the inspection procedures that would be used in service.
In order to allow for variability in fatigue performance for either structure, the estimated mean life N L is divided by a scatter factor to obtain a safe operating period for replacement or inspection of the structure. The scatter factor is obtained by using an assumed probability distribution of fatigue life with an acceptable probability of failure.
DIFFICULTY WITH CURRENT METHODS The difficulty with the previously discussed procedure is that although the safe life to replacement or inspection is based on failure at a given point on the crack growth curve, there is, in service, an increasing risk of failure as the fatigue crack extends and the structure may fail at any stage of the crack propagation.
This difficulty is well illustrated by the measurement of the collapse load of Mustang wings that were fatigue tested to destruction under a random load sequence (ref. 1). In figure 29 of reference 1, the relative frequency distribution is presented for the load at failure as determined by experiment. For the twelve structures tested the results indicate a wide range in the failing load from 30 percent to 60 percent of the ultimate load of the virgin structure. This means that for a given life the safety level in service may be sig- nificantly different from that indicated by the fatigue test result.
Clearly the effect will depend on the shape of the crack growth curve and on the service load spectrum; however to investigate the question further an example of an ultrahigh-strength steel welded structure has been taken. The crack propagation and residual strength curves of this structure are shown in figure 1 and indicate a reasonably typical safe-life construction in that once a fatigue crack has developed there is a very marked reduction in strength which leads rapidly to failure.
The probability of survival has been calculated for this structure by the conventional method, taking two rather extreme cases for the definition of failure as follows: (1) Failure occurs at the limit load. This is a relatively high value of the load, being near the upper limit of loads at which failure would be expected in service.
NL = NsL- (2) Failure occurs at the mean load. This is the lowest load at which service failure can occur and it will give a lower limit to the definition of failing load. N L = NF.
The probabilities of survival corresponding to definitions (1) and (2), L sL and L F, have been evaluated for the two load spectra shown in figure 2 by a log normal dis- tribution of fatigue life.
If NZ is the fatigue life to any crack length 1 and N Z is the median value, then z = NZ Nl has a logarithmic normal distribution and
L F(N) = Y pz (z) dz
(1) NXR LsL (N) = YN/13sLpz(z) dz (2) The results are plotted for the manoeuvre load spectrum and the gust load spectrum in figures 3 and 4, respectively. For both spectra, LF is considerably more than LsL; this indicates that the point on the crack growth curve at which failure is defined will have a significant effect on the safety level.
RELIABILITY ANALYSIS OF FATIGUE FAILURE Consider a more representative model of the fatigue process in which a structure progressively weakened by the fatigue crack may be broken by a service load at any stage of the crack propagation. The structure may survive this risk and continue in service until the fatigue crack has reached the stage where the crack propagation curve is rising practically vertical. The residual strength of the structure then drops rapidly until it reaches the mean load when failure must ensue. This is essentially a case where failure occurs by the fatigue process alone and in this paper the failure is termed "fatigue fracture."
The risk of failure in this mode has been considered in the section "Interpretation of Fatigue Test Results" where the probability of survival LF(N) at the life N has been derived in equation (1) as L F(N) = ^N^&Fpz(z) dz and the corresponding risk of failure is readily obtained as pz (NI N F) r F(N) _ ^ (3) pz (z) dz YNZ&F In addition to the risk due to fatigue fracture, there is the risk of failure due to chance occurrence of a service load on a structure weakened by fatigue cracking although the structure is still able to maintain the steady load. Current methods fail to take full account of this risk which is called herein the "risk of static fracture due to fatigue" and denoted as rs(N).
The total probability of fatigue failure at N is therefore given by r F I,(N) = r s (N) + r F (N) (4) If it is desired to indicate a specified value of the service life, Ns may be used rather than N; therefore, an alternative form of equation (4) is r FT(Ns) = r s(Ns) + rF(Ns) RELIABILITY ANALYSIS WITH VARIABILITY IN FATIGUE STRENGTH First consider the risk of static fracture due to fatigue in the simplified case where there is no variability in static strength but a characteristic distribution of fatigue life at any given crack length. Next consider the probability of failure in the fleet at the Nth load cycle (i.e., the risk of failure at life N) of structures all containing cracks of the same crack length a which may be expressed nondimensionally in terms of the crack length a F at which the structure would fail under the mean load; that is, Z = a/aF.
Let SN denote the Nth service load and R(1) the residual strength of structures with crack length 1. R(1) is a decreasing function of l and may be expressed non- dimensionally in terms of the ultimate strength μ o of an uncracked structure as (5) 0(1) R = μo Hence Pr (Failure at life N I crack length 1) = PF(N/1) J = Pr(SN ' R(Z)) = Pr(SN ' = μ00(l (6) = F S (400[111 where Fs (s) is the probability of exceeding any service load s. The total probability of failure in the fleet at life N (i.e., the risk of failure at N) is then obtained by summing over all crack lengths from 1 = 0 to 1 = 1 F( N/1) p (l) dl rs , μ (N) = J 01 p Fs dl (7) 010$[1])p(1) ^ O j where r s,μ (N) denotes the risk of static fracture at the life N assuming that there is no variability in the static strength at a given crack length.
The probability density function p(l) of the crack length 1 at any given life N is not known but this difficulty is overcome by transposing the variate from crack length at a given life to life at a given crack length. This is done by using the model of the fatigue process shown in figure 5 in which it is assumed that for any structure the life Ni bears a constant ratio z to the median life N1 at the same crack length 1, NZ = zNl or by expressing life nondimensionally in terms of the median life to initial failure Ni N l= nl=znl (8) Ni where z is constant for any structure and is called the life factor. By considering the shaded element in figure 5 it can be seen that structures with crack lengths between 1 and Z + dl at N have initial lives between ni and ni + dni . Hence dl p (l ) = p(ni) dni = p(z) dz ni since z = —. This expression neglects the effect on the probability density function of ni ni of the very few structures that have failed between ni and ns.
If the equation of the median crack propagation curve ( ) (9) = g 1 = g nl (nl/z) is used, equation (7) can now be transformed by changing the variable of crack length 1 to one of fatigue life represented by the life factor z. Taking z = n at 1 = 0 and n z = ,= at 1 = 1, equation (7) can now be written as nF r s μ (n) = J n Fs μo ^(grZll p(z) dz (10) n/n F \ L J J RELIABILITY ANALYSIS WITH VARIABILITY IN FATIGUE STRENGTH AND STATIC STRENGTH In the preceding section it was assumed that there was no variability in the residual strength property, whereas, in general, at any crack length 1, the residual strength R(1) will have a probability distribution about a mean value μR (1). If the dimensionless variate x(l) = R()is assumed to have a characteristic distribution which applies for 11 R (1) all values of crack length, then R(1) = μR (l) x(l) R and μ (1) can be expressed as a decreasing function of I from equation (5) as R(1) = μ o o(l) x(l) This is analogous to equation (6), and integrating over all crack lengths gives as before n Fs xμ o 0(g rnj) dz (11) r s( n p(z) I x(l)^ = J n 4 To obtain the total risk of static fracture at n, integrate over all values of x(l) from 0 to - to get n / r s (n) = Yo J Fs xμ o ^(g[Z] p(z)p(x) dz dx (12) n^n F \ This equation is the general expression for the risk of static fracture by fatigue at life n. As stated earlier an alternative expression using n s instead of n may be adopted where the risk at a specified value ns of the service life is desired. This expression is x400 p(x) dz dx r s(ns) = JO J s n Fs p ( Z) n (g 1 Z ST) F s^ PROBABILITY DISTRIBUTION OF THE LOAD AT FAILURE It is of interest to consider the probability distribution of the load at failure since this indicates how the risk of failure is being affected by the changing residual strength of aircraft in the fleet.
The condition for investigation is the probability that at a given life ns structures will fail with a residual strength less than some specified value Ro.
Requiring R Ro or R Ro x=— -- A R μR then substituting μR = Ao^(Z) Ro X c μoOM or xo x c $ (Z) where Ro xo=— and transposing the variate from crack length L to the life factor z give x° X n
(P(g 1 - z^
From equation (11) Pr (Static fracture at ns with the collapse load < R°) - rs ` ns I R, < ti°x°) n x=xo s / {g[^ZSOF x 13 x z dx dz ^% Jnnfx=0 l μo^(J z p( ) p() ( ) s sJ F where X = Ro ° μo Since the total probability of static fracture due to fatigue at n s is given by rs(ns), the required probability distribution for the load at failure at a specified life ns is as follows: Pr (Failing load ' = μoxo at life ns) X° ns Fs x μ°0(g^Zj p(x) p (z) dx dz {gLZI)
/0
(14) ^n ' J s nF 0 rs(ns) APPLICATION OF THE METHOD To illustrate the method of reliability analysis and to compare the results according to the various risk functions in equations (2), (1), (10), and (12), the risk of failure has been calculated for a nonredundant high-strength steel structure. Sample test data for the structure are shown in figure 1.
The crack propagation curve has been determined from the results of a representa- tive full-scale fatigue test in which fractographic examination of the fracture surface of the critical failures has been used to determine the crack dimensions at various stages of the test life. Although the curve in figure 1 is based on the crack length at the surface of the material, use of the nondimensional relative crack length 1 = aF enables it to represent also the crack depth or any other leading dimension of the crack front.
μ The residual strength curve μ R' _ (P(l) has been estimated from the relationship 1 = A 2 based on fracture mechanics theory, where A is a constant depending pri- 11R) o marily on the fracture toughness of the material and the shape of the crack front.
The variability in residual strength about the mean value μ R was assumed to follow the three parameter Weibull distribution, and with representative data on small steel specimens (ref. 3), the following expression was obtained for the probability distri- bution of the relative residual strength x = 11R 2.55 0.824 _ x - P =Pr ex R x =1- x x () p 1.017 - 0.824 ^μR - The crack length at failure under limit load, according to the relevant fatigue test data used, is approximately 0.08 in., giving a crack depth of 0.04 in. for a semicircular crack.
The distribution of fatigue life about the median value was assumed to be log normal u.2 with variance g N of 0.02.
Two service load spectra were assumed as shown in figure 2. Spectrum I is a spectrum of manoeuvre load derived from data on U.S. jet fighter operations in refer- ence 4. A median life to initial failure of 2000 hours was assumed to correspond to the fatigue test result, and an ultimate load factor of 10 was assumed, which gives a mean load of 10 percent of the design ultimate.
Spectrum II was based on thunderstorm gust load data from reference 5 giving the probability of exceeding a gust load U as Fu (U) = e-0.197U Expressing load non- dimensionally as S Y= Stilt where S is the load due to a gust velocity U and Stilt is the load corresponding to the ultimate design gust velocity of 99 fps with the mean load of the aircraft assumed to be 20 percent of the design ultimate, gives the following equation for the gust load spectrum: Fs(Y) = e- 24.4(Y-0.2) A life to initial failure of 20 000 hours was assumed as typical of this type of spectrum.
The four different risk functions of equations (1), (2), (10), and (12) have been evaluated by using numerical analysis techniques (ref. 6) for both spectra I and H. The corresponding probabilities of survival to life n have been calculated from the relation- - r (t) dt fp ship L(n) = e and are plotted for spectrum I and spectrum II in figures 3 and 4, respectively.
These results show that conventional safe-life estimates as represented by LsL (Ls L corresponds to static fracture of a fatigue cracked structure under limit load and is in accordance with current life estimation procedures) can be inaccurate since they fail to take proper account of the risk of static fracture of the structure weakened by the growing fatigue crack.
Comparison of L s and Ls1μ indicates that the variability in residual strength has a significant effect on the probability of survival (or failure). The probability of survival L F refers to failure due to the .fatigue fracture extending to the stage where the structure is not able to sustain the steady mean load. The risk from this type of failure is often small but as mentioned previously it must be included in the total risk.
RISK OF FAILURE IN STRUCTURES INITIALLY CRACKED With the high-strength materials of low ductility now being introduced into aircraft construction there is a difficulty of detecting very small cracks with current nondestruc- tive inspection (NDI) techniques. This factor together with the susceptibility of these high-strength materials to the formation of flaws in the production process may result in a probability of cracks existing in a number of aircraft structures before they go into service STRUCTURES WITH INITIAL CRACKS OF CONSTANT LENGTH In the most adverse case, all structures are assumed to be cracked in the fatigue which corresponds to the maximum length of critical areas to a relative crack length t o crack that will escape detection. According to this assumption all structures start their service life with a crack of length to present.
In the model of the fatigue process illustrated in figure 5, all the crack propagation curves can be regarded as radiating from a single point or pole P. If all structures are initially cracked to the same length L o , this corresponds to shifting the pole to the point P' with coordinates (no,lo) as shown in figure 6. Each structure now starts its service life h at the life n o which would have produced a fatigue crack of length to in this particular structure. This infers that the initial crack or defect induces the same stress field as a fatigue crack of the same dimensions in the area being considered. It may be regarded as a fair assumption since under repeated loading the defect will rapidly initiate a fatigue crack which can be expected to give rise to a similar stress field as that which would result if the crack had been produced by fatigue alone.
Referring to figure 6 shows that for any structure which has a life factor z = nl/nl, the service life h l to any crack length Z is given by hl = 111 - no = zn l - zno = z ( n l - no) For the median values, hl = n l - no Hence (15) hl = zfil Therefore, the same model of the crack propagation process applies as for structures without initial cracks except that the origin is shifted to (n o ,lo), the service life is given by hs = (ns - no) = z (ns - no) = zhs, and the equation of the median crack propagation curve is transformed to (16) Z = g(fil + no) = g (-z + no) The risk of failure is therefore obtained in the same way as for structures initially uncracked, and by integrating over crack lengths from Z = to to 1 = 1, the following equation is obtained from equation (7) : dl rs,μ(n 110) = (17) Jl Fs^μo0(1^ p(1) Hence if the variable is changed from one of crack length to one of fatigue life at a given crack length as represented by the life factor z, the following equation is obtained from equations (17) and (16) : hs (18) no)] p (z) dz rs,μ(hs 110) = ^hs/(4-flo) FsOOL^Z + where (lo ) denotes the risk of failure at a particular operating life hs of rs,μ(hs structures having initial cracks of length t o and having no variability in residual strength.
The corresponding expression when there is a probability distribution of residual strength x given by p(x) can be derived from equation (18) as x 0 [g (z + no)1 p(z) p(x) dz dx (19) r s(hs 1 Zo) _ ^^ ^^ 11 (p Fs 0 hs^(nF-no) where r s (hs Zo) denotes the risk of failure at service life hs for structures which are all cracked to a length Z o at the start of their service life.
The risk of failure by fatigue fracture for this case follows from the expression given in equation (3) and is hs p 1 z \nF ' no/ rF(hs lo) _ (20) p z ( z ) dz hs / ^nF-no^ The corresponding probabilities of survival can then be calculated as before.
STRUCTURES WITH INITIAL CRACKS OF VARIOUS LENGTHS In the general case the population of structures will contain cracks ranging from zero length up to the detectable length Lo and it can be assumed that there is a proba- bility of a structure containing a crack of length l c between 0 and to as given by the probability density function p(1c) .
Consider the fraction of the population p(lc) dlc which has initial crack lengths between lc and lc + dlc. The probability of failure at hs for these structures is given by r(hs I lc) according to equation (19). Their contribution to the total risk of failure in the population at service life hs is therefore, Or = r (21) s I l c) p(lc) d1c ( h Since hs is the same for all structures whatever their initial crack length l c , the total risk of failure for all structures at service life hs may be calculated by integrating equation (21) over all values of initial crack length from lc = 0 to lc = lo . Then lc=lo (22) p ( l s( h c)) = l c) p(lc) d1c r s I r(hs I
S
1c=0 As was done in the derivation of r s (hs lo) in equation (19), the variable of initial crack length lc is expressed as the corresponding life nc on the median crack propa- gation curve, with lc = g(nc) and ( c) dfic p ( l c) dlc = p n Then, since nc = n i when l c = 0 and nc = no when lc = l o, the following equa- tion is obtained from equation (22) by substituting r(hs I lc) from equation (19): —no x= m cz=00 me ` (23) Fs^xμo0[9^ +nc)] p (z) p (x) p(n`c) dx dz dnc rs(hs I P(l / J J c)) = J-_-_O nc=n1 x=0 z=hs/\nF-°c^ Similarly the risk of fatigue fracture can be derived from equation (20) as [pz(hs/^nF - nc nc) p(nc) - no dil cl F(hs I p(Zc)) = JN (24) r n - no nc=1 c- o pz(z) p(nc) dz dnc f f nc hsAnF-gc) PROBABILITY DISTRIBUTION OF THE FAILING LOAD The probability distribution of the failing load can be determined for the case of structures with initial cracks by a simple extension of the method developed in the sec- tion "Probability Distribution of the Load at Failure."
If one is interested in structures with residual strength R less than some speci- fied value Ro, then as in the aforementioned section this corresponds to structures with xo x Cxo = 1 (25) - c ^^'R^μo) Consider structures with initial cracks of length I c corresponding to a life of ffc on the median crack propagation curve. Now from equation (16) +n c)]
μR- 0(1)=0 Cg^2
Hence substituting this equality into equation (25) gives the following equation: X `= r xo (26) 0[g(ZZ+nc)^ Thus, for structures with initial cracks of length lc it follows from equation (19) that the probability of failure with residual strength - a - than some given fraction xo of the virgin strength is given by h +n l 0 [ g 11 o / o _ hs rs c fx g ^Z + nc) P(x) P(z) (27) μo0[ FS x hs , R ` x Jh n n JO s -^o o /(^F_ c^ The total risk of static fracture due to fatigue at hs is given by rs(hs i lc) and therefore it follows that C, 6 Pr (Failing load _` μ o xo at life hs^ Fs xμo¢^L 9 z ) dx dz ^ + 4@ p ( x) p ( x o /^ [g( Ls +n c)] (28) Yhs/(f!F-fl,) ^0 r h s I Zc) s( Where the population of structures have initial cracks with a probability distribution of crack length represented by p(1c) it follows from equation (23) that the probability of failure with relative strength R/A R less than xo is given by an analogous expression to equation (27) as follows _ hs hs P( l c) (°o xo/^[g(z f l Z) P^nc) dx dz dnc (29) [ Z + nc/^} PAX) PA ( Fs\xμ0 / rs l hs n n JO R<x μ) - Jn. ^h l = 0 D 1 sA R F c^ If equation (29) is divided by rs (hs I p(Zc)), the total risk of static fracture due to fatigue at hs , the probability that R `_ xoμ o at hs is obtained as follows: rxo/^rg(zs+nc)^ F S'0^- s s xlio(plg( -+ii,)I dx dz dnc P(x)P(z)P(nc) P(lc) _ ni hs/(nF-RC) J0 P (30) x o \ h s I J l x o rs(hs I P(lc)) APPLICATION The foregoing theory has been applied to calculate the risk of failure for the ultrahigh-strength steel structures considered previously for which the crack propagation and residual strength curves are shown in figure 1. The load spectrum used in the calcu- lations was the manoeuvre load spectrum shown in figure 2 as spectrum I.
For the case of structures all initially cracked to the same extent, the relative crack length Zo has been taken as 0.075 from a consideration of the crack detection capability of the NDI techniques used in production.
For the case where it is assumed that there is a continuous probability distribution of initial crack size, an exponential distribution of initial crack length Zc has been adopted with the probability density function 20.61c (0 < Zc < 0.075) (31) Z 26.2e- c)- p( The exponential distribution has been adopted since it follows from the physically realistic assumption that the occurrence of a defect in a small element of the material follows a uniform probability law over the whole volume.
The detectable crack length 1 D for in-service inspections has been taken as 0.15.
As stated in the section "Structures With Initial Cracks of Constant Length," the theory assumes that the initial defect produces the same stress field as a fatigue crack the same size as the defect. In applying fracture mechanics theory to deduce crack propagation and residual strength characteristics, the depth of the crack is the important parameter; whereas for crack detection, the length of the crack exposed at the surface is the controlling factor. However, with the nondimensional relative crack length 1= a (32) aF it is immaterial whether crack length or crack depth is taken since both yield the same value of 1, provided the shape of the crack front does not change markedly as the crack propagates.
In establishing the detectable relative crack lengths to and 1D , it has been assumed that the crack length exposed at the surface which will be detected by the best available methods is 0.02 inch for production-line conditions and 0.04 inch for in-service inspections. Assuming a semicircular crack front, which is often characteristic of cracks originating at a surface, gives corresponding crack depths of 0.01 and 0.02 inch.
A value of aF of 0.132 inch was obtained from typical crack propagation data by determining the crack depth at which the crack propagation curve becomes vertical since this is virtually equivalent to failure at mean load. The relative crack lengths to and 1D given previously were thus obtained from equation (32).
With these input data, the risk functions r s *(h 1 0.01") and rs*(h I p(lc)) for the two cases of constant initial crack depth of 0.075 and an exponential distribution of initial crack depths have been evaluated from equations (19) and (23) and are plotted in figures 7 and 9, respectively. The corresponding survivorship functions are plotted in figures 8 and 10. The probability distribution of the failing load at various service lives h s has been calculated from equation (28) and the results are presented in figure 11.
It is apparent that the presence of initial cracks greatly increases the risk of failure at a given life. Also the risk of failure at the beginning of the service life is finite in this case as distinct from the case where all structures are without cracks initially. This arises because with all structures cracked initially every member of the fleet is exposed to the risk of static fracture from the outset.
SAFETY BY INSPECTION As inspection techniques become more highly developed, increasing applications are likely to be found in monitoring structural safety. However, inspections of a complex aircraft structure are both time consuming and costly, and the efficient planning of inspection intervals is becoming an essential requirement. The reliability approach by calculating the risk of failure as a function of life enables the effect of any inspection pro- cedure to be investigated and suitable inspection intervals to be planned.
CONTINUOUS INSPECTION The optimum effect of inspection is, of course, obtained when every structure is inspected continuously. As soon as cracks reach the detectable length 1 D, remedial action is taken and therefore the risk of fatigue fracture is eliminated.
The risk of failure is then equal to the risk of static fracture by fatigue which is determined by calculating the probability of failure for structures with crack lengths between l = 0 and 1 = 1D.
If structures are repaired and replaced when cracks are detected, there is no reduction in size of the fleet and the risk of failure at any life ns is obtained by inte- n s to z = ns since this corresponds to grating in equation (12) between the limits z = — ED integrating over crack lengths between 0 and 1D. (See fig. 5.)
Hence the risk of failure for "continuous inspection with replacement" is given by (33) rI*(ns';lD,ns) s] p (x) p (z) dx dz s f 0 Fs^ xμo.Cg[Z =Sns/"D The corresponding result for structures which are initially cracked is found in a similar manner from equation (20); that is, oo co n — n ] l c (34) Fs xμ o q)[g(z s + n ) p(nc) dz dx dn P(z) x P^Zc);ZD,hs^ _ ( c o ( ( P( rj*(hs c/ n1 J O Jh nc= s/^nD-nc^ When cracked structures are not repaired but are taken out of service after detec- tion, there is a continual depletion of the population since at life n s all structures which have a life less than ns at crack length 1D are eliminated by inspection; that is, the distribution of fatigue life p(z) is truncated at z = and hence the proportion of the S D population remaining at life ns is given by fns/nD p(z) dz.
Therefore, for "inspection without replacement" the risk of failure at ns (which is the probability of failure in the fleet remaining at ns) is derived from equation (33) as rI*(ns;ZD,ns) (35) ri(ns;ZD,ns) dz _ p ( z ) Yn HD In a similar way the risk of failure for inspection without replacement in a population of structures which are initially cracked follows from equation (34) as rI*(hs I P(Zc);ZD,hs) (36) r l( h s I Nlc); Z D, h s^ ° n c =no c) dz dnc _ (_ p(z) P( n i'i C hs/lnD_fQ INSPECTION FOR LIMITED RISK In practice, it is usually not economic or even feasible to inspect structures con- tinuously but inspection is carried out at predetermined intervals. A method is proposed for the efficient planning of inspection intervals in which, when the risk of static fracture by fatigue reaches a prescribed upper limit, an inspection is carried out. The risk of failure is reduced at this stage to the same value as the risk of failure with continuous inspection, but it rises as the life continues until it again reaches the prescribed risk limit when a second inspection is carried out.
Repeated application of this process ensures that each inspection is equally effective in maintaining the risk of failure below a prescribed upper limit. The application of the procedure is shown in a subsequent section, and the expression for the risk function is presented in the appendix.
CRACK DETECTION RATE It is important to determine the probability of cracks being detected at each inspec- tion since this gives the fraction of the fleet that can be expected to require repair and modification before continuing in service.
Reference to the model of the fatigue process in figure 5 shows that in the first inspection at life all structures with crack lengths between 1 = Z D and 1 = 1 are nI(1) nI 1 eliminated. These correspond to structures which have values of z between z = nD and z = fi 1 . Hence the fraction of the population in which cracks are expected to be F n revealed at the first inspection is given by nI(1)/nD r D p(z) dz (37) %n I(1) ; D ^ = YnI(1)/ nF Or in general for the mth inspection, the probability of cracks being detected in a struc- ture is given by n nD z ) dz (38) _ p ( rD*(nI(m);'D,nI(m-1)) = S I(m) N nI(m-1)/nD where denotes the probability of finding cracks at the mth rD*(nI(m);ZD,nI(m-1)) ) following the previous inspection at life It is inspection at life m I ( m nI(m-1)• assumed that cracks with a length greater than Z D will be detected and that structures in which cracks have been detected will be repaired and returned to service.
For structures with initial crack lengths Z = Z o it can be seen by reference to figure 6 that the probability of detecting cracks is hI(m)/^nD-no^ * (h h Z dz r p(z) (39) ^ D^ I(m-1)) D I(m)^ Z o hI(m-1) /^nD-no) where, with a similar notation as for equation (38), rD*(hl(m) I lo;ZD,hI(m-1)) denotes the probability of detection at the mth inspection after a period of operation in service of It is again assumed that all cracks hI(m), following a previous inspection at hI(m-1)• with a length exceeding will be detected and nD and n o denote the lives on the ID median crack propagation curve corresponding to crack lengths of and Zo.
ID If the population of structures has a continuous distribution p(1c) of initial crack lengths between Zc = 0 and Zc = 1 the probability of detection can be derived from equation (39) by integrating over the initial crack lengths from Zc = 0 to l c = Zo, o Shj(m)/(^!D - !Q ^ ( h n P(z)p(lc) ^c r D * hI(m) p (Z c); ZD, hI(m-1)) = JO -n c` I(m-1)/( D or no rhI(n1)/(nD-nc^ p (z) p (nc) dz ^c (40) rD*(hI(m) I p (l c) ;lD,hI(m-1)) _ ^ai hI(m-1)/(nD-nc) expressing in terms of the corresponding life nc according to the median crack lc propagation curve, and integrating with nc = n i at lc = 0 and nc = no at lc = lo.
APPLICATION The foregoing theory has been applied to demonstrate the effect of planned inspec- tion procedures for the case of a high-strength steel structure under a manoeuvre load spectrum (spectrum I in fig. 2) which has been considered previously.
The risk function for fatigue failure with continuous inspection has been calculated by using numerical analysis procedures (ref. 6) for the three cases of structures without initial cracks, structures with initial cracks of constant length to, and structures with a distribution of initial crack sizes given by the probability density function p(lc). The risk functions for periodic inspection with limited risk have been calculated for the same three cases. The results have been plotted in figures 12, 7, and 9, respectively, and the corresponding survivorship functions are shown in figures 13, 8, and 10. The inspection intervals for inspection with limited risk for each of the three cases are shown in table I together with the expected detection rate at each inspection which has been calculated according to the procedure developed in the preceding section.
With periodic inspection, the risk function returns to the continuous inspection curve at each inspection. The continuous inspection curve therefore has a basic significance since it indicates the maximum extent to which the risk of failure can be reduced by inspection.
DISCUSSION OF RESULTS Consider the results of applying the foregoing theory to the case of the high-strength steel structure described previously with particular reference to the suitability of the fail- safe and safe-life procedures.
RISK OF FATIGUE FAILURE Reference to the risk functions r sL and r F in figure 14 illustrates the difficulty with the conventional approach. As the life extends, the difference in these two risks becomes considerable, although as was stated in the section "Interpretation of Fatigue Test Results" they merely represent two rather extreme conditions in the application of the conventional safe-life approach.
In fact, the risks rsL and r F differ only in the point on the crack growth curve at which failure is taken to occur. This difference introduces a problem in the interpre- tation of the fatigue test result since the structure under a representative test load sequence may well fail at a rather different stage of the crack propagation curve as com- pared with the structures that happen to fail at a relatively short fatigue life in service.
This can be seen by reference to the curves of the probability distribution of the failing load in figure 15. These show that at lives typical of service operation (n = 1.0 to 1.25), the expected value of the failing load, for the few structures that fail, is rela- tively high, being above the limit load, whereas at longer lives the expected value of the failing load is considerably reduced. Therefore the fatigue test specimen, representing the average structure, is likely to fail at loads considerably below those at which service failures will occur.
The basic difficulty is that neither r sL nor r F represents the true situation in that they do not take account of the fact that there is some probability of failure at all points along the crack propagation curve as the fatigue crack extends. This effect (the risk of static fracture) is taken account of by L (n) which, as can be seen in figures 3 sI/I and 4, gives an increased probability of failure for the example taken.
Another effect of considerable importance in considering static fracture due to fatigue is the variability in residual static strength of cracked structures since this may have a significant effect on the probability of failure (or survival) depending on the sever- ity of the loading spectrum. This is shown by the comparison between Ls ,4 and Ls for the two load spectra as shown in figures 3 and 4. The probability of survival Ls calculates the increasing risk of failure as the fatigue crack extends in the same way as LS,/-t but it also includes the effect of the variability in residual static strength.
The probability of survival Ls can be applied with equal validity to calculate the probability of survival for structures with initial cracks as outlined in the section "Risk of Failure in Structures Initially Cracked." This has been done for example of the high- strength steel structure taken previously and the results for two cases of initial cracking are shown in figures 8 and 10 where it will be noted that, for an equivalent probability of survival, the fatigue life is greatly reduced by the presence of initial cracks. The short- comings of the conventional methods of life calculation are more marked in this case, since for all structures the whole of the service life involves the propagation of a fatigue crack with continual exposure to the progressively increasing risk of static fracture due to fatigue.
PROBABILITY DISTRIBUTION OF THE FAILING LOAD Curves showing the probability distribution of the collapse load for static fracture by fatigue for the high-tensile steel structure are shown at a series of lives in figure 15.
In the early stages of the life when only small cracks are present the majority of the structures that fail do so from occurrence of a high load in excess of the design limit load. At longer lives, however, when a large percentage of the fleet has developed more extensive fatigue cracks, failure tends to take place by the occurrence of the much more frequent lower loads. The curves for the probability distribution of the failing load have a well defined "knee" which marks the transition from failures of structures with low static strength properties (according to the Weibull distribution of relative strength which has a lower limit at x = 0.82) to structures with low fatigue strength and hence larger crack lengths at any given life.
With the corresponding curves in figure 11, for all structures with initial cracks of a 0.010-inch depth, this knee does not occur. In this case, at any particular life, all structures have substantial cracks and the extent of these is largely independent of the fatigue strength so that the probability distribution of static strength is the controlling factor for all values of failing load.
THE EFFECT OF INSPECTION The effect of inspection on the risk of failure and probability of survival for initially uncracked structures is shown in figures 12 and 13. Although it is not usually a feasible procedure in practice, continuous inspection has an important basic significance which warrants some consideration here.
The risk function for continuous inspection slowly approaches an upper limiting value when there is no repair and replacement of structures in which cracks are detected ("inspection without replacement"). This situation arises because as the initial cracks are propagated by fatigue to the detectable length these structures are eliminated by inspection and a stage is therefore reached where the increase in risk due to the extension of fatigue cracks is offset by the continual removal from service of structures with detectable cracks and high risk of failure.
In the more practical case where structures are repaired and returned to service after detection of cracks ("inspection with replacement") the risk function goes through a maximum value and then eventually approaches zero. The explanation of this behaviour appears to be that, as fatigue cracks extend, the number of cracked structures replaced by sound structures increases until a stage is reached where this counteracts and then outweighs the increasing risk of static fracture by fatigue in the dwindling members of the original fleet.
With this model therefore the original fleet is eventually replaced by new struc- tures which are taken to be free of any fatigue weakness and the risk of fatigue failure decreases to zero. If the service life were to be prolonged to this stage, however, other areas of the structure would become fatigue critical and their risk of failure would have to be considered.
In practice, cracked structures or components are often replaced by new members from the same population as the structures or components in the original fleet. This model of the fatigue process ("inspection with renewal") would show a behaviour inter- mediate between the two procedures considered above.
The risk functions for continuous inspection of structures with initial cracks are presented in figures 7 and 9 and these show a similar behaviour to that found with initially uncracked structures although for the case of a continuous distribution of initial crack size in figure 9 the peak of the "inspection with replacement" curve is much flatter because of the wider range of crack sizes that results.
Turning now to the practical case of periodic inspections designed to limit the risk of failure below a specified value rmax, it can be seen from figures 12, 7, and 9 that in all cases the risk of failure fluctuates between the risk for continuous inspection and the specified maximum value rmax.
For inspection with replacement it can be seen that because of the peak in the curve for the risk function with continuous inspection, the inspection intervals for limited risk at first decrease with each inspection and then increase.
This effect is clearly shown for the three cases considered by the inspection inter- vals given in table I which also lists the expected fraction of the fleet in which cracks will be detected at each inspection.
The curves showing the corresponding survivorship functions for inspection with limited risk are shown in figures 13, 8, and 10, and it is apparent that inspection for limited risk can give a comparable performance to the ideal case of continuous inspection.
At the cost of decreasing the inspection intervals, the probability of survival can be increased by reducing the maximum allowable risk rmax, although this must always exceed the maximum risk for continuous inspection for the inspection procedure with limited risk to be possible.
APPLICATION The reliability approach to structural design has received increasing attention in recent years and it is proposed here that the safety against fatigue of aircraft structures is one of the most important and promising fields of application.
DEVELOPMENT OF THE RELIABILITY APPROACH TO FATIGUE Early work on the probabilistic approach to fatigue of aircraft structures was mainly concerned with efforts to establish the fail-safe philosophy on a more quantitative basis by considering the probability of failure of the structure during the crack propaga- tion stage.
One of the first papers on this subject was concerned with the fail-safe operation of transport aircraft (ref. 7), and a similar approach was used subsequently (refs. 8 and 9) in efforts to develop a proposal for ensuring the airworthiness of fail-safe structures.
In references 10 and 11 reliability analysis was applied to derive the probability of failure for a fail-safe structure by using a sophisticated model to represent the effect of multiple redundancies in the structure.
Probably influenced by the successful application of reliability techniques to electronic systems, the reliability approach to structural safety in general received increasing attention and several papers dealing with the basic development of the phi- losophy (refs. 12 to 15) also dealt at some length with its application to the fatigue of structures.
The reliability approach to structural design has received increasing attention more recently and papers (some relating to the aspect of fatigue) have been represented at a number of International Conferences (refs. 16 to 24).
However, a major difficulty in applying reliability theory to the fatigue of struc- tures is the extensive amount of data required since this is not normally available. The present paper seeks to overcome this difficulty by presenting an approach which allows representative data to be used in conjunction with the full utilisation of the information which can be obtained from the full-scale tests now widely adopted in aircraft design practice.
RELIABILITY ANALYSIS WITH FULL-SCALE TESTING The method proposed in this paper calculates the probability of failure of a structure at each stage of the life with data obtained from full-scale tests on the actual structure in conjunction with other representative data. It therefore estimates the risk of failure in the fleet, and hence the probability of failure (or survival) up to any required life, taking account of the flight loads to be encountered, the progressive reduction in strength due to the growing fatigue crack, and the variability in static and fatigue strength.
The inspection or replacement of structures in service can then be planned to achieve a prescribed safety level using basic data from the fatigue test without requiring any arbitrary decision as to the crack length that constitutes failure or as to whether a structure is "fail safe" or not.
Application of the Method With the risk function having been calculated, the life n I to reach the allowable risk is determined as the life for inspection or replacement.
rmax(nI) From the physical nature of the failure as revealed by the fatigue test and the risk function for continuous inspection with the detectable crack length, a judgement can be made whether to rely on inspection or on replacement.
If replacement is decided on all structures are replaced at nI and the process can be repeated with the constant inspection interval n I until the probability of survival has been reduced to the minimum allowable value.
If inspection is adopted the inspection intervals are calculated as described in the section "Inspection for Limited Risk" and the process is continued up to the life ns at which the probability of survival has been reduced to the minimum allowable value. The fraction of defective structures that can be expected to be revealed at each inspection can be calculated from equation (39). Also the probability distribution of the failing load can be calculated and used to estimate the average value of the failing load at the life for any inspection, from which an indication of the average crack length can be obtained.
It is clear from figures 13 and 10 that the safe operating life can be greatly extended by this type of inspection procedure and therefore as the service life continues other fatigue-prone areas of the structure revealed in the fatigue test may need to be included in the analysis in the same way.
Basic Assumptions The following basic assumptions are involved: (a) The service load S is independent of the failing load of the structure R. This assumption infers that any increase in flexibility of the structure as a fatigue crack extends does not affect its response to the applied loads.
(b) There is no correlation between the residual strength of a cracked structure and its fatigue strength. This is supported by the fact that in a complex structure static ultimate load failure usually occurs in a different area and by a different mechanism to fatigue failure.
(c) The relative residual strength x = Rw of structures cracked to some crack AM length l has a characteristic probability distribution which applies for any value of Z.
For the monolithic structure considered in the section on page 289, the fracture mechan- ics relationship R(1) = K Fis assumed to apply. It can be shown from this that R(1) has the same probability distribution as the fracture toughness K and it is therefore the same for all crack lengths.
(d) The distribution of fatigue life N l'z at a given crack length 1 has a log normal distribution. The log normal distribution is often used in making safe-life esti- mates and it has been supported as a good approximation by comprehensive surveys of fatigue test data (refs. 25 and 26).
(e) At all points on the crack propagation curve of any structure, the fatigue life - 1 = z NZ z bears a constant ratio to the median life NZ at the same crack length ' NZ It can be shown that this follows from the properties of the log normal distribution of fatigue life assumed in assumption (d).
(f) As structures fail by fatigue and are thus eliminated from the population there is no change in shape of the probability density functions of fatigue life z, relative strength x, or initial crack length 1c. In practice some distortion of these functions will occur but for the small probabilities of failure considered it is regarded as a reason- able assumption.
Input Data The following data are required: (a) The service load spectrum Fs(s) which can usually be estimated from the considerable body of flight load data available.
(b) The mean value of the ultimate failing load μo which can usually be obtained from the results of static strength tests on the structure.
(c) The probability distribution of relative strength x = R(^) which must be esti- A R(1) from representative data (as was done for the case of the high-strength steel structure by using data from high-tensile steel specimens) and the results from compo- nent testing during the design stage.
(d) The median crack propagation curve for the structure Z n = g(nl); it is proposed to rely on the crack propagation curve obtained in the full-scale fatigue test of the structure.
CONCLUDING REMARKS From a reliability analysis of the fatigue failure in aircraft structures under ser- vice loading conditions it is concluded that the current procedures for obtaining safety are not entirely adequate. These methods do not take full account of the probability of failure of the structure during the period in which it is being progressively weakened by the growing fatigue crack and they are therefore subject to inaccuracies which may be significant depending on the structural design parameters and the service conditions.
It is also concluded that a reliability approach to the safety in fatigue of aircraft structures must be considered, using the results available from the structural tests and design analysis in conjunction with other representative data.
Such an approach is quite feasible although an extensive body of data and a number of assumptions are involved which warrant some development and testing of the procedure in practice.
However, the reliability approach has major potential advantages by enabling the safety of both safe-life and fail-safe structures to be determined on a quantitative basis, including the planning of efficient inspection procedures and allowance for the possibility of initial flaws in the material where appropriate.
ACKNOWLEDGEMENT The authors wish to acknowledge the efforts of their colleagues in Structures Division of Aeronautical Research Laboratories who have assisted with the preparation of material for this paper.
APPRNTITX TABULATION OF RISKS OF FAILURE AND PROBABILITY OF CRACK DETECTION For simplicity the risk functions in the body of the paper have been expressed in terms of the dimensionless variate z and they have been compared on a common basis in the various figures using the dimensionless variate Ns/Ni . However, in this appendix they are expressed in a form more suitable for practical application, the risk of failure per hour using the relation: r(Ns) dNs = r(z) dz r(Ns) = r(z) ddz s where Ns is the service life in hours.
If the risk of failure were to be required in units other than hours — such as load applications, for example — the dimensional variable N s (or for cracked structures Hs) would have to be expressed in those units.
The footnotes for this appendix are included at the end of the appendix.
STRUCTURES WITH NO INITIAL CRACKS No Inspection Risk with safe-life analysis.- Risk of failure per hour at Ns hours, based on an estimated mean life R L determined from a fatigue test as the life to some crack length L at which failure occurred, is given by NL pz CnL J (Al) rL(Ns) _ p, (z) ^ c" ns^nL where NL is the estimated mean life to the crack length L expressed in hours.
Risk of fatigue fracture a .- Risk of failure per hour by fatigue fracture at a life of Ns hours can be given by pz NF \nF^ r F(Ns) _ 00 pz (z) dz ^ns/ ^ ^F where N F is the median of the life in hours to complete collapse under the mean load.
Risk of static fracture due to fatigue. - Risk of failure per hour by static fracture due to fatigue at a life of N s hours is given by X-00 n 1 (A3) sFs{xμo^(g[zs-P(z)p(x) dz dx r s( N s) = S Zns/ffF x=0 where Fs (s) denotes here the probability of exceeding a service load s per hour of operation b.
Probabilitv distribution of the failin g load. - Pr At life Ns hours that the loads causing static fracture due to fatigue < μoxo rl g [^ s, ^xμo0(g[zs])^ p (x) p(z) dx dz Fs -n X=X zo s z (A4) YX= rs(Ns) ns/i!F Sx=O where rs(Ns) is given by equation (A3), and Fs(s) is taken as the probability of exceeding a service load s per hour of operationb.
Periodic Inspection at NI(1),NI(2),• • •,NI(m) Hours Risk of fatigue fracture with replacement c d . - Risk of failure per hour by fatigue fracture at a life of Ns hours with structures repaired and returned to service after cracks have been detected is given by n n r F * (Ns;ZD, NI(m)) = N pz(" s1N NI(m)i1F D F F/ = 0 (Otherwise) where N F is the median of the life in hours to complete collapse of structures under the mean load.
Note: For continuous inspection the risk of fatigue fracture is zero in this case.
Risk of failure per hour Risk of static fracture due to fatigue with replacement c .- by static fracture due to fatigue at a life of N s hours with structures repaired and returned to service after cracks have been detected is given by z=n x=^ / s^xμoOf g[Z S^1 P(x) p(z) dx dz (A5) r I * (Ns; Z D, NI(m)^ =
S
\
z= n l(m) Z nD x=0
where F s (s) denotes here the probability of exceeding a service load s per hour of operation b.
and ns for nI(m) Note: For continuous inspection substitute Ns for N I(m) Probability of Probability of detecting cracked structures with replacement C . - detection at the mth inspection with structures repaired and returned to service after cracks have been detected is given by )) _ (nI(m)/nD p(z) dz - Pr (Fatigue fracture between NI r *(N ( ) Z N ( m-1 and NI(m) nI(m-1)^nD nD p(Z) ( ' n I( m) I nI(m-1)PiD Since it follows that where an inspection procedure is feasible, the probability of fatigue fracture is relatively insignificant compared to the probability of crack detection.
Note: For continuous inspection the probability of detection per hour at any life Ns hours is given by rD (Ns;l D, Ns) _ — pz * ND C D/ where ND is the median of the life in hours to the detectable crack length 1D- Probabilitv distribution of the failin g load with re p lacement. - At life of N s hours following mth inspection, the loads
Pr^
causing static fracture due to fatigue μoxo n - [ Is s F x ) p(z) dx dz μo^( g [Z]) P( x g z=n s x=xo
- / (A6)
y
^z=nl(m) nD rI*(Ns;lD,NI(m) x=O * s I ( m )) is given by equation (A5), and F s where r I ;l D ,N (s) is taken as the proba- (N bility of exceeding a service load s per hour of operation b.
Note: For continuous inspection substitute Ns for NI(m) and ns for nI(m)• STRUCTURES WITH INITIAL CRACKS (PROBABILITY DENSITY OF CRACK LENGTHS p(i c)) No Inspection Risk of fatigue fracture a . - Risk of failure per hour by fatigue fracture at a service life of Hs hours is given by c =n o ( Pz 1 hs p n c) ^c iiF - nc ^i ' i ' c=1 NF - Nc r F ^H s I p(lc)) _ (A7) nc=no z=0c ( c) dz dnc p(z) p n nc=1 Yz=hs/fF-nc where N F is the median of the life in hours to complete collapse of initially uncracked structures under the mean load, and Nc is the median of the life in hours to produce a crack of length lc for initially uncracked structures.
Risk of static fracture due to fatigue.- Risk of failure per hour by static fracture due to fatigue after a service life of Hs hours is given by c_^ I PA (A$) FS()AO(P[Z + Z ) PAX) P^nc) dz dx dn^ ( 9 Cl)) HS ^ P(lc)^ - Jn c 1 o Z-0 Zh,/(4-i1c) c- // where Fs(s) denotes here the probability of exceeding a service load s per hour of operation b.
Probability distribution of the failing load.- t service life Hs hours that the loads causing
l
Pr
static fracture due to fatigue `_ μ o xo 1 ^ hs y +nc] x=x% g nc=no z-- c) dx dz dnc s xuoo (grZS + i ] I P( F x ) P( z ) P( n L SZ_ hs/(iiF-nc) Sx^ ` Snc=1 (A9) r s( H s I where r s (H s I p(lc)) is given by equation (A8), and Fs(s) is taken as the probability of exceeding a service load s per hour of operationb.
Periodic Inspection at HI(1),HI(2),• • •,HI(m) Hours Risk of fatigue fracture with replacement e d .- Risk of failure per hour by fatigue fracture after a service life of Hs hours with structures repaired and returned to service after cracks have been detected is given by s n D -h I(rn) n F)/( h s -h nF n c-( h I(m)) 1 r h s 1 (Hs PIIP(nc) c HI(m) /I rF*(Hs IPVc);1D,HI(m)) _ nc nD - 1 F - n c =1 NF - Nc z n = o (Otherwise) is the median of the life in hours to complete collapse of uncracked structures where RF under the mean load, and N c is the median of the life in hours to produce a crack of length 1c for initially uncracked structures.
e . - Risk of failure per hour Risk of static fracture due to fatigue with replacement by static fracture due to fatigue after a service life of Hs hours with structures repaired and returned to service after cracks have been detected is given by _- _ I ( /r l n c) dz dx dk Fsrxμo$ Ig z + nc])) x ) P( (A10) P( z ) P( s I PVc); L D, H I(m)) _ (°c-no J r I * ( H L Sx J z ( rn)/(nD iQ nc=1 x=o z=hl - where Fs(s) denotes here the probability of exceeding a service load s per hour of operationb.
Note: For continuous inspection substitute Hs for H I(m) and h s for hI(m)• Probability of detecting cracked structures with replacement e .- Probability of detecting cracked structures at the mth inspection with structures repaired and returned to service after cracks have been detected is given by rnc-no z-hI(m)ARD-nc) Pr Fati e fracture between e z n dz do r H Z Z H P( ) P( R c^ ( I(m) I P( c); D, I(m-1)) = J5 c - D * { HIm _ I and H m ( ) ( ) z=hI(m-1)/(nD-ncl n c =1 nc=n o z=hl(m)/(nD-ncl c) dz dRc _ _ I_ P( z ) P( n ( n c =l z=hI m-1 fQ )/( nD Since it follows that when an inspection procedure is feasible the probability of fatigue fracture is relatively insignificant compared to the probability of crack detection.
Note: For continuous inspection the probability of detection per hour at any ser- vice life Hs is given by * c=nohs _ D, H r D( H s I p ( l c); 1 s) pz p(nc)^c nD - n Y i'i'c=1 ND - Nc where ND and Nc are the median values of the lives in hours to produce crack lengths respectively, in initially uncracked structures.
Of ID and l c , Probability distribution of the failing load with replacement. - aservicelife Hs hours following the mth inspection Pr the loads causing static fracture due to fatigue ` μoxo ^that fn nc=n o z=^ x-xo +nc)] ns _1l r ^[g\z n c) dx dz dnc z x ) P( ) P( Fsl xμo^(g[z + aCl)) P( S J J nc z-hI(m)I(nD-nc^ x 0 =1 r l * ( H I P(Zc);ZD,HI(m)) s where r I * H s is given by equation (A10), and Fs(s) is taken as the I p(lc);ZD,HI(m)) ( probability of exceeding a service load s per hour of operationb.
aThe term in the denominator of this expression is a normalising factor resulting from the truncation of the z distribution by the removal from the population of the structures that fail by fatigue fracture.
However, it is very close to unity for the probabilities of survival that are acceptable in practice.
bIn the body of the paper where rs(ns) has been compared with other risk functions using the dimen- sionless variate Ns/Ni, Fs(s) has been taken as the probability of exceeding a service load s in a time interval Ni.
cWhen there is no replacement of those structures in the fleet in which cracks have been detected, the corresponding probabilities and risk functions are obtained by dividing by the normalising factor P (z) dz. For continuous inspection, nI( m) is replaced by ns.
fnI(m)/ nD dWhen an inspection procedure is applied, the effect on the risk function resulting from truncation of the z distribution, by elimination of structures that fail by fatigue fracture, is so small that it has been neglected here.
eWhen there is no replacement of those structures in the fleet in which cracks have been detected the corresponding probabilities and risk functions are obtained by dividing by the factor z) P(nc) dz ^c Jffc 1 o Jz hI(rn)^\nD-nc) P( is replaced by hs.
For continuous inspection hj(m) REFERENCES 1. Payne, A. O.: Determination of the Fatigue Resistance of Aircraft Wings by Full Scale Testing. Proceedings of Symposium on Full-Scale Fatigue Testing of Air- craft Structures, F. J. Plantema and J. Schijve, eds., Pergamon Press, 1961, pp. 76-132.
2. Raithby, K. D.: A Comparison of Predicted and Achieved Fatigue Lives of Aircraft Structures. Proceedings of Symposium on Fatigue of Aircraft Structures, W. Barrois and E. L. Ripley, eds., Pergamon Press, 1963, pp. 249-261.
3. Lyman, Taylor, ed.: Metals Handbook. Vol. 1.- Properties and Selection of Metals.
8th ed., Amer. Soc. Metals, c.1961, pp. 87-94.
4. Mayer, John P.; and Hamer, Harold A.: Applications of Power Spectral Analysis Methods To Maneuver Loads Obtained on Jet Fighter Airplanes During Service Operations. NASA TN D-902, 1961.
5. Tolefson, H. B.: Summary of Derived Gust Velocities Obtained From Measurements Within Thunderstorms. NACA Rep. 1285, 1956. (Supersedes NACA TN 3538.)
6. Mallinson, G. D.; and Graham, A. D.: A Multiple Integration Technique for the Numerical Evaluation of Probability Integrals. S.M. Rep., Aeronaut. Res. Lab.
(Melbourne). (To be published) 7. Shaw, R. R.: The Level of Safety Achieved by Periodic Inspection for Fatigue Cracks.
J. Roy. Aeronaut. Soc., vol. 58, no. 526, Oct. 1954, pp. 720-723.
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for Study of Fatigue and Reliability, Columbia Univ., 1965.
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Civil Eng., vol. 80, no. 468, Aug. 1954, pp. 468-1 — 468-46.
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AFML-TR-64-401, U.S. Air Force, 1964.
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16. Freudenthal, A. M.: Reliability Analysis Based on Time to the First Failure.
Aircraft Fatigue — Design, Operational, and Economic Aspects, Programme of 5th ICAF Symposium (Melbourne), J. Y. Mann and I. McMillan, eds., May 1967.
17. Black, H. C.: Safety Reliability and Airworthiness. Proceedings of International Conference on Structural Safety and Reliability, Smithsonian Institute, Apr. 1969.
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20. Ang, A. H. S.: Critical Analysis of Reliability Principles Relative to Design. Paper presented at International Conference on Applications of Statistics and Probability to Soil and Structural Engineering (Hong Kong), Sept. 1971.
21. Payne, A. O.; and Grandage, J. M.: A Probablistic Approach to Structural Design.
Paper presented at International Conference on Applications of Statistics and Probability to Soil and Structural Engineering (Hong Kong), Sept. 1971.
22. Cornell, C. A.: The Future of Probabilistic Design. Paper presented at Australian Institution of Engineers Symposium on Reliability and Risk in Structural Design (Melbourne), 1971.
23. Payne, A. O.: Fully Probabilistic Design. Paper presented at Australian Institution of Engineers Symposium on Reliability and Risk in Structural Design (Melbourne), 1971.
24. Itagaki, H.; and Shinozuka, M.: Application of Monte Carlo Technique to Fatigue Failure Analysis under Random Loading. Technical Report No. 16 (NSF-GK3858 and 24925), Columbia Univ., July 1971. (Also presented at the Symposium on Probabilistic Aspects of Fatigue, 74th Annual Meeting of ASTM (Atlantic City), 1971.)
25. Impellizeri, L. F.: Development of a Scatter Factor Applicable to Aircraft Fatigue Life. Spec. Tech. Publ. No. 404, Amer. Soc. Testing Mater., 1966, pp. 136-156.
26. Ford, D. G.; Graff, D. G.; and Payne, A. O.: Some Statistical Aspects of Fatigue Life Variation. Proceedings of Symposium on Fatigue of Aircraft Structures, W. Barrois and E. L. Ripley, eds., Pergamon Press, 1963, pp. 179-208.
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FATIGUE OF COMPOSITES* By Michael J. Salkind Sikorsky Aircraft Division, United Aircraft Corporation, United States INTRODUCTION During the past decade, the extensive development activity in composite struc- tures has indicated the promise of substantial improvements in the performance of aerospace systems. This experience, however, has shown that composite materials are substantially different from our former materials of construction, and new con- cepts in analysis, design, fabrication, quality assurance, and even systems manage- ment will be necessary.
A major difference between composites and metals exists in their respective behavior in a fatigue environment. Whereas metals usually fail by crack initiation and growth in a manner which has come to be predictable through fracture mechanics analysis, composites exhibit several modes of damage including delamination, matrix crazing, fiber failure, void growth, matrix cracking, and composite cracking. A par- ticular structure may exhibit any or all these damage modes, and it is difficult to pre- dict, a priori, which mode will dominate and cause failure. The selection of fiber and matrix can produce predictable fiber or matrix-dominated failure in simple unidirec- tional specimens. (See refs. 1 to 4.) In real structures, however, the complex multi- directional loadings and complex reaction of nonsimple laminates precludes easy prediction of failure modes. Also, joints and attachments in composite structures generally result in failure modes which are peculiar to a particular design.
A characteristic of composite materials which differs substantially from metals is the relative difference between low- and high-cycle fatigue behavior. Whereas most metals behave according to the so-called Coffin-Manson relationship (refs. 5 to 7) in low-cycle fatigue, composites have been shown to be more sensitive to strain range (ref. 4). This sensitivity results in the high-cycle fatigue strength of composites being high with respect to static- and low-cycle fatigue strength. Many structures designed for fatigue experience a spectrum of high as well as low stresses, and whereas the more numerous low stresses may be the critical design factor for a metal structure, the same structure made from a composite material may well be critical in low-cycle fatigue.
A problem arises in the design of composite structures for fatigue loading because of the lack of an adequate definition of failure. A large part of the fatigue *Also published in ASTM STP 497.
data in the literature is based on time to fracture. For high-cycle fatigue, metals are generally structurally adequate to the point of crack initiation (and to some extent beyond that), which is usually a large part of the time to fracture. Although it is preferable to use fatigue data based on crack initiation, the error introduced by designing metal struc- tures using fatigue data based on fracture is usually not significant. Using such an approximation for composites, however, could lead to disastrous results. Composites generally begin to exhibit changes in properties very early in the total life to fracture.
Such changes in elastic properties could lead to structural failure long before the struc- ture is in danger of fracturing. Rotating airfoils such as helicopter rotor blades or gas turbine blades are subject to aeroelastic instabilities if the fundamental frequency shifts because of early fatigue damage that causes stiffness changes. A composite spring whose spring constant changes beyond an acceptable value would be considered failed even though it was in no danger of fracturing. The same composite used for a tension cable application for which stiffness is not critical might have an acceptable fatigue life to fail- ure several orders of magnitude higher than the stiffness critical spring under the same loading conditions. A further complication to this problem is the fact that composites are anisotropic, and for any number of cycles, the change in stiffness in one direction may be unrelated to the change in stiffness in a second direction.
The requirement for an adequate failure criterion, coupled with the challenge of providing adequate damage detection schemes for multiple damage modes, clearly indi- cates the requirement for a new approach to the design of fatigue-critical composite structures. This paper includes a review of the fatigue behavior of composite materials and structures and a proposed approach for design of fatigue-critical components.
FATIGUE OF COMPOSITE MATERIALS A large body of small specimen fatigue data has been generated over the past 10 years. These data are primarily for unidirectional laminates and, as mentioned pre- viously, are based upon fracture as the definition of failure. Hence, much of it is of limited value for use in design. A survey of pertinent observations is included in this section.
Fiber-Reinforced Polymers The most widely used class of composite materials, glass-fiber-reinforced poly- mers, has been the subject of extensive fatigue testing (refs. 8 to 23). Although the data in references 8 to 23 are based upon fracture as the failure criterion, they give us an indication of the effect of significant variables, such as resin composition and content and fiber composition and orientation on fatigue. Boller (ref. 11) has evaluated a variety of matrix systems and found epoxides to be superior in fatigue. His data, seen in fig- ure 1, is more than 15 years old, and improved surface treatments and processing have since been developed; however, the relative ranking remains unchanged (ref. 19). As seen in figure 2, varying the resin content between 20 and 37 percent has a negligible effect on fatigue behavior for t5 0 glass-fiber composites. The effect of fiber orientation is rather complex. Although the tensile strength of unidirectional composites is a maximum at 00 to the fibers (ref. 24), in fatigue the unidirectional construction is not optimum, as can be seen in figure 3. The best explanation for this phenomenon is the fact that unidi- rectional material is subject to splitting and rapid crack propagation in the matrix parallel to the fibers. Fatigue data for t5°, 677, 00/337,90 0 , and Style 181 satin weave (00/900) are compared in figure 4. In general, nonwoven materials are superior to woven mate- rials in fatigue. Note also the low notch sensitivity of these materials. A comparison of the behavior of S-glass and E-glass composites (ref. 15) is seen in figure 5. The higher modulus S-glass is consistently stronger in fatigue than E-glass. The effect of mean stress is seen in figure 6 for tension-compression and tension-tension behavior.
There have also been some measurements of the compression-compression fatigue behavior in low-cycle fatigue (ref. 20). These data indicate that the effect of mean stress is similar to that for metals, that is, the Goodman diagram is approximately linear.
In recent years, the realization that fracture was not an adequate design criterion for failure has led to studies of failure mechanisms in fatigue which provide a foundation for design. Broutman (ref. 25) studied the mechanisms of failure in glass-fiber- reinforced polymers subjected to fatigue loading. He noted cracks originating at fiber- matrix debonds propagating through the matrix and being deflected by fibers. Recent studies (refs. 26 to 30) have quantitatively described the changes in elastic and strength properties associated with this type of damage. Smith and Owen (ref. 26) evaluated eleven X different composite systems with modulus values ranging from 0.5 10 6 to 6.5 X 106 psi and found that the initial damage debonding occurred at 0.3% strain as seen in figure 7.
Thus, the limiting factor in fatigue is not the fiber but the interface or the matrix. As described in the following section, studies with metal matrix composites confirm this behavior. The data seen in figure 8 for chopped-strand mat-reinforced polyester lami- nates confirm that initial damage occurs at stresses well below those required for frac- ture. The effect of such damage on structural capability will determine whether the part has failed. Based on the observation of a critical strain, Smith and Owen postulated a critical maximum stress independent of mean stress for any material. As seen in fig- ure 9, this postulation was found to be incorrect (ref. 26).
Cessna et al. (ref. 27) performed constant-deflection flexural fatigue tests on glass- reinforced polypropylene and monitored the load decay (proportional to modulus decay) with cycles as seen in figure 10. They also monitored the temperature rise, as seen in figure 10, due to viscoelastic energy dissipation, which is common for polymeric com- posites. (See refs. 31 to 37.) In addition to indicating progressive fatigue damage, the temperature rise also contributes to weakening the material and shortening its fatigue life. As seen in figure 11, by cooling their specimens to maintain isothermal conditions, Cessna et al. (ref. 27) were able to extend both the cycles to onset of stiffness change and the fracture life by an order of magnitude.
Broutman and Sahu (ref. 28) have related the changes in residual tensile strength and modulus to the development of cracks in 0 0/900 crossplied material as seen in fig- ure 12. Although the decrease in residual strength and primary modulus is expected because of the increasing crack density, the initial increase in secondary modulus remains unexplained. A quantitative relationship between modulus change and crack den- sity (fig. 13) has been developed on the same material. Fujii and Mizukawa (ref. 30) have also determined the change in elastic and strength properties with cycling for laminates consisting of several combinations of roving cloth, chopped mat, and woven cloth.
The higher modulus composite materials, graphite and boron, have exhibited higher fatigue strengths than glass-reinforced polymers, as seen in figure 14 (refs. 15, 38 to 41). This difference is primarily attributed to the higher modulus resulting in less strain in the matrix and interface at the same cyclic stress level. The phenomenon of low fatigue strength at zero mean stress for the high modulus composites as seen in fig- ure 14 was first noted for boron-reinforced aluminum. It is thought to be the result of low transverse strength of unidirectional composites resulting in splitting under cyclic compressive loads. This behavior severely limits the use of unidirectional composites as discussed above.
A major variable which can affect the data obtained in a composite fatigue test is the specimen geometry. This variable is very much a function of the particular laminate orientation being tested, as interlaminar shear can be a primary controlling factor (refs. 42 and 43). Although this problem is negligible for a unidirectional material, it becomes a major factor in fatigue testing of ±45 0 laminates. Figure 15 compares the axial tension-tension fatigue behavior (based on fracture) for ±450 1002 E-glass compos- ites for three different specimen configurations (ref. 43). The straight-sided specimen is flat, and each fiber terminates at the edge, thus, high interlaminar shear stresses are created. The x-type specimen has all fibers continuous from grip to grip; thus, inter- laminar shear stresses at the edge are precluded. The latter type has the disadvantage of having a vanishingly small gage length and very uniformly loaded fibers, which are not representative of the types of loading experienced in most structures; thus, the resultant data are considered to be too optimistic for design. The tubular specimen has a uni- formly loaded gage section and no fiber edges; thus, interlaminar shear is precluded. It is felt that such a specimen comes closest to yielding representative material properties for design. Edges are usually handled as a separate factor in design. Although the dif- ference between the straight-sided and tubular specimens is only 5% for glass, it is approximately 50% for boron, as can be seen in figure 16. The reason for this effect is that the interlaminar shear stresses are higher for high modulus materials.
Fiber-Reinforced Metals Although fiber-reinforced metals considerably lag reinforced polymers in terms of development and usage, some of the earliest and best fundamental studies of fatigue have been accomplished with metal matrix composites. Forsyth, George, and Ryder (ref. 1) demonstrated that the inclusion of steel wires in an aluminum-alloy sheet reduces the rate of crack propagation substantially (fig. 17), although the improvement in total fatigue life to fracture is small (fig. 18). Baker and Cratchley (refs. 2, 44 to 48) performed extensive studies of the fatigue behavior of silica- and steel-fiber-reinforced aluminum alloys. Although silica-reinforced aluminum did not show promise as a fatigue-resistant material, Baker and Cratchley made important observations concerning failure modes and anelastic behavior. They identified the crack-diverting capability of strong fibers (ref. 2) and made important observations concerning the stress-strain behavior and damping capability of composites as seen in figure 19 (ref. 44). In addition, Baker quan- titatively defined the effect of fiber length on fatigue behavior (ref. 46) and evaluated the effects of fiber fatigue behavior and the interface (ref. 47).
Extensive studies have been made of the fatigue behavior of composites made by unidirectional solidification of eutectic alloys (refs. 4, 49 to 52). Because these com- posites have very regularly distributed fibers and well-bonded interfaces, they serve as excellent systems for studying the mechanical behavior of composites without the variable fabrication effects common to other composites. The Al-A1 3Ni (10% reinforcing A13Ni whiskers) and the Al-CuAl 2 (50% reinforcing CuAl 2 platelets) composite materials exhibit markedly different fatigue behavior as seen in figure 20. A comparison of the stress-strain behavior of the two materials showing fatigue failure at the same stress amplitude (ref. 49) reveals that Al-CuAl2 appears to work-harden more rapidly with narrower hysteresis loops than Al-A1 3Ni. It can be speculated that the wide CuAl2 platelets are more effective at blocking plastic flow than the A1 3Ni whiskers (which have a spacing at least an order of magnitude too large for optimum dispersion hardening). In addition, the greater volume fraction of CuAl 2 is more effective at blocking plastic flow in the matrix. If matrix strain is the controlling factor, then the behavior seen in fig- ure 20 would be an expected consequence of the difference in stress-strain behavior.
The fatigue behavior of metals has been found to obey a simple empirical relation- ship (refs. 5 to 7, 53 and 54) = MNz (1) AEr Ny + E Plastic Elastic where AE T total cyclic strain range E elastic modulus number of cycles to failure N M, G, z, y material constants This relationship is depicted schematically in figure 21, and it is seen that the plastic component (first term of eq. (1)) dominates at low cycles (high strain amplitudes), and the elastic component dominates at high cycles. Although most metals exhibit values of z of -0.5 to -0.6 (refs. 53 and 54), Al 3Ni whisker-reinforced aluminum exhibits much lower values as seen in figure 22. It has been proposed (ref. 4) that the low-cycle fatigue behavior is not governed entirely by the plastic behavior of the aluminum (z = -0.5) but also by the elastic behavior of the A1 3Ni (y < -0.1). This type of behavior would be expected for most composites having fibers which behave elastically in the stress range of use (glass, boron, graphite, highly cold-worked steel) and accounts for the relatively flat S-N (that is, stress S — number of cycles to failure N) curves discussed in the Introduction.
As seen in figure 23, the flexural fatigue behavior of Al-Al 3Ni is substantially higher than that for the matrix alone. The mode of failure is matrix cracking, the fibers serving to reduce matrix strain. Testing in a protective atmosphere such as argon results in higher fatigue strength as seen in figure 24, which further verifies the fact that failure is matrix dominated. Although the aluminum is susceptible to attack by moisture in the atmosphere, the A1 3Ni whiskers are not.
The fatigue behavior of boron-reinforced aluminum has been extensively studied (refs. 55 to 59). The very high modulus of the reinforcing fiber keeps the matrix strain low for any given stress level. This factor, coupled with the excellent fatigue resistance of boron fiber itself (ref. 60), provides extremely good fatigue resistance as seen in fig- ure 25. The data by Young and Carlson (ref. 56) is particularly valuable as it records changes in deflection for torsion, tension, and combined-load fatigue testing.
Gates and Wood (ref. 61) performed detailed studies of the microstructural changes which accompanied the torsional fatigue testing of copper reinforced circumferentially by tungsten or molybdenum wire. They noted that work hardening followed by crack initia- tion occurred in the matrix between fibers.
FATIGUE OF COMPOSITE STRUCTURES In order to define a design base for structures, it is necessary to determine the full-scale fatigue behavior of composite materials to identify the effects of size, manu- facturing variation, and combined loads. A limited amount of experience now exists with full-scale components (refs. 62 and 63); however, much of it relates to specific geome- tries and constructions and few generalizations may be drawn. Two things which are clear from this experience is the fact that composite structures are very fatigue resis- tant in aerospace applications relative to metal structures, and joints and attachments remain a major design problem, especially in fatigue.
The most substantial body of structural fatigue data exists for helicopter rotor blades (refs. 62 and 63). Jarosch and Stepan (ref. 62) have done fatigue testing of root end and outboard sections of the BO-105 fiberglass/epoxy rotor blade. The blade con- struction, seen in figure 26, consists of a C-spar of unidirectional E -glass -reinforced epoxy wound around a pin fitting at the root end, a skin of woven-glass cloth/epoxy oriented at ±45°, and a foam core. Measured values of the spar and skin elastic modulus in the spanwise direction were 6.0 x 10 6 and 2.6 x 106 psi, respectively. The root end was fatigue tested, as seen in figure 27, with equal flapping and lagging loads of 1900 ± 2600 ft-lb and a steady centrifugal load of 24 000 lb. Fatigue lives varied to 13 x 10 6 cycles. Failure generally occurred in the unidirectional roving at the root-end pin attachment and was accompanied by considerable heating due to interlaminar friction.
Readily visible delamination and gradual changes in stiffness and damping also occurred.
Outboard specimens were tested in flapping resonance at a fatigue strain level of ±0.870, which is ten times the maximum strain in flight. Typical fatigue lives were more than 106 cycles, and failure was preceded by obvious visible delaminations and accompanying changes in damping and stiffness.
Fatigue tests of boron/epoxy and glass/epoxy CH-47 rotor blades (ref. 63) have also indicated excellent fatigue resistance although failures occurred in the metal root- end fitting. Similarly, fatigue testing of the boron/epoxy F-111 horizontal tail resulted in failure associated with the attachment of the composite to the titanium root end.
Spectrum testing of components of a boron/epoxy wing box has shown excellent fatigue resistance, as has sonic fatigue testing of a boron/epoxy C-5A slat component. Both of these items have exhibited failure in fittings of composite bonded to metal.
COMPOSITE FATIGUE DESIGN CONSIDERATIONS A successful design procedure for composite materials in fatigue applications will not be a simple extrapolation of procedures used for metals. Metal parts exhibit cracks when they begin to fail in fatigue, and the cracks generally propagate in a predictable manner to failure. Thus, the metal part may be inspected at specific intervals and removed from service prior to failure. Composites, on the other hand, do not fail in the same manner.
The difference between fatigue behavior of a composite and that of a metal structure is depicted schematically in figure 28. The primary mode of damage in a metal struc- ture is cracking. Cracks propagate in a relatively well defined manner with respect to the applied stress, and the critical crack size and rate of crack propagation can be related to specimen data through analytical fracture mechanics. In this discussion, the critical damage size is defined as that amount of damage at which the composite will be no longer structurally adequate. In general, the crack initiation time (defined as the time to detec- able cracking (inspection threshold)) occupies a large part of the fatigue life of a metal part (ref. 64). It should be noted that all structures have some initial damage in the form of microcracks, surface imperfections, inclusions, and other stress risers and that much of the so-called crack initiation time involves propagation of this damage to detectable size. With composite structures there is no single damage mode which dominates.
Matrix cracking, delamination, debonding, voids, fiber fracture, and composite cracking can all occur separately and in combination, and the predominance of one or more is highly dependent on the laminate orientations and loading conditions. In addition, the unique joints and attachments used for composite structures often introduce modes of failure different from those typified by the laminate itself.
The composite damage propagates in a less regular manner and damage modes can change. (See fig. 28.) Present experience with composites, although limited, indicates that the rate of damage propagation in composites does not exhibit the two distinct regions of initiation and propagation. Although, as mentioned previously, the crack initiation range in metals is actually propagation, there is a significant quantitative difference in rate. This quantitative difference appears to be less apparent with composites. This observation is very subjective and apparently dependent upon the observer's definition of initiation. Some investigators have observed matrix crazing and other indications early in their tests but have reported short-time rapid propagation because they define the latter based upon their experience with metals as crack propagation. Indeed, composite cracking may occupy only a small part of the fatigue life at the very end, but we can cer- tainly snake use of all the earlier indications which are prevalent.
It is expected that composite materials will be more damage tolerant than metals.
Again, this expectation is based upon limited experience and will depend upon the lami- nate orientation (unidirectional composites are subject to splitting) and loading conditions, but, in general, it can be argued that each fiber is a separate load path and that a com- posite is therefore highly redundant. Our present analytical fracture mechanics tool must be supplemented for use with composites before we have a better understanding of this behavior. Several investigators have indicated that, in general, composites exhibit good fracture toughness (refs. 65 to 67) and, unlike metals, increase fracture toughness with increasing strength. It is thus reasonable to predict the critical damage size in composites to be greater than that for metals (fig. 28), although the multiple failure modes make this value a band for composites. Similarly, the inspection threshold is depicted as a band in figure 28 because there are multiple failure modes and multiple inspection methods The problem then is to determine the critical mode or modes of failure and develop detection schemes in order to insure fail safety in critical components. One such pro- cedure involves the determination of changes in the static or dynamic stiffness properties of the component. A change in the resonant frequency or damping behavior of a part is an indication of damage. Failure criteria can be developed from data such as those seen in figures 10 to 12 as substantial changes occur early enough in the fatigue life to allow safe detection and removal from service. This characteristic may provide excellent fail safety for rotor blades in that the aeroelastic behavior may degrade noticeably long before the part has sustained damage of critical size. Other detection schemes such as temperature rise measurements (fig. 10), embedded conducting wires, radiography, sonics, ultrasonics, holography, infrared inspection, dye penetrant, and visual inspection will probably be used separately or in conjunction with dynamic measurements.
As mentioned earlier, a major consideration for developing a valid design method- ology is a definition of failure. A problem exists however, in that a single failure crite- rion may be inadequate for all applications. This situation is seen schematically in fig- ure 29. The example considers two structures, a spring and a tension cable, and two candidate materials, a metal and a composite, for each application. The failure criterion for the spring is a specified loss in stiffness, whereas that for the cable is fracture.
Since metal structures exhibit little change in stiffness until cracking is extensive, the metal spring and metal cable have approximately the same life, and a single criterion based on fracture is probably adequate for design. The composite material spring would lose sufficient stiffness to be considered failed at only a fraction of its fracture life, whereas, the tension cable made of the same material and subject to the same loading would have a much greater useful life. In order to provide for such design considerations, it will be desirable to record fatigue data as depicted schematically in figure 30.
CONCLUDING REMARKS Composite materials appear to offer excellent resistance to fatigue loading and, as such, will likely find use in dynamic components. A second factor which makes com- posites attractive for these applications is the opportunity for tailoring of the stiffness in different directions, thus the designer is given the capability of tuning dynamic com- ponents. As composites find wider application, it will be necessary to provide more precise definitions of failure and to couple these definitions with proper damage detection schemes. New, sophisticated damage detection methods will probably not be necessary; however, because of the multiple damage modes possible, it will be necessary to utilize multiple detection schemes. The apparent high damage tolerance of composites will allow somewhat relaxed inspection requirements and will provide for improved repair- ability procedures. At this writing, the cost of high modulus composites is still high and must be further reduced to allow wider usage.
REFERENCES 1. Forsyth, P. J. E.; George, R. W.; and Ryder, D. A.: Some Preliminary Tests on Aluminum Alloy Sheets Reinforced With Strong Wires. Appl. Mater. Res., vol. 3, no. 4, Oct. 1964, pp. 223-228.
2. Baker, A. A.; and.Cratchley, D.: Metallographic Observations on the Behaviour of Silica Reinforced Aluminum Under Fatigue Loading. Appl. Mater. Res., vol. 3, no. 4, Oct. 1964, pp. 215-222.
3. Morris, A. W. H.; and Steigerwald, E. A.: An Investigation of the Fatigue Behavior of Tungsten-Reinforced and Steel-Reinforced Silver Composites. Trans. Met. Soc.
AIME, vol. 239, 1967, pp. 730-739.
4. Salkind, M. J.; and George, F. D.: Fatigue and Bonding of A1 3 Ni Whisker Reinforced Aluminum. Rep. G910583.4 (Contract No. 0019-68-C-0016), United Aircraft Corp., July 31, 1968. (Available from DDC as AD 838 871.)
5. Tavernelli, J. F.; and Coffin, L. F., Jr.: A Compilation and Interpretation of Cyclic Strain Fatigue Tests on Metals. Trans. Amer. Soc. Metals, vol. LI, 1959, pp. 438-453.
6. Manson, S. S.: Behavior of Materials Under Conditions of Thermal Stress. NACA Rep. 1170, 1954. (Supersedes NACA TN 2933.)
7. Sachs, G.; Gerberich, W. W.; Weiss, V.; and Latorre, J. V.: Low-Cycle Fatigue of Pressure-Vessel Materials. Proc. Amer. Soc. Testing Mater., vol. 60, 1960, pp. 512-529.
8. Boller, K. H.: Fatigue Tests of Glass-Fabric-Base Laminates Subjected to Axial Loading. Rep. 1823, Forest Prod. Lab., U.S. Dep. Agr., May 1952.
9. Stevens, G. H.; and Boller, K. H.: Effect of Type of Reinforcement on Fatigue Prop- erties of Plastic Laminates. TR 59-27, U.S. Air Force, May 1959. (Available from DDC as AD 213 835.)
10. Kimball, Kenneth E.: Supplement to Fatigue Tests of Glass-Fabric-Base Laminates Subjected to Axial Loading — Effect of Notches. Rep. No. 1823-C, Forest Prod.
Lab., U.S. Dep. Agr., Oct. 1958.
11. Boller, Kenneth H.: Resume of Fatigue Characteristics of Reinforced Plastic Laminates Subjected to Axial Loading. ASD-TDR-63-768, U.S. Air Force, July 1963.
12. Boller, K. H.: Effect of Pre-Cyclic Stresses on Fatigue Life of RP Laminates.
Modern Plastics, vol. 42, no. 8, Apr. 1965, pp. 162, 165-166, 168, 171, 173.
13. Boller, Kenneth H.: Effect of Tensile Mean Stresses on Fatigue Properties of Plastic Laminates Reinforced With Unwoven Glass Fibers. ML-TDR-69-86, U.S. Air Force, Mar. 1964. (Available from DDC as AD 605 412.)
14. Boller, Kenneth H.: Effect of Pre-Cyclic Stresses on Fatigue Life of Plastic Laminates Reinforced With Unwoven Fibers. ML-TDR-64-168, U.S. Air Force, Sept. 1964. (Available from DDC as AD 606 769.)
15. Boller, Kenneth H.: Fatigue Strength of Plastic Laminates Reinforced With Unwoven "S" Glass Fibers. AFML-TR-64-403, U.S. Air Force, Dec. 1964.
16. Boller, Kenneth H.: Fatigue Characteristics of Two New Plastic Laminates Rein- forced With Unwoven "S" Glass Fibers Under Cyclic Axial or Shear Loading.
AFML-TR-66-54, U.S. Air Force, Mar. 1966.
17. Boller, Kenneth H.: Effect of Notches on Fatigue Strength of Composite Materials.
AFML-TR-69-6, U.S. Air Force, Apr. 1969. (Available from DDC as AD 853 045.)
18. Boller, K. H.: Fatigue Fundamentals for Composite Materials. Composite Materials: Testing and Design, Spec. Tech. Publ. No. 460, Amer. Soc. Testing Mater., c.1969, pp. 217-235.
19. Broutman, Lawrence J.: Fiber-Reinforced Plastics. Modern Composite Materials, Lawrence J. Broutman and Richard H. Krock, eds., Addison-Wesley Pub. Co., Inc., c.1967, pp. 337-411.
20. Cornish, R. H.; Nelson, H. R.; and Dally, J. W.: Compressive Fatigue and Stress Rupture Performance of Fiber Reinforced Plastics. Proceedings 19th Annual Technical and Management Conference, sec. 9-E, Soc. Plast. Ind., Inc., Feb. 1964.
21. Mettes, David G.; and Lockwood, Paul A.: The Mechanical Properties of Laminates Reinforced With High Performance Glass Fiber Fabric. Proceedings 21st Annual Technical and Management Conference, sec. 4-G, Soc. Plast. Ind., Inc., Feb. 1966.
22. Davis, J. W.; McCarthy, J. A.; and Schurb, J. N.: The Fatigue Resistance of Rein- forced Plastics. Mater. Des. Eng., vol. 60, no. 7, Dec. 1964, pp. 87-91.
23. Cutler, Martin B.; and Pinckney, Robert L.: Static and Fatigue Test Properties for Woven and Nonwoven S-Glass Fibers. USAAVLABS Tech. Rep. 69-9, U.S. Army, Apr. 1969. (Available from DDC as AD 688 971.)
24. Kelly, A.; and Davies, G. J.: The Principles of the Fibre Reinforcement of Metals.
Metallurgical Rev., vol. 10, no. 37, 1965, pp. 1-77.
25. Broutman, L. J.: Failure Mechanisms for Filament Reinforced Plastics. Modern Plastics, vol. 42, no. 8, Apr. 1965, pp. 143-145, 148, 150, 153, 214, 216.
26. Smith, T. R.; and Owen, M. J.: Fatigue Properties of RP-1. Modern Plastics, vol. 46, no. 4, Apr. 1969, pp. 124-125, 128-132.
27. Cessna, L. C.; Levens, J. A.; and Thomson, J. B.: Flexural Fatigue of Glass- Reinforced Thermoplastics. Proceedings 24th Annual Technical and Management Conference, sec. 1-C, Soc. Plast. Ind., Inc., Feb. 1969.
28. Broutman, L. J.; and Sahu, S.: Progressive Damage of a Glass Reinforced Plastic Annual Technical and Management Conference, During Fatigue. Proceedings 24th sec. 11-D, Soc. Plast. Ind., Inc., Feb. 1969.
29. Lavengood, R. E.; and Anderson, R. M.: Matrix Properties Controlling Torsional Fatigue Life of Fiber Reinforced Composites. Proceedings 24th Annual Technical and Management Conference, sec. 11-E, Soc. Plast. Ind., Inc., Feb. 1969.
30. Fujii, Taichi; and Mizukawa, Kiyoshi: The Effect of the Combination of Roving Glass Cloth and Mat Upon the Fatigue Strength of Reinforced Polyester Laminates.
Proceedings 24th Annual Technical and Management Conference, sec. 14-D, Soc.
Plast. Ind., Inc., Feb. 1969.
31. Hagerup, E.: Flexural Fatigue Testing of Polyesters. J. Appl. Polymer Sci., vol. 7, no. 3, May 1963, pp. 1093-1116.
32. Lazan, B. J.: Some Mechanical Properties of Plastics and Metals Under Sustained Vibrations. Trans. ASME, vol. 65, no. 2, Feb. 1943, pp. 87-104.
33. Lazan, B. J.; and Yorgiadis, A.: Behavior of Plastics Under Repeated Stress.
Symposium on Plastics, Spec. Tech. Publ. No. 59, Amer. Soc. Testing Mater., Feb. 1944, pp. 66-94.
34. Boller, Kenneth H.: Fatigue Characteristics of RP Laminates Subjected to Axial Loading. Modern Plastics, vol. 41, no. 10, June 1964, pp. 145-150, 188.
35. Thompson, A. W.: Fatigue and Creep Properties of Reinforced Plastics. Plastics Inst.-Trans., vol. 30, no. 85, Feb. 1962, pp. 39-50.
36. Owen, M. J.: New Fatigue Testing Machine for Reinforced Plastics. Plastics Inst.-Trans., vol. 35, no. 115, Feb. 1967, pp. 353-357.
37. Dally, J. W.; and Broutman, L. J.: Frequency Effects on the Fatigue of Glass Rein- forced Plastics. J. Compos. Mater., vol. 1, no. 4, Oct. 1967, pp. 424-442.
38. Shockey, P. D.; Anderson, J. D.; and Hofer, K. E.: Structural Airframe Application of Advanced Composite Materials. Vol. V — Mechanical Properties — Fatigue.
AFML-TR-69-101, Vol. V, U.S. Air Force, Mar. 1970. (Available from DDC as AD 867 017.)
39. Hayes, R. D.: Flightworthy Graphite Fiber Reinforced Composite Aircraft Primary Structural Assemblies. Vols. 1 and 2. FML-TR-70-207-Vols. 1 & 2, U.S. Air Force, 1970. (Available from DDC as AD-877 234 and AD-877 235.)
40. Holmes, R. D.; and Wright, D. W.: Creep and Fatigue Characteristics of Graphite/Epoxy Composites. ASME Paper 70-DE-32, Amer. Soc. Mech. Eng., May 1970.
41. Owen, M. J.; and Morris, S.: An Assessment of the Potential of Carbon Fibre Rein- forced Plastics as Fatigue Resistant Materials. Proceedings 25th Annual Technical and Management Conference, sec. 8-E, Soc. Plast. Ind., Inc., Feb. 1970.
42. Puppo, A. H.; and Evensen, H. A.: Interlaminar Shear in Laminated Composites Under Generalized Plane Stress. J. Compos. Mater., vol. 4, Apr. 1970, pp. 204-223.
43. Pipes, R. Byron; and Pagano, N. J.: Interlaminar Stresses in Composite Laminates Under Uniform Axial Extension. J. Compos. Mater., vol. 4, Oct. 1970, pp. 538-548.
44. Baker, A. A.; and Cratchley, D.: Stress-Strain Behaviour and Toughness of a Fibre- Reinforced Metal. Appl. Mater. Res., vol. 5, no. 2, Apr. 1966, pp. 92-103.
45. Baker, A. A.: The Effect of Fibre Volume Fraction and Interfacial Bond on the Fatigue of Aluminum Reinforced With Stainless Steel Wires. Appl. Mater. Res., vol. 5, no. 3, July 1966, pp. 143-153.
46. Baker, A. A.: The Effect of Fibre Diameter and Discontinuous Fibres on the Fatigue of a Fibre-Reinforced Metal. Appl. Mater. Res., vol. 5, no. 4, Oct. 1966, pp. 210-217.
47. Baker, A. A.; Mason, J. E.; and Cratchley, D.: High-Strain Fatigue Studies of a Composite Material. J. Mater. Sci., vol. 1, no. 3, Aug. 1966, pp. 229-237.
48. Baker, A. A.: The Fatigue of Fibre-Reinforced Aluminum. J. Mater. Sci., vol. 3, no. 4, July 1968, pp. 412-423.
49. Salkind, M. J.; George, F. D.; Lemkey, F. D.; and Bayles, B. J.: Investigation of the Creep, Fatigue, and Transverse Properties of A1 3 Ni Whisker and CuAl 2 Platelet Reinforced Aluminum. E910344-4 (Contract NOw-65-0384d), United Aircraft Corp., May 11, 1966. (Available from DDC as AD 633 241.)
50. Salkind, M. J.; Lemkey, F. D.; and George, F. D.: Whisker Composites by Eutectic Solidification. Whisker Technology, Albert P. Levitt, ed., Wiley-Inter science, c.1970, pp. 343-401.
51. Thompson, E. R.; George, F. D.; and Kraft, E. H.: Investigation To Develop a High Strength Eutectic Alloy With Controlled Microstructure. Rep. J910868-4 (Contract No. 0019-70-C-0052), United Aircraft Corp., July 31, 1970. (Available from DDC as AD 873 832.)
52. Hoover, W. R.; and Hertzberg, R. W.: The Fatigue Characteristics of Unidirectionally Solidified Al-A1 3Ni Eutectic Alloy. Trans. Amer. Soc. Metals, vol. LXI, 1968, pp. 769-776.
53. Manson, S. Stanford; and Hirschberg, Marvin H.: Fatigue Behavior in Strain Cycling in the Low- and Intermediate-Cycle Range. Fatigue — An Interdisciplinary Approach, John J. Burke, Norman L. Reed, and Volker Weiss, eds., Syracuse Univ. Press, 1964, pp. 133-178.
54. Coffin, L. F.: A Study of the Effects of Cyclic Thermal Stresses on a Ductile Metal.
Trans. ASME, vol. 76, no. 6, Aug. 1954, pp. 931-950.
55. Forest, J. D.; and Christian, J. L.: Development and Application of Aluminum- Boron Composite Material. AIAA Paper No. 68-975, Oct. 1968.
56. Young, J. R.; and Carlson, R. G.: Advanced Composite Material Structural Hardware Development & Testing Program. AFML-TR-70-140-Vol. I, U.S. Air Force, July 1970. (Available from DDC as AD 872 264.)
57. Shimizu, H.; and Dolowy, J. F., Jr.: Fatigue Testing and Thermal-Mechanical Treatment Effects on Aluminum-Boron Composites. Composite Materials: Testing and Design, Spec. Tech. Publ. No. 460, Amer. Soc. Testing Mater., c.1969, pp. 192-202.
58. Kreider, K. G.: Mechanical Testing of Metal Matrix Composites. Composite Materials: Testing and Design, Spec. Tech. Publ. No. 460, Amer. Soc. Testing Mater., c.1969, pp. 203-214.
59. Toth, I. J.: Creep and Fatigue Behavior of Unidirectional and Cross-Plied Composites. Composite Materials: Testing and Design, Spec. Tech. Publ.
No. 460, Amer. Soc. Testing Mater., c.1969, pp. 236-253.
60. Salkind, M.; and Patarini, V.: Fatigue of Boron Filament. Trans. Met. Soc. AIME, vol. 239, 1967, pp. 1268-1270.
61. Gates, R. G.; and Wood, W. A.: Evaluating Potential Fatigue Performance of Composites (Cu/W and Cu/Mo) From Microstructural Behavior. Metal Matrix Composites, Spec. Tech. Publ. No. 438, Amer. Soc. Testing Mater., c.1968, pp. 218-228.
62. Jarosch, E.; and Stepan, A.: Fatigue Properties and Test Procedures of Glass Reinforced Plastic Rotor Blades. J. Amer. Helicopter Soc., vol. 15, no. 1, Jan.
1970, pp. 33-41.
63. Stratton, Warren: The Potential of Advanced Composites for V/STOL Propellers.
Proceedings of the V/STOL Technology and Planning Conference, U.S. Air Force, Sept. 23-25, 1969.
64. Manson, S. S.: Fatigue: A Complex Subject — Some Simple Approximations. Exp.
Mech., vol. 5, no. 7, July 1965, pp. 193-226.
65. Salkind, M. J.; and George, F. D.: The Charpy Impact Behavior of A1 3Ni Whisker- Reinforced Aluminum. Trans. Met. Soc. AIME, vol. 242, 1968, pp. 1237-1247.
66. Cooper, G. A.; and Kelly, A.: Tensile Properties of Fibre-Reinforced Metals: Fracture Mechanics. J. Mech. Phys. Solids, vol. 15, no. 4, July 1967, pp, 279-297.
67. Tetelman, A. S.: Fracture Processes in Fiber Composite Materials. Composite Materials: Testing and Design, Spec. Tech. Publ. No. 460, Amer. Soc. Testing Mater., c.1969, pp. 473-502.
Phenol ic >i - resistont epoxide \ Heot Po I yeste r --\ i v 30 a E Heat-fesistont polyester Epoxide m c E° _e 5 it i cone 10 102 103 104 105 106 107 108 Cycles to fuilure Figure 1.- Effect of matrix material on fatigue of glass fabric composites (from ref. 18).
:t a 80 26% E `- d
N 60
N 20% 32%
^o
^a
N Q and 37% C 20 a^ Q .2 10 5 107 1 10 10 10 4 10 6 Number of cycles to failure Figure 2.- Effect of matrix content on fatigue of ±50 glass-fiber-reinforced epoxy (from ref. 13).
s „ E 60 c N N m CD c C m Q 10 103 105 Cycles to Failure Figure 3.- Effect of fiber orientation (from ref. 18).
X h 45 \ V' Notched — O^ c 2.1 a c ^0 E E Unnotched X Cb 0--^ — 103 104 105 106 107 Cycles to Failure Figure 4.- Fatigue of woven and nonwoven materials (from ref. 18).
A 9 O e 'S' GLASS 25.000 PSI A MEAN STRESS 0- N 8 'S' GLASS (L q ZERO O 7 O MEAN STRESS q e O O e 6 O A A C] 'E' GLASS^^^^ O 25,000 PSI ^^^ q U) MEAN STRESS w 5 U) 4 'E' GLASS---- ZERO O MEAN STRESS `^^^` C^ L J 0- O X Q 2 O 1 O i iU iU iU j i NUMBER OF CYCLES TO Figure 5.- Fatigue of E- and S-glass composites (fl N Y w 80 a m E 60 D E X Cycles to Failu Figure 6.- Effect of mean stress level (from I 8 ^- Z )7 N Cx M 0 8 —3000 psi {\ b Q Opsi C3
i
+ 2000 p s ^ 0 0.1 1 10 10 2 103 10 4 10 5 106 107 Number of load repetitions Figure 9.- Effect of mean stress on debonding of glass-mat-reinforced polyester (from ref. 26).
s X V a i' 2' r7 40 LL', • 0 8 w x Q d 4 X/ ono f w In x In w cc 2 .n 1000 10,000 100,000 10 100 CYCLES ENDURED Figure 10.- Apparent stress and temperature rise in glass- reinforced polypropylene (from ref. 27).
120 ISOTHERMAL TESTS DATA POINTS W M O 100 C P Z q 500 C P M A1000CPM Ie:T1LE
U_ O
FAILURE P M O 1080 C G C P M O 1800 0 q q Q q q ^ oco `'no Q
--Il i
co Z 60 T T I NONISOTH(RMAE ES S SOLID LINFS N^ M ePITTLF 0 1000 P n 500 C P M Q 40 720 C r M U_ DUCTILE AIOOOC PM g P M Al oo C O 20 e H 1A) ISOT ERMAL FA ILU R E POND 0 1 I ri t 10 2 104 105 10 6 107 CYCLES ENDURED Figure 11.- Stiffness decay during fatigue of glass-reinforced polypropylene (from ref. 27).
Ir W fn PLIES OO P ERPENDICULAR ^ Y 1
D U
O Z rt w U 5 i ^w QO PARALLEL PLIES J W Ir O PRIMARY I MODULUS Q.
4.5 I O i I 4.0 O J SECONDARY 3.5 MODULUS O 3.0 moult =124 kM PSI W J Z = 80 I- w w w 60 > O (D 40 J w O O 3 4 7 1 2 5 6 8 CYCLES,10 4 Figure 12.- Changes in strength, modulus, and cracking of 00/900 glass-reinforced epoxy (from ref. 28).
0.20 0.15 WlW d N J 0.10 Z u) 0.05 a W cr U W Q 0.00 1.2 1.4 1.6 1.8 2.0 2.2 CRACK PITCH TO PLY THICKNESS, P Figure 13.- Change in modulus with density of cracking for 0 0 /90 0 glass-reinforced epoxy.
1Dc UNIDIRECTIONAL 10 1 C.YCLESTO FRACTURE R=0 , R=01 R-03 In a.
-------- ^0 a V) V) W a m m 2s bu 0 100 150 200 STEADY STRESS 10 1 PSI Figure 14.- Comparison of fatigue behavior of unidirectional boron, graphite, and glass-reinforced polymers.
R=0.1 T o o -.—TVPE o O o 6.5 0 0 0 0 0 fn 5.25 —1 Y 20 W rJ ir H 15 TUBULAR \ r 14 –-- X 10 Q STRAIGHT-SIDED 15 — —^j 1 1 l O i 10 1 104 105 106 107 10n CYCLES TO FRACTURE Figure 15.- Effect of specimen configuration on axial fatigue behavior of ±45 0 1002 E-glass/epoxy.
R=0.1 "X" TYPE 32— Y N ` 24 N Ili N TUBULAR X Q STRAIGHT SIDED O' 10^ 10 10, 106 10' CYCLES TO FRACTURE Figure 16.- Effect of specimen configuration on axial fatigue behavior of ±45 0 boron/epoxy.
z 4.0
ALUivyIINium W/O
WITH
REINFORCEMENT STEEL
3.0
WIRES
CD Z 2.0 w Y 1.0 U Q
1 3 4 5
0 2
U
CYCLES X105
Figure 17.- Effect of steel wire mesh on the crack growth behavior of aluminum alloy sheet (from ref. 1).
LOADING P± P
. L REINFORCED L73
73 ^
16 0
O
10 6 107 108
ENDURANCE---so- (CYCLES)
Figure 18.- Fatigue behavior of aluminum alloy with and without 13.5 volume percent steel wire (from ref. 1).
L J `^ 1 J O 0 7 IV If IL I.7 IV (ton/in2) Stress — ► Composite 1: 2: Grey cast iron 3: Scotch ply 1009 4: RR58 AI alloy 5: Silver steel Figure 19.- Vibrational damping capacity (b) as a function of stress for silica-reinforced aluminum compared with conventional engineering materials (from ref. 44).
Z n n M • U3 O • n fy A O O n O O O n o• n o ^ o- 0 o- e A • 0- o- a 20 SOLIDI 9 1CATION ROTE Cn 0 0.3 CM/HR V) W O 08 CM/HR N CM/HR A 2 tn O 11 CM/HR FILLED SYMBOLS - A]-AI 3N, OPEN S YM BOLS-AI-Cu Alt ARROW INDICATES SPEC IMEN DI D NOT FAIL 1 100 1000 10,000 CYCLES TO FAILURE N Figure 20.- Comparison of fatigue behavior of lamellar (AI-CuAl2) and fiber (AI-A1 3 Ni) composites (from ref. 49).
e m ARRO—. DEMOTE SPECIMEN DID MOT FAIL Q Q u e Q AI-AI?N. - Ilc^'IM n Q o ^ O e AI -at l N. -) c... k.
w'S a r n n- o— s 0 AI MAY.- O - W !O T to a CYCLES TO FAILURE Figure 23.- Flexural fatigue behavior of Al-Al 3 Ni in air (from ref. 4).
AR GOM P A SLIGMT SURFACE I 0- O^ a CRAC11MG MDTED O— t r^ n AIR e IS IN e— s ARROWS DEMOTE SPECIMEN DID MOT FAIL I I i0 5 106 DT 10, CYCLES TO FAILURE Figure 24.- Effect of environment on the flexural fatigue behavior of AI-Al 3 Ni (from ref. 4).
loc 8C -10 2 AI-B DATA\ (^\ \ 10 4 Y 106 \ \ 6C z a 4( w Q '0' 60 ," -l6 , T 2( 10 6 II I 60 80 100 20 40 0 MEAN STRESS, KSI Figure 25.- Fatigue behavior of 40 volume percent boron-reinforced 6061 aluminum, compared with unreinforced aluminum alloys (from ref. 57). I 81ade -Root-Tests -- 1 Outer Blade- Bending Tests – 01 8 It -- – -- t--- — --13.8 It -- --- -- Foam Core G R E - Skin G R.E (Rovin g ) Nose Cover Endurance-Test specimen cut out of production Blade with Erosion and Roving Samples.
De -icing protection 0 24 x 0.59'; 1 0.39 x 0 59x2.40" 0.32x0.59" 1=70" 0 47x 0.47 ) For Bending Tests For Shear Tests Figure 26.- Glass/epoxy 80-105 rotor blade (from ref. 62).
Full—Size Blade Root Sam Complete Btade Root Attachment M iag M flop = = 1900=2600 ft Ibs Tension (C.E 1 = 12 t Figure 27.- Root-end fatigue test specimen of BO-105 rotor blade (from ref. 62).
DAMAGE SIZE METALS CRACKLENGTH COMPOSITES BROKEN FIBERS LCLAMINAIION MATRIX CRACKING COMPOSITE CRACKING DEBONDS VOIDS ER F EU IONS INITI AL Figure 28.- Comparison of fatigue behavior in metals and composites.
IT E RE FATIGUE DESIGN PROCEDURE FOR THE AMERICAN SST PROTOTYPE By Ralph J. Doty Th e Boeing Company, Seattle , Washington, U.S.A.
SUMMARY For supersonic airline operations, significantly higher environmental temperature is the primary new factor affecting structural service life. Methods for incorporating the influence of temperature in detailed fatigue analyses are shown alon g with current test indications. Thermal effects investigated include real-time compared with short- time testing, long-time temperature exposure, and str ess -temperature cycle phasing.
A method which allows deSigners and str ess analyzers to check fatigue resistance of structural design details is the primary theme of this paper. A more communicative rating system is presented which defines the relative fatigue quality of the detail so that the analyst can define cyclic-load capability of the design detail by entering constant-life charts for varying detail quality. If necessary then, this system allows him to determine ways to improve the fatigue quality for better life or to determine the operating stresses which will provide the required service life.
A supersonic vehicle structure , which is subject to major airload center-of - pressure shifts as well as to the addition of thermal-gradient stresses to mechanical stresses, experiences a relatively large percentage of damage from ground-air-ground (GAG) cycles. In studying the Ig thermal-gradient history of a design detail , the analyst will produce a Ig stress history. Application of simple factors to this history allows determination of dynamically instantaneous maximum and minimum stresses statistically realized once per flight which represent the GAG cycle. The relationship of GAG dam- age to total damage on various parts of the vehicle is used to facilitate a quick fatigue- resistance check.
A quick fatigue- check method for deSigners and stress analysts benefits the design by making designers and stress analysts more cognizant of fatigue problems throughout the detail design phase of an aircraft development.
THE PROTOTYPE TASK At the 1967 ICAF meeting in Melbourne, Australia, the philosophy and scope of an integrated program of analysis, development testing, and verification testing for the American supersonic transport (SST) were presented. Since that time the program has developed to the point where the prototype configuration is being designed and fabricated.
Figure 1 shows the SST in take-off and cruise configuration and figure 2 gives an idea of the structural configuration. Attention to fatigue and fail-safe requirements in the detail design of the prototype will assure a structure representative of the 50 000 flight hour and 20-year service life design goal for a production SST.
If a total SST program schedule is reviewed, the significant location of the proto- type job becomes apparent. Figure 3 presents the essential schedule elements. A 30- to 40-year time span is needed to include a 20-year operating period. The prototype design release, which is labeled NOW on figure, comes fairly early in the program after a company study period, a research and competition period, and a prototype design devel- opment period. Careful planning and implementation of investigation programs with extensive testing will provide the required structural confidence for the production design.
For the prototype, fatigue resistance representative of production design must be engi- neered into the structure with a strictly fundamental analysis without a great depth of titanium structural component tests. This paper presents the basic tools used along with discussion of the significant factors affecting fatigue and how they are accounted for in the prototype design.
Good fatigue design is most effectively accomplished when both designers and design analysts understand and implement fatigue requirements in the drawing release process.
Design analysts on the SST prototype are required to check their designs for production requirements specifying 50 000 flight hours of normal usage. The projected composite airplane usage includes 49 250 hours of revenue service used in 22 000 flights and 750 hours of training containing 1500 full-stop landings and 2600 touch-and-go landings.
Application of these service life requirements in addition to other loads criteria truly makes the prototype design an exercise in production design.
The fatigue analysis procedure, made available to the design analyst in handbook form, allows him to determine the service life capability quickly. A rating system which gives the relative fatigue quality of a design detail so that the analyst can determine cyclic-load capability by entering constant-life charts for varying detail quality is pre- sented. Consequently, he can determine whether to improve quality for known life improvement or to establish operating stress levels which will provide satisfactory service life. With a minimum of experience with different details, an engineering under- standing of relative fatigue values is developed.
THE SUPERSONIC TRANSPORT FATIGUE PROBLEM In the transition from subsonic to supersonic transport operations, the major new parameter influencing structural fatigue resistance is elevated-temperature exposure.
There are many other more subtle influences in this operational transition, but the thermal environment necessitates development of new tools for fatigue-performance evaluations.
Figure 4 shows schematically a comparison of equidistant subsonic and supersonic transport operations. The supersonic mission is clearly a high-speed high-altitude type of operation with a lower percent of time spent in cruise operation. High-altitude opera- tion puts the SST in a less damaging gust environment during cruise. Also, because the SST must be designed for efficient high-speed supersonic cruise, the effects of relatively large center-of-pressure shifts between the subsonic and supersonic operation are appar- ent on this type of vehicle. When the relative parts of the damage resulting from gust, maneuver, taxi, take-off, landing, and ground-air-ground (GAG) operation are considered, it is apparent that a large part of fatigue damage will be due to the GAG cycle on critical parts of the primary wing and body structure. This conclusion is used to advantage in developing a simple fatigue-check procedure.
The subsonic operation produces no significant thermal environment but supersonic operation at Mach 2.7 subjects the airplane to a stagnation temperature of 500 0 F. Fig- ure 5 shows the stabilized temperatures existing during cruise. Realizing that the mis- sion requires climb and acceleration into and finally descent and deceleration from such a condition, the design analyst knows that fatigue analysis must account for many thermal effects. For convenience in the development of analytical procedures, the total thermal effect will be evaluated as thermal-gradient loading, long-time temperature exposure, and an interrelated cyclic exposure of stress and temperature.
After analysis of projected operational SST route structures, a mean mission was selected to establish representative fatigue damage for the SST prototype structural design. Figure 6 shows the details of this mission. The consequences of this operation on a structural detail are illustrated in figures 7 to 9. Figure 7 shows a typical 1g stress and external temperature history at a wing lower surface location. Figure 8 shows the thermal-gradient stress and temperature history as it will develop on two types of typical wing surface structures. Figure 9 shows a combined total stress and temperature his- tory for the structural detail being analyzed. The design analyst studying the load and temperature effects on any structural detail will prepare these histories to understand his problem. These histories provide him with the initial tool leading into the fatigue- check procedure.
The first step in the analysis procedure is to define the stress level of a primary GAG cycle from the data obtained in producing figure 9. It is not the intent of this report to discuss in detail the criteria loadings for gust, maneuver, taxi, take-off, and landing.
However, with a clear definition of a GAG cycle, a statistical factor can be determined to apply to the maximum and minimum stresses of figure 9 to establish dynamically instan- taneous maximum and minimum stresses that are realized 1000 times in 1000 flights.
These factors, indicated in figure 9, are used by the design analyst to establish the stress limits of a primary GAG cycle.
From the general aspect of fatigue analysis the analyst now has viewed the effects of the thermal cycle associated with supersonic flight and has established the GAG stresses for his design detail. It is now important to again realize that temperature is the primary new factor affecting fatigue and that the balance of the factors affecting fatigue are handled in the same manner as those on subsonic transports. Consideration of the primary factors affecting service life will point out how they are evaluated and how the effect of the thermal cylce is included in the analysis.
FACTORS AFFECTING SERVICE LIFE Based on broad scope categories, the primary factors influencing service life of an operational vehicle are (1) Selection of structural material (2) Type of design and fabrication (3) Service reliability (4) Operational environment Each of these categories is handled in a particular manner to facilitate the application of a fatigue-check procedure at the point of drawing release.
All factors associated with the SST mission, service life, and vehicle production are considered in selecting the structural material. Annealed Ti-6A1-4V was selected as the primary structural material because good fracture and fatigue properties are combined with a good strength-weight ratio, particularly in the SST operating environment. High- strength steels, as applicable, augment the primary structural material. For analysis purposes, after the selection decision, the material is represented by S-N curves for varying quality of structure. In addition, when considering service reliability, the level of backup test and service knowledge for the material and type of detail application influ- ence the selection of reliability factors.
Type of design and fabrication with its many facets is controlled in this procedure by establishing a detail fatigue rating (DFR) number. Effectively, the DFR of a design will direct the analyst to the correct quality of S-N data for determining the service life. Surface finish, fabrication techniques, geometric design details, fastener installa- tions, and design assembly patterns are typical influencing factors determined by the type of design and fabrication. Based on test data and service experience, DFR values are determined with formulas or established in charts.
Service reliability must account for the variability of fleet statistics, loading envi- ronment, test representation, and structural material properties. In a well defined loading environment on a fail-safe design detail with good test and service background, the analyst can consider going as low as 2.0 for a fatigue reliability factor (FRF) to be applied to specified life for analytical life requirements. As background data becomes minimum in the design of a good fail-safe structure, FRF values of 4 to 6 are required.
In cases where fail-safe design is difficult or impossible, safe-life design must be devel- oped with FRF values twice those that would be required for fail-safe design. For the analysis procedure, FRY values are specified in general terms and the design analyst consults with fatigue specialists if further refinement is necessary.
The operational environment is usually well defined at the current state of develop- ment of specifications and investigation studies. Gust, maneuver, taxi, take-off and land- ing criteria for the SST are very much like that required for subsonic vehicles with fairly well defined adjustments to account for SST operation. The airline operation effects are included by developing a pattern of missions to represent the total scope of SST operation.
The means of including all these effects in determining service life are practically the same for subsonic and supersonic operation and have been developed from a history of subsonic transport operation. The new influence on service life not significantly present in subsonic operation, is the thermal cycle associated with a Mach 2.7 transport. The effects of this thermal cycle require special attention to assure a proper accounting in analytical procedures.
ENGINEERING THE TEMPERATURE EFFECTS Investigations of thermal cycle considerations required for Ti-6A1-4V structure in environments in the region of 5000 F indicated that developing the following areas of influ- ence will properly account for the thermal cycle: real-time and short-time test correla- tion, long-time temperature exposure, and phase-cycle relationship of temperature and stress. As indicated in figure 9, the mechanical stress and thermal-gradient stress are added directly when studying the history of stress with temperature on a design detail.
Consideration of these factors shall provide the corrections necessary to account for thermal effects.
Temperature and time have always been two variables strongly related in establish- ing material properties. Some indication of real-time and short-time test correlation is shown in figure 10. Initial testing reported under this Department of Transportation con- tract began in 1963 and is continuing at this date. The program data shown here was designed to compare a 65-minute flight cycle with three accelerated tests. An acceler- ated load spectrum was run at 900 F constant temperature, 5000 F constant temperature, and a 900 F to 500 0 F cyclic temperature. The accelerated tests on sheet and extrusion material both showed a deterioration in life at higher constant temperature and also showed deterioration at cyclic temperature, although not as great as at 500 0 F constant temperature. Real-time tests have completed in excess of 36 000 flight cycles, only one sheet specimen out of a total of 12 sheet and extrusion specimens failing. These test results encourage further analyses with a hope that accelerated tests may correlate with real-time tests somewhere near a factor of one. Testing is continuing and other tests are underway to augment this data.
The effect of long-time temperature exposure was conveniently included in the basic S-N data by developing the data with specimens previously exposed to 500 0 F for 500 hours. This procedure is justified by data shown in figures 11 to 13. Figure 11 shows the ratio of exposed to unexposed cyclic maximum stresses and gives 10 5 cycles of life at a stress ratio R = 0.06 for Ti-6A1-4V baseline specimens heat soaked for the indicated hours and then tested at room temperature. Figure 12 shows the same ratio for Ti-6A1-4V lap joints with varying fastener installations exposed to both load and tem- perature for 500 hours and 1000 hours. These data demonstrate a reduction in allowable stress for equivalent life with temperature exposure for 500 hours. Further exposure produces little change. Figure 13 shows results of similar more extensive testing con- ducted in Ti-8A1-1Mo-1V center-notched specimens exposed to both steady-state and cyclic load and temperature. In this case subsequent fatigue testing is at 500 0 F after the specified exposure. With varying exposure up to 20 000 hours cyclic and 30 000 hours steady state, all data, independent of how much exposure, falls into a reasonable scatter band. For analysis of the SST prototype, this type of data justified a convenient, 500 0 F, 500 hours (3 weeks) exposure before life testing. Thus, the effect of long-time tempera- ture exposure is included in the S-N curves used for fatigue-check analysis.
In the accelerated test data of figure 10 with the same maximum temperature, there is an indication that fatigue life improved over that at constant temperature when tempera- ture and stress were both cycled. From many sources the data of figure 14 establishes a life ratio curve for life at constant elevated temperature. A comparison in figure 15 of this curve with data from tests wherein temperatures were cycled in phase with stress, shows an improvement in fatigue life for the 0 0 phase difference stress-temperature cycle. Extending this basic idea through all phase-angle differences develops the life ratio factor rl of figure 16 as a means to correct service life computations for varia- tions of the phase angle between stress cycles and temperature cycles. The design ana- lyst reviewing his temperature and stress history, in addition to determining GAG stress limits, must determine the maximum temperature and the significant phase-angle differ- ence between his stress and temperature flight cycle.
In order to engineer temperature effects into a simplified fatigue-check procedure for prototype design, the following guidelines are offered: (1) Accelerated test procedures can be established to assure real-time and short- time test correlation near a factor of one.
(2) Long-term temperature exposure is accounted for by exposing test specimens for S-N data to 500 F for 500 hours and then testing at room temperature.
(3) The stress-temperature cycle phasing correction factor TJ of figure 16 will account for the balance of temperature effects.
TOTAL DAMAGE RE LA TED TO GAG DAMAGE Since a method has been provided for the design analyst to define the primary GAG stress cycle, one key to establishing a quick fatigue-check procedure is to relate total damage to GAG damage on the elements of primary structure. By extensive use of com- puter programs to define internal load distribution and conduct fatigue analysis on dis- crete parts of typical primary structure, the ratio 6 of GAG fatigue damage to total fatigue damage can be determined. Typical plots of the GAG dama ge ratio developed for handbook use are shown for the wing lower surface in figure 17 and for the body sec- tions in figure 18. It is now possible to set up a simple formula which determines a number of GAG cycles NGAG which will produce equivalent total fatigue damage.
(FRF) NGAG = nGAG 7]15 where number of cycles to produce equivalent total fatigue damage the number of flights in which the primary GAG cycle is determined for a 50 000 flight hour service life, or where a primary GAG cycle is not appar- ent, a number of primary load cycles in a 50 000 flight hour service life for which the damage ratio 15 is known or can be estimated FRF fatigue reliability factor defined in handbook tables ratio of fatigue life at stress-temperature cycle phasin g to room-temperature fatigue life ratio of GAG fatigue damage to total fatigue damage Since N , GAG a ' and GAG a are known, it is now necessary to determine GAG MAX MIN the proper quality level of S-N data which can be used to determine service life.
RATING OF STRUCTURAL DETAILS It has been common practice to rate structural details by determining apparent stress concentration factors Krr and using S-N curves with the same apparent stress concentration factor to determine fatigue life of that detail. Many textbook and handbook sources are available to determine apparent stress concentration factors. For communi- cation to the design analyst, who likes to do his thinking with loads, load paths , and stresses, Krr gives some feel for fatigue quality but does not necessarily provide good communication. High values of apparent stress concentration KT give low values of service life. The quantity Krr defines some local magnification of stresses that reduce life. Although for calculation purposes the detail fatigue ratings (DFR) defined in this report depend on values of KT' D FR values are a more useful communication term with an engineering feel closer to the design analyst's pattern of thinking.
The DFR number found useful in this report is defined as the maximum cyclic stress u in a constant-amplitude loading cycle at which the design detail will withstand MAX 10 cycles at a stress ratio R of 0.06. This stress ratio is a convenient testing ratio and 10 cycles represents a re liability factor of 4 on 25 000 flights, which is near the fatigue life range of Significance on the SST prototype. Figures 19 and 20 show ranges of value of the DFR number for various detail coupon tests and for various lap joint tests, respectively. If this DFR number is plotted against l/Krr for variations in a type of structural detail, it will develop, within test scatter, as a straight line, as shown in fig- ure 21. Consequently, for the convenience of the design analysts, tables can be produced with governing constants specified for various design details. Somewhat more convenient, as more test data and experience develops, charts similar to figure 22 are prepared and added to the analysis handbook.
For communication purposes the DFR number communicates a stress number; the greater it is, the better the fatigue quality. A value of 65 ksi is high quality in Ti - 6Al-4V structure and is achieved in basic skin - stringer structure with high-quality fastener installations. Low-quality values can go below 20 ksi in the low-quality joint installations.
The Significance of the DFR number in specifying S-N data is illustrated in figures 23 and 24. Figure 23 is a set of S-N curves for a DFR of 30 ksi and fig- ure 24 is for a DFR of 45 ksi. In each case this rating number establishes the rela- tive quality of each set of curves by being the u giving 10 cycles at R::: 0.06.
MAX If on each plot the design analyst considers a design detail for which he has determined GAG u = 50 ksi and GAG u = 20 ksi, the service life variation is apparent.
MIN MAX (U is the minimum cyclic stress.) At DFR = 30 ksi, the fatigue life is about M1N 4 5 5 x 10 cycles; at DFR = 45 kSi, the fatigue life is about 2 x 10 cycles. The higher quality provides four times the fatigue life.
CONSTANT-LIFE CHECK CHARTS After development of a family of S-N curves for a range of design quality, it is a simple procedure to prepare detail fatigue-check charts for a range of constant-life val- ues. As shown for N = 10 5 cycles in figure 25, this procedure allows a plot of the two and DFR, in a form most useful to the design analyst. These variables, GAG AMAX two variables plot as a family of lines for different values of stress ratio. With a family of these detail fatigue-check charts covering the range of cyclic interest, interpolation can be conducted for a design detail at any NGAG to establish the required relationship at a known value of R.
of DFR and GAG AMAX The design analyst can enter the fatigue-check charts with either or DFR UMAX and determine important design trades. Entering the chart with a calculated cyclic 'MAX might represent a case where a desired level of working stress is apparent from other design considerations. Figure 26 illustrates this case and points out the design terms established for the case where N = 200 000 cycles. The ordinate value defines a minimum detail quality required for this c' MAX . If DFR is actually higher or lower, the design analyst moves up or down the R value line to determine an appropriate allow- able AMAX . Entering the chart with a trial DFR is illustrated in figure 27. In either case the design analyst can quickly determine the value of improving his design quality or of changing his cyclic stress level.
FATIGUE ANALYSIS PROCEDURE The fatigue-check procedure is made available to each design analyst on the SST prototype by a structural fatigue handbook. By management directive, a design has not been structurally reviewed unless it has been checked for its repeated load environment as well as for its strength and stiffness requirements. Unless a specific exception can be justified for prototype only, the prototype design details shall qualify for the specified production service life of 50 000 flight hours.
To illustrate the fatigue-check procedure, assume the design analyst is looking at a wing lower surface skin-stringer detail forward of the rear spar at buttock line (BL) 550.
(See fig. 17.) He would like to use standard rivet installations in order to minimize assembly costs. The procedure would be (1) Following through the segmented sections of the mean mission of figure 6, com- putations of internal load distribution and the gradient effects of the thermal cycle will produce a normal operating stress and temperature history similar to that of figure 9.
From such data the primary GAG stress cycle is determined as 'MAX=25ksi(R=-0.5) Also from a plot similar to figure 9 it appears that the stress-temperature phase rela- tionship is near 900 with a maximum temperature of 430 0 F.
(2) It is now necessary to determine the number of GAG cycles NGAG that will produce equivalent total fatigue damage. By referring to figure 16, the stress- temperature cycle phasing correction is = 0.85 By referring to figure 17, the GAG damage ratio is 5 = 0.80 From handbook tables and test data considerations, the fatigue reliability factor for this detail in Ti-6A1-4V is FRF = 5.8 Conservatively, including full-stop landings in the number of required flights, GAG - 23 500 cycles n Consequently, R bF = 200 000 cycles NGAG - nGAG F (3)With N at R = -0.5 known, the design analyst enters fig- GAG and oMAX ure 26 and determines the minimum DFR required to provide 50 000 flight hours of ser- vice life; that is, a required DFR of 40 ksi.
(4) With the geometric, fabrication, and installation details, the design analyst must determine the actual DFR. From figure 22, Actual DFR of 56 ksi > Required DFR of 40 ksi Therefore the installation provides more than satisfactory service life. If surrounding installations are compatible, weight may be removed from the installation by increasing stress levels to match the actual DFR. The weight reduction is only possible if static strength and stiffness requirements will permit.
If testing or previous experience had not provided a chart of DFR values for this installation, the structural fatigue handbook would have provided the constants needed in figure 21 to calculate an actual DFR. By the use of this procedure the design analyst can develop an understanding of the stress or detail quality modifications necessary to qualify for service life.
CONCLUDING REMARKS A fatigue-check procedure requiring minimum additional effort is proposed for use by design analysts who must review structure and "firm up" design details before drawing release. The concept presented here satisfies part of the need of leaving the designer of structural details cognizant of the good and bad points of design for service life.
As compared with subsonic transports the primary new environment variable influencing fatigue design on the American SST is the thermal cycle associated with a Mach 2.7 cruise speed. The effects of this thermal cycle can be included in fatigue- check procedures by accounting for real-time and short-time test correlation, long-time temperature exposure, and phase cycle relationship of temperature and stress. Because of the SST type of operation, relatively large parts of fatigue damage develop on wing and body primary structure from ground-air-ground (GAG) cycles. By determining the rela- tionship of GAG damage to total fatigue damage on typical primary structures, fatigue- check procedures can be greatly simplified.
By using a detail fatigue rating (DFR) designated by a maximum cyclic stress instead of using the apparent stress concentration factor directly, a better communica- tion term is available to evaluate relative fatigue quality of design details.
c '" .~ '- <1> E « <1> .s::: I- , N \ \ \ \ V' -.J co SST PROGRAM SCHEDULE 1960'S I NOW 1970'S 1980'S 8 1 91 0 11 1 2 ! 3 1 4 15 16 17 18 1 91 0 i :l ! 2 I 3 1 4 15 16 I 71 8 1 1 0 11 I 21 31 4 15 I 6 1 71 8 1 91 0 11 PROTOTYPE (pT) COMPANY DESIGN CONSTRUCTION PRODUCTION AND STUD IES 100 HR. FlI GHT TEST A I RlI NE SERV ICE
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, PT 1 ST FlI G HT I
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BODY STATION F igure 1 8.- Fuse l age primary G AG fat i gue damage rat io.
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iv v ^„^^^ ^ rr^v^ EDING PAGE BLANK NOT FI Yttr.^%k^Ullvu d q PRACTICAL ASPECTS OF DESIGNING FOR AND EVALUATING STRUCTURAL INTEGRITY By Marcel Peyrony and Daniel Chaumette Avions Marcel Dassault Saint-Cloud, France INTRODUCTION The objective of this paper is not to show the results of very scientific studies, but only to put forward some points which can be of practical use to the designer. The following procedures apply generally in the tests discussed: (1) Skins are machined, either chemically or mechanically (2) Their surfaces are blasted with glass beads and wet sand (3) They are given a surface protection and painted (4) No bonding is used.
FATIGUE PERFORMANCE IMPROVEMENT It is well known that bolts with tight fit give a definite increase in fatigue life.
However, this increase is guaranteed only if every bolt is mounted with the right fit and if no undetectable fault may change the assumed condition.
Conical Fasteners For a long time we have been using bolts or fasteners with tight fits of 5 to 30 microns, with very satisfactory results. But it is quite a problem to achieve a guaranteed fatigue life of 40 000 hours while saving much weight, especially in the joints or in the lower skin of the wing. The search for a higher admissible stress is then a constant undertaking.
Conical bolts had at first sight appeared most interesting. There was indeed the danger of stress corrosion when a tight fit of 90 microns was used with alloys such as 2024-T3 and 2014-T6, but riveting on short transverse components is infrequent, and less sensitive alloys may be used. A test program was started with two types of test specimens, a "dog bone" type and a lap joint. (See fig. 1.)
The first test results (fig. 2) were most encouraging, until a test specimen broke after a disappointingly low number of cycles. A more thorough inspection of the test piece (which had been inspected prior to testing) showed a reaming fault as in figure 3.
The bolt bears only on four regions.
It was necessary to determine why this fault existed and why it had escaped inspec- tion. The first problem was easy to resolve. It took many years to learn how to drill a perfectly circular cylindrical hole. Conical holes, because of their high drilling torques, will surely require still more development and tooling for reliable results.
With limited tooling, we succeeded in drilling correct holes up to 6 mm in diameter and 8 mm deep. But for larger diameters, very rigid jigs and expensive tooling were needed.
Both the cost of tooling and the drilling time were found to be prohibitive for an extensive conical fastening.
Furthermore, inspection was most difficult, with the necessity of blueing checks at every hole, which increased the cost of the total operation. Finally, a subsequent test with holes purposely drilled incorrectly showed a dramatic decrease in fatigue life. (See fig. 4.) These results, added to the danger of stress corrosion, led to the decision not to use conical fasteners in the Mercure.
Hole Preparation In an attempt to increase the fatigue life of structures, the following processes were examined: (1) The way in which the hole is made: (a) Normal reaming (b) Heli-Armor reaming (c) Broaching (2) The finish given after reaming: (a) Deburring (b) Roll over Significant differences were found between treated and untreated holes without rivets (fig. 5). On the other hand, once the bolt is set, these differences decrease and even disappear (fig. 6).
Interference Fit On one hand, interference fit has a positive influence on fatigue life, but on the other hand, beyond a certain level of interference (30 microns), fretting under the fastener becomes too important unless special care is taken. Figure 7 shows the type of failure in each case. With the free bolt, the crack started in the cylindrical part of the hole, but with the interference-fit bolts, the cracks started by fretting in the countersink.
Antifretting Protection In all previously described tests standard sealing and surface protection treatments were used; that is, rivets were wet mounted with PR 1422 or Blendexite and the test specimens were painted with PR 1460 or Cellolac 78-28. Figure 8 shows the effect on fatigue life when one of these two protections is omitted. The fatigue life was reduced by fretting underneath the fastener collar when the specimen was not painted, and in the countersink when the rivet was dry mounted.
Selecting Parameters for Mounting a Fastener The results of these experiments led to the selection of the following procedures: (1) Use of a moderate amount of interference (bearing in mind the problem of stress corrosion) (2) Painting and wet mounting The influence of the way in which the hole is obtained is not so obvious. Broaching and Heli-Armor give comparable results, but broaching is an extremely reliable method of obtaining holes of a high standard, while Heli-Armor may be less reliable. The "miracle" alloy for the best life has appeared to be 2024-T3. (We have not tested 7075-T73.)
FAIL-SAFE DESIGNS General Considerations The greatest risk of crack initiation is surely incurred in joints. Multiplying stress concentrations by using, for example, riveted reinforcements around door openings should be avoided as much as possible. Integral structures mechanically or chemically milled might seem a good solution, but then the difficult problem of fail-safe design enters the picture.
We have already made some remarks about this problem at Melbourne, having been unfavorably impressed by some examples of so-called fail-safe design, the most classic being a structure cut in two pieces and bolted back together. Since then the situation has apparently worsened, judging by the design of some recent tail-unit hinges and control- surface bearings.
Are the regulations responsible? It is certain that FAR 25-573 encourages a designer who does not want to put questions to himself to demonstrate that a structure can sustain the required static load when one of the elements has failed. This test allows him to claim that his structure is fail-safe. Moreover, the same paragraph allows a failure to be considered only partial if it is obvious.
As far as fatigue is concerned, the basic idea, in itself quite legitimate, of assuring security by means of residual strength has been put in a wrong way.
Fatigue and Fail-Safe Of course a fatigue test is not a fail-safe demonstration by itself, but it is not neg- ligible in assessing structural fail-safe designs. Also, fatigue testing is a good method for determining inspection schedules for the various parts of the airplane.
We do not believe that an element cut in two, but in which cracks appear and grow rapidly, is sufficiently fail-safe. What happens to the half of this element carrying the whole load when the other half has broken?
Some recent mishaps with elements working in parallel should prove of interest.
One instance was the F-14 prototype, in which two hydraulic tubes used on separate cir- cuits, but subjected to the same fatigue duty, gave up in a 5-minute interval.
Another example of a more structural nature was found during a fatigue test on a military aircraft. The main frame supporting the bending moment of the wing was made of two rings working in parallel. (See fig. 9.) Cracks appeared and grew almost identi- cally in the two rings, and a rupture occurred in each, the load being then supported by the remaining structure outside.
Another example concerns a wing attachment (fig. 10). Cracks grew at the same time from five holes and, what is more, on both wings. To have separated the attachment into halves would only have given a formal fail-safe structure without increasing enough the safety of the design.
These problems occurred because the fatigue life was short enough for all the pieces involved to be damaged. A quite different case appeared in the test of the Mercure main frame. An artificial crack in the flange of the frame grew only on one half of the flange, not passing the "wall" of the web, and at a rate low enough to be found in inspections.
Here the stress was lower, and this explains most of the difference. Thus a fatigue test may give important indications for fail-safe designs.
There is a still worse method for obtaining fail-safe. Take a beam with an I-section, the tensioned flange of this beam being perfectly smooth, without any hole. Then replace the integral tension flange by riveted flanges, the tensioned area being the same. Fail- safe is not definitely guaranteed and fatigue life is severely decreased.
If you feel unable to insure safety with such a monopiece structure, you can design a double load path while avoiding putting rivets in the tensioned zone. You will keep good fatigue life and get a double load path at the same time, but perhaps you will have some trouble with fretting or corrosion.
Fail-Safe and Unexpected Cracks The double load path finds its soundest justification in unexpected cracks. However, this should not deter the designer from looking at the types of remaining risks and finding a solution to them. These risks can be defined as flaws in the material, fretting, and stress corrosion. With correct designs, care, and inspection these difficulties can be overcome, and we have to work for that in any possible way.
Important Conclusions Regarding Fail-Safe Certainly a low stress level is an important factor for fail-safe guarantee. For less important elements where weight loss is small, no regrets should be had in designing with important margins for a theoretically infinite life. But this is not enough. During the fatigue tests and after, it is necessary to monitor the crack propagation rates at every point which may be critical. The results should be linked with the inspection schedule of these particular points.
Double load path must not be neglected. But its reliability must be assured with regard to fatigue considerations as well as corrosion and fretting, and the structure must not be weakened by a bad design.
OUR FAIL-SAFE APPROACH It must be admitted that we have often used the classic fail-safe methods described here. However, even in these cases we applied the procedures described in the following paragraphs to investigate crack propagation.
Photoelastic Tests For the Mercure design, we had previously developed tests on photoelastic models and on metal parts coated with photostress material (figs. 11 to 13). Thus, we were able to study stress concentrations on a particular component, and even on an entire element of the fuselage. Also, we were able to determine critical areas where we could provoke cracks.
Partial Fatigue Test Usually the area where we want fail-safe capability of a one-piece structure is greatly overdimensioned for fatigue. So we perform tests with normal fatigue loads, followed by cycles at higher loads. During these tests, cracks must not originate.
Crack Propagation Next we artificially provoke cracks in critical areas — that is, areas where calcu- lations and photostress investigations show stress concentrations. (See fig. 14.) The crack growth rate is plotted against time in order to define a schedule of inspections that will provide detection in service before the risk of dangerous failure is encountered.
This implies that the tests are based on particular conditions.
It is best to have two types of cycles. The first, with only normal fatigue loads, is applied on specimens to monitor the crack growth rate. The second, including the same normal fatigue loads, also includes "fail-safe" loads, and is applied on other specimens to evaluate the critical length of crack beyond which a static failure may occur.
Another possible application for fail-safe design is found in secondary effects (fuel leakage, for instance).
CONCLUSIONS The double load path, although a good fail-safe concept in many cases, is not entirely satisfactory. It may be insufficient when fatigue life is too short, and superfluous when the stress is low, detection is easy, or fail-safe capability is achieved by other means.
The best procedure is to rely on crack growth-rate studies and guaranteed crack detection by inspection in service.
The use of double load path to cope with unexpected phenomena such as stress cor- rosion or flaws seems rather makeshift, and it is better to seek specific action (improved forgings, inspection, protection) in each case.
The easier the inspection, the better for fail-safe.
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ON THE CYCLIC STRESS-STRAIN BEHAVIOR AND LOW-CYCLE FATIGUE OF AEROSPACE MATERIALS By J. Burbach Krupp Forschungsinstitut, Germany The elastic-plastic deformation behavior under cyclic stress of a number of dif- ferent engineering materials was experimentally investigated with the aid of high- precision methods of measuring, some of which had been newly developed. (See refs. 1 to 4.) The report covers, in particular, experiments made with a variety of steels, the titanium alloy Ti-A16-V4, a cobalt (tungsten) alloy, the high-temperature material Nimonic 90 and Dural (Al-Cu). The theory given — in an attempt to explain these experiments — is aimed at finding general formulas for the cyclic stress-strain behav- ior of engineering materials.
The experimental and theoretical investigations made can be summarily described as follows: (1) Geometric relationships of stable mechanical hystereses at a given variation of stress or strain and normal strain-rate dependence at cyclic deformation (plain and notched specimens) (refs. 5 and 6) (2) Accurate and direct measurement of the second-order elastic constants of polycrystals and their influence on the test result (3) Accurate balance of elastic and plastic energy in cyclic deformation, particu- larly in microscopic inhomogeneous plastic deformation (4) Spreading of Luders bands in cyclic deformation; phenomena of strain hard- ening and removal of strain hardening (5) Inverse strain-rate dependence for aluminum-copper alloys (6) Investigations relating to cumulative damage at irregular cycling of stress.
The investigations, unfortunately, showed that cyclic stress-strain curves do not provide sufficient information for developing cumulative damage formulas that are suffi- ciently accurate from the physical aspect or suitable for engineering application. For this reason, it is not possible for the time being to give up practical simulation of actual material stresses with modern fatigue-testing machines.
The accuracy of the measurements made is exemplified by the cyclic stress- strain behavior of a round bar specimen with a sharp notch. (See figs. 1 and 2.) The stress — related to specimen cross-sectional area in the notch root — is plotted against the plastic deformation of the full-length specimen. It is clearly seen how the gradually propagating crack causes a "nose" in the cyclic stress-strain curves; that is, the opening and closing of the crack becomes apparent.
In figure 1, the stress given is related to the notch-root cross section. The hyster- esis curves shown were written with rising values of the plastic-strain amplitude. Strain measurement was made as usual at a distance between the edges of the inductive exten- someter of 40 mm; thus, the mean value of the inhomogeneous extension was obtained.
The test represented by figure 1 was continued in such a way that with (approxi- mately) constant amplitude of plastic strain, cyclic deformation proceeded. Continuation of the test eventually led to fracture of the specimen. See figure 2.
REFERENCES 1. Burbach, J.: A Tensile Machine With a Particularly High Spring Constant. Techn.
Mitt. Krupp, Forsch.-Ber., Bd. 24, 1966, pp. 79-88.
2. Burbach, J.: The Static Tensile Test. Recent Methods of Metallurgical Investigation.
Ver. Dt. Eisenhuttenleute (Dusseldorf), 1970, pp. 19-36.
3. Burbach, J.; and Vierling, P.: Experimental and Theoretical Studies of Strain Gauges, Particularly With Respect to Their Transverse Strain Sensitivity. Experimental Stress Analysis (Dusseldorf), VDI-Rep. 102, 1966, pp. 131-136.
4. Burbach, J.: Unavoidable Influences of the Loading Speed on the Indication of Load Cells. Precision Measurements With Strain Gauges for Force Measurement and Weighing (Dusseldorf), VID-Rep. 137, 1970, pp. 83-87.
5. Burbach, J.: Recent Investigations on the Plastic Behavior and Fracture Process of Hard Metals. Techn. Mitt. Krupp, Forsch.-Ber., Bd. 26, 1968, pp. 71-80.
6. Burbach, J.: Zum Zyklischen Verformungsverhalten Einiger Technisher Werkstoffe.
Techn. Mitt. Krupp, Forsch.-Ber., Bd. 28, Heft 2, 1970.
riAl 6V6 gekerbte Rundprobe Figure 1.- Cyclic stress-strain behavior of a notched round bar specimen. Notch angle, 600; notch-root radius, 0.15 mm; notch-root cross-sectional diameter, 3 mm; Ti-A16-V4.
rlAl6V6 gekerbte Rundprobe Figure Z.- Continuation of test measurements shown in figure 1 into the cracking stage. Ti-A16-V4.
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PRECEDING PAGE BLANK NOT MMED A PARAMETRIC APPROACH TO IRREGULAR FATIGUE PREDICTION By T. H. Erismann Federal Laboratories for Testing Materials and Research Dubendorf, Switzerland SUMMARY The method proposed consists of two parts: empirical determination of certain characteristics of a material by means of a relatively small number of well-defined standard tests, and arithmetical application of the results obtained to arbitrary loading histories. The following groups of parameters are thus taken into account: the varia- tions of the mean stress, the interaction of these variations and the superposed oscil- lating stresses, the spectrum of the oscillating-stress amplitudes, and the sequence of the oscillating-stress amplitudes. It is pointed out that only experimental verification can throw sufficient light upon possibilities and limitations of this (or any other) pre- diction method.
FUNDAMENTALS OF PARAMETRIC APPROACH The fundamental procedural scheme of the method evolved in this paper consists of the following phases: (1) Determination of a number of characteristics of the material by means of standard tests (2) Prediction of the fatigue life of the material on the basis of these characteris- tics and an analysis of the expected loading history.
The problem thus raised can, in principle, always be solved since for a specified accuracy there will always be a finite number of tests from which the necessary data for a satisfactory processing of the second phase can be drawn. There is, consequently, a problem of interpolation which can be solved with a finite number of base points. The question remains how to attain the goal economically. In view of the present state of development of servo-hydraulic testing equipment and digital computers, neither irregu- lar stress sequences in the standard tests nor extensive algorithms in analysis and evaluation are prohibitive.
The progress of our knowledge of fatigue strength has in the last few decades become an alarming "parameter explosion." Thus, in order to avoid undue complica- tions, no mention will be made of parameter groups connected with notch effect or environmental influences and nothing but the loading history will be considered.
Consequently, the following effects will be taken into account: (1) Mean stress effect (index M), influence of the chronological curve of the mean stress (2) Interaction effect (index J), influence of systematically occurring correlations between the effects of mean and oscillating stresses (3) Spectral effect (index P), effect of the statistical distribution of the oscillating- stress variations (4) Sequence effect (index Q), effect of the sequence in which the individual stress variations follow one another.
The parameters linked to these effects will be called in this paper "M.I.S.S. parameters" from their initial letters.
Owing to the inherent complexity of the problem, a certain number of simplifying assumptions must be made. In particular it is assumed that (1) Miner's rule is applicable with sufficient accuracy to sufficiently narrow sec- tions of a stress spectrum (2) The influence of the mean-stress effect can be described with sufficient accuracy by the statistical amplitude distribution of the variations occurring in the mean stress (3) Every increment of a loading history produces an incremental interaction effect approximately proportional to its mean stress level and to its "linear-damage increment" (according to Miner's rule) (4) The effect of the sequence extends mainly to the "coarse sequence" (that is, to changes of the spectrum over longer periods of the loading history), whereas the "fine sequence" (that is, the individual sequence of the single-stress cycles) is of minor impor- tance in practice, provided the process under consideration can be described with suffi- cient accuracy by stochastic characteristics (5) The effects of the M.I.S.S. parameters allow with sufficient accuracy a linear (in one exceptional case, a quadratic) interpolation when the logarithm of the "Miner sum" (1) L^ u Ni (which according to Miner's rule should always be equal to 1) is used as the interpolation value. In equation (1), n i is the number of cycles applied at stress level whereas Nj is the total number of cycles to cause failure at stress level.
It is not possible here to justify these assumptions. A justification of these assump- tions is given in reference 1.
OUTLINE OF THE M.I.S.S. METHOD The method outlined here starts from relation (1); it being clearly understood, how- ever, that a sum not equal to 1 is permissible. In accordance with the assumptions made, the four M.I.S.S. parameters P M , PJ , PP , and PQ are defined and (2) f(PM ,PJ ,P P ,PQ ) .
is postulated. This postulation means that the spectrum, as in Miner's rule, is still the most important group of parameters, but not the only decisive one.
Thus, the first phase of the method results in the performance of an unequivocally defined series of standard tests with well-defined M.I.S.S. parameters and the determina- tion of the resulting standard Miner sums which are to be considered as charac- L_js teristics of the material.
The second phase, that is, the application to an expected loading history with a given nominal fatigue life, is divided into the following partial phases: (1) Analysis of the loading history according to equation (1). The result is the Woehler-Miner sum (2) Analysis of the loading history according to well-defined formulae for deter- mining their M.I.S.S. parameters.
(3) Application of the M.I.S.S. parameters as a means of interpolation in the results field of the standard Miner sums. The result is the Effective Miner sum vE (4) Formation of the quotient I /11W which indicates the chances of survival of E the specimen. For &/^ W > 1, survival of the loading history is to be expected.
The first and fourth phases are carried out according to the known algorithms of Miner's rule. The interpolation in the third phase must mainly be carried out linearly
for log I. Figure 1 shows the interpolation for PM and PJ , with Pp and PQ
held constant. The heights of the column at its four edges represent the results of four standard tests. The result of the interpolation is the height (heavy dotted line) for PM and PJ . Only the standard tests and the stress-history analysis need to be considered in more detail.
MATHEMATICAL TREATMENT OF PARAMETER GROUPS It would be impossible to give a complete review of the mathematical deductions applied to obtain appropriate equations for the calculation of the M.I.S.S. parameters.
It must be referred, therefore, to more detailed works on the subject. (See refs. 1 and 2.)
The following remarks are made in order to give a general idea of the logical structure of the method.
All the equations used in this connection are based solely on the simplifying assumptions made. For instance, the second assumption means only that the mean stress effect for given values of the other parameters is determined by the "spectrum of the mean stress" so that Miner's rule may be considered as applicable to the mean stress. Thus, an extremely simple definition of the mean-stress parameter is obtained; that is, - Ill P (3) M N O), L.1W where N o is the number of mean-stress variations of the value a, and N Q is the cycle number pertaining to Q according to the Q-N curve. The division by the Woehler-Miner sum ^ W is used for normalizing purposes.
The spectrum of a loading history is represented in principle by a parabolic approximation so that theoretically, three parameters are needed for the mean value, the average slope, and the curvature of the parabola. The first of these parameters, how- ever, is insignificant since in the chosen representation, the mean value of the parabola is given. It is a particular feature of the method that the ordinal numbers i of certain well-defined stresses ai are used as values of the independent variable of the approxi- mation so that the respective numbers ni are expressed by (4) nl =c0+c1 • i+c2 •i2. . .
Ni 1W where co , c l , and c 2 are the spectral parameters PP.
III more or less analogous way, the parameters for interaction and sequence, P and PQ, are deduced from the assumptions made. Both are connected with variations of the spectral parameter c l ; thus, predominance of high- or low-stress amplitudes under particular conditions is indicated. Although P establishes a correlation with the mean stress am (taking into account such phenomena as the increased dynamic forces due to increased payload of a vehicle), P Q accounts for variations undergone in the course of the loading history as a whole (as encountered owing to more frequent over- load when an aircraft is transformed from passenger to cargo transport); thus, it serves as a safeguard against unpleasant surprises, because many materials have a shorter fatigue life when first subjected to low- and then to high-stress amplitudes.
The influence of parameter variations upon loading histories is illustrated in fig- ures 2, 3, and 4. In figure 2, the oscillating stresses are not present for negative mean stresses because of the choice of constants in the equations. In figure 3 the stress amplitudes are higher in section II than section I; thus, a higher value of c l is indi- cated. In figure 4, the variation of c 2 results in predominance either of extreme (high and low) or of medium amplitudes. It will be observed that in figure 3, section II shows higher stress amplitudes than section I; thus, a higher value of c 1 is indicated. Vari- ation of c2 results in predominance either of extreme (high and low) or of medium amplitudes (fig. 4).
STANDARD TESTS AND PRACTICAL APPLICATION Since linear interpolation of log has been accepted for all parameters (excluding c l), variations through all possible combinations other than the meaningless ones (PM = Oi ; PJ + 0) would give 36 base points which can be found from 36 tests (plus repetitions). The cost is considerable but is certainly justified for important materials.
Experience will show whether all 36 standard tests are really required. The num- ber depends on how far the multidimensional functions of figure 1 can be approximated by plane surfaces. If, for example, it should be found that, apart from P P , the function surface can be considered as sufficiently plane, then only the inclinations of this plane would have to be known; that is, for every additional parameter only one single base point would have to be determined and nine tests would suffice. Probably the truth lies between these two extremes.
An actual "cooking recipe" for the details of the method is found in reference 1.
There the individual steps are not only commented on but are also compiled in tabular form so that the economic establishment of suitable computer programs is possible.
POSSIBILITIES AND LIMITATIONS By the method described, it is possible to determine the probable fatigue life of a Z, material under a given loading history without having to carry out a large number of loading tests. As a matter of fact, the standard Miner sums as characteristics of a material, together with the u-N curve, should contain enough data to predict the fatigue life of a material with sufficient accuracy even in irregular stress sequences. The main point obviously is 'What is meant by "sufficient accuracy" T Of course, the M.I.S.S.
method is more expensive than the determination of a number of u-N curves, although not impossibly so. In return, it refines the results obtained from Miner's rule (which are derived only from Q-N curves). Only systematic tests with different materials can give a definite answer. Such tests should prove worthwhile, for even Miner's rule in its present form is better than it is usually believed to be. Thus, it should usually be possi- ble to supplement it by introducing additional parameters (mean stress, interaction, and sequence) so that the result can satisfy the demands of practice.
It must be stressed in this connection that the testing equipment available should be improved in the sense of cheaper and faster execution of large numbers of irregular fatigue tests. Only such a development will guarantee in reasonable time the acquisition of the information necessary for an efficient verification of the methods proposed here or elsewhere.
REFERENCES 1. Erismann, T. H.: Ein Verfahren zur Abschatzung der Lebensdauer von Materialien bei unregelmassigen Belastungsfolgen. Schweizer Arch. angew. Wiss. Tech. 36, 1970, pp. 57, 103.
2. Erismann, T. H.: Fatigue-Life Prediction Under Irregular Stress Conditions. J.
Strain Analysis, vol. 5, 1970, p. 207.
BIBLIOGRAPHY 1. Miner, M. A.: Cumulative Damage in Fatigue. Trans. ASME, Ser. A, J. Appl. Mech., vol. 67, 1945, p. 159.
2. Palmgren, A.: Die Lebensdauer von Kugellagern. ZVDI, Bd. 68, 1924, p. 339.
l o . g Z
(3 4, Figure 1.- Interpolation for PM and PJ.
P M =0; P=0 P M # 0; =0
P
P M 7' P=1 Figure 2.- Characteristic stress curves for various values of P M and P.
P Q - = 0 P Q
# 0
Figure 3.- Characteristic loading histories for P Q = 0 and P Q # 0 and P M = P = 0.
C 2< 0 AAA A"
—AAAA ^^OA
C2>0 Figure 4.- Characteristic stress curves for various values of the spectrum curvature parameter c2.
NW -ag70
FRACTURE CONTROL PROCEDURES FOR AIRCRAFT STRUCTURAL INTEGRITY By Howard A. Wood Air Force Flight Dynamics Laboratory, U.S. Air Force United States SUMMARY This report reviews the application of applied fracture mechanics in the design, analysis, and qualification of aircraft structural systems. Recent service experiences are cited.
Current trends in high-strength materials application are reviewed with particu- lar emphasis on the manner in which fracture toughness and structural efficiency may affect the material selection process.
General fracture control procedures are reviewed in depth with specific refer- ence to the impact of inspectability, structural arrangement, and material on proposed analysis requirements for safe crack growth. The relative impact on allowable design stress is indicated by example.
Design criteria, material, and analysis requirements for implementation of frac- ture control procedures are reviewed together with limitations in current available data techniques. A summary of items which require further study and attention is presented.
"Fracture Mechanics has, in fact, been a boon to the metal producing industry; it has made the finite crack in a structure reputable and even fashionable." (Quoted from A. M. Freudenthal, Miami Beach, Florida, December 1969.)
INTRODUCTION Primary aircraft structural components generally contain flaws or defects of variable shape, orientation, and criticality which are either inherent in the basic mate- rial or are introduced during the fabrication or assembly processes.
From an industry survey (ref. 1) it was concluded that the majority of cracks found in aircraft structures were initiated from tool marks, manufacturing defects, and the like. When not detected, these flaws experience the combined driving forces of environment and service loading and may grow to serious proportions resulting in reduction of service life or complete loss of the aircraft. The final fracture process is most often sudden, unexpected, and almost totally devoid of gross plastic deformation or yielding. While this "brittlelike" behavior is most spectacular in the so-called high- strength alloys, it is seen to occur to some degree in most of the commonly used air- craft structural materials.
Recent cases of catastrophic failure in primary structure of first-line aircraft have emphasized the need for a "fresh" new look at the structural integrity process cur- rently used to design and qualify structural systems. Under such an improved process, fracture control would insure the reduction in the probability of catastrophic failure due to the presence of undetected flaws and cracks. This assurance can best be achieved by the intelligent material selection based on fracture as well as common strength con- siderations and by assuming the existence of flaws in "new" structures and accounting for their probable growth during service.
Linear elastic fracture mechanics analysis and testing techniques have reached the state of development where they may be used with a moderate level of confidence to assess the degree of flaw criticality, to predict the extent of subcritical flaw growth prior to fracture, and to determine the resultant failure modes (ref. 2). Much of the basic groundwork for the current application of linear elastic fracture mechanics to "real" structures can be attributed to the investigation associated with fracture control of metallic pressure vessels for space applications (refs. 3 and 4). While attempts to translate this technology to aircraft usage have been moderately successful, limitations must be recognized which are due to the complex spectrum of loads, temperatures, and chemically aggressive agents that comprise the aircraft environment.
Fail-safe procedures in aircraft have resulted from civil requirements and from independent regulation within the particular airframe company. These efforts have been beneficial on many Air Force aircraft.
Application of fracture mechanics within the Air Force has been almost exclusively "after the fact" to determine remaining safe life with cracks, residual strength, and safe inspection intervals for older systems in which flaws have developed and progressed to near-critical dimensions. Some examples of service application in which the Air Force Flight Dynamics Laboratory (AFFDL) actively participated are summarized in table I (see refs. 5, 6, 7, 8, 9, and 10). In practically all cases, however, attempts to formulate reliable solutions were hampered by the lack of an adequate material-environmental data base and deficiencies in analysis techniques, particularly those techniques which must account for load interaction and environmental effects. One purpose of this paper is to review those areas of application where deficiencies in the technology exist and to offer suggestions for alleviating these deficiencies.
Under the F-111 Recovery Program (ref. 9), basic fracture mechanics data are cur- rently being amassed for D6ac steel by the contractor and several laboratories. (See refs. 8, 11, and 12.)
Specific criteria, guidelines, or requirements for considering fracture mechanics principles in the design and procurement cycle for Air Force aircraft have not existed in the past. Only recently have requirements been levied for new systems. It is too early to assess their impact. In the proposed revisions to the Air Force Airplane Structural Integrity Program (ASIP) which is given in reference 13, damage tolerance considerations are outlined. These changes are currently being reviewed prior to being formally incorporated.
There exists a natural unwillingness amongst many to accept the "preexistent flaw" concept in aircraft design because of the weight penalties normally associated with damage-resistant structures. There are those who cite system performance degrada- tion and the time and cost of implementing fracture requirements as deterrents. The imposition of arbitrary fracture requirements should be done cautiously under current state -of -the -art limitations in analysis methods and testing techniques are resolved and material-environmental behavior is better understood.
In this paper, recent structural material utilization cases are summarized to indi- cate those problems associated with the use of high-strength material. General fracture control procedures are reviewed with specific reference to the impact of safe crack growth and remaining strength requirements on system design. Examples are cited, including recent laboratory efforts in the analysis of crack growth under variable- amplitude spectrum loading. Limitations in basic design criteria, material data, and analysis are reviewed.
SYMBOLS crack size, length or depth, inches a acr critical crack size, inches ap proof-test crack size, inches Aa change in crack size, inches B,t thickness, inches C one-half surface crack length, inches E modulus of elasticity, ksi f frequency of test load application, cycle/minute stress intensity factor, ksi- in.
K Kc critical stress intensity factor, ksi- in.
plane strain fracture toughness, ksi- in.
KI c critical stress intensity factor for stress corrosion cracking, ksi-in.
KISCC maximum stress intensity factor, ksi-Fin.
Kmax minimum stress intensity factor, ksi-in.
Kmin AK = Kmax - Kmin, ksi- in.
M,N number of load cycles material density, lb/in3 P Kmin R= Kmax ry ,Ry radius of crack tip yield zone, inches a stress, ksi OQ change in stress, ksi limit stress, ksi 9L yield strength, ksi uys da/dN fatigue crack growth da/dt environmental crack growth Subscripts: 0,1,2,3,... reference values A,B,C,D,E,F,G requirements critical c i initial f final maximum max min minimum MATERIALS UTILIZATION IN STRUCTURAL DESIGN — RESISTANCE TO FRACTURE With the advent of higher performance air vehicles, weight minimization has neces- sitated optimum design and construction techniques and greater utilization of the high- strength, high-efficiency, and limited-ductility materials. The process also has evolved increased operating stresses and, thus, lower tolerance to flaws and cracks.
These applications have resulted in critical flaw dimensions of the order of the material thickness which make positive detection by current nondestructive inspection (NDI) practice questionable. Current trends in the structural design utilization of high- strength alloys for resistance to catastrophic fracture can be evaluated by examining trends in two basic material parameters, the plane strain fracture toughness index KIc and the conventional yield strength Qys.
For a specific application, the designer must select a material of reasonably high strength in order to meet static strength requirements and still achieve minimum weight.
A parameter for evaluating structural efficiency (Qys/p) is mentioned later. In the selection process, however, fracture toughness must be a consideration. The achieve- ment of maximum yield strength and maximum fracture toughness is often difficult as is illustrated in figure 1. It is generally recognized that within certain material groups, toughness decreases with increasing yield strength. This trend is illustrated in figure 1 for aluminum, titanium, and several selected steels where material data from table H have been plotted. Variations in KIc can be expected for any given alloy and strength level, and these variations are generally due to metallurgical aspects, impurities, or manufacturing processing. This variability makes the selection of a "design allowable" extremely difficult.
In specifying a particular material and strength level (minimum acceptable ays), the designer usually would not be concerned about those quantities of material which possessed strength levels on the upper end of the normal range. However, because of the dramatic decrease in KIc , he must in many cases limit the upper bound of acceptable range of yield strength. This is current practice in specifying titanium alloys. In fig- ure 1, KIc ranges for two common titanium alloys are noted. These data are shown at one yield strength value to illustrate the fallacy in specifying only Qy s minimum.
Recent F-111 experience with D6ac steel has indicated a similar phenomenon; however, the variation of KIc is dependent upon the heat treatment procedure (ref. 9). In this case, two specimens of material from different lots might possess the same measured oys and yet have a two-to-one range in KIc• The material selection process is therefore a trade-off procedure wherein many concurrent requirements must be satisfied. For the case in point, the designer must establish criteria for accepting either a reduced toughness or a reduced strength level.
The choice might be dictated by overall flaw tolerance. This is illustrated in figure 2 where the ordinate (KIc/uys)2, a parameter indicative of crack size, is used. Since structures are designed to withstand (statically) a percentage of the yield strength, this parameter may be conveniently used to illustrate flaw tolerance sensitivity. Examination of figure 2 indicates a more dramatic reduction in the crack length parameter with increased yield strength.
The same trend is repeated in figure 3; however, the yield strength has been nor- malized with respect to the material density p. The parameter Qys/p is one form of structural efficiency used to select materials. Note that material ranking has changed, with titanium being superior to steel. One exception illustrated is that 18Ni-Co-Mo maraging steel and 9Ni-4Co-2C fall beyond the bounds illustrated. There are recogniz- able limits on the values of both (Klc/oys)2 and Qysp for materials in use today.
The bounds are illustrated in figure 3.
The data presented in figure 3 clearly illustrate the relationship of nondestructive inspection (NDI) capability and material selection to resist brittle fracture. For example, a through-the-thickness crack will experience plane strain fracture when K = KIc = Q7Tacr• If fracture is assumed to occur at the design limit stress, the value of critical crack length a cr can be computed. For many aircraft structures, design K ( K Ic \2 limit stress is of the order of = 0.6Qys and acr = 0.6 Q o Thus each oL C ys^ YJ point in figure 3 might be considered the critical characteristic flaw dimension for plane strain fracture and thus would describe the sensitivity level required for fleet inspection.
For this type of selection criterion, many materials may be prohibited because of the extremely small flaws which must be detected. Limits of NDI practice are not well defined.
With the technological trend in material utilization growing toward greater strength- density ratios, it seems logical also to define more realistic limits on the material selec- tion based on uncontrollable "human element" defects. Thus, the crack size definition of figure 3 might indicate limits produced by normal tool marks, scratches, or gouges pro- duced during manufacture or maintenance. If these limits are recognized as sound, then more effective means of inspection may be required, such as proof testing, if use is to be made of these alloys (fig. 4).
All the data from table II has been plotted in figure 5 with both and oys KIc normalized with respect to density p. This plot indicates an apparent technological limit which material producers might find difficult to exceed (ref. 2).
In the previous discussion it was assumed that plane strain fracture is dominant.
Fortunately, this is not always the case because of the effect of thickness, plasticity, and geometry (figs. 6 and 7). The question does remain, however, as to what role K Ic has in the material selection and analysis process.
It is perhaps safe to conclude that the selection of candidate materials for fracture considerations can be made on the basis of superior KIc , as long as the materials are similar. The decision, however, rests upon the thickness required to fulfill the task. In figure 7, the variation of critical stress intensity factor with thickness is illustrated for several alloys (ref. 2).
MATERIAL SELECTION — RESISTANCE TO FLAW GROWTH UNDER REPEATED LOADS In the preceding discussion, KIc and oys were shown to be effective parameterE in selecting a material class and alloy to resist brittle fracture under plane strain condi- tions. Wide variations in strength and toughness were indicated within a given material.
Toughness was also seen to vary within a given alloy group.
Material selection based on cyclic growth considerations is not as clearly defined, since observed trends in rate data for a nonaggressive environment indicate that mate- rials within a group or class generally fall within a narrow scatterband, with little, if any, dependence on toughness. Average growth-rate curves have been included in figure 8 to illustrate the relative relationship between materials. Hahn (ref. 6) has observed that the rate da/dN can be approximated for many materials as da = 8 (AK)2 E dN in the central or log linear portion of the growth-rate curve. Several points are shown in figure 8 which were obtained by using the Hahn expression. Because of the relation- ship of growth rate to modulus E, the data can be normalized with respect to the mate- rial density p as indicated in figure 9 where rate curves are seen to converge. It is apparent, then, that a material's advantage can only be assessed on an individual applica- tion basis. Growth under variable-amplitude spectrum loading, for example, may produce different trends in growth retardation due to the interaction of loads. Generally speaking, however, the time to failure from an initial flaw is dependent primarily upon the toughness This is illustrated in figure 10, with cutoffs for several levels of toughness. The KIc .
relative effect, however, may be dependent upon the shape and severity of the spectrum.
While the preceding discussion has been concerned with the cyclic flaw growth behavior, the selection of materials for repeated load application in the presence of flaws may be seriously influenced by the chemical and thermal environments in which the struc- ture must operate. No attempt is made in this paper to cover these trends. The reader is referred to several excellent publications (refs. 6, 11, 14, and 15).
FRACTURE CONTROL — BASIC CONSIDERATIONS The traditional Air Force approach to structural integrity (ref. 13) requires that "safe life" be evaluated through the cyclic test program. The success of this approach in determining the overall fatigue resistance of full-scale structures has been well documented (refs. 6 and 16). The achievement of "fatigue quality" through careful work- manship, surface finishes, and detailed design (local stress levels) and the demonstration of resistance to crack initiation are basic and reasonable goals. Therefore, before pre- senting suggested procedures for fracture control, it is important that two basic tenets be stated: (1) Damage tolerant design and fracture control philosophy should not be considered as substitutes for adequate fatigue considerations.
(2) Consideration must be given to the probable existence of flaws within all basic primary structures.
Crack initiation resistance and fracture resistance should be considered as complementa objectives.
By virtue of its complex nature and varied operational regimes, an airframe encounters a wide variety of natural and induced environments. While this makes the application of fracture theory a rather difficult task, the general overall goals which must be achieved are rather simply stated, as follows: (1) Encourage the intelligent selection of fracture-resistant materials, manufac- turing processes, and so forth (2) Provide an incentive to design for inspectability with damage-resistant structural configurations (i.e., multiple load paths) (3) Aid in establishing effective and realistic inspection procedures (4) Assist in selecting and controlling safe operating stresses In the Materials Utilization section, materials data were presented to illustrate how strength-density ratio (efficiency) could result in the selection of material with an unde- sirable level of toughness. Likewise, the choice based on fatigue alone might lead to serious difficulty since many high-strength materials (steels, for example) may have acceptable fatigue resistance but possess low resistance to brittle fracture and subcritical flaw growth (stress corrosion cracking, for example).
Structural configurations which possess multiple load paths, crack stoppers, and so forth, are necessary and desirable; however, their ability to function and meet specific preassigned goals must be demonstrated early in design.
Controlling design stress levels for common structural materials can have untold benefits from both the strength and fatigue points of view and can prevent costly field maintenance problems. For example, multiple load path, redundant, and fail-safe arrangements may effectively prevent the loss of aircraft, so long as adequate and fre- quent inspections are planned. The sole dependence on the fail-safe approach to achiev- ing fracture control without regard to limiting design stresses may result in frequent member failures, costly unscheduled maintenance, and aircraft downtime. This situation can be alleviated by requiring each member in the multiple or redundant set to be inher- ently resistant to flaw growth within prescribed bounds (i.e., it must have a safe life with cracks).
The ability to detect and quantify flaws and cracks, both in the raw product form and the final assembled structural article, remains as the most significant measure in deterring catastrophic fracture. Instituting fracture control procedures is, in fact, a frank admittance that serious flaws can and often do go undetected. This fact was dramatically pointed out by Packman, Pearson, Owens, and Young (ref. 17) in a study for the Air Force Materials Laboratory. The data in figure 11 have been obtained from that report and depict the sensitivity and reliability of common NDI methods in controlled laboratory experiments. The results are quite surprising because relatively large flaws were not detected. This does not mean that all hope is lost of improving present methods and procedures. On the contrary, continued development of improved NDI techniques is mandatory.
Fracture control procedures are most beneficial if effectively implemented and managed. Implementation consists of satisfying specific requirements for analysis and test based on established ground rules and definitions of required strength, assumed damage, service life, and inspection intervals. A balanced design within the goals of damage tolerance is thus insured. It is important that the basic definitions, goals, and fracture requirements be established early in the design phase in order to impact trade studies. Implementation requires a firm material data base, knowledge of operational environments, design criteria, and an analytical capacity to perform complex flaw-growth and strength analyses.
If fracture control procedures are instituted early, they form a portion of the basic design criteria and no weight penalties can then be attributed to their existence. Weight penalties are only recognized if the requirements are levied after the design is frozen.
FRACTURE CONTROL — REQUIREMENTS It should be acknowledged that the preparation of detailed step-by-step require- ments for fracture control is a difficult task because of the numerous classes of aircraft (i.e., fighter bombers, trainers, etc.) in use today by the Air Force and because of the various types of structural arrangements which comprise these airframes. With regard to the structural aspects, the term "Damage Tolerant" is perhaps most common and is used within the Air Force (ref. 13) to describe those configurations "which will minimize the loss of aircraft due to the propagation of undetected flaws, cracks, or other damage."
Supplemental requirements for the ASIP (ref. 13) and various military specifica- tions (ref. 18) are currently being formulated to insure the achievement of damage- tolerant design. Such requirements will be applicable to all primary structures, the failure of which would reduce the strength level below specified limits and endanger the safe operational flight characteristics of the aircraft.
In general, requirements to insure adequate fracture control take on the form of specific directives in the areas of (1) design, (2) analysis, and (3) test.
In the following discussion, a representative set of specifications for fracture con- trol is described to indicate the relative levels of importance placed on structural arrangements, inspections, and so forth.
It is generally recognized that there are two major design steps which are required to produce a damage-tolerant structure: (1) Controlled safe flaw growth (safe life with cracks) (2) Positive damage containment (remaining or residual strength) Neither of these should be considered separate and distinct, however, since it is the judicious combination of both that is required for effective fracture control.
Since the assumption is made that flaws do exist in new structures and can go undetected, full compliance with this philosophy requires that consideration be given to the probability that flaws will exist in any and/or all members, including each element of a redundant or multiple load path group. This is important because it is easy to rational- ize that each member of the multiple set could be flawed. For example, if stress cor- rosion is responsible for the existence of subsurface cracks in one member, there is no assurance that each adjoining member does not contain cracks of a similar character.
The first major requirement for fracture resistance must, therefore, dictate that any member must have a safe life with assumed cracks present.
For any given application, the overriding factors which govern the details and com- plexity of the fracture requirements and demonstrations are (fig. 12) (1) The class or type of structure (2) The quality of production and assembly NDl (3) The accessibility of the structure (4) The assurance that the member will be inspected in service (5) The probability that a flaw of subcritical size would go undetected even though periodic inspections are made Most structural members can be classified by load path (fig. 13): (1) Single load path (2) Single primary load path with auxiliary crack arrest features (3) Multiple and redundant load path Class 2 includes such items as pressure cabins and pressure vessels, where rela- tively large amounts of damage may be contained by providing tear straps, stiffeners, and the like. While some load shedding does take place, the primary load path is singular.
Detection of damage for such cases is likely, because of fuel or pressure leakage.
Class 3 structures are generally designed so that some percentage of original strength is retained during and subsequent to the failure of one element (often called fail safe). Assurance of this capability should be mandatory by analysis and tests. The con- tainment of damage is often produced by natural barriers such as production splices and so forth.
Accessibility and inspectability were indicated in the section on Basic Considera- tions for Fracture Control as major items in fracture control. This point cannot be overemphasized. Not only should the structure be inspectable, but assurance must be given that it will be inspected periodically after assembly. Because of recent experi- ences with high-strength materials, speculation has arisen whether or not subsurface cracks of near-critical size can be found in service by use of routine inspection proce- dures and equipment. A positive criterion such as "leak before break" may have to be levied in order to assure their detection. Otherwise, an inspectable structure would have to be classified as noninspectable. (See fig. 14.)
Engineering Criteria — Definitions Before specific fracture requirements for design, analysis, and test can be levied, certain aspects of loading and service must be defined for each type of aircraft. In most cases, these items will be unique for each particular system and will be specified in the basic design criteria.
Strength limits.- The percentage of unflawed static strength which is to be main- tained with prescribed amounts of damage must be established. This load is generally the limit load but may vary with aircraft types.
Dynamic factors.- The effect of dynamic load amplification due to the release of energy as the damage is introduced must be included.
Inspection intervals.- Inspection intervals shall be consistent with required safe crack growth intervals and the requirements for residual strength.
Damage limits.- The size of initial flaws which may be expected to slip by inspec- tion must be established from NDI capability studies. Final damage limits will be based on fracture and inspection requirements. In addition, the number and locations of mem- bers which are to be considered failed for residual strength purposes must be identified.
Damage limits should be established for each system based on individual requirements, materials applications, and so forth.
Design Trade Study Analyses A primary function of the fracture control requirements during early design stages is to assist in the selection of damage-resistant materials and structures, with some incentive offered to those that are easily inspectable and those that include multiple or redundant load paths. In figure 15, key factors which influence these trade studies are summarized. Each member is first classified as to structural type, inspectability, and so forth, and a candidate material is selected. Limits of assumed initial damage size are assigned together with the engineering criteria for life, strength, and final damage size. The analysis is then performed by utilizing the appropriate cyclic and sustained loads and environments. The process is then iterated until a satisfactory combination of material and stress level is selected which fulfills the strength and life requirements.
The resultant information is then incorporated with other design considerations until a satisfactory design is achieved.
Analysis — Detailed Requirements The analysis consists of determining the growth rates of initial flaws under cyclic loading and environment and insuring that these flaws remain subcritical for the specified time period. Initial flaw sizes generally reflect the NDI capability but may be influenced by such criteria as proof tests and manufacturing processes. The flaws are generally assumed to be normal to the maximum principal stress field. The character and shape of the flaws are usually influenced by such aspects as (1) Materials and processing (2) Manufacturing and assembly (3) Handling and service conditions Experience has indicated that the flaw types shown in figure 16 are most representative in aircraft.
In table III, a set of hypothetical analysis requirements have been tabulated for the three classes of structures, based upon whether or not the assemblies will be inspected in service. l The information from table III has been translated into figures 17, 18, and 19 for clarity. As is indicated, each class is designed for a safe crack growth period from an initial flaw. The final fracture dimensions are governed by plane strain fracture at limit load unless conditions indicate that this mode of fracture is unlikely. Some motivation to design with inspectability and with high-toughness materials (and thus higher stresses) is offered for (a 3 > a5) and (a4 > a5). The final crack dimensions a3 and a4 must truly be detectable however; otherwise, the structure should be reclassi- fied as noninspectable. It was previously stated that subsurface flaws most likely should be put in the noninspectable class (for service inspections). However, in most cases, it is possible to achieve through-the-thickness cracks and thus "positive detection" with proper selection of materials and stresses.
A safe life period of two inspection intervals has been indicated for the class 1 and class 3 inspectable cases. This will result in a slight reduction in allowable design stresses but will offer more chance to detect the subcritical crack.
For the class 1, single load path, structure the requirement to satisfy a safe life with cracks is easily accepted because of the consequence of losing the member.
1 These requirements are presented for purpose of illustration only and do not represent USAF policy.
However, as previously stated, the preexistent flaw concept requires that all members, including each member of a multiple load set, be assumed flawed. It is not sufficient simply to design the multiple load path structure to a remaining strength criterion with one principal member failed. This does not insure that initial flaws in a member will not grow to critical size in a relatively short period of time and result in broken mem- bers and unscheduled, costly maintenance. Therefore, the safe life requirements C and E as listed in table III and indicated in figure 18 are applicable to every member of the structure. However, since there should be some incentive to design class 3 structures, the size of the initial assumed flaws in the class 3 structure is reduced from that in the class 1 structure for the noninspectable case (a 1 < a2). By doing this, the designer is admitting that the design is more comfortable and that he is willing to take a larger risk of operating with cracks.
Supplemental safe life (with cracks) requirements (F and G) for the class 3 struc- ture are listed in table III and are applicable to the remaining structure after the one principal member has failed. In these requirements, the assumption is made that the element could fail at any time during the life (or inspection period) and go undetected.
The remaining structure (assumed to be flawed) would then be required to carry the maxi mum load for the duration of the remaining specified time period. The stresses which result from requirements F and G most likely will dominate the design. In actual prac- tice, studies would have to be conducted to determine the most appropriate time to assume the member failure. In requirement F, the remaining growth period would be one inspection interval regardless of when the member was assumed to have failed. As is indicated in figure 19, the total growth in any one member is equal to the amount which occurs prior to the failure of the principal element plus the amount which occurs subse- quent to the failure at an increased stress level.
Alternate Scheme to Assess Remaining Life In the previous section, requirements F and G (table III) were presented to satisfy the requirement for some remaining life in the multiple load structure after the failure of any principal member. An alternate scheme, and one which may be less restrictive, has recently been prepared for use in the Air Force. The principal difference is that the remaining structure is considered to be intact (unflawed) subsequent to the failure of the principal element. The requirement is stated as follows in reference 18: " Fail Safe. Primary structure that is designed fail safe shall be read- ily inspectable and meet the following requirements after failure of a principal structural element: (1) the remaining structure shall sustain without failure, the maximum expected load or limit load, whichever is greater, (2) the air- plane shall be controllable within the design speed limits, and (3) catastrophic failure of the remaining structure will not occur under repeated load condi- tions during the time period to the next opportunity to detect the failure.
Verification of the ability of the remaining structure to withstand the repeated loads shall be accomplished by determining the crack growth period from an initial flaw to failure of the principal element, and then insuring that the life (including a factor of four) of the remaining structure will equal or exceed the time interval established for the next inspection.
Inspection intervals shall be as agreed to by the procuring agency . . ."
Fracture Control — Verification and Demonstration In the preceding discussion, requirements for analysis were presented. In certain instances, experimental verification or demonstration of compliance should be required.
Safe crack growth tests (class 1 and class 3).- Although basic growth-rate data will be generated to support analysis techniques, it is desirable to augment the constant- amplitude tests with spectrum crack growth tests conducted on a meaningful flight-by- flight basis. This is particularly true where reliance has been placed upon positive detection by surface flaws penetrating the member thickness. In most cases, these experiments can be conducted on representative coupons, or small specimens if stresses are well known. If the geometry is complex, it is more desirable to utilize prototype component structure and run the growth tests in conjunction with the static or cyclic preproduction tests.
Demonstration tests utilizing full-scale structures (i.e., complete aircraft) should not be necessary since it is generally quite easy to duplicate localized conditions sur- rounding the crack tip.
Damage arrest (class 2).- Demonstration of crack arrest capability and subsequent cyclic life should be required. These tests may be conducted on representative speci- mens or on the full-scale aircraft at the conclusion of the static or fatigue test. In most cases, critical damage is introduced mechanically to simulate service condition (battle damage, etc.).
Establishment of Inspection Procedures An additional function served by the safe crack growth analysis is the establish- ment of inspection procedures for an individual structure or for all members in the air- craft which are manufactured from the same material. The use of fracture analysis procedures allows inspection or rejection with more confidence by classifying parts and regions within a part according to the required NDI sensitivity.
The development of such an inspection procedure for a typical application is illus- trated as follows. Spectrum crack growth information is plotted in figure 20(a) as a function of the initial crack size (only a0 is shown) for various degrees of spectrum severity (maximum stress). In this example, the required safe growth period is N hours, and a0 is the largest crack size that can be tolerated for this material application. The maximum expected spectrum stress is Q4 . NDI procedures must insure the reliable detection of a 0 during fabrication and assembly.
This spectrum growth information is translated into more meaningful form in fig- ure 20(b) where, for any level of design stress, the largest tolerable flaw which would grow to failure in N hours is plotted. Rather than using fracture at N hours, a criterion based on positive detection could be substituted and produce a similar diagram.
Application of Requirements While the full impact of the proposed fracture requirements can only be assessed through an extensive design application study on an existing system, the relative severity can be assessed by studying typical examples. The following example illustrates the values of design stress for a single material which would result under each requirement listed in table III: Example: Tension cover; aircraft type, fighter Material, 7075-T6 KIc = 30 ksi- in.
Thickness = 0.375 in.
Initial flaw assumptions (surface flaw) (a/2c = 0.5): a l = 0.050 in. (for all inspectable cases) a2 = 0.150 in. (for all noninspectable cases) Final flaw size: a4 = Minimum detectable size = 0.375 in.
a3 = Minimum acceptable equivalent = 0.500 in. for single load path structure Stress information: The fighter spectrum information is contained in table IV in terms of a unit of maximum stress value a = 37 ksi. These occur- rences in table IV are the equivalent of 40 hours of flight. The maxi- mum limit stress for design purposes is: UL = 1.5Q = 55.5 ksi Spectrum growth-rate data: By utilizing constant-amplitude growth-rate data (ref. 19), the CRACKS computer routine (ref. 20), and the AFFDL crack growth retardation model (ref. 10), the stress spectrum (table IV) was translated into plots of crack depth a as a function of number of flights starting with an initial crack length a l = 0.050 in. (fig. 21) and a 2 = 0.150 in. (fig. 22). All levels of stress from table IV were increased or decreased proportionally to achieve the variation in growth due to spectrum severity.
Material toughness: The cutoff line for KIc = 30 ksi- in, is indicated in figures 21 and 22. The effect of varying this parameter was not investigated in this example.
Life requirement: Service life = 160 blocks = 160 x 40 = 6400 hours. Inspection intervals are planned each 1/4 lifetime of 40 blocks = 1600 hours.
Requirement A: Initial crack depth: al = 0.050 in.
Final crack depth: a3 = 0.500 in. (based on positive detection) Life requirement: NA = 80 blocks = Two inspection intervals Design stress QA: This goal cannot be achieved with this material since K Ic is limited to 30 ksi-in, and the inspection requirement of 0.500 in. is not possible. A material change would most likely be required.
Requirement C: Initial crack depth: a1 = 0.050 in.
Final crack depth: a4 = 0.375 in. (based on positive detection) Life requirement: NC = 80 blocks Design stress, maximum: 0C (allowable) = 1.270 = 47 ksi Requirement D: Initial crack depth: a2 = 0.150 in.
Life requirement: ND = 160 blocks = One lifetime Final crack depth: a 5 = Plane strain fracture > 1.0 in.
Design stress, maximum: 0D (allowable) = 0.810 = 31 ksi Requirement E: Initial crack depth: al = 0.050 in.
Final crack depth: a 5 = Plane strain fracture = 0.58 in.
Life requirement: NE = 160 blocks Design stress, maximum: 0E (allowable) = 1.080 = 40 ksi Requirement F: Coupled with requirement C is the additional requirement that the struc- ture remaining after failure of the principal member will be capable of carry- ing limit load for one additional inspection period, or 1/4 lifetime. The lower portion of the growth data from figure 21 has been replotted in figure 23.
(a) Assume that the member breaks accidentally after the first flight and remains undetected until the next inspection interval. The stress is assumed to increase by 20 percent, with the requirement being no failure at limit load in 1/4 lifetime or 40 blocks. From figure 23, it can be seen that a stress level of approximately 1.6Q = 60 ksi would grow to failure in 40 blocks.
Therefore 160 0 = 50 ksi aFa (allowable) = (b) Assume the member failure to be at 1/4 lifetime (just subsequent to inspection). The crack in the remaining structure has grown an amount Da during the first inspection period. Thus, New initial a = al + Da = 0.050 + Aa This condition can be satisfied by trial and error by using figure 23. The result indicates that crFb z 1.2a = 44.4 is appropriate for this condition.
Failure at any other time could be checked to see whether a lower stress would result. Note that no criterion for positive detection was required since at the next inspection the broken member would be found.
Requirement G: In a similar manner, requirement E should be checked for life after member failure.
(a) Assume failure on first flight (from fig. 21) Q E =1.08Q=40 ksi Q a 12-33.3 ksi " gG (b) Assume failure at 1/2 lifetime. The incremental growth during the first 1/2 lifetime must be added to a l . The requirement for 1/2 remaining life shall then be determined. From figure 21, by trial and error, a stress level of uGb = 1.Ou = 37.0 ksi is seen to satisfy the requirements.
Summary: The following table is a summary of the previous example: Requirement Design stress, Q, ksi Condition A Not satisfied Inspectable class 1 C 47 Inspectable class 3 D 31 Noninspectable class 1 E 40 Noninspectable class 3 Fa 50 Inspectable class 1 Fb 44.4 Ga 33.3 Noninspectable class 3 Gb 37.0 The results clearly indicate the advantages offered by designing for inspectability since the allowable stresses for requirements C and F are greater than for require- ment G. The incentive for multiple, in lieu of single, load path design is seen in the resultant allowable design stresses for requirements E and G being greater than for requirement D.
ANALYSIS AND DATA REQUIREMENTS FOR IMPLEMENTATION The successful implementation of the fracture control analysis requires the ana- lytical capability for cyclic and environmental flaw growth, aircraft usage information, and basic strength and fracture data for proposed candidate materials.
Criteria Requirements Initial considerations for fracture resistance and control of subcritical flaw growth must be established during the criteria development stage and must reflect appropriate chemical, thermal, and operational loads environments. For example, recent materials usage has necessitated the generation of data on sustained-load flaw growth in aggressive environments such as fuel and water (fig. 24(a)). Because loading rate and dwell times are important in the assessment of environmental effects, it has become important also to generate load-time spectra of the type indicated in figure 24(b).
Material Data Requirements The major material strength and fracture properties required to perform the ana lyses and trade studies for fracture considerations are illustrated in figure 25. In all cases (except KIc) no approved standard test methods exist to determine these proper- ties. Through experience, however, various test techniques and specimens have evolved.
(See fig. 25.) As is often the case, a specimen developed for one function or application is used to generate a multitude of data. Testing techniques and data interpretation may mask important material responses or indicate false reaction to stress and environment.
For example, in a recent comparison of cyclic growth-rate behavior in D6ac steel (refs. 9, 11, and 12) comparative growth rates obtained from compact tension and surface- flawed specimens indicated a predominant stress-level effect for the surface-flawed specimen, whereas no clear dependency was observed for the compact tension case (fig. 26). These effects are currently being investigated.
Fracture Analysis Methods Prediction of fracture and growth behavior requires a means of translating external applied loads into stresses in the region of the crack tip. Finite-element techniques offer a vast potential in the area, particularly in complex structural arrangements (refs. 21 and 22). A rather broad collection of stress intensity solutions exists (ref. 4); however, their use is limited in many cases and extrapolation is often required to pro- vide the best estimate of K.
Considerable effort is being expended in the development of computer routines to "integrate" growth-rate (da/dN) data (ref. 20), for example, and to account for the retar- dation effect of overloads in variable-amplitude spectra. As an example of this type of activity, the AFFDL has recently developed a mathematical model for predicting the growth delay effect (ref. 10). The basic model is concerned with the effect of the over- load plastic zone on the subsequent rate of growth as indicated in figure 27. A hypotheti- cal residual or reduction stress is then computed which suppresses the subsequent cyclic loads. Retardation is accomplished in three modes, depending on the relative size of the overload in relation to the subsequent cyclic level (fig. 28). Effective OK and R values are computed and reduced rates obtained from normal da/dN and OK relation- ships. Note that growth can be completely stopped (fig. 28). An extensive testing pro- gram is being completed at AFFDL to evaluate the merit of the model. In figure 29 are some early correlations with single overloads in aluminum (ref. 6). Fairly good correla- tion is noted also with randomized block spectrum data for D6ac steel (fig. 30).
Growth analysis schemes need to be extended to include the effects of loading rate and delay time (sustained load growth). Free surface effects and flaw shape changes, including the transition of a surface flaw to a through crack, must be included.
SUGGESTED AREAS OF STUDY The suggested areas of study for the application of fracture mechanics in struc- tural integrity have been summarized and are presented as table V. This table is obtained from reference 23.
CONCLUDING REMARKS AND RECOMMENDED TOPICS FOR STUDY The author has attempted to present the significant impact of fracture mechanics and fracture control in the overall program of airframe structural integrity. The true weight, cost, and performance trade-offs associated with the implementation of these or any requirement can best be judged by experience and application to existing systems.
A fair assessment can only occur, however, if continued materials and structures devel- opment efforts are directed toward upgrading existing fracture mechanics and fracture analysis technology.
The author has summarized in tabular form a rather extensive "shopping list" of items which require attention. In many cases, a relatively high degree of proficiency exists and application experience is all that is necessary while others require new thought and new direction.
REFERENCES 1. Donaldson, D. R.; and Anderson, W. E.: Crack Propagation Behavior of Some Air- frame Materials. Proceedings of the Crack Propagation Symposium, Vol. H, Sept. 1961.
2. Wilhem, D. P.: Fracture Mechanics Guidelines for Aircraft Structural Applications.
AFFDL-TR-69-111, U.S. Air Force, Dec. 1969.
3. Anon.: Fracture Control of Metallic Pressure Vessels, NASA Space Vehicle Design Criteria (Structures). NASA SP-8049, 1970.
4. Anon.: Fracture Toughness Testing and Application. ASTM STP 381, June 1964.
5. Wood, H. A.: A Study of the Residual Strength of Damaged Heavily Stiffened Sheet Structure. AFFDL-TR-(to be published).
6. Anon.: Proceedings of the Air Force Conference on Fatigue and Fracture of Aircraft Structures and Materials. AFFDL-TR-70-144, U.S. Air Force, Dec. 1969.
7. Gran, R. J.; Orasio, F. D., Jr.; Paris, P. C.; Hertzberg, R.; and Irwin, G. R.: Investigation and Analysis Development of Early Life Aircraft Structural Failures.
AFFDL-TR-70-149, U.S. Air Force, Nov. 1970.
8. Wood, H. A.; and Haglage, T. L.: Crack Propagation Test Results for Variable Ampli- tude Spectrum Loading in Surface Flawed D6ac Steel. Tech. Memo FBR-71-2, U.S. Air Force, Feb. 1971.
9. Hinders, U. A.: F-111 Design Experience — Use of High Strength Steel. AIAA Paper 70-884, July 1970.
10. Willenborg, J. D.; Engle, R. M.; and Wood, H. A.: A Crack Growth Retardation Model Using an Effective Stress Concept. TM-FBR-71-1, U.S. Air Force, Jan. 1971.
11. Masters, J. N.; and White, J. L.: Development of Fracture Toughness Properties of D6ac Steel for F-111 Application. AFFDL-TR-70-310, U.S. Air Force, Nov. 1970.
12. Harmsworth, C. L.; and Cervay, R. R.: Fracture Toughness Evaluation of D6ac Steel in Support of the F-111 Aircraft Recovery Program. AFML/LAE 71-2, U.S. Air Force.
13. Anon.: The Air Force Airplane Structural Integrity Program (ASIP) Program Require- ments. ASD-TR-66-57, U.S. Air Force, May 1970.
14. Wei, R. P.: Some Aspects of Environment Enhanced Fatigue Crack Growth. Paper presented at ASTM Fall Meeting (Atlanta, Ga.), 1968.
15. Hartman, A.; and Schijve, J.: The Effect of Environment and Load Frequency on the Crack Propagation Law for Macro Fatigue Crack Growth in Aluminum Alloys.
NLR MP 68001U, 1968.
16. Lowndes, H. B., Jr.: Air Force Flight Dynamics Laboratory, Correlation Between Full Scale Fatigue Test and Service Experience. Paper presented at the Eleventh Conference of the International Committee on Aeronautical Fatigue (ICAF) (Stockholm), May 1969.
17. Packman, P. F.; Pearson, H. S.; Owens, J. S.; and Young, G.: The Applicability of a Fracture Mechanics — NDT Design Criterion for Aerospace Structures. WESTEC Conference (Los Angeles, Calif.), March 10, 1969.
18. Anon.: Airplane Strength and Rigidity — Reliability Requirements, Repeated Loads, and Fatigue. Mil . Specif. MIL-A-008866 A, Mar. 31, 1971.
19. Hudson, C. Michael: Effect of Stress Ratio on Fatigue-Crack Growth in 7075-T6 and 2024-T3 Aluminum-Alloy Specimens. NASA TN D-5390, 1969.
20. Engle, R. M., Jr.: CRACKS: A FORTRAN IV Digital Computer Program for Crack Propagation Analysis. AFFDL-TR-70-107, U.S. Air Force, Oct. 1970.
21. Chan, S. K.; Tuba, I. S.; and Wilson, W. K.: On the Finite Element Method in Linear Fracture Mechanics. Eng. Fracture Mech., July 1970, vol. 2, no. 1, Pergamon Press, pp. 1-17.
22. Byskov, E.: The Calculation of Stress Intensity Factors Using the Finite Element Methods With Cracked Elements. Int. J. Fracture Mech., vol. 6, no. 2, June 1970, pp. 159-167.
23. Wood, H. A.: The Role of Fracture Mechanics in the Air Force Airplane Structural Integrity Program. AFFDL-TM-70-5-FDTR, U.S. Air Force, June 1970.
TABLE 1.- TYPICAL SERVICE APPLICATIONS OF FRACTURE MECHANICS Type of System Problem Material Solution Reference structure App ea rance of in-service C-130 Aluminum Multiple load Analytical estimate of remaining 5 cracks in center wing area . sheet path, heav - strength with relatively l arge Extremely heavy usa ge of ily stiffened cracks. Stiffened case.
aircraft due to mission "planks" In-house experimental verifica- change. Structure readily tion of K solution for stiffened inspectable. Plan e stress structure. Simulated and case.
actual panels.
F-100 "Thunderbird" acci d ent. Aluminum Single load Inspection pro g ram to determine 6 path skin Discovery of small cracks plate maximum probable flaw sizes.
in fastener holes during Analysis of spectrum gro wth (no inspection. Structure not retardation assumed). Esti- readily inspectable.
mate of residual strength.
Laboratory tests of spectrum g rowth with actual flaws from service and manufactured cracks.
T-37 Main spar failure, plane Aluminum Single load Estimate of stress intensity strain, crack originated in "TEE" path factor for complex geometry.
fastener hole. Structure extrusion Growth estimate for safe moderately inspectable.
inspection interval F -111 Fatigue test failures. Plane Steel plate Single load T est failure analysis.
8,9 , strain cases. and path cases and 10 Spectrum gro wth tests and ana- forging Service failure (A/C) # 94).
lysis techniques for deter- Surface flaw during manu- mination of inspection inter- facture, l oss of aircraft.
vals following proof test.
Structure not readily inspectable.
i TABLE 1I. - TYPICAL MATERIAL PROPERTIES [so ur ce : Air Force Materials Laboratory] Plan e strain Yield strength, u KIc toughness, ys (KIC)2 2 (KIC)2 Material u (typical), p ys u U P KIc' ys ys ksi ksi- ..fin.
(a) (b) Steel 724 177 (318) 205- 50 to 90 0.120 to 0.38 0.06 to 0.19 D6ac 220 53 .12 .06 777 247 69 .16 .08 872 300M 285 89 .20 .100 1007 18Ni-Co - Mo 1039 141 294 40 .04 .02 H-11 180 to J90 110 to 170 1.22 .61 600 9Ni-4Co-2C Aluminum 0.44 0.22 660 310 7075-T73 (for gi ng) 66 31 .32 .16 580 230 2024 -T851 (plat e) 58 23 .23 580 280 2024 -T851 (extruded) 58 28 .46 .56 .28 660 350 2014-T6 66 35 26 .22 .11 780 260 7075-T651 (plate) 78 .44 .22 750 350 7175-T73 (for g in g) 75 35 76 27 .26 .13 760 270 7075-T6 (plate) 75 27 .26 .13 750 270 7075-T6 (for g in g) 30 .38 .19 690 300 7079-T6 69 Titanium 0.26 (0.38) 0.13 (0.19) 856 312 (375) Ti-6Al-4V (ann) 137 50 to 60 41 .14 .07 988 256 Ti -6Al-4 V (ST A) 158 .10 (.22) .05 (.11) 937 219 (312) Ti - 6Al-6V - 2Sn (ann) 150 35 to 50 .08 .04 1018 212 Ti-6Al-6V -2Sn (STA) 163 34 .04 1050 156 Ti-13V-11Cr-3Al (STA) 168 25 .02 a ASTM thickness required for plane strain fracture.
bEquiv a l ent to a for u = 0.6 u ' ys cr L TABLE III.- FRACTURE CONTROL ANALYSIS REQUIREMENTS Inspectabl e class Noninspectable class (a) (a) 1 2 1 3 Safe crack g rowth Requir ement A Requirement B Requirement C b Requirement D Requirement E b (fig . 17) (fig. 18) (fig. 17) (fig. 18) b b Initial flaw .. a a1 a1 a1 c c d Shall not grow to critical size . a a3 a6 a5 a5 In the specified time of Inspection period One fli g ht Inspection period One lifetime One lifetime e Critical stress Limit load stress Limit load stress Limit load stress Limit load stress Limit load stress Inspectable class 3 Noninspectable class 3 Remainin g strength additional safe life. Class 3 Re{uirement F b Re quirement G b fi g. 19(a)) (fig. 19(b)) Subsequent to failure f of one principal member, the remain- ing structure shall be capable Limit e load stress of carrying . Limit e load stress At the en d of . One inspection period One service lif etime a Class 1 = Single load path.
Class 2 = Single load path (crack arrest features).
Class 3 = Multiple load path.
b Each member of class 3 structure shall be assumed to be flawed. The safe crack growth requirements shall be continuous throughout the specifi ed time p erio ds prior to and subsequent to the failure of the element.
ca 3 and a4 are de termined by fracture considerations but must be lar ge and detectable (Le., throu g h-the-thickness cracks).
Otherwis e, classify as uninspectable. (Note: a3 » a4') d a must be re a dily inspectable (L e., pressure loss). Otherwise, classify as noninspectable class 3 structure.
~ e Will vary with aircraft type .
c;..., f Member can fail at any time durin g specified period.
TABLE IV.- STRESS SPECTRUM FOR FIGHTER AIRCRAFT EXAMPLE a amin, am ax , amin, amax, Layer Cycles Layer Cycles ksi ksi ksi ksi 1 0.06 16.6 63 30 7.94 34.9 2 2 7.04 27.0 76 31 3.64 16.1 3 .45 13.7 371 32 7.57 16.8 367 4 5.90 26.4 37 33 7.15 25.6 109 .79 17.5 111 34 7.91 37.0 1 6 10.60 25.4 2 35 1.63 265 6.3 7 .76 14.2 363 36 .79 20.8 34 8 4.02 28.7 5 37 7.81 20.2 9 1280 3.64 10.7 38 3.68 11.8 6 10 6.77 22.9 62 39 0.0 21 11.3 3.64 16.6 1 40 7.18 17.9 374 6.07 17.5 89 41 2.01 13.9 478 8.64 21.8 41 42 1.59 8.8 46 9.51 19.1 57 43 .06 11.9 300 15 3.78 14.0 491 44 1.59 11.3 10 16 0.0 13.9 6 45 7.91 31.7 4 17 3.81 17.5 74 46 0.0 16.4 4 7.88 13.4 682 47 7.57 14.5 306 .72 10.4 1376 48 8.26 24.9 15 20 9.37 16.0 66 49 7.98 26.1 5 .52 17.2 34 50 8.19 12.9 6.76 8.6 1621 51 7.98 10.7 1338 7.98 11.8 1589 52 .06 19.8 19 24 .45 10.6 1374 53 3.85 10.4 1546 25 0.0 8.8 67 54 0.0 6.4 238 7.08 28.5 1 55 .48 16.1 114 27 7.39 22.8 250 56 7.08 14.9 370 28 .06 22.1 8 57 3.85 20.8 7 29 1.63 13.9 2 58 2.01 13.9 478 a Single block is equivalent of 40 flight hours.
TABLE V.- SUGGESTED AREAS OF STUDY F OR THE APP LICAT IO N OF FRACTURE MECHANI CS IN STRUCTURAL INTEGRITY Implement rationa l fracture mechanics theory into the design criteria, material selection, PR OGRAM : analysis, qualification, and utilization of aircraft structural systems.
TO P I C AREAS: I Criteria II D ata requirements and applications Fracture analysis met hodology ill Qualification for fracture resistance IV V Utilization - structural concepts SUBJECT BREAKDOWN: I Criteria a. Definition chemical and thermal environment for fracture requirements b. Review past experience, structural failure, and so forth c. Catalog critical structural materials arrangements and previous desi gn considerations in order to establish wh ich areas require extensive investigation d . Establish fracture criteria for materia l selection and trade-off studies e . Establish analogous "leak before break" criteria for aircraft application f. Assemble design data and criteria for fracture applications g. Definition of mission and analySiS, including estimates of time at load factor h. Incorporate criteria in basic specifications including ASIP modification II Data requirements and applications a. Establishment of measurable parameters Kc , K ' K ' da j dt, da/dN, Ic ISCC and others, including testing standards b. Application of Kc and K in design Ic c. Fatigue crack growth data d. Subcritica l crack growth rate, environment, and temperature e. Effect of loading seq u ence on cyclic growth or growth retardation f. Nonpropagating crack study, threshhold of ~K g. Parametric growth data, mission segments h. Extension of fracture mechanics testin g standards to new classes of materials i. Study of statistically derived crack sizes and shapes based on nondestructive inspection (NDI) and nondestructive testing (NDT) j . Effect of stress state of fracture k. Mixed mode fracture study "'" TABLE V.- SUGGESTED AREAS OF STUDY FOR THE APPLICATION OF FRACTURE MECHANICS IN STRUCTURAL INTEGRITY - Concluded 0) 0) Fracture analysis methodology SUBJECT BREAKDOWN: III a. Assemblage of currently applicable K factor relationships including application b. Guidelines for estimating K or approximate K for complex cases (including superposition) c. Development of K for complex cases, elastic solutions d. Finite-element studies, crack growth, subcritical growth development of K, model crack element for finite-element technique e. Plasticity and free surface effects f. Tabulation of equivalent cracks in complex flaw geometries g. Analytical crack model for growth under variable loading h. Routine for crack growth and life estimates including environment, rates, and load sequence effects i. Analytical study of variation of flaw shape and surface flaws j. Statistical analysis to establish confidence levels for toughness and life estimates, scatter factor for application to analysis results k. Residual strength and static considerations 1. Handbook preparation and design guidelines m. Development of semiempirical methods for estimating K n. Fracture arrest, damage-tolerant analysis methods o. Study of the effect of crack bluntness on fracture behavior IV Qualification for fracture resistance a . Real-time flaw growth testing including temperature and environment (specimens) b. Rea l -time flaw growth (structures) c . Crack growth resistance and crack arrest testing d . Damage tolerance or fail-safe testing e. Test time reduction for (a) and (b) above f. Proof testing: Repeat work of Tiffany (Boeing) for typical aircraft struct u res Extend knowledge and techniques to satisfy environment and requirements Statistical assessment of the risks and merits of proof testing V Utilization - structural concepts a . Concepts for flaw and crack arrest b. New mater i al ut il ization c . Performance and weight trade:..off st u dies d. Fabrication of structural concepts and full-scale testing e. Inspection, fracture mechanics interfa,ce, and flaw classification f. Proof testing, full sca le o^ n \i D6ac 80 I U p Ti-6A1-4V Ti-6AI-6V-2Sn z O o A CD ZD t° n ° ° \ •• z STEEL ALUMINUM ° TITANIUM z a J d 0 100 200 300 YIELD STRENGTH, 6ys, ksi Figure 1.- Trends in toughness variation.
N N T b U 0.3 • CIE TITANIUM Q 0.2 I I STEEL I c^ I z 0. 1 LLj J ALUMINUM n Y U ° d Cif i U 300 200 YIELD STRENGTH, 6ys, ksi Figure 2.- Variation of crack length parameter with yield strength.
0.3 T_6A ALUMINUM • f DESIRED TREND N 0.2 N • - _ o b U HYPOTHETICAL • NDT ''LIMIT'' i HYPOTHETICAL TITA- MANUFACTURING z NIUM o oDEFECT LIMIT d 0.1 d d z • ALUMINUM ° c^ I STEEL o z STEEL LL, J o TITANIUM o Y I U d U 0L STRUCTURAL EFFICIENCY PARAMETER , GyS/p Figure 3.- Variation of crack length parameter with structural efficiency parameter.
/ PROOF STRESS IN ITIAL FLAW WHICH ap ^ ASSES PROOF TEST P CRITICAL FLAW SIZE a MAX. OPERATING e cr AT MAX. OPERATING / STRESS STRESS w I_ _ CONSTANT Klc i ii d / GROWTH PERIOD ap I a c r A y
j
FLAW S I ZE , a - Figure 4.- Proof test concept.
A 4 APPARENT 0 0 UPPER BOUND O^^ K IC /p x 100 O O A g ^ • ALUMINUM A STEEL O TITANIUM 1 1 1 1 1 1 1 1 1 1 1 , I -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Gys/p x100 STRUCTURAL EFFICIENCY PARAMETER, - normalized variation of yield strength with fracture toughness.
Figure 5.- Density PLANE STRAIN FLAT w U Z Q Q w d MIXED w MODE r-- U Q w JE STRESS z S LANT OR V—SLANT 0 0.2 0.4 0.6 0.8 1.0 RADIUS OF PLASTIC ZONE r B THICKNESS Figure 6.- Trend in fracture mode appearance as a function of crack tip plastic zone parameter (ref. 2).
c 200 Y" 160 U Q " 120 } t- N Z Z N K F- N Q 40 U K U L 0 0 0.
THICKNESS, B, in.
Figure 7.- Nominal critical stress intensities for several materials as a function of thickness (ref. 2).
U >- = 20 U Z 3^: 6 Y 4 U Q 3 4 5 6 7 8 9 10 20 30 40 50 60 STRESS INTENSITY RANGE , LK, ksi-V Figure 8.- Fatigue-crack-growth data for typical aircraft structural materials.
U V N w z z w Y U 3 Q U 20 30 40 50 1.00 200 300 400 DENSITY-NORMALIZED STRESS INTENSITY . OK/p Figure 9.- Comparative crack growth data.
i K3 > K2 > K 1 K2 K1 w I I I N 1 1 L) SPECTRUM I B SPECTRUM A I LI FE INTERVAL L^LIFE ^1 'INTERVAL SAFE CRACK GROWTH LIFE - Figure 10.- Effect of fracture toughness life for various shape spectra.
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CLASS 1 CLASS 2 CLASS 3 SINGLE LOAD PATH MULTIPLE LOAD PATH SINGLE LOAD PATH DAMAGE ARREST CAPABILITY REDUNDANT LOAD PATH Figure 13.- Structural arrangements.
• POSITIVE CRACK GROWTH THROUGH
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THICKNESS INSURES DETECTION t PRIOR TO CATASTROPHIC FAILURE a Cr (a) UNDETECTED • MAY BE ACHIEVED BY SELECTING MATERIAL TOUGHNESS AND/OR INITIAL FEW GEOMETRY TO PRODUCE TRANSITIONAL GROWTH BEHAVIOR t
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acr (b) DETECTED Figure 14.- "Leak before break" criteria for positive detection.
f MAT'L STRESS LIFE STRUCTURE ANALYSIS SATISFY EFFICIENCY? DAMAGE CLASS —INO • SAFE CRACK GROWTH • NO ai -STRENGTH 1, 2, 3 • YES •WEIGHT • DAMAGE CONTAIN.
' a f STRENGTH YES I INSPECT I IENVIRON.
OTHER I TRADE CONS.
Figure 15.- Fracture control analyses for design trade studies.
SURFACE INTERIOR CORNER FLAWS ORIGINATING AT HOLE Figure 16.- Representative flaw shapes found in service.
K I C at GL a3 I MUST BE DETECTABLE K I C a5 © I at 6L f FLAW SIZE ^ I > PECTA B LE I a2 I I I al ,r 1 INSPECTION SERVICE I NTERVAL(S) LI FE Figure 17.- Safe crack growth life requirements for class 1 structure.
I K I C at 6L a 4 MUST BE KIC a DETECTABLE at GL FLAW SIZE C E NONINSPECTABLE al SERVICE INSPECTION I NTERVAL LI FE TIME Figure 18.- Safe crack growth life requirements for class 3 structure (any member).
ONE INS PECTI ON INTERVAL -KIC KIC at 6L of of at 6L I ^^ / I ^P^ ^ PQi FLAW v^ Qk F FLAW SIZE ^4 SIZE 6 F2 0a `, a l a ONE MEMBER FAILS a l +Da MEMBER FAILS Aa al al I GF2 ' GF1 1 ONE SERVICE LIFETIME 6F1 " , INSPECTION INTERVAL TI ME TI ME (a) Requirement F. Class 3 inspectable. N Requirement G. Class 3 noninspectable.
Figure 19.- Safe life requirement for remaining structure after failure of single principal element.
E Q3 6 5 FAILURE IN 0 p N HOURS - 6j E Q5 0 °3 C D 2 t U C Q 6l A U `f a0 B N ( a 3 a 0 a l a 2 a4 A ^l 2 ^3 CRACK SIZE LI FE a (a) (b) Figure 20.- Illustration of inspection procedure based on safe crack growth analysis.
. 9U . 70 . 60 C .50 w .40 Q .30 U .10 120 160 180 200 220 240 260 280 0 20 40 60 80 100 140 CRACK GROWTH BLOCKS AFTER al = 0.050 in.
Figure 21.- Spectrum growth data. Fighter example. a l = 0.050 in.
1.1 1.0 . 90 b .80 0 7075-T6 SPECTRUM, TABLE IV GO . 70 o' SURFACE FLAW c 6 - 37 ksi .60 ca a _ .50 4Cr) CL w ° .40 0.7 U .30 v I NS PECTI I NTERVAL ONE LI FETI ME 0„ 20 40 60 80 00 CRACK GROWTH BLOCKS AFTER a2 = 0.150 in.
Figure 22.- Spectrum growth data. Fighter example. a 2 = 0.150 in.
1075-T6 K I c - 30 ksi - V/in.
SURFACE FLAW SPECTRUM, TABLE IV a - 37 ksi
40 "^f r
l\ .35 1 NS PECTI ON ' F a 1.336 INTERVAL .^ .30 .25 1.50 1.25a a .20 o 1.6a Y .15 a ^ MEMBER FAILURE 1.00 A 1.446 a = 1.2o F 0 10 20 30 40 50 60 70 80 90 100 CRACK GROWTH BLOCKS AFTER a 1 = 0.050 in.
Figure 23.- Spectrum growth data. Fighter example. Data from figure 21.
PLANE STRAIN TOUGHNESS, Klc Y d' O H U Q LL MATERIAL (b) MATERIAL (a) - -- z KISC W z w N -2 -1 3 iu W iu TIME TO FAILURE, hr (a) Schematic of sustained load flaw growth.
J W Z Q H N N PERCENI OF TIME Al LOAD (b) Schematic of sustained load spectrum.
Figure 24.- Sustained load growth and spectrum information requirements.
O i i t t / COMPACT DOUBLE SURFACE CENTER CRACKED TENSION CANT. BEAM FLAW SHEET FATIGUE CRACK • • • • GROWTH, da/dN PLANE STRAIN TOUGHNESS, Klc PLANE STRESS • TOUGHNESS, KC ENVIRONMENTAL CRACK • • GROWTH, da/dt FATIGUE GROWTH • • SPECTRUM EFFECTS Figure 25.- Material fracture properties required for analyses and trade studies.
N N L") CD CD CD COMPACT TENS I ON DATA CD -3 ^ TEST CONDITIONS: U 8 TEMP. = 75°F / ENVIR. =DRY AI ^ 6 f = 60 CPM z -a PREDICTED SURFACE FLAW RATES ( a 1 2c = 0 ) j i I i i j I j( 1 L 10 20 30 40 50 60 80 100 200 300 Z^K, in.
ksi - Figure 26.- Surface flaw data adjusted to a/2c = 0 and compared with compact tension data from reference 11.
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II w - II F-- w p Z p U b w N LLJ Q ::D ^z N f- b p N d w w e MATERIAL, 2024-T3 M=1 22.5 ksi 15 ksi n, 0 0 N=300 N TEST DATA (REF. 6) PREDICTED (AFFDL MODEL) (REF. 10) 0 50 100 150 200 250 300 350 400 X 103 N, CYCLES Figure 29.- Comparison of test and predicted crack growth. Single overload.
.25 PREDICTION PREDICTION AFFDL MODEL NO RETARDATION .20 TEST P1M16 (REF. 8) z w a ° 10 V Q t^0.30 U .05 MATERIAL, D6ac STEEL RANDOMIZED BLOCK LOADING (REFS. 8 and 10) 0 10 20 30 40 50 60 70 80 90 100 N, TEST BLOCKS Figure 30.- Comparison of test and predicted crack growth. Randomized block spectrum loading.
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pR,ECEDING PAGE BLANK NOT FILMED N-79 , THE INFLUENCE OF MODIFICATIONS OF A FATIGUE LOADING HISTORY PROGRAM ON FATIGUE LIFETIME By J. Brangex Eidgenossisches Flugzeugwerk Emmen, Switzerland SUMMARY Rectangular specimens of 7075 and 2014 aluminum alloys with two holes (stress concentration factor of 3.24) have been tested under axial fatigue loading on a six- rod test bed with modifications of the loading program, the surface particulars, and the frequency. The length of the precrack stage was investigated by use of a new crack detector.
In most cases the two alloys behaved similarly, with similar life to crack start under the same loading. Some overloads lengthened the life. Truncation by omission of the lowest peak loads should be limited to about 20 percent of the ultimate load.
Simplifying counting methods gave misleading results. Very thin surface layers of anodizing, protection by vinyl, dry nitrogen atmosphere, as well as stepwise reaming or grinding the surface of the holes, lengthened the life; thick anodized layers short- ened the life. Compressing the hole surface by rolling had no influence. Frequencies at about 210 to 240 cpm produced shorter lives than those at 40 cpm. At 5.4 cpm the life was considerably longer. A model to better understand the precrack-stage fatigue mechanism is discussed.
INTRODUCTION Fatigue test programs are usually designed to fit available test installations.
Since the capability of most test facilities is limited, such test programs have to be simplified. The genuine sequence of the loading occurring in real flight usually has to be neglected. The influence of this neglect and also the influence of blocking cycles on the result of a fatigue test cannot be calculated by present methods nor can it be estimated because of many gaps in the knowledge of the fatigue mechanism. The need to remove these restrictions by appropriate tests is obvious. Test series considering the effect of variation of one or two parameters can help to find explanations of the fatigue mechanism or can at least prove whether proposed theories are possible or not.
Figure 1 represents a survey of the investigation of the influence of program modifications on the fatigue life of light alloy specimens. This paper is especially dealing with the precrack stage of a specimen representing safe-life aircraft elements machined from bars and plates. Also, the crack-propagation life is considered to some extent.
Loading history which does not neglect the genuine sequence of the loads seems to be the only test approach to solve the problem. Moreover, since full loading history pro- grams take a long time to run, means to shorten them without influencing the life to fail- ure should be evaluated.
SYMBOLS chemical affinity A a index for arithmetical
index for probable, or for bending N
b C crack-stage length, C = F - P a l ,b l ,c 2 ,c 3 material, surroundings, and loading parameters c' quasi-cycle (asymmetric) D damage D' amount of damage produced by R', that is, by the effective amount of reaction per cycle D" amount of damage produced by R", that is, by the reaction of one half-cycle e eccentricity F life to failure (number of cycles, flights or periods) f function fi flight number fq flight number per period fs scatter factor, F50 P99.9 Hq number of quasi-cycles of one period intensity of incitation of chemical activity, I = f(v) • f(s) I index for number of cycle, flight or period i K1 stress concentration factors, calculated by RAS Data Sheets K2 L load Lq highest peak load in one period N number (of cycles, flights or periods) n number of specimen; index for nominal P life to the end of the precrack stage, that is, to crack start (number of cycles, flights or periods) p duration of reaction = persistence (time) q period, index for period reaction (chemical) R R' effective amount of reaction per cycle R" amount of reaction in one half-cycle S strain, range of strain ]1,2 n empirical standard deviation s = n 1 1 (log Ni - log N)2 s i=1 s for the number of periods up to failure s s for the number of periods up to the end of the precrack stage, that is, up s to crack start t time index for ultimate u v rate of straining, dS/dt y probability of survival z electrical resistance 0 lowest considered load step V rate of reaction (chemical), f (I • AA) a stress, load per unit of area cp function of ordinate values for the third asymptotic extremal distribution (Smirnow) P 11x 0 chemical resistance W frequency of cycles A bar over a symbol denotes a mean value.
MEANS AND METHODS The means and methods used by the Swiss Federal Aircraft Establishment (called F + W) for the investigation and evaluation of the influence of program modifications involve a six-rod test bed, a crack detector, test rods, fatigue loading history, and prob- able mean and scatter. For test specimens which are not too large, this problem can be investigated on the six-rod fatigue test bed (fig. 2), developed and built by F + W (ref. 1), because this facility is capable of simulating the genuine sequence of loads up to 8 tons for each specimen. A structural component of a shape commonly used in aircraft, already mentioned in reference 2, was chosen as the test specimen (fig. 3). It is a slightly eccentric, axially loaded, notched specimen of rectangular cross section. A better insight into the behaviour of fatigue is due to the crack detector (figs. 4 and 5), also developed by F + W and operational since 1969 (ref. 3).
Figure 6 defines fatigue loading history, that is, a loading in which all actual service loads essential for fatigue are applied in their genuine sequence, magnitude, and fre- quency, and only rest times and steady loads are omitted. Figure 7 presents the symbols and also explains how the results of the tests are evaluated. Since six test specimens, each with two identical notches, are run simultaneously, each run is giving the scatter of 12 precrack stages and the scatter of the crack-propagation life of the faster growing crack in each specimen. As Freudenthal (ref. 4) explained, it is the time to the first fail- ure which is important, especially for safe-life elements. Therefore, all the tests are evaluated in the manner presented in figure 7. The log-extremal paper was devised by Smirnow (ref. 5). Moreover, figure 7 defines the scatter factor.
The properties of the investigated 7075 and 2014 light alloys are presented in fig- ure 8. The 2014 alloy plate was delivered in the prestretched (2 percent) condition. The test specimens machined from this plate were fully heat treated after they were machined.
The main data of the loading programs are listed in table I.
The investigation has four main considerations: influence of omission of low loads and addition of overloads (group A), influence of different counting methods (group B), influence of surface particulars (group C), and influence of frequency (group D). A survey of the test-run numbers is given in figure 9.
INVESTIGATIONS Group A The aim of group A (fig. 10) is to disclose the influence of omitting the lowest load steps, as well as the influence of adding some overloads (fig. 11). The history program applied is the VENOM Program (ref. 6) consisting of 350 flights; the full program is called VENOM Program II. By omitting the smallest air and ground loads, program XIV was deduced from program II. In similar manner, programs XV (only the smallest air loads omitted) and XVI (only the smallest ground loads omitted) were deduced from pro- gram II. On the proposal of Hooke of ARL in Melbourne, program XVII was deduced from program XIV by omitting the next smallest air and ground loads, whereas program XVIII was deduced from program II by addition of some high peak loads exceeding the design limit load. At each fifth period an overload of 107.5 percent and at the tenth period one of 115 percent were applied. All these programs strictly observe the genuine load sequence in all 350 flights.
Figure 12 presents the results of the investigations of group A. The data are listed in tables II and III.
Group B There is still much speculation about the influence of different counting methods of the occurring fatigue loads on the fatigue life. Group B (fig. 13) is aiming to clear this.
Although programs V' and VI' are deduced directly from program II by counting the peaks between the mean level crossings (these are the +lg level for V' and the zero-g level for VI'), LBF at Darmstadt composed two new programs: program XX by counting program II with the "level crossing" method and program XXI with the "range pair" method defined by Schijve (ref. 7), both furthermore pooling positive and negative peak loads and grouping the same cycles within each flight into blocks. This is represented on the right side of fig- ure 13 by the hatching. The ground loads had to be presented separately.
More of the character of these program modifications is visible in figure 14. The differences from the basic program are evident.
Figure 15 and table IV present the results of group B, in which some comparative tests for specimens which were taken transversely from the plate were also included.
Group C On the basis of a hypothesis proposed by Schaub (ref. 8) in 1955, the investigation project was completed by considering the influence of surface particulars. Figure 16 and table V give a survey of this test series and the results. Anodic surface treatments are very widely applied where cladding is not possible. Their influence on fatigue is not suf- ficiently known. It was decided to test surface-layer thicknesses of about 20 μ and 6 μ for anodic oxidation in sulfuric acid and 3 to 4 μ for the anodic oxidation in chromic acid, known as the BF 4 procedure (a better defined version of Bengough). In most cases these treatments are applied before the holes are reamed; the same procedure was followed for these test specimens. It is of rather academic interest to hinder the chemical activity by a thin protective layer of vinyl as it is used to protect transistors or to lower the chemical affinity by an artificial atmosphere of commercially available dry nitrogen.
Similar to the tests of Schaub, test runs 69 and 71 were performed in such a man- ner that from time to time the holes 6.0 mm in diameter of the test rod were reamed or ground in steps of 0.1-mm diameter, up to five times, to a final diameter of 6.5 mm.
Although by this procedure the net area was reduced by 2.5 percent and the stress con- centration factor was increased from 3.24 to 3.30, the last crack started only at 115.2 peri- ods on the reamed specimen and at 195.8 periods on the ground specimen (compared with 40.1 periods for the last crack start of those specimens which were reamed only once to a diameter of 6.0 mm). Therefore, to find the reason for the end of the precrack stage, one needs to look only in the surface layer. This result confirms the findings of many authors. The very long life of the last three specimens after the last grinding is difficult to explain. Perhaps the workman did his job with extraordinary care because he knew what was expected and then produced a surface of higher quality than before.
No gain resulted from rolling the hole, notwithstanding the fact that it was made by a specialist.
Group D The frequency effect on the fatigue life is still debated. It is therefore necessary to investigate its influence. Figure 17 and table VI present the results.
On a chain test bed 36 test rods of the same design were fatigue loaded parallel and simultaneously with the full-scale fatigue tests of three VENOM aircraft. The loading program I differs from program II only by those orders which were needed for the full- scale test; the loads, their sequence, and their number were exactly the same as with pro- gram II on the six-rod test bed. Both test beds are in the same room. The only differ- ences were the frequency, 5.4 cpm (this test lasted
2 years'), and the shape of the cycles
(figo 18). As an intermediate frequency to 210 or 240 cpm, 40 cpm was selected because it can be run on the six-rod test bed and at the same strain rate as for 210 or 240 cpm.
For program II the increasing (56 and 340 percent) life with decreasing frequency from 240 cpm to 40 cpm and 5.4 cpm is remarkable. Another comparison test was run with program XX, once with 96 cpm and once with 173 cpm. The opposite behavior is noteworthy.
PRECRACK STAGE Student's test was used to determine the significance of the difference indicated in the tables by the ratio of the precrack-stage lives P 50 . The probability levels for the differences considered are listed in table VII. Levels of about 90 percent or higher indi- cate a significant difference; lower ones may indicate a trend, whereas very low levels indicate that the modification had no influence on the life. In some cases the actual thick- ness of the anodized layer must be taken into account and in some cases also the fact that the specimens were manufactured from different bars (as indicated by the test number).
Generally, table VII hints that the significance is higher for 2014 alloy. The reason is the higher loading relative to the ultimate load.
Influence of Alloy The test specimens of 7075 alloy, as well as those of 2014 alloy, were loaded to exactly the same absolute load values. Relative to the ultimate strength, the 2014 speci- mens were thus loaded about 33 percent higher than the 7075 specimens. Nevertheless, the fatigue life of 2014 is only 19 percent shorter than that of 7075 (table VIII). This result confirms the well-known fact that the fatigue strength of the different aluminum alloys is nearly independent of their static strength. By the way, a part of the difference may be contributed to the 7075 specimens being machined from bars 15 by 60 mm, whereas the 2014 specimens were cut in the longitudinal direction from plates 32 by 1220 by 2290 mm.
This also explains the slightly higher scatter for 2014.
Influence of Overloads As expected and as reported and explained by many authors for program loading, the overloads lengthened both stages (table II) but much more so with 2014. For this alloy the relative overload (relative to the ultimate strength) was much higher: The highest peak load applied (+6075 kp) is 53 percent of the nominal ultimate load for 7075 but 71 per- cent of that for 2014. Nevertheless, overloads should not be taken into account because not all service aircraft experience them.
Influence of Omitting Cycles With the Lowest Peak Loads For 7075 anodized to 20 μ the omission of the lowest and the next lowest peak loads (table III) has no significant influence on the life although the number of cycles is reduced by 81 percent. It seems that a favourable effect is abolished by another, unfavourable effect. In contrast, 2014 suffers a decrease in lifetime of 45 percent when the lowest peaks are truncated but has an increase of 63 percent when the next lowest peaks are also truncated. Relating programs XVII to )UV, this increase is as much as 195 percent. This increase of life may be explained by the truncation of the positive peaks at a relative level of 27.5 percent (relative to the ultimate load), whereas truncation at a level of 20.5 percent with 7075 has a slightly unfavourable effect. Taking into account the stress concentration factor of 3.24, the level of 27.5 percent is just at the nominal 0.2 yield strength of 2014, whereas the level of 20.5 percent is only at 77 percent of the nominal 0.2 yield strength of 7075. That is about the same for the lowest peak level omitted (program )UV) with 2014 (75 percent of 0.2 yield strength) where the effect is on the same side but faster. For these alloys, axial tension and compression, and a stress concentration factor of 3.24, the critical limit thus lies between 20.5 and 27.5 percent. Omitting loads smaller than this limit shortens the life, which seems to be very astonishing; whereas the omission of loads greater than this limit lengthens the life, as is expected. The strange shortening effect may be due to a recovery or a re-creation during the application of these lowest loads.
This very interesting effect will be discussed further, in connection with surface influences and frequency.
Before the crack detector type 02 was developed, tests were performed with the same specimen and 7075 anodized to only 6 μ. For the arithmetical mean of six specimens, the ratio of program )UV to II was 0.89 at failure. Later tests on 2014 at a higher relative load level had a similar, more pronounced trend. The influence of omitting some of the ground load cycles will be discussed subsequently.
Influence of Counting Methods The important decrease in the life by counting by the level-crossing method (pro- gram XX) has to be attributed mainly to the pooling of positive and negative peak loads into combined cycles. In the Swiss Review 1967 (ref. 1) a simplified test with the same 7075 specimen for the investigation of the pooling effect was reported. The pooled pro- gram (VIII) had a life ratio of 0.43 to that of the nonpooled program (XI), which is very near the ratios 0.34 for 7075 and 0.38 for 2014, when F 50 of program XX is compared with F 50 of program II.
The order-of-magnitude longer life with the program designed by the range-pair method (program XX) has to be attributed to the diminution of all positive peak loads, although such a big difference was not expected. It is noteworthy that both alloys behave nearly identically. Therefore, both counting methods have to be rejected. The same has to be said of the mean-crossing-peak counting method if this mean is zero (program VI') because this crude method omits too many cycles (fig. 14). The resulting increase of life was expected but perhaps not by this amount. About the same increase is valuable for the transversely machined 2014 specimens, as may be seen by comparing runs 100 and 97 in table IX. By putting the mean mainly at +1 of the air loads, only the ground loads are concerned. This will be discussed subsequently.
Influence of Surface Particulars The unfavourable effect of a thick 20-4 anodized surface layer, which is hard and cracks easily, thus forming stress raisers, is well known. The decrease of only 30 per- cent is even less than expected by many people. In contrast, the important favourable effect of a thin anodized layer was not expected, certainly not by this amount. It may be that these thin layers are so elastic that they do not crack and hence fulfill their protec- tive task. The influence of the thickness of the anodized layers was more important than had been expected. Therefore, measurements of the layer thickness of all test specimens were made after the tests. These measurements disclosed considerable differences in the nominal thickness. By this way, a part of the scatter was better explained. The only procedure which regularly gives the same thickness with a high reliability seems to be the BF 4 process.
The smaller favourable effect of the vinyl protection may be due to low porosity, which also explains the greater scatter. The fact that the life in a nitrogen atmosphere was only doubled (other authors reported much higher ratios) may be explained by the test conditions: Commercially available dry nitrogen was used, the specimen was not cooled down, and testing was at room temperature. But a very important fact has to be noted: By simple chemical means the crack stage, as well as the precrack stage, can be length- ened considerably although the mechanical fatigue strengthening of the specimen is strictly the same.
Removing about 0.05 mm of the surface layer, by reaming or grinding, confirms the work of Schaub and his collaborators. The removal was accomplished by the same man- ner in which the hole was machined at the beginning. To avoid the effect of a further fac- tor, the specimens were not electropolished. Although the crack detector was working perfectly, the removal procedure was made too late in some cases. Nevertheless, the increase of the life of the last four ground specimens is extraordinary.
In contrast, the test with the surface compressive treatment by a rolling procedure was disappointing. The main reason may be that the crack always starts at the edge of the hole because the special shape of the test rod has a slight eccentricity. This reveals the doubtful effect of treatments like this — doubtful because eccentricities are not com- pletely avoidable in actual designs.
Influence of Frequency Up to now there have been only a few reports on tests with increasing life at decreas- ing frequency. A note from Schutz related Weller's (Dresden) work, who reports (ref. 9) on both trends and who advocated in 1966 (ref. 10) that there must exist a frequency- dependent minimum of life with increasing life in both directions, that is, by decreasing the frequency and by increasing it from that minimum. Weller's assumption is obviously right, as will be discussed later.
There are three factors contributing to the frequency-dependent effect: 1. The genuine corrosion of unstrengthened aluminum alloys (in the present test series this influence may be neglected).
2. The strain rate, which in most cases increases with increasing frequency. Test runs 67/68/73 and 64, 57, and 55 (table VI and fig. 18) eliminate this factor because the strain rate is the same in all cases.
3. The proper frequency effect. This one is of special interest and must be dis- cussed in connection with other influences, for example, the influence of omitting cycles, counting methods, and surface particulars.
For test run A (program I, fig. 18) the strain rate was greatly reduced. This test reflects the influence of two factors, which may explain the very long life.
The opposite trend of test runs 57 and 55 is remarkable and may be attributed at first to the very different program and cycle shape. This difference seems to move the frequency of the minimum of life to about 100 cpm, whereas for the loading history pro- gram shape this minimum lies at about 200 to 250 cpm.
In 1956 Wade and Grootenhuis (ref. 11) found that the life still increases if the fre- quency is increasing from 24 Hz to 3835 Hz (1440 to 230 000 cpm). But Wood and Mason (ref. 12) reported in 1968 and 1969 that by increasing the frequency from 1700 cpm to the ultrasonic range of 17 000 Hz (1 million cpm), the life decreased considerably. Two new factors (resonance and concentration in a few localities) are responsible for this result.
Thus, after the minimum proposed by Weller, there is a maximum, detected by Wood and Mason, at about 5000 times higher frequencies, as presented in figure 19. This down- up-down configuration comes about by the effects of different factors which predominate in turn. This will be discussed by means of a model.
Influence of Compressive Loads In these tests compressive loads are applied by ground loads and negative air loads.
As the latter are very few compared with the ground loads, the findings reflect the impor- tance of the ground loads.
Table X reveals opposite behaviour of 2014 and 7075 alloys. Program XVI, which omits all small ground load alterations (5 percent of ultimate load for 7075, 7 percent for 2014), gives shorter lives than program II in all three 7075 comparison tests (21 to 16, 76 to 67/68, and 104 to 92). This result is in accordance with the similar findings for program XIV for 7075. But in the 2014 comparison test the life with program XVI was longer than that with program II (test runs 88 to 91), which is not in accordance with the result of program XIV but with the result of program XVII. From this it may be deduced that the limit for ground loads, the omission of which has a life-lengthening effect, lies between 5 and 7 percent of the ultimate load, whereas the same limit for tension loads lies between 20 and 27 percent (as discussed in the section on omitting cycles). This result underscores the importance of compressive loads. The same trend of different behaviour appears in program V'.
Material Flow Because of the integral design of modern wing skins, thick plates are needed which are machined as a whole. These plates are stretched to about 2 percent before machining.
This procedure outweighs the effect of rolling the plates in respect to fatigue loading his- tory, as can be seen in table IX. The time to failure is shorter only for the transverse- directed material with program V'. This result indicates a ground-load effect.
MODEL OF THE PRECRACK STAGE In 1955 Schaub (ref. 13) put forward the following hypothesis: There must be two conditions for the start of a fatigue crack. One consists of the well-known physical- mechanical alterations due to fatigue loading; the other consists of a chemical reaction with the surrounding medium, which is derived from observations made by Kramer, Pepperhoff, and Churchill (ref. 13). On the same occasion it was mentioned that Gough and Sopwith, Weibull, Freudenthal, and others had found an important influence of the sur- rounding medium in classical constant-amplitude tests. Therefore, the inclusion of a chemical reaction for the explanation of the fatigue mechanism seems to be a more prom- ising approach to clear the mystery of the precrack-stage fatigue mechanism than the physical-mechanical aspect alone. With the results of the tests on two aluminum alloys, this hypothesis may be refined by analysing a corresponding model of the first phase of fatigue damage, a scheme of which is presented in figure 20, and which may be called the "chemical phase."
1. Stress is inflicting strain (with all the well-known rules, especially important are those on the stress concentration factor and the residual stress originating from previous loadings (ref. 14)).
2. Strain, that is, the strain rate and the range of uninterrupted application of the variation of strain, is inciting chemical activity (apart from the well-known rules on the physical effects) between both mediums. By the way, steady strain is often the reason for stress corrosion, which should not be confused with the following description.
3. The intensity of incitation of this chemical activity, that is, the rate of reaction, is increasing with increasing strain rate and with increasing range.
4. This rate of reaction is more lively the better the affinity of these two mediums is and the lower the chemical resistance is.
5. The reaction may begin with a very short time delay after the inciting event but continues some time after it with decreasing intensity, like the persistence of a television screen.
6. The effect of this reaction is a new chemical product, most probably some com- position between the two mediums concerned, that is, in most cases an oxide of the metal, in other words, damage.
7. The very thin layer of the genuine product of their affinity, for example 4 to 9 ang- stroms (10- 10 m) of oxidation of aluminum alloys, does not hinder this activity if the incit- ing strain rate and range exceed a certain limit.
8. The (genuine) product produced at rest and the (artificial) product produced by strain rate and range are probably of the same nature, but the quantity of the latter is by far more rapidly increasing with continuing strain rate and range (called fatigue loading) than the former at rest.
9. Therefore, this accelerating (if not inciting at all) effect of the fatigue loading may be compared with the catalysis. Fatigue loading is, so to say, a dynamic catalyst.
10. This catalysis is producing an increasing thickness of the layer of the composi- tion, for example, of the oxide, as long as fatigue loading continues.
11. There is no reason for a decomposition at rest.
12. The rate of increase in thickness will decrease with increasing thickness, as this effect begins to hinder the activity because of its chemical resistance. The rate of damage increase is thus decreasing. This is very important because a slowly increasing amount of damage explains the big scatter in the precrack stage of fatigue life, as will be seen later.
After this first phase of fatigue damage, a second phase, still in the precrack stage probably follows, which may be imagined as follows: 13. The layer of the new composition, for example this oxide layer has a Young's modulus different from that of the underlying metal, also a different yield strength. It is probably more brittle.
14. If the thickness of the layer exceeds a certain limit (which itself depends on the three-axial stress state), this layer may crack under a tension strain or form flakes under a compressive strain.
15. Those parts of the underlying metal, which are set free by these incidents and which get direct contact with the other medium, for example, with the atmosphere, will again be chemically activated, and so on.
16. Finally, the surface may get an aspect like the one which Wood (refs. 15 and 16) saw by scanning electron microscopy and on which a fatigue crack is starting.
The second part of the precrack stage may therefore be called the flake phase and is schematically presented by figure 21. Both these phases, that is, the whole process, is in fact a corrosion by fatigue and may be called fatigue corrosion, in contrast to corrosion fatigue, where a relatively quick genuine corrosion exists (and thus facilitates the fatigue corrosion). This definition differs somewhat from that given by McAdam (ref. 17), whose process "differs only in degree from stressless corrosion, but does not imply ordinary fatigue."
Most of these explaining steps are more or less evident. Step 2 was supposed by Schaub (ref. 8) 16 years ago and then supported by others. Step 15 was mentioned in 1960 by Broom and Nicholson (ref. 18). They also assumed a relation between fatigue deforma- tion and hydrogen diffusion. Step 16 was detected only one and a half years ago by Wood (refs. 15 and 16) The increased oxide layer thickness (step 10) remains to be shown.
The most important supposition is step 5, the time-delaying activity, because by this persistence of a chemical process, the frequency influence may be explained as displayed in figure 20(g): By increasing the frequency, the reaction initially increases because of the not-yet-settled reaction of the preceding cycle; however, further increases in fre- quency decrease the relative damage per cycle. Obviously, together with step 3, the shape of the cycles (fig. 18) and their sequence are influencing the frequency at which the minimum life (fig. 19) is found; thus the seemingly opposite behaviour of programs II and XX is explained. Similar to figure 20(g) the omission of less effective, very low peaks (step 3) increases the value of the effective amount of reaction per cycle (and thus shortens the precrack life), whereas the crack-stage length increases by this same omission as expected (in table III compare test runs 74 with 73 and 86 with 91), thus supporting the hypothesis that the reason that the omission of the lowest peaks has a life-shortening effect originates entirely in the first damage phase.
Step 7 may explain the endurance limit to some extent. Finally, the larger scatter of the precrack stage may be explained by figure 20(h), as outlined in step 12.
The ultrasonic frequency range is not mentioned in this model because other factors are predominant and because frequencies higher than about 300 cpm do not occur in pri- mary aircraft structures. But the model should still be valuable for acoustic fatigue (most at about 200 000 cpm).
CRACK-PROPAGATION STAGE Because the crack-propagation stage is not the topic of this paper, only some unusual observations are mentioned.
1. The type F + W crack detectors can detect the crack depth as well as the fatigue crack surface before final failure. Figure 22 presents a fatigue failure surface and the corresponding record from the detector. The record is not a linear, but an exponential, function. Its character also depends on the shape of the specimen.
2. The crack stage is short, much shorter than often reported or assumed, when differentiated from the precrack stage.
3. The crack stage is, on the whole, of an astonishingly constant length (fig. 23), which was computed as outlined in the appendix by P. Gschwind.
4. Crack-stage lives decrease with decreasing probability of survival (i.e., longer life), for example, by some hardening effect. (See test runs presented in fig. 23(a).) A low frequency combined with a small strain rate showed a remarkably large effect (run A, fig. 18). Nitrogen atmosphere (72), high overloads (90), and low frequency (64) also had an effect.
5. Crack-stage lives increase with increasing precrack-stage lives, for example, by some weakening effect. (See test runs in fig. 23(c).) This result was most pronounced for run 100 (transverse, most simplified program).
6. Very short crack-stage lives were experienced with program XX.
C50 7. The computation of the relative crack-stage life, that is, 100, reveals F50 astonishingly high and consistent values of 10 to 30 percent.
8. As was shown in Stockholm (ref. 19), the fatigue-cracked surface, as recorded by the crack detectors, is increasing by a simple law and with a very low scatter, which can be seen in figure 24.
CUMULATIVE DAMAGE The different character of the damage cumulation of the three phases of the model is presented in figure 25. The poor correlation of actual life until crack start with simple linear cumulative damage hypothesis originates mainly from the first phase, which reveals the influence of load sequence, cycle shape, and frequency. The proposed model is still a simplification and needs many tests to find quantitative coefficients, but it is hoped that the model helps for a better approach to the problem.
CONCLUSIONS Up to now results from the test project permit the following conclusions: 1. There is no important difference in time to crack start between these two alloys (2014 and 7075) if loaded to identical values. This result confirms earlier findings.
2. Overloads have a favourable effect. This result is also in agreement with find- ings of earlier and less sophisticated tests. This should, nevertheless, not be considered for calculations of time to failure.
3. Omission of low peaks does not affect the time to failure of tests if this omission concerns peaks lower than about 20 percent of the ultimate load at tension and 5 percent at compression.
4. Counting load occurrences by the so-called peak between +lg mean-crossing method, peak between zero-g mean-crossing method, level-crossing and range-pair methods (both combined with pooling and blocking) is giving misleading results and must be rejected.
5. While thick ( -20 μ) sulfuric anodized surface layers have an unfavourable effect on the lifetime, the contrary is true for thin (-6 p) layers or BF 4 treated elements, which lengthen the life.
6. Stepwise reaming or grinding of holes can lengthen the life considerably, which may be useful for maintenance people; whereas rolling of hole surfaces alone has no effect.
7. There is a definite frequency effect with a minimum and a maximum.
8. There is a strain-rate effect — decreasing rate giving increasing life.
9. A model, assuming a catalytic effect of fatigue loading on the chemical activity of the surface, with a persistence of this activity, is presented, which could explain the influ- ences of frequency, strain rate, and load sequence, as well as the trend of decreasing life by omission of the lowest (and most numerous) peaks. The model also reveals an impor- tant reason for the scatter in the precrack stage.
10. The crack stage, now easier to observe by a new crack detector, is (for machined specimens) short — much shorter than often reported. It is, on the whole, of an astonish- ingly constant length, with a lower scatter than the precrack stage, which also diminishes the scatter of the life to final fatigue failure.
ACKNOWLEDGMENTS Many thanks are extended to the collaborators for their help: Mr. P. Gschwind for the mathematical part, Mr. E. Eberle for evaluation and figures, Miss L. Meierhans for typewriting, Mr. L. Richiger for tables, and Mr. K. Steiner and his team for the editing of this report, also many thanks to Mr. E. Kindlimann (hydraulics) and Mr. H. Widmer (electronics) and their teams for keeping the test beds and recorders running day and night.
This paper is published with the permission of G.R.D. (Armament, Technology and Procurement Group of E.M.D.), Berne, Switzerland.
APPENDIX
APPENDIX COMPUTATION OF THE MEAN CRACK-STAGE LIFE By P. Gschwind Let P(y) be the most probable line of precrack-stage life on log-extremal paper and F(y) be the most probable line of fatigue failure, both functions of life expectancy y.
The mean crack-stage life must be computed, (1) C (y) = F'(y) - P (y) On log-extremal paper (u,Y) a straight line is defined by two constants Y=a2u+al and u= -al)
a2(Y
For F and P, then = 1 F (Y - a1F) u F a2 \ and up =1P CY - a1P) a2 Because u is the common logarithm of F and P, 1F(Y-a1F) a F=10 2 (2) 1P(Y-a1P) a P = 10 2
APPENDIX — Concluded
APPENDIX — Concluded Otherwise on log-extremal paper, -eY y=e or Y = log(-log y) (3) Introducing equation (3) into equations (2) and (1) yields 1F og(-log L[og(-log Y)-alp] Y)-a1F] C - 10a2 C (Y) = 10 a2 The constants a l F , a2 F , a l p , and a2 are to be calculated with the least-square method from experimental data.
REFERENCES 1. Branger, J.: Swiss Review 1965 - 1967. ICAF Doc. 412, Minutes of the Tenth ICAF Conference, J. Y. Mann, ed., 1967.
2. Branger, J.: Swiss Review 1961 - 1963. ICAF Doc. 271, Minutes of the Eighth ICAF Conference, V. Villa, ed., 1963.
3. Branger, J.: Life Estimation and Predicting of Fighter Aircraft. Proc. Int. Conf. on Structural Safety and Reliability, A. M. Freudenthal, ed., 1969.
4. Freudenthal, A. M.: Reliability Analysis Based on Time to the First Failure. Proc.
of Fifth ICAF Symposium, J. Y. Mann and I. S. Milligan, eds., Pergamon, 1967.
5. Smirnow, N. W.; et al.: Mathematische Statistik in der Technik. VEB Deutscher Verlag der Wissenschaften, 1963.
6. Branger, J.: The VENOM Program, F + W 5-197 (not yet published).
7. Schijve, J.: The Analysis of Random Load-Time Histories With Relation to Fatigue Tests and Life Calculations. Fatigue of Aircraft Structures, W. Barrois and E. L.
Ripley, eds., Macmillan Co., 1963, pp. 115-149.
8. Schaub, C.; and Liedtke, W.: Der Mechanismus des Dauerbruchs metallischer Werkstoffe. Colloquium on Fatigue, W. Weibull and F. K. G. Odquist, eds., Springer, 1956.
9. Weller, J.: Die Bedeutung der Lastspielfrequenz beim Dauer schwingversuch metallischer Proben a.s.o. in Neue Hutte, 6. Jg., Dez. 1961.
10. Weller, J.: Kritischer Vergleich einer Auswahl von Aluminium- Konstruktionswerkstoffen a.s.o. in IfL-Mitt. 5, Heft 12, 1966.
11. Wade, A. R.; and Grootenhuis, P.: Very High-Speed Fatigue Testing. International Conference on Fatigue of Metals, I. Mech. Eng., 1956.
12. Wood, W. A.; and Mason, W. P.: Fatigue Mechanism in Iron at Ultrasonic Frequency.
J. Appl. Phys., Oct. 1969.
13. Lissner, O.: Einige Versuche uber die Vorgange in der Oberflachenschicht von Ermudungsproben. Colloquium on Fatigue, W. Weibull and F. K. G. Odquist, eds., Springer, 1956.
14. Haibach, E.; Schutz, D.; and Svenson, O.: Forschungsbericht FB 78/68 des LBF.
ICAF Doc. 508, 1969.
15. Wood, W. A.: Fatigue Crack Initiation as Viewed by Scanning Electron Microscopy.
Technical Report No. 1, George Washington Univ., Jan. 1970.
16. Wood, W. A.: Elastic Fatigue in Titanium Studied by Scanning Electron Microscopy.
Technical Report No. 2, George Washington Univ., Apr. 1970.
17. McAdam, D. J.: The Influence of Stress Range and Cycle Frequency on Corrosion.
Proc. ASTM 30 (1930), Part 2, pp. 411-447.
18. Broom, T.; and Nicholson, A.: Atmospheric Corrosion-Fatigue of Age-Hardened Aluminium Alloys. Journal of the Institute of Metals, vol. 89, 1960.
19. Branger, J.; and Ronay, M.: High Strength Steels Under Fatigue History Loading.
ICAF Doc. No. 499, Proc. of the Technical Session of the 11th ICAF Meeting, G. Wallgren and S. Eggwertz, eds., 1969.
TABLE 1.- DATA OF LOADING PROGRAMS C yc l es Hq in Highest peak l oads Lq one period q Pro gram in one period q, kp of 350 flights I----- Air Ground Total Positive Negative I I 20033 18515 38548 5265 -1600 V' 19553 350 19903 5265 -1600 V I I 350 988 5265 -1600 XIV 9180 3405 12585 5265 -1600 XV 9180 18515 27695 5265 -1600 XVI 20033 3405 23438 5265 -1600 XV I I 6499 835 7334 5265 - 16 00 XV I I I 20033 1 8515 38548 6075 -1600 XX 10150 5010 -1580 XXI 10150 4800 -1580 These data are valuable for both alloys investigated , also for all surface particulars and for all frequencies. All tests were run with the test rod (fig. 4) and all in the same test room at a room temperature of 15 to 20 C.
<:.n o <:.n UI o m T ABLE II. - OVERLOAD ------ Alloy 7075; 240 cpm Alloy 2014; no anodic treatme nt; 210 cpm C Anodic P C sp Test s F sF sp F50 P50 FSO Test 50 50 50 Pro gram treat. , run run J-L 0. 0699 0.0939 6.3 37.1 30.8 16.5 XV I I I 4l.6 53.1 11. 5 0.1015 0.0673 90 73 . 040 8 .0550 4.9 32.8 27.9 20.3 I I 30.4 38.3 7.9 .0774 .0576 91 1. 71 1. 71 1. 28 1. 13 T. 10 XV I I I 1. 37 1. 38 l.46 1. 31 1. 17 I I TABL E Ill. - TRUNCATION All oy 707 5; 240 cpm All oy 201 4; no anodic treatment; 210 cpm Ano di c Test Test
Prog ram r
sp sp
tso f50 P"so (5 0 sF
s F '\0 run run 50 treat . , /l ..::..
67/ 32 . 9 26.2 23.7 I I 30 . 4 38.3 7.9 0.0774 0. 0576 91 0.0630 0. 0882 6.7 .0939 4.9 20. 3 I I 73 .0408
32.8 I 27. 9
7( XIV 16 .8 2 5.9 9. 1 . 1 44 8 . 11 07 86 .0999 .1249 8.2 34 . 3 26. 1 20.5 19. 7 X V 23 .8 35 .1 11. 4 .0 7 53 .0 900 87 75 .1103 .1362 9.3 32.2 22. 9 X VII 49 . 7 12 . 1 .0823 .06 06 89 79 .0628 . 1 020 7.0 3 1. 3 24.3 24 61. 8 R atios : 74 /7 3 86 /91 0. 55 0. 68 1 .15 l. 87 1. 92 2.45 1. 33 1. 67 1. 05 0.94 1. 05 1.00 1. 16 1. 04 .95 .93 79 / 89 / 91 1 .63 1. 61 1 . 53 1. 06 67 t6 8 1 . 82 .85 .9 1 . 93 79 /7 4 89/86 2. 95 2. 38 1.33 . 57 . 55 .63 1. 45 1. 90 .9 8 . 82 75/73 87/ 91 . 78 . 92 1.45 . 97 1. 56 2.70 1. 09 1. 13 . 94 .8 8 75/74 87 /8 6 1. 42 1.35 1. 25 . 52 .81 1. 1 0 F 86 .2 5.2 I I 16 0.0452 = a 7 6.8 7. 7 X IV 20 .0602 97.3 7. 9 XV 19 .1064 Ra ti os: 1.77 1. 27 19/20 1. 33 .89 20/ 16 ~~ ~ ~- - c:Jl o ~ CJl o <Xl TABLE IV.- COUNTING METHODS Alloy 2014; no "modic treatment; 210 cpm Alloy 7075 Test Test Anodic Program Freq., run run treat. , sp sF E50 1\0 P50 (50 sp F\O F50 sF cpm fJ.
67/ 0.0630 0.0882 6.7 32.9 26.2 240 23.7 I I 30.4 38.3 7.9 0.0774 91 0.0576 96 .0629 .0880 6.8 35.9 29.1 210 22.8 V' 54.4 64.7 10 .3 .1347 .1265 101 V I II I 1.00 1. 00 1.02 1.09 1.1 1 1. 79 1.69 1. 30 1. 74 2.20 0.0825 0.0688 13.8 210 92 81.9 68.1 5.5 I I VI I 102 .0561 .0716 1 9.2 ~22.0 102.8' 210 3.3 74.8 93.4 18.6 0.1208 0.1078 99 1 03 .0952 .0965 12.3 83.0 70.7 210 5 V' VI I II I 0.68 l. 04 1. 39 1. 49 1. 51 2.44 1.56 2.46 2.35 1. 87 .59 .74 1.5 6 1. 47 V I I /V ' l.45 1. 37 1.44 1.81 .90 .85 Alloy 7075 Alloy 2014 ; no anodic treatment; 96 cpm 54/ 0.0478 0.0547 7.9 46.5 38.7 240 I I 21.6 see above .0445 .0893 3.5 15.8 12 .3 21.2 55 96 XX 10.2 1 4.5 4.3 0.1 1 02 0.1034 93 . . 1 490 84 .0709 .0 813 12.0 121.0 109.0 96 25.5 XXI 25.5 143.0 17 .5 . 13 03 94 0.93 0.44 l. 63 .0.34 0.32 t.X/ I I 0 .34 0.38 0.54 1.42 1.80 1.46 l. 12 2. 18 3.70 4.0 XXIIII 4. 15 3.73 2.19 1.93 2.26 I 1. 57 .69 5.0 10.9 12.5 XXI/XX 12 . 2 9 .8 4 .1 1. 36 1. 26 -- I TABLE V.- SURFACE Alloy 2014; program II; 210 cpm Alloy 7075; program II; 210 to 240 cpm Surface Test particulars
run e r r G Test run
sp sF P50 P"50 sp sF 50 50 50 50 .- No treatment 30.4 67/68 0.0478 0.0737 8.0 45.6 37.6 38.3 7.9 0.0774 0.0576 91
.. CD
Std. atm.
@.
73 0.0408 0.0939 4.9 32.8 27..9 20.3,u 67/68 .0630 .0 882 6.7 32.9 26.2 23.7 f'
@
CD
92 0.0825 0.0688 13 .8 8l.9 68.1 35.3 44.7 9.4 0.1513 0.1201 98 Anodic BF4 5 .5f' 3'0f« 70 0.0779 0.1023 10.6 64. 1 53.4 Vlny1 No treatment 72 0.0516 0.0716 15 .3 92.7 77 .4 105
CD
Nitrogen Ratios: 0.85 1. 27 0.6 1 0.72 0.74
~ /
l. 32 l. 20 .84 .72 .70 2b /
ffi
l. 73 .94 l. 73 l.80 l.81 1.1 6 2.08
Q) / l.17 l.19 l. 95
CD
1. 63 1. 39 l. 33 1. 41 1.42
0 /
CD
l.08 .97 l. 91 2.0J 2.06
@ /
CD
No anodic
®
80 0.0760 0.0641 7.5 44.5 37.0 Rolled surface l. 59 0.87 0.94 0.96 0.98
@ / G)
- ------ CJ1 o to ~ o TABLE~.- FREQUENCY Alloy 7075 Alloy 2014 ; no anodic tr ea tment Pro g ram - - - - Frequ e ncy, -
Test -
Anodic C P C Test run cpm s p SF sp F50 P50 F50 run SF treat. , 50 50 50 J.l
I
-I I II I i 67/ I I 22 .0 68/ 0. 04 87 1 0 . 0728 5 . 5 32.7 27 . 2 240 210 30 .4 7.9 0.077 4 38 .3 0 . 0576 91 , I I I I
21 . 2 1 07 (3 j
64 0.0484 0.0724 8.0 50 . 5 42. 4 40 40 rods A r I I 19 .7 30 . 0
0.0286 I 0.0630 150. 0 120.0 Ni trogen I
5.4 40 atm I J ( 107.3 r j I 40 / I 40 / l. 00 I 1.00 l.46 1. 55 1. 56 I 5.4 / .59 .86 5.5 4.6 4.4 40N / I Pro gram XX Freq. , cpm 57 21. 7 0.0693 0 . 0671 3.7 1 8.2 14.5 173 55 21 . 2 .0 445 .0893 3. 5 15.8 1 2.3 96 0.64 1. 33 0.95 0.87 0.85 96 1 1 73 j TABLE VII.- STUDENT'S SIGNIFICANCE TEST Test run considered }
CD
Actual thickness of anodized layer in jJ.
Test run compared with
CD
Probability level for the difference
G)
..... Analogous relation for 2014 and 7075 alloy and same trend " )I( Analogous relation for 2014 and 7075 and opposite trend
CD CD
CD CD CD CD
No. No. % N o.
jJ. jJ. No . % jJ. jJ.
67/68 no 91 no 89 67/68 no 67/68 23 .7 99 86 no 91 no 99 74 20.5 73 20.3 26 87 no 91 no 99 75 19. 7 73 20 . 3 " 67/68 88 no 91 no 98 76 22.5 23.7 60 104 7.5 92 5. 5
> 99
89 no 91 no 99 ) 79 24 . 0 67/68 23 .7 75 ...
90 no 91 no 99 77 16 . 5 73 20 . 3 51 93 no 91 no ) 99 ~ 55 21.2 54/56 21.6 »99 ... ~
94 no 91 no » 99 84 25.5
67/68 23.7 »99 91 no 96 97 no BF4 91 no ~ 98 85 67 / 68 no 92 5. 5 no 91 -4 99 no 99 102 3.3
92 5.5 > 99
...
100 no 97 no )99 1 01 no 91 no )99 103 5.0 92 5.5 40 ...
96 22 .8 67 / 68 23 . 7 49 105 N2 ...
91 no 72 N2 67/68 no 99 106 Vinyl 91 no 70 Vinyl 67/68 no 97 ...
no 91 no 64 21 .2 , 73 20 . 3 99 95 no 101 no )99 55 21.2 57 21.7 65 100 no 99 no 20 80 roll. 67/68 no 10
99 no 101 no 92 1 02 3.3 > 99
103 5 .0 ~ ) 99 100 no 95 no 87 no 86 no 98 75 19.7 74 20.5 85 , ' 86 )1-99 89 no no 79 24.0 74 20.5 90.5 <:.TI ......
t-.:) T ABLE VIII. - ALLOY Test Surface P50 F50 1[ 50 sp Alloy sF Pro gram Frequency , cpm run treatment 67/ 7075 None I I 240 37.6 45.6 8.0 0.0737 0.0478 91 2014 None I I 210 30.4 38.3 7.9 .0774 .0576 Ratio
-- .......... 0.81 0.84 0.99 1.05 1 20
1 .
TABLE IX.- MATERIAL FLOW -
-
Test -
Flow I Surface Fr eq ue ncy, P e sp F5 0 s F
so run Alloy Program
direction
I treatment cpm
I
i
I
Long. I I None 91 2014 2 10 30.4 38.3 7.9 0.0774 0.OS76 I
I
97 2 014 Trans. I I None 210 36 . 7 42.5 5.8 .0705
j .0514 I
"- I Transverse / L ongit udin al . . . . . . . . . . . . . . . . . . . .
1. 20 1 . 1 1 0. 73 0.91 0.89 V' ') 4.4 101 20 14 Long. 210 1. 347 0. 1 265
None 64 . 7 1 : 0.3
I
I I
V' None 9b (0 14 Trans . 2 10 3').0 .1473 . 1283 ,
38 . 1 i 3.1
j
I !
..
Tr ansverse / Lon git udinal ...................................... 0 . 64 59 0.30 1.09 1. 01
0. 1
- --- ~.
VI' 99 20 14 Long. None 2 10 74.8 93.4 T 18.6 0.1208 0.1078 V[ , 2014 _ Trans.
100 None 210 72 . 1 .0729 .0869
87. 4 ~ . 15. J
I
d
Transverse / Longitudinal . . . . . . . . . . . . . . . . . . . . 0.96 0.94 0.82 0.60 0.81 ~'-- .. - .-- -- - -- Ratio 100/ 97. . . . . . . . . . . . . . . . . . . . . . . . . . .
1.97 2.06 2. 64 1.03 1. 69 100/ 95 ............... ... .........
.50 .68 2.06 2.30 4.94 - ~ -- -
-
c:.n I-' v.:l CJ1 ~ ~ TABLE X .- GROUND LOADS Alloy 7075 Alloy 2014 ; no an odic t r eatme nt Pro gr a m ,tst
- - -
Anodic - - -
run P sp C Test run C C' tr ea t. ,· F50 P50 F50 sp s F 5 50 s F J.L 67/ 23.7 0.0882 0.0630 6. 7 32.9 26.2 I I 30.4 38.3 7.9 0.077.4 0.0576 91 . 0407 .0729 6 .2 27 . 0 20 . 7 XV 1 43.6 76 22 . 5 52.2 8.6 . 1367 .1085 88 54·4 64.7 10.3 .1265 . 0880 29.1 V' .1347 96 22.8 .0629 6. 8 35.9 101 0. 79 0. 83 0.93 0. 32 0.79 XV I II I 1.43 1. 36 1.09 1.77 1.88 V I II I 1. 00 1. 01 1. 02 1. 09 1.11 1.79 1.69 1.30 1. 74 2.20 Anodic Alloy 7075 Test tr ea t. , 7075: Fa SF run J.L 92 5. 2- 5.5 0.0825 0. 06 88 13 .3 81. 9 68.1 II 86.2 0.0452 '6 7.5 .0902 . 11 4 8.0 56.6 48.6 5.3 XV I 66 . 5 .07.80 5.0 .0952 .0965 12.3 83 . 0 70.7 V' 1.09 1. 62 0.58 0. 69 0. 71 XVI/II 0. 77 1. 73 1.15 1. 40 .89 1 .01 1.04 V' II I Survey of the Investigation of the Influence of Program Modifications on the Fatigue Life of Light Alloy Specimens Sheet Rod, Boom Plate j s Light Alloy Element or ~/VT~ r
~ ~ ~ •
Component
~
lJ U tJ
Crack Propagation slow fast very fast safe Life Fatigue Behaviour Fail safe safe Life Field of this Precrack Stage Report
I I
!
Crack Propagation Life
I I
Life to Fai lure --- Figure 1 C}1 I-" C}1 C)1 ~ m Six-Rod Fatigue Test Bed (F+W) • For axial loads on 6 rods, tension and compression, up to 8 tons for each rod .
• Frequency 1 to 240 cpm • Genuine sequence of loads • 127 Load levels available • Fully automatic electronic control, up to 120000 orders in an unique and uninterrupted sequence .
Figure 2
"ICAF"- Test Rod for Light alloys
O'n = L L
·- +- 1 - t jJ ) t ~
10(25-6) = 190 kp/mm
e=0,8 reamed after anodic surface / treatment (if any was appli~d) K2 KI
len
~
a.
0.
l eT :J
51 1 :$ C=f
I I I , ,I B
B
A I I
B-B
A-A
KI = 3.24
~ ~ = 0.48 ,if elastic
K2 = 0. 95
d~formation by calculated by bending is neglected RAS Data Sheets (universal suspension)
1 Loading L t
Figure 3 C)l I-' -1 c.n .....
CP Eddycurrent Crack Detector Type 02 (F+W) • For non - ferromagnetic alloys • For holes 4 to 50 mm diameter I) and flat - surfaces I) • 5 to 1 Volt output per 0.1 mm crack depth • Range up to 50 Volts • Indication independent of scratches or undulations up to 0.5 mm or of conical holes up to 50 Figure 4 test run No.90
Story of 12 Holes In 6 Rods
Crack
program XVIII/100/5265
automatically recorded by the Crack Detector Type 02 crack I
rod No . hole start failur~ No. of periods 40 50 periods 0 10 20 30 60 E-144 0
- -
~ E-144 u 34,4 47,821
--
51,4 61,406
/ l E-143 0
f-- E-143 56,4 u
- -
I I : I ~
1. 52,406
E-142 0 43,4 " life to Failure F ./' "~ Fatigue ~ / ICrack E-142 u 44,4
-
- f-......:T Len th
Precrack Stage P C h' 11 at g
Crack Stage C ~ 1 / 1 Failure
E-141 0 43,4 54,406 ...crack ~ ~ ~ Failure E- 141 u 45,8
-
E-140 0 37,4
~1 o
36,4 45,839 ~ E-140 u E-139 0 27,4
-
_ Y1I O I
27,4 38,406 E-139 u
I
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- --
q ( Hq I fq I Tq I Lq )
• --
Fatigue Loading History
c' quasi - cycle l:l. lowest considered load step f flight type q period I consisting of the unique sequence of aU flights Hq Number of quasi - cycles of a period fq Number of flight types of a period (different or uniform) Tq Number of the simulated service flight hours in one pe'riod Lq highest peak load in one period Figu re 6
Symbols sand N
probability n :: number of holes (two per specimen) P(l-'+"')'100 Log - Extremal Paper N :: Number of periods q (350 flights p~r p~riod) -7 + 1 999 P C F s :: empirical standard deviation :: p
-6 + 1 • I : I 9(g [\ i
~ ] 1/2
n~l ~ (tog Ni -log Nb) 2
[
Na:: arithmetical mean::
-5 + 1 99 1 1 i 1 \'\~
-4 i-n )
~ ~Ni
-3 (
I ' r
I Test run ®
Nb = 0 = probable mean:: -2
\.\
line of least squares at 50 % probability of survival 80 I I -t I.
I I.
I ' -1 I F50
P = crack start (N)
J 1---
F = Failure (N)
50 t
'1
o
P50 I
C:: F - P = Crack stage
\
I P50 = probable mean of crack start } - - - I I
- . C50 = F50 - P5Q
I
F50 = probable mean of faIlure
0, ~ 2 ~ 1 b 1 2 '. 5 1 0 2
fs = scatter factor = F50 I I I ~ y P99 .9 N periods q tabled by Smirnow Fi gu re 7 c.n 1:\:1 ......
t,]l I:\:) I:\:) Bar ) Plate ) ( ( Investigated Alloy Types
7075 15x60mm 2014 32x 1220x 2290mm
Spec , Spec.
actual actual Unit (nominal) (nominal)
0.2 yield strength kplmm2 52 56 40 48
tensile strength kp/mm2
60 62,5 45 52
long. 9900
Ultimate Load of test rod 11400 12000 8500
kp transl0000 Ti
Composition Cu Zn Mg Mn Cr Fe Si
A
1 Spec . 1 0 - 2,5 5,5-7,0 2,0-3,0 0,2-1,0 I 0,1-0,4 I 0,6 0,6 0,3 rest
7075 r t I 0,3 0,15 0,2 0,2 <0,05 rest 1,6 ac ua 6,3 2,3 Spec . 0,2-0,8 0,4-1,2 I <0,1 I <0,5 I 0,5-1,2 I <0,2 rest 3,9-4,8 <0,25 2014 r actual 4,7 <0,1 0,6 0,95 0,07 0,5 0,9 0,04 rest kP/mm't Stress ~ constant universal suspension •• of test rod wi th eccentricity e unloaded
· 71//1
so loaded
;;:;;:;?
..
deformation of ~ 12000 eccentric rod, " ..,./" -' lO e'= actual ( 7075) , ~~ ' , reducing e to e' ,. , ~ . '>;. . e= 0 ~ .". - ,.
lA f'4 (2014) height /length "' <q, "<q, q.
' ~ J ~ '~ s~ .~ '~ .~ .~ Load Kp Scale 2 1 Figu re 8 Survey of the Jnvestigation - Project: Test run No.
Fre- alloy 7075 quen- trans .
cy flow longitudinal longitudinal ground lrotled BF4
no I N 2 t lVinyl no ~ N2 IVi nyl reamed no
xvm 77 1
210 ~ II 73- , 92 t 69
71 '1 80
67J58t72 i70 i 98 91 105 106 97
- XIV 74 --.., f-- -+ to L XV 75 j f' I- -~ -
-
XVI 76 104 '-
xvn 79 89
, - -1- I-
101 95
V' 96 103 f- -- f-
1 -=-
VI' 102 99 --- XX 173 - - - 96 XX 1 55 93 96 XXI 84 94 -
40 II 64 107
--- 5,4 I A
- --,- -- '-
20.522.723.720.3 '
•
II 54 ~ S6 , ~ 7~ : 73
'--- .
Figure 9 CJ1 t-:) c..J C]1 t-:) ~ up load
History Load Spectra Group A
down load --------
this I ·w· .;:: 1 omitted is program XIV and XV
of one ' period q this ~ omitted is program XIV and XVI of Venom program II this r:;ti8SI%J omitted is program. XVII (200 hours, 350 flights) this f ::::::::::: :::: ::::::: J added is program XVIII 1015 2014 ing
loa4 ! kp 1.'.C 1
u
"nno ~10
f »';;';;';;>4'7»~<b»( /,/, // A~r'" - - '/" - 4/ 1 , iN iN i i d~ --1-- -+- 1 4000 30 ,40
v ~
-1 1/ '-r - • --- - ~
I "''''_ '' _ '_~ J __ ~ ___ • ..J 1000 I 10
+ I" " I' " I II ' '''A , ! I,!", 0 0
o
--7- T r r 7 - r 'T" T7 J .... -r~p..- r 7-r-r
-t- ;: I I 100J 10
of ,quasi - cycles ~ c' 3 4 0,01 0,1 10 10 Figure 10
Program - Modification Group A
Program I No. of cycles per q
actual flight No. 9 Schematic presentation No . in air Ion XVIII 20033 18515 II 20033 18515 XIV 9180 3405 XVII 6499 835 XVI 20033 3405 XV 9180 18515 Figure 11 C}l t-.:) C}l CJ1 ~ O'l
Influence of Modifications A on the Fatigue Life
Schemes of Lo~d Spectra No. of cycles Hq in one period q 38548 q XVIII .
N frequency 210 to 240 cpm 38548 II crack
?
propaga ti on
~ 91
12585 XIV 74
~
~ e50 XVII 79
[>
23438 XVI ~ L;
•
27695 XV 75 Figure 12
Load Spectra Group B
for one period q derivations from Venom program II : L __ ] basic Venom program II -- up load c=J program XX : level crossing method -- --- down load positive and negative peaks pooled t::. '- J this omitted is program V' r-; ...... 'J program XXI : range pair method only peaks between + 19 - cross i ngs counted positive and negative peaks pooled lV Ji.:Zi? il this omitted is program VI'
[ .. -:=~ ground loads in program XX and XXI
only peaks between zero - crossings counted 2 3 2 3 10 10 10 10 10 10 10 0,1 Number of quasi - cycles --. c' Number of quasi - cycles --. c' Figu re 13 c.n ~ -:J c.n t-:> co
Program - Modification Group 8
Program No of cycles per q Actual program No . in air Ion ground f9 basic program II reduced to the following 18515 20033 count methods= f lO ~
-
mean - crossing peak, V' 19553 350 mean = + 19 air f ll mean -crossing peak, VI' 638 350 mean = 0 g level
~I '
level crossing
xx
10150 (pooled blocks per flight) o range pair XXI 10150 (pooled blocks per flight) Figu re 14
Influence of Modifications B on the Fatigue Life
. ~ of loed ~etra n N
~~ 111903, 'f
I VI'
-
10150
, xx , :~ ,_ 212"
10150 (XXII::
~
Figure 15 CJ1 ~ ~ tJl W
Group C: Influence of surface particulars
Loading : program 11 (highest peak load 5265 kp Test I Surface Frequency : 210 to 240 cpm
\AllOY I
treatment type Number of periods at crack start and failure 0 100 1 Std Atm none none Std Atm Std Atm anod.
92 Std Atm anod.
98 Std Atm BF4 3 ~ Na Vinvl 70 Std Atm
80 I Sid Aim
UI nun: tJ 0
I
I I
-
! St~p of 0,1 mm on tJ
I I hole ~ 6 7075 ~~~~~ "'-. '\1 69 I Std Atm
I reamed in steps
_~ijy//ff hl ' j1:~ 'i'/PhJ':;;'
Ni
~~ &
---
I hol~ 4 7075
." I Std Atm ground I n steps F igu re 16
Group D: Influence of the Load Frequency
on the Fatigue Life
Test Number of periods at crack Alloy Surface prg. Frequency run start and failure type treatmt . No . c pm No.
150 200
7075 II 67/68/73 240
22 . 0J.l
7075 II 64 40
21.1 J.I
7075 I A 5,4
19.7J.1
7075 XX 57 173
21.7J.1
7075 XX
21.2J.1 55 96
2014 none 11 91 210
2014 none II 107 40
2014 Nitr. II 107 40
Figure 17 CJl v.:>
-
C)l v.:> ~
Shape of loading Cycles
Frequency Program Actual record cpm No .
II - --- - _ .- - II
o ~
u -- -- - I 5.4
xx
o
xx
o 20 30 40 sec
o 10
Figure 18
o
0'
Frequency Dependence
N(q) N(c) 150 10 I . / /'
"""'- /'
/' ' .
/' \ /' ,Y' 6 \ /' 100- 10 /' \ . / / ~ ./ \ -.-.- .- . -.- ' ..-"" ."".
pur~ fr~qu~ncy effect \ \ Reversed bending \ (Wade and Grootenhuis) II \ 5 50 10 "~ combin~d frequency \
,';, I and rate effect
\
,,,,,~, ...
,
-. ... --- ... -::>' -"" '- R~versed bending (Weller)
\ -- .. . -- .. --- ... _ r:."""' ... .-"""" ... \ and Mason ' "'- xX-· ·- ~ deduced from Wood Frequency 2 3 5 n 10 10 10 10 10 10 cpm_ ,------ -- - T -~ 2 3 0.1 10 10 10 10 Hz mano~uvr~s gusts rotors engin~s acoustic fatigue iultrasonic History Loading Rand~~~~~~dln;'j Constant- amplitude loading S~rvo - controll~d t~st beds ~ resonant test beds ~ c ryslal re,> v n~n c p Figu re 19 CJ1 c:..:> c:..:> c:Jl v.:> >I'>- Scheme of the Influence of the chemical Activity 5 = Range of strain in one half - cycle V . . dS
®
R f t v = ate 0 s raining = Cit R' ...
~ -- -j ...... p = Intensity of incitation of chemical activity = t(v) · t(S) \ \ \ 'V = Rate of reaction = f (I . ~J I v W \ \ A = chemical Affinity between the contacting mediums \ \ .I'\. = chemical Resistance (e . g. oxide -layer) = f (N, I, A) I p = Duration of reaction = persistence = f (v ) ~ , R"= amount of reaction in one half-cycle = t(p,v,w) I D" = Damage produced by R" (e . g. oxide) = f( R") I V I / W = frequency of cycles R' = effective amount of reaction per cycle = f (R",w)
/
/ N = Number of cycles, periods / N D' = amount of damage produced in one cycle = f (N , R') v R = Reaction @) I,A,D,.J'\..,v, p,R D = Damage (6) II L ® ~;, r ... p V
o
. - . - . - . - . - . j ~~ . - . - . - . - .
.n..
II L @ ~!S
--------- K ef/fCC ///( ~ ! ~ P
--
---
----- R - --- V,p, -><--- ~
CD
- -- ------ -- ---
---
"I ® 0"
L c ~ I,A,d,. ~ ~ p
~ ... N Fi gu re 20
Scheme of the flake phase
tension compression ,. L . ' , I - chemical phase
I
,' , 1· . .
" ' If l) flake phase L fracture phase Figure 21 C)1 w C)1 CJl c:.:> O'l
Fatigue Crack Surface
of test rod E 1 02
Record of Crack Detector
before failure
Static failure Load :
new (mean value) 9900 kp
E 102 with fatigue crack 5890 kp
Fa i lure surface
Figure 22
Probable Crack - Stage Life
as a function of the probability of survival N N N = Number of periods q
®
for probable crack stage 15
• / 89 _. ± . .. . 7~ ... * . .. __ _ ml ~ _. ___ u .... _ .. u _ _ _ . -c>
life C = F-P
:::::: : ~ ' 9 ' .. .. - ~J. . _ .. . --
101 77 ~ ~_ ~==-~ ---; ~1
5 , 54~ ~ .. =t= .. . .:;; _ .~ 8
@
..., ·· - ·I ·· --- .. -~- · t . . - .. ~ .. -.- .. ~
76 84(xxl) 94(XXI) 67/68(1l,23,7~ )
o 1 ~
0.7 0.5 0.3 0.1 y 0.9 N Ie . .
20 ,...---_.c.~_'--~~ ________ ... ____ ___ _ _ . __ ___ .. _._ ._
72 (0, H2, 1075) ~ .. -.- .. - .. - .- .. -.- . -.- .- - ---.
Qf\ • ----.... ._ ._ ._ . --- ._ ._ .
~-~ -. . ...
104 ~ &1!'6"~"'''''tr_'
~ ¥---+-- -=y
!II ~" --0 i~ - -==:::~::: ___ :-- 73
~"J'!!',"l"' ----- • ~ eo
... 55,cxx) 0 ~ ~
0 1 ~
o I 7 ~
0.9 0.3 0.1 y 0.7 0.5 0.3 0,1 y 0.9 0.7 0.5 probability of survival Figure 23 C}l c..J -l c.n w co 'c ,z
I ,! " "
I - , .. t T . I - r -' ! '
" t j- nTl _ _ . r" t I If'
"
. . ., . . - , ' "7 I , . I , } . t i
.:: t
f ' Q,415 (Volt : mm) !lt O , 56(rn ~ c lack, ~rt " c) ! I : I ' .~ I
ArM 1'lPpr~nting rmistanC¥.if , .r , n~ . ,I' I I ", ,I ' j ~tw •• n r~ i &tanc. disotribu ion at crack \ F ' 711 , ". d tro - I POl i hti d I I I
t
3 ·
start and a\ the- 9wn ' btor ¥ ~ . $ . I : , ~ ~: : "r : \
Thi. arM S proportional t th ~ crack .u fac. . I, • ~ • • • • I I I I t I I • • • , , ' : ,
-
1 "
1 , • " t I ' I ' , , t I I
i I I :J I 1 .1 f I
0'
, I I I ' 1
B · I ~ I ' ' . '
, I I .r. ' ; I I : I
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5 · ~ I , , ' / ,1 / , 1 I I F ~I I , • .. "- F II '1_ I I I I ' I ' I ' ' I J L.
' I
I , , F "3 ,-
I : .. "' \ I , r ' / _ Pr'ogtess ' ot I jl ' I ; 1 . } 2·
I
fatigue ~ : C r ac~ ! I i< : ; I; : tfi ' 1
for Steel F , _ --->-_ . , I
I , , , , , a , , . . , .
I) , , 1
, '
.5 ...
I ' I.
, 1 .
, I I , , 1 .1
, I j !: i ; · • • '
I
Fe , --
: t- : I i
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:t tr ' l I" 1 · td, od' : , },
:1
L ,.
10 "1
I
t. 5 t. 5 5 7 8 9 10 ' 2 3 I. 5 5 7 8 9 10' 2 3 Figure 24
Scheme of the three damage phases
log 0
o o o
OF ~ .-- --- . r --- , /
I OF = 01 + 02 u~ [h]
" / --- / / " / / , / / st 2nd phase 3 rd phase ./ // 1 phase (flake phase) (fracture phase) // (chemical phase) / ,/ / /' / / -' / /
01(W,N)=.~Di'(a1 }(j)+b )''¥ i (w)
1 02 = c2N2
" / 1=1 .u.
--- / / -- / / / / / / / / / / , / / / / main origin __ -' '- ' ~ . - - - __ N of final failure of scatter _ --- ~;;~;.-;..- ::.:. --..-- 02
,.---- .... --------~-; . :-.,. . .., ~~ ~:: -- ----
log 03 = C3 . log N3
log N3 N1 N2 Figu re 25 c:Jl c.v to PRECEDING PAGE BLANK NOT 1l'tfMf1U STATISTICAL ANALYSIS OF MISSION PROFILE PARAMETERS OF CIVIL TRANSPORT AIRPLANES By Otto Buxbaum Laboratorium fUr Betriebsfestigkeit Darmstadt-Eberstadt, Germany SUMMARY To evaluate fatigue life, manufacturers must define and use typical mission pro- files. The probability with which a mission profile (or one of its parameters) occurs can be used to quantitatively describe the term "typical." The airplane weight at any point in the mission is, of course, a very important parameter; the present paper pre- sents some weight data and analyses from several types of airplanes. Severallong- , medium-, and short-range airplanes, flown either in passenger or in cargo service of Lufthansa German Airlines, were observed between January and April 1969.
The statistical analysis of flight times as well as airplane gross weights and fuel weights of jet-powered civil transport airplanes has shown that the distributions of their frequency of occurrence per flight can be presented approximately in general form. Before, however, these results may be used during the project stage of an air- plane for defining a typical mission profile (the parameters of which are assumed to occur, for example, with a probability of 50 percent), the following points have to be taken into account.
Because the individual airplanes were rotated during service, the scatter between the distributions of mission profile parameters for airplanes of the same type , which were flown with similar payload, has proven to be very small. Signifi- cant deviations from the generalized distributions may occur if an operator uses one airplane preferably on one or two specific routes.
Another reason for larger deviations could be that the maintenance services of the operators of the observed airplanes are not representative of other airlines.
Although there are indications that this is unlikely, similar information should be obtained from other operators. Such information would improve the reliability of the data of the present report.
INTRODUCTION The airworthiness standards for transport category airplanes require that the fatigue strength evaluation include the typical loadin g spectrum expected in service.
(See ref. 1.) The loading spectrum , however, depends on the mission profile, which has been chosen in agreement with the requirements of the customers. Since the operational conditions will vary from flight to flight and probably different customers may operate the same type of airplane differently, several mission profiles will always be discussed for an airplane that is in the project stage. (See ref. 2.) The manufacturer then has to combine the various mission profiles into one or two so-called representative or typical ones on which to base the fatigue-life evaluation.
A quantitative description of the term "typical " may be obtained by defining the probability with which a mission profile or one of its parameters will occur. This defi- nition can be achieved possibly for parameters like flight altitude and airspeed by means of results from measurements which have been carried out on airplanes of similar design features, for example, from VGH recordings. There is, however, still a lack of informa- tion insofar as parameters such as flight-time airplane weight and weight distribution are concerned.
In order to investigate the variation of mission-profile parameters and to gather information which could be used for the design of similar airplanes, the following analy- sis has been performed.
The author is indebted to the German Government, Ministry of Defense, for finan- cial support and to the departments of structural engineering and performance and opera- tion engineering of Lufthansa for their assistance and collaboration.
AIRPLANE TYPES, ANALYZED PARAMETERS, AND PERIODS OF OBSERVATION Several long-, medium -, and short-range airplanes flown either in passenger or in cargo service of Lufthansa German Airlines have been observed during a period lasting from January 'to April 1969. As far as it was possible, the following parameters have been taken for each flight from flight and fuel logs as well as from the so-called "load sheets:" airborne time, take-off gross weight, landing gross weight, fuel take-off weight, and fuel landing weight. Information about the individual airplanes and their characteris- tics is presented in table 1. In addition to the analysis performed for the airplanes and the period of observation as mentioned, results from earlier similar investigations have been included for information.
PRESENTATION AND DISCUSSION OF RESULTS The results are . presented for each of the mission-profile parameters in form of cumulative frequency distributions , from which the number of occurrences per flight and the respective magnitude can be read, and in form of cross plots for any two parameters, ~ - - -- ---------------------- which have occurred during the same flight. In order to achieve the intended generaliza- tion, the airplane and fuel weights have been related to the maximum allowable weights as specified in table 1.
Airborne Time The cumulative frequency distributions of airborne times for the different types of airplanes are presented in figure 1. The longest flight time has been observed for a 707C airplane in cargo service; its flight time was 9.75 hours. Also a difference in flight times between cargo and passenger airplanes of the same type can be noted.
If the cumulative frequency distributions of airborne times are plotted on Gaussian probability paper with a logarithmic grid for the variate , then the distributions for the individual airplanes may be approximated by one or by a combination of several straight lines (fig. 2); that is, they correspond to logarithmic normal distributions, as it was demonstrated in reference 2. Only those data have been included in figure 2, which were obtained during the same period of observation. The following conclusions can be drawn: (a) The scatter between airplanes of the same type which were flown with similar payload is very low.
(b) The distributions can be separated into three groups which actually correspond to short-range , medium-range, and long-range airplanes.
(c) The difference between passenger and cargo airplanes increases with the rang e .
(d) All long - range airplanes show the same asymptotic behaviour, which has been observed in a previous investigation. That behaviour could be caused either by the specific station-to-station distances as flown in service by the operator concerned, or by the limitation of fuel capacity , or - and that seems to be very likely - by a combination of the two reasons.
If it is assumed that other airlines operate Similarly and the scatter for very short flights (which occur with probabilities above 99.5 percent) is neglected, then the following generalized information may be derived for the airborne times of jet - powered civil trans- port airplanes. The logarithmic mean value of the airborne time amounts for short-range airplanes to 37 minutes and for medium - range airplanes to 60 minutes . (See fig. 3.) The corresponding standard deviations , by which the slope in the probability paper is defined, are 0.155 and 0.215. The two logarithmic normal distributions intersect at a flight time of 11 minutes and are assumed to occur with a probability of 99.5 percent. At the same point also, the distributions for the long - range airplanes are assumed to have their origin.
As has been mentioned before, the long - range airplanes show an asymptotic behaviour, which may be expressed by a mean value of 440 minutes and a standard deviation of 0 .040; they do not, however , follow this distribution completely but only to a certain percentage, which is about 25 for the passenger and 70 for the cargo airplanes. As the distribution for the long-range passenger airplanes leaves the asymptote already at a probability of 25 percent, its mean value is about 245 minutes instead of 440 minutes for the cargo version.
Two distributions for short- and medium-range airplanes can be used directly for an estimation of an airborne time belonging to a typical mission profile; in the case of the long-range airplanes a distinction has to be made between cargo and passenger service, and prior to the estimation, an assumption has to be made about the percentage of flights which will follow the asymptote, that is, which actually can be called long-range flights.
Take-Off Weight A similar analysis has been made for the take-off gross weights. As it has been said before, the results are presented in relation to the corresponding maximum allowable take-off weight. (See the cumulative frequency distributions . in fig. 4.) It has to be noted here that for the 737 type airplanes only those take-off weights which have occurred at flights departing from and arriving at Frankfurt airport could be obtained. The data for the other airplanes resulted from succeeding flights in the periods of observation as given in table 1.
The scatter between the cumulative frequency distributions for the individual air- planes of the same type, which flew with the same payload, was very small. (See, as an example, that of passenger and cargo long-range airplanes in fig. 5.) This graph shows also that the cargo airplanes are generally flown with a much higher take-off weight than the passenger airplanes. An indication that this happens not only with the long-range air- planes as investigated for one operator but also with the whole fleet of aU airplanes from all operators may be derived from the fact that a certain type of fatigue failure in the wing structure has occurred at a significantly shorter service life for cargo airplanes than for passenger airplanes. A careful fatigue-life evaluation has demonstrated that the reason why cargo airplanes have the shorter life must result from generally higher air- plane gross weights. The data as presented in figure 5 confirm that prediction.
In order to obtain the intended generalization, the data as observed during the same period of time for jet-powered short-, medium-, and long-range airplanes have been plotted on probability paper. (See fig. 6.) The distributions for the short- and medium-range airplanes can be apprOXimated by a rather small scatter band of two straight lines with a standard deviation of 0.03. It says that 99.95 percent of all flights were made with a take-off weight exceeding 70 to 75 percent of the maximum allowable one, and that in about 5 percent of all flights, 100 percent of the maximum take-off weight was reached. The variation of the relative take-off weight of long-range airplanes is larger than that of short- and medium-range types. But also the difference between passenger and cargo service is larger for the long-range airplanes, because only 0.5 per- cent of all flights of passenger airplanes took place with the maximum allowable take-off weight, whereas in the case of cargo airplanes it was almost every second fligh!.
As supplementary information, a cross plot of the variation of take-off weight with airborne time as observed on three long-range passenger airplanes is shown. (See fig. 7.)
This example has been selected because it was the best correlation which has been obtained. For the other types of airplanes, the trend was not as clear. More details about this subject are given in reference 3.
Landing Weight If the cumulative frequency distributions of relative airplane landing gross weight (fig. 8) are compared with those of the take-off weight as shown in figure 4, it is evident that the curves for the landing weight of the individual types of airplanes are much more consistent and conformable. When plotting these distributions on logarithmic probability paper and approximating them by straight lines (fig. 9), it becomes apparent that for all types of airplanes, between 2 and 15 percent of all landings occurred with the maximum allowable landing weight. The distributions have almost the same slope with one excep- tion, which is again the long-range cargo-type airplane. It has to be mentioned further that the scatter between the distributions for the individual airplanes of the same type was similar to that of the take-off weight and was very small. Unfortunately, for the short- range airplanes, only the landing weights for flights from and to Frankfurt airport could be obtained because of matters of organisation. This fact seems, however, to be of secondary importance with regard to the result.
In order to investigate the relation between airborne time and the respective landing weight, cross plots have been made which showed that the landing weight is more or less independent of the flight time. An example of this type of plotting is shown for three long- range passenger airplanes in figure 10.
Take-Off Fuel Weight The definition of a mission profile to be used for fatigue analysis has to include not only the airplane gross weight but also the appropriate weight distribution. Since the weight of the fuel, which the airplane is carrying, allows information to be derived about the weight distribution, an analysis similar to that for the airplane weights has been per- formed also for the fuel weights.
Figure 11 shows the cumulative frequency distributions of take-off fuel weights for the different types of airplanes in relation to the respective maximum fuel weights. This form of presentation is not very suitable for deducing a general trend, because the indi- Vidual curves intersect at several points. Therefore an attempt was made to plot the ratio between take-off fuel weights and the respective allowable airplane take-off weights on logarithmic probability paper. (See fig. 12.) The distributions appear as a family of curves with increasing standard deviation for increasing airplane size. They are Clipped at the respective value of the ratio of maximum fuel to maximum allowable airplane take- off weight. Only the distributions for the long-range cargo airplanes behave as excep- tions because they consist of two parts, each of which can be described by a logarithmic normal distribution. It has been demonstrated that almost every second flight of long- range cargo airplanes is made with the maximum allowable take-off weight. (See fig. 6.)
If the maximum allowable payload was reaChed, the fuel weight had to be restricted in order not to exceed the maximum allowable airplane gross weight. That may have led to this combination of two logarithmic normal distributions. Furthermore, it can be seen in figure 12 that the variation between the cumulative frequency distributions as observed for airplanes of the same type which flew with similar payload is very small.
A generalized presentation and a good approximation to the results is obtained when the scatter as occurring in the range of probabilities between 90 and 99.5 percent is ignored and is replaced by a fictitious point at 95 percent, where all distributions are assumed to intersect at a weight ratio of 13 percent. (See fig. 13.)
Landing Fu. el Weight In opposition to the fuel weights as observed during take-off, it is not necessary to relate those occurring during landing to the respective airplane gross weight, it is suffi- cient for obtaining general information to relate them to the maximum fuel capacity of the airplane type. The results of the analysis are presented again in form of cumulative fre- quency distributions for the different types of airplanes. (See fig. 14.) From this graph, a further confirmation can be derived for the assumption which was made when explaining the fuel take-off weights of long-range cargo airplanes because it shows that these air- planes have generally the lowest percentage of maximum fuel weight during landing.
From the presentation of the distributions in a probability paper (fig. 15), the percentages of maximum fuel weight as occurring during every second landing can be defined as 14.5 for the car go and 20 for the passenger long-range airplanes. The corresponding figures for medium- and short-range airplanes are 38 and 49 percent, respectively. The latter value seems to be very high; it can, however, be explained by the fact that in short-range service, up to three flights were flown without refueling. It is interesting to note that the distributions for the individual airplane types are almost parallel to each ' other, a tendency which already has been observed for the airplane landing weights. (See fig. 9.)
CONCLUDING REMARKS The statistical analysis of flight times as well as airplane gross weights and fuel weights of jet-powered civil transport airplanes has shown that the distributions of their frequency of occurrence per flight can be presented approximatively in general form.
Before, however, these results may be used during the project stage of an airplane for defining a typical mission profile (the parameters of which are assumed to occur, for example, with a probability of 50 percent), the following points have to be taken into account.
Because the individual airplanes were rotated during service, the scatter between the distributions of mission profile parameters for airplanes of the same type, which were flown with similar payload, has proven to be very small. Significant deviations from the generalized distributions may occur if an operator uses one airplane preferably on one or two specific routes.
Another reason for larger deviations could be that the maintenance services of the operators of the observed airplanes are not representative of other airlines. Although there are indications that this is unlikely, similar information should be obtained from other operators. Such information would improve the reliability of the data of the present report.
REFERENCES 1. Anon.: Airworthiness Standards: Transport Category Airplanes. Federal Aviation Regulations, Pts. 25 and 25.571, FAA, May 8, 1970.
2. Buxbaum, 0.; and Gassner, E.: Haufigkeitsverteilungen als Bestandteil der Lastannahmen fUr V er kehrsfl ugzeuge Z eitschr . Luftfahrttechnik - Raumfahrttechnik, Bd. 13, Nr. 4, 1967, pp. 78-84 . (Also available as Library Translation No. 1303, Brit. R.A.E., June 1968.)
3. Buxbaum, 0.; and Reinhold, P.: Statistische Auswertung der das Einsatzprofil von Transportflugzeugen kennzeichnenden Parameter. Tech. Rep. TB-88, Laboratorium fur Betriebsfestigkeit, 1971. (To be distributed as lCAF-Document.)
U1 ""- ex> TABLE 1 AIRPLANE CHARACTERISTICS AND PERIODS OF OBSERVATION Maximum allowable weights , Number of thousand lb airplanes Payload Period of observation Type of airplane observed Take-off Landing
~)l
97.5 72.2 2 150.9 Boeing 707 B Passengers 112.0 72.2 2 150.9 Boeing 707 C Cargo 61.2 21.7 2 69.2 Boeing 727 A Passengers Jan. 1969 to Apr. 1969 1 72.8 64.6 21.7 Boeing 727 C Car go 40.7 10.7 3 44.2 Boeing 737 A Passengers 1 50.2 46.7 10.7 QC (Passenger / Cargo) Boeing 737 C 97.5 72.2 1 150.9 Boeing 707 B Passengers Apr. 1968 to July 1968 79.4 Jan. 1964 to Dec. 1964 1 106.1 Boeing 720 B Passengers 1 32.8 29.0 Bickers Viscount Passengers Apr. 1959 to Jan. 1961 -- 3.
aAssumed fuel density: 0.8 kp/dm • Boeing 707 B, 3 A/C, 505 Flights 707 C , 2 A/C, 320 Flights II 720 B, 1 A/C, 571 Flights 727 A I 2 A IC, 880 Flights
•
~ 727 C , , A/C, 566 Flights
x
737 A, 3 A/C, 1634 Flights c: - + Vickers Visco A/C , 481 Flights , 1
E
c:
.-
~
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•
I X x-~x_
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x
I
10 - 2 10- 10 - Cumulative Frequency per Flight Figure 1.- Cumulative frequency distributions of airborne time for different types of transport airplanes.
c:.n ~ to 737 A
----
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----
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--- 707 B
99.95
---- 707 C
99 .5 c
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\
\ 0.05 0.01 2 3 10 10 10 Airborne Time in min .
Figure 2.- Cumulative frequency distributions of airborne time for 10 airpfanes during the same period of observation.
r----- --- ---- 707 C --- 707 B --. -- 727 A and C 99.99 ---- 737A 99.95 ,
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0.040 0.215 Standard Deviation sl = 0.155
0.01
Airborne Time in min .
Figure 3.- Fl igh t t imes of je t -powered short-. med i um- , and long-range ai rplanes.
CJl CJl t-:> .....
c ~ .
u ~ ~ .
~ °
~ ~ c ~ 80 • Boeing 707 B , 3 A IC , 503 Flights
..... -
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•
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•
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3 10- 10- 2 10 - Cumulative Frequency per Fl ight Figure 4.- Take-off gross weights of different types of transport airplanes in percentage of maximum allowable take-off weight.
-
c
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10 - 2 10- ) 10- Cumulative Frequency per FL i ght Figure 5.- Variation of cumulative fr equency distributions of take-off gross weight for individual long-range airplanes.
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40 80 100
Take-Off Weight in Percent of Max . Allow . lO .W.
Figure 6.- Take-off weights of jet-powered short-. medium-. and long-range airplanes.
Max . Allow. Take-Off Weight
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Fi gure 7.- Re l ation between take - off weight in megaponds and fl i ght t i me as observed f or t hree l ong-range airp l anes in p assenger service.
U1 U1 U1 CJ1 CJ1 Q') )( ......
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c - "0 0 ~ 727 C • lAIC. 549 Flights C X 737 A. 2 A/C. 172 Flights (FRA) o .....J 737 C • lAIC. 147 Flights (FRA)
•
50~1~--------------~~-------------:'~--------------~
10 - 10- 10 - Cumulative Frequency per Flight Figure 8.- Cumulative frequency distributions of landing weight in percent of maximum allowable landing weight for different types of transport airplanes .
99.99j
99.95 ,
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0.5 0.0 I +----r----r----r--.......----....-----r---~--+-- 70 80 90 Landing Weight in Percent of Max. Allow. l.W.
Figure 9.- Landing weights of jet-powered short-, medium-, and long-range airplanes.
t,)l t,)l 0) Max . Allow. Landing Weight •• • 0 • .0 0 • IItP u:r- .x"1 0"'01> •• '..
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0- A BUL '/ 200 300 400 Airborne Time in min .
Figure 10.- Relation between landing weight in megaponds and flight time as observed for three long-range airplanes in passenger serv i ce .
100-1 x ! X
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ell U ....
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ell )( 707 C , 2 Ale 320 Flights :J a 727 A , 2 Ale, 866 Flights u...~
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O~I-----r--------------------r--------------------r------------------~~ 10 - 3 10 - 2 10- Cumulative Frequency per Fl ight Figure 11.- Cumulative frequency distributions of take-off fuel weight for different types of transport airplanes.
CJl CJl to 737 A 99.99 727 A 99.95 727 C
----
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707 C 99.5
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Take-Off Fuel Weight in Percent of Max. Allow. A/C Figure 12.- Ratio of take-off fuel weights to airplane take-off weights for 10 airplanes during the same perioo of observation. Each line indicates a different airplane.
- -~-- ---- - 99.99 13 Percent 99.5 C
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727 A
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10 20 30 40 50 60
Take-Off Fuel Weight In Percent of Max . Allow. Ale T.O . W.
Figure 13 .- Take-off fuel weights of jet-powered short-. medium-. and long-range airplanes .
c.n en ~ • Boeing 707 B 3 A/C 504 Flights c 707 C 2 A/C 320 Flights c
-
727 A 2 A/C 868 Fl ights
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41 ::l 3 ' LL - X x, 41 CI x ~~ 01- .f 0 "U c CI ...J O~I----~---------- ----------r--------------------r------ -- ------------r 10 - 10 - 10- Cumulative Frequency per Fl i ght Figure 14.- Cumulative frequency distributions of landing fuel weight for different types of transport airplanes .
99.99 99 .95 99 .5
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727 A and C 0.05 737 A 0.0 I 5 10 40 20 60 80 100 Landing Fuel Weight in Percent of Max . Fuel Weight Figure 15.- Landing fuel weights of jet-powered short-, medium-, and long-range airplanes.
PR ECED lliG PAGE BLANK NOT FILMED STATISTICAL LOAD DATA PROCESSING By G. M. van Dijk National Aerospace Laboratory NLR, The Netherlands SUMMARY In designing against fatigue the assessment of the loading environment still is a major problem. Especially with military trainer and fighter aircraft which may be used for a variety of duties, regular or continuous load recording programs have to be considered mandatory . Such load recording programs may serve either to assess the consumed fatigue life of operating aircraft or to select design spectra for future air- craft designs and a fatigue-test setup. Within this scope the National Aerospace Laboratory has carried out a tentative load mOnitoring program.
A recorder system has been installed on two operational fighter aircraft. Signal values from a c.g. -acceleration transducer and a strain-gage installation at the wing root were sampled and recorded in digital format on the recorder system. To analyse such load-time histories for fatigue evaluation purposes, a number of counting meth- ods are available in which level crOSSings, peaks, or ranges are counted. Ten differ- ent existing counting principles are defined. The load-time histories are analysed to evaluate these counting methods.
For some of the described counting methods, the counting results might be affected by arbitrarily chosen parameters such as the magnitude of load ranges that will be neglected and other secondary counting restrictions. Such influences might invalidate the final counting results entirely . The evaluation shows that for the type of load-time histories associated with most counting methods, a sensible value of the parameters involved can be found at which the counting results are rather unique.
Besides assessing the influences of secondary parameter values, the different counting methods are compared with each other. The analYSis shows that the counting results obta.ined by level-crossing count methods and peak count methods compare rather well. For most of these counting methods the differences actually turned out to be surprisingly small, especially for the c.g. -acc eleration load-time history. The results of the range count methods exhibit larger differences. Also, with the range counting methods the differences appear to be larger for the strain-gage history. The comparison of the different counting methods with each other is concluded by com- paring the level-crossing and peak count methods with the range count methods.
Three different ways are used to convert level-crossing and peak countings into range countings. The results show that level-crossing and peak count methods do not com- pare well with range count methods.
Finally, the described counting methods are evaluated from the fatigue point of view while bearing in mind the purposes they will have to serve. It is concluded that in assessing the life consumed by individual aircraft, a sophisticated range count method applied to strain-gage histories should be preferred. For the selection of design spectra of future aircraft or a fatigue-test setup, level-crossing and peak count methods may be suitable ; in fact , they may even be preferred.
INTRODUCTION A major question in designing against fatigue concerns the assessment of the loading environment to which the aircraft will be subjected during their service life.
Civil and military transport aircraft generally appear to be fatigue sensitive with respect to gust loads. This gust loading environment is substantially independent of the aircraft itself. In the past, extensive measurement programs have been carried out which enabled the assessment of the quantitative rules determining this loading environment .
Hi g h-performance aircraft appear to be relatively insensitive to gust loads with respect to fatigue. With this type of aircraft, fatigue damage will be primarily due to maneuver loading. However, in contrast with gust loads the maneuver loading depends greatly on both the tasks to be carried out and the maneuverability of the aircraft and is substantially independent of external conditions. On the one hand, the maneuvering cap- abilities of the aircraft as well as the intended usage differ enormOUSly from aircraft to aircraft. On the other hand, the way in which the intended composite tasks are carried out will be highly dependent on training philosophy, pilot experience, and such .
Therefore , the resulting loading severity will be somewhat unknown and, in addition, will exhibit important differences from aircraft to aircraft. Consequently , to assure adequate structural integrity (especially with fighters and military trainer aircraft) , load monitoring - either individual monitoring or sample monitoring - has to be con- sidered mandatory. Such load monitoring will provide the means to assess the life con- sumed by the individual aircraft and will also provide information reg a rding load spectra to be used in future aircraft designs and fatigue testing. Within this scope the National Aerospace Laboratory has carried out a tentative load monitoring program under con- tract for the Royal Netherlands Air Force. Continuous load-time his tories became available from both the c.g. acceleration and a wing-root - bending - moment strain-gage installation.
To analyse such load - time histories for fatigue evaluation purpo s es, a numbe r of counting methods are available in which the number of certain loa d occurrences is counted. In the past, these counting methods were compared to each other with respec t to gust loads. Bearing in mind the nature of a gust loading environment, the results of that evaluation are not self-evidently applicable to maneuver-induced load-time histories.
The main theme of the present paper is to evaluate the basic counting methods with respect to maneuver-type loading. The results will be discussed from the fatigue point of view while taking into account the purposes they might serve.
PRINCIPLES OF DATA ANALYSIS Actual load-time histories will consist of a number of load excursions with an irregular pattern and in irregular random sequence. The analysis of load-time his- tories has to be such that the amount of damage caused by these load excursions is somehow quantitatively reflected in the final results. With all analysis procedures of present interest, the actual time scale is irrelevant. Actually, the assumption is made that for fatigue evaluation purposes load-time histories are fully characterized by all peak values in their actual sequence irrespective of the time elapsed between succes- sive peaks.
A number of different counting methods do exist in which specific occurrences within such simplified load histories are counted. The occurrences of interest are the following: (1) Crossings of fixed levels with either a positive or a negative slope (2) Peak values (either maxima or minima) (3) Load variations (either load increments or decrements) With counting procedures of type (1) and type (2), the counting results usually do not provide any direct information about those load variations known to influence the fatigue process. Additional information about the load patterns that do occur will gen- erally be needed. Thus, secondary counting prinCiples should be applied to account for sequence effects.
The different counting methods will be described in the next section. The dis- cussion of each method will comprise these two distinct elements: (1) Uniqueness of the counting method (2) Usefulness of the counting results The aspect of uniqueness will be discussed in connection with the secondary counting principles. In applying these secondary counting prinCiples arbitrary param- eter values may have to be adopted which may influence the final counting results.
Self-evidently, such influence (if considerable) would reduce the validity of the counting method, and the results would no longer be unique.
The usefulness of a counting method is influenced by its application; this relation- ship forms the basis for the discussion of the counting methods. The basic purposes are as follows: (1) Estimating the life consumed by individual aircraft (2) Estimating load spectra for future aircraft designs (3) Selecting the loads for fatigue testing The discussion will take into account the state-of-the-art in realiSing these three purposes.
DEFINITION OF COUNTING PROCEDURES Ten different counting procedures are considered in the present evaluation, enumeration of which can be found in table I. It should be noted that although all methods are derived from the literature (refs. 1 to 7), slightly different names have been adopted for some of the methods to emphasize the characteristic differences between them.
Simple Level-Crossing Count Method The simple level-crossing count method is the simplest way of analysing load histories. A number of preset levels are chosen . . Each time the load crosses one of these levels with positive (or negative) slope, a count is made. Obviously, it does not matter whether level crossings are counted with positive or negative slope. Both pro- cedures will provide almost exactly the same results (maximum difference will be 1 count at each level for each load history analysed). With this method only momentary load values are of interest. Information regarding the actual load patterns is fully lost.
In order to interpret the counting results for fatigue evaluation purposes, additional information will be needed regarding the expected load patterns. The insufficiency of this counting method is clearly demonstrated by figure 1. Although the load patterns shown on the left-hand and right-hand sides of this figure are highly different, the same counting results will be obtained. Small intermediate load variations, which virtually are of minor tmportance in the fatigue process, will give rise to additional countings.
Generally, interpretation of the counting results will be such that the number of crOSSings of a level is assumed to equal the number of maxima above (or minima below) that level. Figure 1 also clearly demonstrates the incorrectness of this assumption.
Obviously, small intermediate load variations seriously hamper the validity of this counting method. In practical applications a secondary restriction may be applied to compensate to some extent for this setback. It may be decided to neglect level crossings which are associated with load variations smaller than a certain range value.
This decision would actually mean skipping all load variations which do not exceed that assumed range value. This range filtering may be carried out by means of a logical system or may be due to the type of load transducer used, as for example with scratch gages (ref. 8).
Restricted Level-Crossing Count Method The restricted level-crossing count method applies the same primary counting principles as the simple level-crossing count method. Different secondary counting principles are applied, however. A crossing of a level with positive (or negative) slope is not made until the load also has crossed a second lower (or higher) preset level in opposite direction. This counting method is associated with the so-called "Fatiguemeter" developed at the British Royal Aircraft Establishment (RAE) and is normally referred to in the literature as the Fatiguemeter count method. Although the Fatiguemeter was developed to count acceleration occurrences, the method may also be used to monitor other parameters such as strains. The adjustment of the secondary counting levels generally is of arbitrary nature. The drop or rise required to satisfy the secondary counting condition may be the same for all counting levels or may be chosen in a pro- gressive way. With the progressive adjustment, the higher (or lower) the primary counting level concerned, the larger is the drop (or rise) required to satisfy the second- ary counting condition. Still, however, interpretation is hampered by intermediate load cycles as is clearly demonstrated by figure 2. Rather different load patterns are depicted on the left-hand and right-hand sides of this figure but, as in the simple level- crossing count method, they will produce equal counting results.
Simple Peak Count Method With the simple peak count method all peak values are counted. The counting results are presented separately for the maxima and the minima. From the definition it is understood that with this counting method, as well as with all other peak count methods, the load patterns that actually occur are taken into account to some extent since application of this method implies a peak detection. However , the counting results will not provide any information regarding the sequence of the maxima and the minima themselves. It is not possible to tell whether a counted peak was actually associated with small or large load variations. Again interpretation is seriously hampered by the smaller intermediate load variations. Much the same as with the simple level-crossing count method, a secondary counting condition may be introduced to more or less com- pensate for this setback by disregarding peaks which are not associated with at least a certain load range. It sometimes is decided to count only maxima above a specified mean level and minima below that level. This Simplification does not improve the validity of the counting results at all. For example, minima associated with minor load ranges are sometimes neglected whereas the adjacent maxima would still be counted.
Level - Restricted Peak Count Method The principles of the level-restricted peak count method are very much the same as those of the restricted level - crossing count method (Fatiguemeter counting). In con- trast, however, with the restricted level - crossing count method, only a count is made pertaining to the highest primary counting level that has been crossed before the second - ary counting condition was met, after which all othe.r previous crossings of primary counting levels are disregarded. Actually, the crOSSings of primary and secondary counting levels are considered merely to detect a peak associated with at least a certain load range. Figure 3 shows a comparison of this method (see fig. 3(b)) with the restricted level-crossing count method (see fig. 3 (a)) . The final counting results do not provide definite information regarding the actual sequence of the maxima and the minima.
The method has been widely used in association with VGH recording programs (ref . . 3) .
Range-Restricted Peak Count Method With the range-restricted peak count method, the intention is to count merely the more significant peaks. The method will merely count peaks that are associated with major load variations. The counting is restricted to peaks beyond mean threshold levels (e.g., minima below O-g and maxima above 2- g) . The peaks to be counted are those which are both preceded and followed by drops (or rises) of at least a certain magnitude (e.g., I-g increment) or exceeding a fixed percentage of the incremental peak value (e.g., 50 percent), whichever is the greater. Here the incremental peak value is defined as the difference between the peak value itself and the mean load level. The counting con- ditions for a maximum count are illustrated in figure 4. From the definition it is under- stood that intermediate load fluctuations are disregarded rather rigorously by this method. The method also neglects some load fluctuations which are not truly insignifi- cant. However, counts pertaining to the higher maxima and the lower minima have become more relevant. The method has been used extensively with VGH recording programs (ref. 6).
Peak - Between-Mean - Crossings Count Method The peak-between-mean - crossings count method is also intended to count only the more Significant peaks. Only the highest maximum or the lowest minimum between two successive crOSSings of a specified mean level is counted. With this method intermediate load fluctuations are disregarded most rigorously. However, all counts are now known to be associated with major deviations from the steady-flight level. A further refine- ment of the counting procedure may be obtained by applying two mean threshold levels as references. The highest maximum will be counted between any two successive crossings of the upper threshold level, as well as the lowest minimum between any two successive crossings of the lower threshold level. The method is illustrated in figure 5.
With this refinement, peaks associated with minor deviations from the steady-flight pattern will also be neglected. On the other hand, less high maxima and lower minima will be disregarded in applying this counting procedure. The method has been used extensively in evaluating VGH records (ref. 9).
Simple Range Count Method With the simple range count method as well as with all other range count methods, the load fluctuations are of direct interest. The fluctuations are known to be a primary influence in the fatigue process. A range is defined as the difference between two suc- cessive peak values. With the simple range count method all ranges are counted. It should be noted here that counting ranges essentially implies a peak detection procedure.
With this simple range count method the loading sequence is taken into account to some extent; that is, with each count two succeeding characteristic values of the load history are considered. However, information regarding the peak values themselves is com- pletely lost.
In practical applications it may be decided to neglect small load fluctuations which are not of much importance for the fatigue process. As is illustrated in figure 6, dis- regarding such small load fluctuations does affect the final counting results seriously.
Apparently, the final counting results will depend on the magnitude of the smallest load range that will be counted.
It may also be decided to count only ranges pertaining to load increments or load decrements. One should bear in mind, however, that the counting results for the positive ranges might differ appreciably from the counting results for the negative ranges.
Consequently, such a Simplification might yield less relevant reSults.
Range-Mean Count Method The prinCiples of the range-mean count method are very much the same as with the simple range count method. However, this counting method does provide additional information. Not merely the load ranges are counted. With each count the corresponding mean value of the load range counted will also be taken into account. So each count is now associated with two values which completely describe the load variation concerned.
As is clear from the definition, the counting results will again be sensitive to the smallest load range regarded.
Range- Pair Exceedance Count Method The range-pair exceedance count method is intended to analyse load histories in terms of load cycles rather than load ranges (half cycles). Since fatigue properties are generally presented in terms of load cycles, this is of course a favourable property.
To accomplish a count two conditions must be met. Each count of a range-pair exceedance of a certain specified magnitude, say R, will have to be associated with a load increment (positive range) of at least R succeeded by a load decrement (negative range) of at least R. By proceeding as such and consecutively conSidering a number of different range values, the counting result will finally give the number of range pairs (load cycles) exceeding a certain range value R. The counting procedure is illustrated in figure 7. The Vickers- Armstrongs strain range counter (ref. 10) is an example of a counting device operating according to this counting method. In conSidering figure 7, it becomes clear that the method will primarily count the major load fluctuations. Small intermediate load fluctuations will be regarded as superpositions on the major load patterns. Obviously, this counting method does take into account the loading sequence.
Fatigue test experience indicates that this characteristic feature is desirable. The counting procedure also has the advantage of being insensitive to the magnitude of the smallest load range regarded.
Another interesting feature of this counting method will become clear by con- sidering the largest range-pair value that will be present in the final counting results.
By nature, the range-pair exceedance count method will combine the largest load incre - ment and load decrement that both occur in the load history concerned and will count them as one load cycle of that specifiC magnitude. Likewise, the counting procedure will also combine the next largest load increment with the next largest load decrement, and so on. From fatigue experience it is known that extreme negative load excursions do actually influence the damage caused by a succeeding extreme positive load excursion.
So it may be stated that fatigue experience is indeed reflected in the counting prinCiples.
Nevertheless, this feature does imply a complication. It certainly is not relevant to combine a very low minimum with a very high maximum which occur at instances very much apart. In practical applications the method should be carried out separately on segments of the load history to avoid irrelevant countings. Treating each flight as such, a separate load-history segment seems to be a both obvious and rather practical approach.
Another example of a counting device operating according to this counting proce - dure is the Schenck range-pair counter (ref. 5). With this counting device, however, the starting procedure is not altogether in accordance with the basic counting principles.
In . starting the counting process the device will analyse the load history as if the starting point of the load history were an extreme minimum. This actually means that for the first count to be made, merely the second condition of the basic counting prin- ciples will have to be met. The effect is illustrated in figure 8 and demonstrates that the Schenck procedure will produce higher counting results than the basic procedure. In applying the counting procedure on a flight-by-flight basis, the effect on the final counting results might be significant.
Although the range-pair exceedance count method does apply rather sophisticated counting principles, the method is still hindered by two shortcomings: (1) No information will be provided regarding the mean values of the load cycles counted.
(2) Not all load excursions will be fully counted (see fig. 9).
Both shortcomings are offset by the next counting method.
Range- Pair- Range Count Method The range-pair-range count method is also intended to count load cycles. The counting procedure operates in two phases. In the first phase all intermediate load cycles are detected and counted in connection with the associated mean values. Each intermediate load cycle will be eliminated from the load history after being counted.
The procedure is continued until the load history does not present any more intermediate load cycles. As may be easily verified, the residual load history will necessarily have a divergent- convergent envelope such as depicted in figure 9. In the second phase of the counting procedure, this residual load history is analysed according to the range-mean count method, These counting prinCiples are illustrated in figure 10. The range-pair- range counting procedure is referred to in the literature as the NLR counting method (ref. 2) and the rain-flow counting method (ref. 4).
This range-pair-range counting method generally has the same advantages as the range-pair exceedance count method without being hindered by its previously mentioned shortcomings. It should be noted that this counting method also is intended to analyse load histories on a flight-by-flight basis.
NUMERICAL EVALUATION DATA Under contract for the Royal Netherlands Air Force a tentative load monitoring program has been carried out. This load monitoring program was intended to serve the following primary purposes: (1) To demonstrate the feasibility of a digital load recording system (2) To demonstrate the feasibility of a strain gage as a load transducer in opera- tional conditions for long-term load monitoring (3) To emphasize the desirability of recording strain histories instead of accelera- tion histories (4) To evaluate different counting methods Two operational fighter aircraft have been equipped with both an accelerometer transducer at the aircraft c.g. and a bending-moment strain-gage installation in the wing root section. Signal values from both transducers were sampled at a scanning rate of 24/sec. After being digitised, the data were stored on a magnetic recorder medium with a 15-hour recording capacity. The beginning of each flight could be recognized by a series of marking numbers which were automatically entered on the recorder medium at the activation of the aircraft electrical power. Every 15 flight hours the recorder medium was removed for further proceSSing on ground-based facilities. By means of a digital computer the data were checked for spurious readings after which a data com- pression was carried out.
The data compression reduced the enormous amount of data to a relatively small number of characteristic data resembling the peak values that did occur. The com- pressed load-time history still comprises all Significant information for fatigue evalua- tion purposes. During the data compression phase more than just peak values are detected. Peaks which are not associated with at least a certain relatively small varia- tion are disregarded to reduce the number of data and to remove data that are of less importance for the purposes concerned. The minimum load range thus left in the com- pressed load-time history amounted to approximately 7 percent of the aircraft limit load level. When applying the counting procedures just described, such a range filtering is either obligatory or does not significantly . affect the counting results since other more stringent restrictions are applied. Consequently, the load histories resulting from the final data compression phase are still suited to evaluate the different statistical load counting procedures. A plot of such a compressed load-time history for a typical fighter mission is shown in figure 11. Such load histories - covering some 75 flight hours - were used to evaluate the different counting methods. The results of this numerical evaluation are presented in the next section.
--- . --- - -- ---- - ---------------- ------ ---- --------- NUMERICAL RESULTS General Comments The counting procedures which have been described herein were simulated by means of a digital computer to analyse the available load-time histories. The results obtained with the c.g.-acceleration history and the wing-root-bending-moment strain- gage history are presented separately. It should be noted that this paper is not intended to present a quantitative comparison of the counting results obtained for the acceleration history with those obtained for the strain-gage history.
The load data are presented in arbitrary units as a result of the digitisation process. In general, the counting results were calculated with an interval width of 8 units. The results have been plotted without any fairing.
Application of some counting methods did imply the definition of a mean level.
For the c.g.-acceleration data the 1-g steady-flight level has been defined as such, although in terms of mathematical statistics this level is not actually the mean value but rather the most probable value. An "equivalent" 1-g level has been assessed to be used as mean reference level in the strain-gage data analysiS. Actually, the equivalent 1-g strain-gage value is not a constant value. Nevertheless, the definition remains relevant since, on the one hand, merely a reference level has to be chosen while, on the other hand, with high-performance aircraft the ' variations in this 1-g strain-gage value are relatively small in comparison with the load fluctuations of general interest.
Before discussing the numerical results, it should be mentioned that the counting results obtained with different counting procedures are not all fully independent of each other. The following relations do exist which will all be easily understood by considering the definitions given for the various methods: (1) Simple level-crossing counting results may be derived from the counting results obtained with the simple peak count method.
(2) Simple peak counting results may be derived from both the counting results obtained with the range-mean count method and those obtained with the range-pair-range count method.
(3) Simple range counting results may be derived from the range-mean counting results.
(4) The results obtained with the simple peak count method and the peak-between- mean-crossings count method will be the upper and lower limits of the counting results obtained with all other level-crossing and peak count methods described.
(5) Peak-between-mean-crossings counting results may be derived from the range-pair-range counting results.
Results From Level-Crossing and Peak Count Methods The results obtained with the level-crossing and peak count methods are pre- sented in figures 12 to 15 and table IT.
As previously stated, parameter values associated with secondary counting prin- ciples may influence the final counting results. The effect is illustrated in figure 12, figure 13, figure 14, and table II for the counting results obtained with the simple level- crossing count method, simple peak count method, peak-between-mean-crossings count method, and restricted level- crossing count method, respectively.
In figures 12 and 13 it is shown that the value of the smallest load range regarded does indeed affect the counting results obtained with the simple level-crossing and simple peak count method. The effect of doubling the basic range-filter value (Ro) from 13 to 26 units does not seriously affect the counting results for the higher load values. Apparently the countings which were additionally disregarded were mainly associated with load cycles near the steady-flight level. Further increasing the range- filter value hardly changed the counting results for the higher load values. However, applying a smaller range-filter value yielded hIghly different counting results. The main conclusion to be drawn is that if a sensible range-filter value is adopted, the counting results for the higher load values are rather unique. It is nevertheless inter- esting to note that the counting results obtained by analysing the strain-gage history appear to be more sensitive to the adopted range-filter value than the results obtained by analysing the acceleration history. In conSidering both load histories in more detail, the major load excursions from the strain-gage history presented small intermediate load fluctuations more frequently than did the major load excursions from the acceleration history. This effect is most probably due to dynamic effects (dynamic overshoot and buffeting) .
By definition it is clear that the restricted level-crossing count method, the level- restricted peak count method, and the range-restricted peak count method are intended to apply secondary counting principles which at least override the applied basic range filtering. From the preceding results the effect of the applied secondary parameter values may be expected to be rather limited. This limited effect is indeed confirmed by the data from table IT, in which the restricted level-crossing counting results are tabu- lated by applying two different adjustments of the secondary counting levels. The counting results came out to be only slightly different. Similar results were obtained with the level-restricted and range-restricted count methods. Also with the peak- between-mean-crossings count method (fig. 14), the influence of the secondary parameter values (e.g., mean threshold levels) was rather limited. From these findings it may be concluded that the majority of the load fluctuations of interest were separate excursions from the steady-flight level.
All the level-crossing and peak count methods described are compared in figure 15.
As might be expected from the aforementioned findings, the differences are not large, although they are more pronounced with the strain-gage data than with the acceleration data. Nevertheless, when accurate data are required, the results obtained with different counting methods are not fully compatible (number of counts may differ by a factor of 2).
Results From Range Count Methods The results obtained with the range count methods are depicted in figures 16 to 18.
It should be noted that these results have been plotted without distinguishing between positive and negative ranges. This effect has been studied in connection with the simple range count method. Comparative results showed that when applying the basic range- filter value of 13 units, the number of positive and negative ranges counted did not differ very much. However, when applying a smaller range-filter value, the differences appeared to be much more pronounced. The counting results pertaining to the negative ranges appeared to be far more sensitive to the applied range-filter value than the :!ounting results pertaining to the positive ranges. Apparently, small intermediate load fluctuations more frequently occurred after the load had reached a maximum. The over- all effect of the applied range-filter value on the results obtained with the simple range count method is illustrated in figure 16. Doubling the basic range-filter value from 13 to 26 units does appreciably affect the counting results, especially the results obtained by analysing the strain-gage history. When applying a smaller range-filter value than the basic one, the differences were even more pronounced. It should be noted that further increasing the applied range-filter value (>26 units) still yielded appreciably different counting results. Consequently, it is stated that the results obtained by the simple range count method are not unique even when intermediate load fluctuations are disregarded.
The counting results from the various range count methods are compared in fig- ure 17. The curves presented illustrate that the range-pair-range count method and both variants of the range-pair exceedance count method do not produce very different results. The simple range counting results, however, appear to be very different. It is interesting to note that with the strain-gage data, both variants of the ra,nge-pair exceed- ance count method coincide completely because of the presence of the Ground-Air-Ground (G-A-G) cycle (with every flight the strain-gage history will exhibit a relatively low starting value).
In comparing the mean countings as obtained by the range-mean count method and range-pair-range count method, the results have been averaged - that is, all mean ---- - ------------ countings pertaining to a specified range interval have been averaged while a corre- sponding standard-deviation value has been calculated. The averaged means thus derived are represented in figure 18. With the c.g.-acceleration data as well as with the strain-gage data, the range-pair- range count method yielded lower averaged mean values than did the range-mean count method. However, the differences are much more pronounced with the strain-gage data. This fact may be easily understood by considering the counting principles of the range-pair-range count method and bearing in mind that m every flight the strain-gage history will both start and end with a low minimum due to the G-A-G cycle. These results clearly demonstrate that with the range-pair-range count method the G-A-G cycle is certainly accounted for .
The calculated standard-deviation values corresponding to the averaged means are not plotted in figure 18. It is interesting to note, however, that these standard-deviation values were approximately equal for all range intervals considered and, besides, appeared to be relatively small (order of magnitude of 10 units). From this finding it may be concluded that most load fluctuations of equal magnitude apparently occurred between approximately the same levels.
Comparison of Range Count Methods With Peak Count Methods By nature the results obtained by the range count methods are not directly com- parable with the countings resulting from the level-crossing and peak count methods since different types of occurrences are counted. To enable a comparison the counting results have to be converted. The present comparison will be accomplished by applying different ways of converting simple peak countings into range countings. Reference will be made especially to the range-pair-range counting results since this method is believed to represent best the amount of fatigue damage caused by the load history con- cerned. The following three conversion procedures are considered (see fig. 19): (A) Maxima and minima are supposed to occur in random sequence.
(B) Maxima and minima are supposed to occur in random sequence; however, maxima below a certain level (e.g., 115 units) and minima above a certain level (e.g., 95 units) are neglected. Although the additional assumption seems a curious one, the case is relevant since actually the data disregarded generally are not available.
(C) Maxima are to be combined with minima having the same probability of exceedance (equal cumulative frequency).
The results of these converted simple peak countings as well as the range - pair- range countings and simple range countings are plotted in figure 19. As is illustrated, the applied conversion procedures do produce highly different results. Again the strain- gage data reveal the largest differences. However, none of the applied conversion procedures produce counting results which approximately coincide with the range-pair- range countings . From these findings, it is concluded that a quantitative comparison of range countings with simple peak countings as well as with all other types of peak and level-crossing countings is hardly feasible for the type of load histories concerned.
DISCUSSION Basically the counting methods as described herein are intended to interpret irregular load-time histories by counting the number of specific types of load occur - rences. In the preceding sections the uniqueness of the information has already been discussed and illustrated. In discussing the usefulness of the counting results, one should primarily take into account the purposes these results are meant to serve - that is, the type of information required.
In assessing the life consumed by individual aircraft, reference has to be made to experimental fatigue data, either simple S-N data or full - scaie fatigue test data.
Accomplishing such life calculations, however, will be useful only if the final counting results are sufficiently accurate. Thus, in assessing the life consumed by individual aircraft, a counting method should be used which fully takes into account the actual load- time history and which does not need the application of additional assumptions to be interpreted. Besides, the fatigue damage caused by the actual load-time history should be reflected in the counting results (interaction effects). By conSidering its definition and bearing in mind the aforementioned requirements, it is felt that the range-pair-range count method is best suited for asseSSing the individual aircraft fatigue damage. Also, the range-pair exceedance count method may be rather useful; however, with this method the counting results are not definite since no information is provided about the means of the range pairs counted. Consequently, less accurate results are to be expected. It should be noted that the same remarks hold when the counting methods are meant to compare with any degree of accuracy the life consumed by individual aircraft of the same type. Here, however, the requirements perhaps could be less stringent since it may be known that the aircraft are operating according to the same type of load patterns. In this case, restricted level - crossing or restricted peak count methods may be suited as well.
In estimating load spectra for future aircraft designs or selecting the loads for fatigue testing of an aircraft type that possibly has not even been in service operation, the requirements are somewhat different. Here, great accuracy would be more apparent than real. The load patterns as well as the sequence in which they occur may be entirely different with different types of aircraft. In particular, the number of intermediate load fluctuations at the higher load levels may be expected to be strongly related to the aerodynamic performance capabilities, which may be highly different for different air- craft types. Estimating loading spectra as well as selecting loads for fatigue testing usually implies a mission analysis procedure. The number of exercises (during a mission) that will be carried out has to be estimated. The assumption made is that each separate exercise is associated with major load excursions from the steady-flight level ("characteristic events"). Small intermediate load fluctuations are considered of less or even irrelevant importance. A counting method should be chosen which will provide the number of such major load excursions and the peak levels they are associated with.
As will be understood, the peak-between-mean-crossings count method is very well in accordance with these requirements. However, a restricted level-crossing or peak count method may be suited as well. To obtain a loading program for fatigue testing, the number of "events" counted may be arranged in a realistic sequence. Interaction effects will then be accounted for to some extent.
It can be concluded that the range-pair-range count method apparently has the best general validity. On the one hand, the method embodies some of the characteristics of the other counting methods mentioned (simple level-crOSSing countings, Simple peak countings, and peak-between-mean-crossings countings may all be derived from the results of this range-pair-range count method). On the other hand, the load histories are taken into account by this method as much as possible from the fatigue point of view.
Consequently, general application is recommended.
CONCLUSIONS (1) Some counting methods require secondary counting restrictions involving the choice of an arbitrary parameter value which may influence the final counting results.
With the exception of the simple range count method and the range-mean count method, a sensible parameter value can be found which will yield rather unique counting results for maneuver-type load histories.
(2) The restricted level-crossing and restricted peak count methods will yield approximately equal counting results, especially at the higher load levels. The simple level-crOSSing and Simple peak count methods, however, will yield conservative counting results.
(3) Level-crOSSing and peak countings virtually do not compare very well with range countings.
(4) The range-pair-range count method and the range-pair exceedance count method will produce approximately equal range counting results.
(5) Both the simple range count method and the range-mean count method will pro- vide irrelevant information since the counting results are very sensitive to the magni- tude of the smallest load ranges regarded.
(6) Both the range-pair exceedance count method and the range-pair-range count method provide relevant information in assessing the life consumed by individual air- craft. However, the range-pair-range count method is to be preferred since this method provides additional information about mean values of the ranges.
(7) In comparing individual lives .of aircraft that are of the same type and that operate according to the same kind of duties, a restricted level-crossing or restricted peak count method may be sufficiently relevant.
(8) In estimating spectra for future aircraft designs or in selecting load events for fatigue testing, the peak-between-mean-crossings peak count method will provide relevant data.
(9) The range-pair-range count method will have the best general validity. The results obtained by this method are unique as well as definite and do suit . all purposes.
REFERENCES 1. Schijve, J.: The Analysis of Random Load-Time Histories With Relation to Fatigue Tests and Life Calculations. Fatigue of Aircraft Structures, W. Barrois and E. L. Ripley, eds., Macmillan Co., 1963, pp. 115-149.
2. De Jonge, J. B.: The Monitoring of Fatigue Loads. ICAS Paper No. 70-31, 1970.
3. Wells, Harold M., Jr.: Flight Load Recording for Aircraft Structural Integrity.
AGARD Symposium on Flight Instrumentation, Paris, Sept. 1965.
4. Tucker, Lee E.: A Procedure for Desi gning Against Fatigue Failure of Notched Parts. Thesis, State University of Iowa, 1970.
5. Anon.: Instrument Combination for Counting According to the Range-Pair Method.
Schenck Pamphlet Nr. P2047e.
6. Morton, W. Wallace, Jr.; and Peckham, Cyril G.: Structural Flight Loads Data From F-5A Aircraft. Technical Report SEG-TR-66-51, 1967.
7. Pitts, Felix L.; and Spencer, J. Larry: An Electronic Strain-Level Counter for Air- craft Structural Members. NASA TN D-5944, 1970.
8. Tipps, Daniel 0.: F-5 Scratch Gage Correlation Data Report. Technology Incor- porated, Report No. TI-375-71-1, 1971.
9. Donely, Philip; Jewel, Joseph W., Jr. ; and Hunter, Paul A.: An Assessment of Repeated Loads on General Aviation and Transport Aircraft. Paper presented at 5th I.C.A.F. Symposium "Aircraft Fatigue - Design, Operational and Economic Aspects" (Melbourne, Australia), May 1967.
10. Teichmann, A.: The Strain Range Counter. Vickers-Armstrongs Ltd., Technical Office VTO/M /416.
BIBLIOGRAPHY Incarbone, G.; and Padovano, E.: Methods of Evaluation of Extensiometric and Accelerometric Data To Determine Load Spectra on Aircraft. Paper presented at the First National Congress on Aeronautical Fatigue, Rome, May 16-19, 1960.
Jost, G. S.: The Fatigue of 24-ST Aluminium Alloy Wings Under Asymmetric Spectrum Loading. ARL/SM 295, 1964.
Ravishankar, T. J.: Simulation of Random Load Fatigue in Laboratory Testing. UTIAS Review No. 29, 1970.
Roth, George J.; and West, Blaine S.: Parametric Fatigue Analysis of USAF Fighter Aircraft. Technical Report AFFDL-TR-69-85, U.S. Air Force, 1970.
Schijve, J.: Cumulative Damage Problems in Aircraft Structures and Materials. NLR MP 69005 U, 1969. Aeronaut. J. Roy. Aeronaut. Soc., vol. 74, no. 714, June 1970, pp. 517-532.
Schijve, J.; Broek, D.; et al.: Fatigue Tests With Random and Programmed Load Sequences With and Without Ground-to-Air Cycles. A Comparative Study on Full-Scale Wing Center Sections. NLR-TR S.613, 1965.
- - - - --- -- -
TABLE I: COUNTING PROCEDURES
SIMPLE LEVEL-CROSSING COUNT METHOD
RESTRICTED LEVEL-CROSSING COUNT METHOD
SIMPLE PEAK COUNT METHOD
LEVEL-RESTRICTED PEAK COUNT METHOD
RANGE-RESTRICTED "
"
"
PEAK-BETWEEN-MEAN-CROSSINGS COUNT METHOD
SIMPLE RANGE COUNT METHOD
RANGE - MEAN " "
RANGE-PAIR EXCEEDANCE COUNT METHOD
RANGE-PAIR-RANGE COUNT METHOD
TABLE n: RESULTS OF RESTRICTED LEVEL-CROSSING COUNT
METHOD FOR C.G.-ACCELERATION HISTORY
SECOND . COUNTING LEVEL (G)
NUMBER OF COUNTS
PRIMARY
COUNTING
EQUIDISTANT PROGRESSIVE EQUIDISTANT PROGRESSIVE
LEVELCG)
ADJUSTMENT ADJUSTMENT
ADJUSTMENT ADJUSTMENT
-1.0
0 -
-0.5 -
0 0.5 0.5 17
- - -- r------ f--- - - - -
- - - - - -- - --
2.0 1.5 1.5 1019 1019
1.5 402 343
3.0 2.5
194 180
3.5 3.0 20
4.0 3.5 2.0 76 70
4.0 2.5 29
4.5 27
4.5 3.0 10 9
5.0
10 LEVEL CROSSINGS COUNTED
LOAD LOAD ~----~~-------ff~------ 3 ~--~~~~ -------- ----- 3
f
t
~--~ ----~~~ -------- 2 --TIME -TIME Figure I. - Simple level-crossing count method.
a FIRST COUNTING CONDITION SATISFIED
• SECOND" " " LOAD LOAD ~~4--q~---------------- 2
t
t
-- 1' -11 --TIME -1 1-- ----- --{:\t---::z-....---±- --I. stJ-- _ _ 2' 1----- - ~+- --- ~~~ - -2 ~ -------- -4~ -- liH --------- -2 Figure 2.- Restricted level-crossing count method.
o FIRST COUNTING CONDITION SATISFIED
• SECOND" " " ~ --~;---~rr ----- 2
I RESTRICTtD LE.VEL - CROSSINGS
LOAD
t
2 x CROSSING OF LEVEL 2 1x
" "
"
- - .. 1· ----- TIME ( a )
LOAD I LEVEL -RESTRICTED PEAK COUNTING
t
2 x MAXIMUM EXCEEDING - LEVEL 2
i
~ ~--~~---+----- , ., 2x " ~TlME ( b ) Figure 3.- Comparison of level-restrict ed peak count method with restricted level - crossing count method .
LOAD , t-t--f---------t- THRESHOLD LEVEL 1 (2 - G)
1-------------1-- MEAN LEVEL (1-G)
-- TIME t------------ THRESHOLD LEVEL 2 (O-G) ICONDITIONS FOR A MAXIMUM COUNT o PEAK LOAD EXCEEDING LEVEL 1 o R1 AND R2 ARE AT LEAST A FIXED VALUE (1- G) o R, AND R2 " " " " " PERCEN TAGE OF ~ L (50 PERCENT> Figure 4.- Range - restricted peak count method.
5 86 o MEAN THRESHOLD CROSSING LOAD • PEAK TO BE COUNTED
t
i-fA-t\}--------Ef}-----tir- UPPER THRESHOLD MEAN LEVEL ~~~--~-- --- -LOWER THRESHOLD -.. TIME Figure 5.- Peak-between-mean-crossings count method.
LOAD
r
WITH SMALL . RANGE: SMALL AND INTERMEDIATE RANGES COUNTED -'- TIME LOAD " DISREGARDING SMALL RANGE: LARGE RANGE COUNTED -TIME ' Figure 6.- Effect of ' disregarding small ranges with the simple range count method .
LOAD
t
o FIRST COUNTING CONDITION SATISFIED
• SECOND --TIME Figure 7.- Range-pair exceedance count method.
LOAD
t
o HIGHEST MAXIMUM
• LOWEST MINIMUM AFTER THE HIGHEST MAX.
X LOWEST MIN . BEFORE THE HIGHEST MAX .
ONE FUGHT
I •
..I LARGEST RANGE-PAIR COUNTED: BASIC METHOD R1 SCHENCK VARIANT; R2 Figure 8.- Comparison of basic range - pair exceedance count method with Schenck variant.
LOAD EXCURSIONS COUNTED BY LOAD RANGE-PAIR COUNT METHOD
t
-TIME ONE FLIGHT I ..
.1
Figure 9.- Fl igh t record with omission of intermedi a te load cycles .
LOAD FIRST STEP:
t
RANGE - PAIR R, COUNTED WITH MEAN M, -TIME FIRST PHASE OF COUNTING PROCEDURE LOAD , SECOND STEP: RANGE - PAIR R2 COUNTE R2 WITH MEAN M2 -TIME _ __ _ --L LOAD RESIDUAl RECORD TO
t
SECOND PHASE OF BE ANALYSED ACCORDING COUNT ING PROCEDURE TO RANGE-MEAN COUNTING --TIME Figure 10 .- Illustration of range-pair-range count . method.
5 89 KGF/MM 10 MIN ,- .-l IWING-ROOT BENDING STRESsl 0 - G t --TIME Figure 11.- Compressed load-time history of a typical fighter mission.
LOAD LEVE r L-- -,-- --._~,_._--,_--_,_,rI_,--_,r_--~_r_r~--_r--_.--._"
t
• RANGE -FILT ER VALUE Ro=13 UN I TS 2 ~ -------------- ~~ ----------_+-- ~ (BASIC CASE) o RANGE -F ILT ER VALUE Ro - 26 UNITS l50 r- ---- --------~------------~------ ~~ --~------------ ~ 100 l -G MEAN LE VEL - NUMBER OF CROSS I NGS (a) R esults for c.g. acceleration.
Figure 12.- Simple level-crossing counting results .
LOAD ~ fE. ~L---'--~-'~~-'--~ -' IT~--~~~ ~~~~~ ~~~ 20 "- ----------""::O ""l<il:- ~c-------------+____l • RA NGE-F IL TE R V AL UE % - 13 UNITS ur ( B ASIC CA SE ) o RA NGE- FILT ER V ALUE Ro"26 UN I TS l50 ~------~-------~---~~ ---+------- ~ 100 • EClU IV ALENT" · l- G MEAN LE EL _ NUMBER OF C ROSS I NGS (b) Results for wing - root bending stress.
Figure 12 .- Concluded.
LOAD LEvErL __ -, ____ ,-,-.-,- __ .- __ _r--~_r--_,r_--.__r_r._--_r-- _. --._"
t
200 r- ------------~ ~ c-----------+_-------------+------------ ~ • RANGE-FILTER VALUE (BASIC CASE) ® RANGE-FILTER VALUE 100 r-~ 1- ~ G ~ M~E~AN ~ L~E ~ VE~L ~~------------~--------------+, ~ -------- ~ ~ NUMBER OF {MAXIMA ABOVE lMINIMA BELOW (a) Results for c.g. acceleration.
Figure 13 .- Simple peak counting results .
LOAD LEVEL t ,--,--~,-~--,---,_IT.--.---.-.~--~--~~~ 200 r- ------ --~~~~ ---------- ~------ -- -----+------------ ~ .. EQUIVALENT"" 1- G 100 MEAN LEVEL 10 10 __ NUMBER OF{MAXIMA ABOVE MINIMA BELOW ( b) Results for wing-root bending stress .
Figure 13 .- Concluded.
LOAD LEVE~L ____ '- __ '--' -'-' __ -''- __ '--'-'-' __ -' ____ .- -.-.'- __ -' ____ r--.-..
t
BASIC CASE 200 ~------------~ ~-------------- _r~ o APPLYING MEAN THRESHOLD f-- - ----1 LEVELS A AND 8 150 ~--------------~------------~~ ---- ~~----_4-------------- ~ - - - - - - - - - - - LEVEL A 100 1-G MEAN LEVEL -+----- - --f------ - --!------ ---jJ>- --j - LEVEL B NUMBER OF (MAXIMA ABOVE MINIMA BELOW Figure 14 .- Peak-between-mean-crossings counting results for c. g. acceleration .
200 ~------------ ~~~ ----------+--------------+------------ ~ • SIMPLE PEAK COUNTING (BASIC) X .. LEVEL CROSSINGS( .. ) 6 RESTR . .. ..
150 • LEVEL - RESTR. PEAK COUNTING 1-----+----- ~~P\. ~__1-------------- *_l [!J RANGE.. ..
o PEAK-BETWEEN-MEANS COUNTING (BASIC) 100 l-G MEAN LEVEL -+----------+-------+------ ~ 10 CUMULATIVE FREOUENCY (a) Results for c.g . acceleration.
Figure 15.- Comparison of level-crossing and peak count methods.
LOAD LEVE~L~~~,,--~ro----r_--._._,_r_--._--.__._.._--_r--_,_,'" t 200 ~---- --~ ~~~~ ----------~------------_+----------_. ~ • SIMPLE PEAK COUNTING (BASIC) X .. LEVEL CROSSINGS ( .. ) 6 RESTR . .. ..
• LEVEL-RESTR. PEAK COUNTING [!J RANGE.. ..
o PEAK-BEnNEEN-MEANS COUNTING ( BASIC) "EOUIVALENT" 1- G 100 MEAN LEVEL ~~------------~--------------~-------- ~~~ CUMULATIVE 10 10 FREOUENCY (b) Results for wing-root bending moment.
Figure 15.- Concluded .
C I J
a o RANGE- FILTER VALUE Ro 13 UNITS 100 ~ -------------+ ~~~ --------+_ ~ (BASIC CASE) ® RANGE-FILTER VALUE Ro=26 UNITS 50 ~------ ------~-------- ----r-----~~r-~------------~ 10 10 - CUMULATIVE FREQUENCY (a) Results for c. g. acceleration.
Figure 16.- Results of simple range count i ng.
o RANGE-FILTER VALUE Ro°13 UNllS 100 i-- --- ----= -....:::c -- P-< ;::-----------l -----1 <BASIC CASE) ® RANGE-FILTER VALUE Ro= 26 UNITS 50 ~----------+-------- ------+_---- ~~~ --_+------ ----- ~ 10 - CUMULATIVE FREQUENCY (b) R e sults for wing-root bending stre ss.
Figur e 16 .- Concluded.
'1. RANGE - PAIR COUNTING (BAS I C) <SCHE VARIANT o RANGE-PAIR-RANGE COUNTING 100 I--------F=":O"~_=__' ..::s:,:::s;:- --+-____j & SIMPLE RANGE COU NTING 50 1-- ------r-------r---- ~~ -_+------ ____j 10 10 10 ~ CUMULATIVE FREQUENCY (a) Re sul ts for c.g . a cce leration .
Fi gure 17.- R ange c oun t in gs.
LOAD t~~--~~~--~~~ ~ --~-- ~~~ ~~~~" • RANGE - PAIR- RANGE METHOD & RANGE - PA IR METHOD (BOTH VAR I ANT S) I-----=:....:::::, '""""'=: :---II-----">..; ~ ---I- ----j 0 SIMP LE RA N GE COU NT ING <BA S IC) 50 ~--------+_------------_r----~ ~._--_+------------ ~ 10 10 - CUMULATIVE FREQUENCY (b) R esu l ts for wi n g- r oot b end in g stress.
F igure 17 .- Co ncl uded.
WI NG-ROOT BENDING RANGE VA L UE / /
t
/ 100 f- --- ®-; -----:,r----i r·~R~A~N~G~E--~M=E7AN ~ C~ O~ UN~T~ I N~G~ o RANGE-PAIR-R A NGE METHOD 50 f- -~---~- --i M: AVERAGE MEAN VALUE WITH REF . TO " l-G " MEAN LEVEL / (3 50 - M 50 - M F igure 1 8.- Comp ar ison of a ve r aged me a ns.
0SIMPLE RANGE COUNT METHOD • RANGE - PAIR - RANGE METHOD FROM SIMPLE PEAK COUNTING : X CONVERSION A El " B fA " C 100 ~-----~ ""':::", ~~~~~J-- -'=========F======== ~ -l 50 r- ------------~r_---------- --_1-------- ~~~~ -------------- ~ CUMULATIVE FREQUENCY (al Results for c.g. acceleration.
Figure 19 .- Pe ak countings compared wi th range countings.
o SIMP LE RANGE COUNT I NG • RANGE- PA I R-RANGE FROM SI MPLE PEAK COUNT I NG .
x CONVERS I ON A EJ " 8 fA C 100 ~-- ~ ~-= --4-~~~~~~-- ~=======+======== ~ - ro r- ------------~--------------~---- ~~~~~ ------------~ 10 -CUMULATIVE FREQUENCY ( bl Results for wing-root bending stress.
Figure 19 .- Concluded .
DETECTION OF STRUCTURAL DETERIORATION AND ASSOCIATED AIRLINE MAINTENANCE PROBLEMS By H. D. Henniker British European Airways United Kingdom and R. G. Mitchell British Overseas Airways Corporation United Kingdom STRUCTURE INSPECTION The requirement to operate a civil transport aircraft on scheduled operations for a period of perhaps 15 to 20 years, with a constant level of safety , creates a need for a system of continuous monitoring of the structure. At the same time it is implicit that no unnecessary work should be done and that the time out of service should be minimal.
It is perhaps necessary first to outline the approach to the maintenance and inspection of the components and systems of the aircraft. It has become apparent that most components, and therefore systems , suffer primarily from random effects . In a relatively few cases a life can also be dictated by a wear-out rate , but random defects predominate and have to be dealt with by inspections and functional checks so that the defect is detected at the earliest opportunity.
By duplication , or triplication , the integrity of the aircraft can be maintained , and the study of reliability levels can set the periods for inspection or checks which limit the period of dormant failure. Since a large number of components are functioned on each flight, the number of additional checks required to reveal a dormant fault is reduced.
It can be seen that for systems and components , the optimum periods for insp e c- tion , maintenance , and overhaul can be safely developed in respect of a particular air- craft type and a particular operation by a process of recording and analysing data on failures and strip reports and by general experience g ained in service. The aircraft itself determines its own maintenance schedule.
In respect of structures , a different approach has to be adopted. With the advent of fail-safe structures , the duplication of load path which provides failure survivability has been achieved. Unfortunately , no ready indication of failure is available. The purpose of inspection is therefore to detect failures before they become catastrophic , and to detect such deterioration with time and use which, in itself , will lead to failure.
The object of maintenance is to restore the structure to its original condition and to main- tain the failure survivability originally built into it.
It is natural that there should be a desire to use the same downtime of the aircraft to deal both with structure and systems. Improved component life and improved relia- bility lead to longer intervals between major maintenance inputs. There is therefore an inevitable clash of requirements because the structure tends to deteriorate with age and demands increased vigilance.
The structure inspection that emerges is therefore a compromise influenced by opportunity, and it changes with time. In deciding initially on the nature and extent of inspection, the design philosophy and the background of fatigue and fail-safe substantia- tion tests are of paramount importance. A structure inspection schedule for the lead fleet of a new type of aircraft is arrived at by extracting the structure content from the total schedule. A typical structure schedule is outlined as follows (in this schedule flight- hours and flights are approximately the same): At each departure and at each 72 hours elapsed time: A general walk-around check which would detect gross damage , due to either serious structural failure or damage inflicted on the ground.
At each 300 hours or flights: A general visual inspection of the complete exterior, supplemented by opportunity inspection of such areas where access is required for maintenance and servicing. This check is also used to monitor any item on special surveillance.
At 2000 hours (12 to 15 months): A more detailed visual inspection of the lower fuselage, externally and internally , including pressure bulkheads, and door- surround structure. This is aimed primarily at detecting corrosion. Ultrasonic checks are also made at this interval on bonded stringers in the lower fuselage , and radiographic inspection is made in those areas of the lower fuselage not acces- sible for visual inspection.
At 5000 to 6000 hours or flights (2 to 2t years): The major maintenance check in which all access panels are removed and all structure inspected visually.
This represents the most detailed routine visual inspection of the structure possible by normal access, that is, without stripping out interior trim and lagging. At the same intervals - but not necessarily at the same time - radiographic inspections are made of closed structures such as Horizontal stabilizer Fin Primary control surfaces Slats, flaps , air brakes , and so forth All these inspections are carried out on all aircraft in the fleet. The extensive areas of the internal structure of the upper fuselage (above floor level) are the subject of a sampling procedure. This approach is made because of the extensive downtime involved if all trim, soundproofing, thermal lagging, air ducts, and so forth are removed.
Experience has shown that the area below floor level is that most prone to corrosion.
This can occur early in the aircraft life and can progress relatively rapidly. Experience also suggests that the upper areas dry out more rapidly, and corrosion is only likely at a later stage and will develop less rapidly.
The sampling programme is therefore started in about the 5th year of operation (10 000 to 12 000 hours). Because of the large work load and downtime involved, radio- graphic inspection is used extensively but is supported by visual inspection as follows: . In each of the 5th, 6th, 7th, and 8th years of operation, one composite aircraft is examined, 25 percent by visual means and 75 percent by radiographic means. The samples involve not less than 60 percent of the fleet, and at the end of this period one complete composite fuselage will have been examined visually; and three, radiographically. It is planned that after the 9th year the sampling will be extended so that by the 20th year all aircraft in the fleet will have been examined completely both visually and radiographically.
The choice of inspection method is basically economic. Where visual inspection is viable, it is preferred. Radiography is an adequate tool to detect the Significant craCking of internal structure such as frames, stringers, and cleats. It can also indicate corro- sion and paint flaking - but requires considerable skill in interpretation. A 10-percent reduction in material thickness can be reliably detected , provided the corrosion deposits are not retained. The critical corrosion along the heel line of a stringer or lap joint is detected mainly by evidence on the adj oining surface.
In a particular case where this inspection schedule has been applied up to an aver- age aircraft life of 12 000 flights or 6 years, 38 defects have been identified. Of these , 16 involved fatigu~ cracks, in secondary structure, and two involved corrosion in primary structure. Most of these defects were detected on the major check. In the period con- cerned , the major check period has been progressively increased from 3000 to 5000 hours, or flights, on the basis that those items which have shown up and are not subject to modi- fication action are retained as specific items on the annual or 300-hour inspection.
For detection of deterioration that could be the cause of fatigue, this increase in the major check period is feasible. If, however, the major check is to form the basis for detection of fatigue cracks concerned with the fail-safe design concept, then the period between inspections must have some finite limit. This should be the interval assumed in the design concept from first detectable crack to the point at which crack propagation reduces the static strength to proof load. Ideally, this should be demonstrated by a full- scale test for all fatigue-critical regions of the structure. For the aircraft concerned the period is not less than 5000 flights, with proof load applied each 2500 flights. On this basis each aircraft structure must be examined in detail at maximum intervals of 5000 flights. It might well be argued, however, that when the aircraft life is relatively low , so that this interval represents a Significant part of the probable scatter between identical failures on aircraft of the same fleet, then staggered inspection over a longer period is perhaps justified on the basis that no cracked aircraft will fly more than 5000 flights before the defect is detected in another of them. It is implicit that all aircraft will be checked within a short period from the discovery of the first defect.
As the aircraft life increases, so that the safe period of crack propagation becomes small in relation to the probable scatter in failure , the inspection would have to be increased to cover each aircraft in 5000 flights. As the aircraft life increases still fur- ther so that the probability of failure is high and simultaneous failures become probable, it would be prudent to reduce the inspection interval.
Finally, it would seem logical that whilst the ratio of test life to aircraft life is 5 or more, inspection can be done on a sampling basis only, to assess the general deterio- ration, such as corrosion. Thus, an ideal structure inspection schedule would result and would be based on aircraft life and test life. (See fig. 1.) The practical problem would then be to integrate this schedule with the remainder of the maintenance requirements and the seasonal demands on aircraft.
If there are several operators involved in making up a Significant fleet of "lead" aircraft , there is a case for spreading the initial sampling across all the aircraft to thus reduce the requirement on the individual operator. This involves a reporting system so that the manufacturer can coordinate results. There are possibly limitations to this approach, since each operator tends to operate on a different route structure and in a different environment.
Most aircraft types operated by British European Airways (B.E .A.) have carried some form of in-flight recording equipment , either fleetwise or on selected aircraft. In some cases this has been a condition in the terms of the warranty on the fatigue life of the primary structure. The recording equipment has fallen into two categories: (1) Continuous recording of acceleration thresholds or strain-range thresholds on entire fleets (2) Continuous recording of acceleration thresholds together with other flight data on a limited number of aircraft In the first category , counting accelerometers mounted at the center of gravity record threshold counts at increments of 0.2g between 0 and 2g. Total counts in each level are read and recorded at each 300-hour check.
Fatigue-meter data are fed back to the respective manufacturers at intervals, together with operational data from which a typical flight plan, representative of the route network, can be deduced. This is done by taking significant samples of summer and winter operations and includes take-off weight, fuel state at take-off , cruise altitude, and flight duration . Fuel burn-off is computed and thus actual weight and fuel state at each phase of flight are deduced. The aircraft manufacturer then computes fatigue dam- age rate and compares this with the damage rate used in the fatigue test or calculated fatigue life.
Similar procedures are adopted in the case of strain-range counters, except that these give 'a more direct indication of damage rate and require less operational data.
In both cases the manufacturers concerned have stated that an increase in service life of up to 30 percent has been possible compared with the service life that would other- wise be imposed. So far, this has all been in respect of those parts of the structure which are on a "safe life" basis.
Both these types of recording instrument are such that they are quite practical for an airline to carryon all aircraft. They need little attention and are reasonably reliable.
As long as there are safe-life items in the primary structure, the improvement in life that has been possible would appear to be adequate return .
The more comprehensive type of observer unit is more questionable. Attempts have been made on two types of aircraft to get a simultaneous record of acceleration counts, speed, height, time of flight, and so forth by use of film recorders, switched on at take-off and off on landing by an airspeed switch. " They have been installed in perhaps two aircraft of a new fleet with the object of obtaining more complete data for an initial period. The problems with film recorders have been (1) Short duration of film leading to either much lost recording time, or very frequent film changes (2) Unserviceability revealed only after film development (3) Reference still required to flight documents to obtain aircraft weight and other data (4) Low order of reliability The authors have found from experience that only about 10 percent of the total hours flown by the aircraft equipped with the film recorders were satisfactorily recorded. It does not seem practical to use this type of equipment in the environment of day-to-day airline operation.
It has been B.E .A. policy to record manually maximum cabin differential pressures for each flight on all aircraft. The pilot records this in an appropriate box in the techni - cal log. This information is extracted and the total flights in each band of pressure, in increments of 1/2 psi, are computed. Where there are maximum lives prescribed for modification or replacement of structure, this information is forwarded to the manufac- turers and to the airworthiness authorities at six monthly intervals. All unrecorded flights are assumed to be at maximum differential pressure, and a factor of 10 percent is added to the recorded pressures to allow for inaccuracies of recording. At the same time, the equivalent flights at maximum differential pressure are computed and forwarded to the inspection department to allow mandatory life requirements to be monitored.
This policy has yielded Significant benefits where safe-life situations have existed.
It allows advantage to be taken of all flights where only low pressures are needed, yet retains the advantage of operational flexibility, such as cruise altitude on longer flight sections and occasional high rates of descent. This flexibility is otherwise lost if pres- sure is permanently reduced. On one type of aircraft it has allowed an extension from 12 500 to 30 000 flights before a major modification, with its accompanying weight penalty, was required and from 17 000 to 50 000 flights before wholesale replacement of fuselage skins.
It is true to say that the advantages so far gained by continuous recording in airline operation have all been associated with safe-life structure situations. It is questionable whether real advantages can accrue in the case of a truly fail-safe structure. One of the advantages, to the manufacturer, of a fail-safe philosophy is that the duration of the full- scale test can be reduced. If the structure is designed for a long fatigue life, it is prob- able that natural failures will not be produced on test. Provided adequate fail-safe tests are carried out, this may be satisfactory from an airworthiness point of view, but it would seem pointless, in this case, to try and correlate test and actual aircraft usage in order to try and predict the operator's long-term planning requirements.
Only if full-scale testing is extended until fatigue failures occur - and perhaps only if these then indicate the need to impose a finite life when action must be taken - can better data on actual aircraft usage yield some dividends.
MAINTENANCE ASPECTS It will be appreciated that although the modern public transport aircraft is a highly complex and sophisticated engineering product, it is also the means by which the air- lines earn their revenue. The aircraft utilisation rate, which varies during the year and reaches its peak during the summer months, is laid upon a foundation of known work pro- grammes which stipulate that various aircraft will be undergoing maintenance for block periods of time during the year. It will be seen, therefore, that in order to support the commercial plans, an extremely well-devised maintenance programme is required. For an airline to operate at optimum efficiency , the maintenance programmes are planned to ensure that the work requirement is matched by the necessary spares, materials , tools , equipment , and labour at the commencement of the hangar check.
The unexpected and nonscheduled problem is, therefore, strictly an economic embar- rassment. The discovery of a fatigue crack, corrosion, or any of the other mechanical faults which beset airline operators from time to time and which must be repaired on an urgent basis are the ones which really cause the headaches.
Ideally, the airline engineering base should be a facility carrying out planned main- tenance and changing or repairing wornout components. This is, of course , an ideal sit - uation which never exists in practice. For instance , a piece of ground-support equipment could be run into the side of an aeroplane and thus cause a delay to the service. Simi- larly , the work necessary to repair the unexpected crack in a major piece of structure can soon seriously upset the best planned engineering commitment and rapidly lead to nonavailability of aircraft.
It must also be remembered that there will be an internal conflict of interests within the airline. The production and maintenance departments are charged with producing aeroplanes for service to meet the commercial demands, and an engineering require- ment which may extend the hangar check times or takes aircraft out of service is reSisted, unless vital to continued safe operation. Also, since modern aircraft construction is making ever-increasing use of integrally machined components , which in themselves are much more difficult to repair in terms of time and complexity than the riveted skin- stringer combination , it also follows that the flow of spare parts from the manufacturer in the event of a rash of fatigue problems across the fleet could be inadequate to meet the demand.
All aircraft exhibit cracks in various structural components. Many of these , hav- ing relieved a local stress condition, will then remain static in length for a considerable period of time, and the aircraft will continue in service with these known defects. Nor- mally such defects are examined for signs of propagation at each scheduled inspection until the part can be replaced or repaired, ideally at a convenient hangar check. This applies mainly to multi-load-path and secondary structure, but of course all cracks and defects are evaluated and a course of action decided upon which is dependent upon the significance of the defect. In the case of more serious defects the normal procedure is to raise a special check on the remainder of the fleet to determine the extent of the prob- lem fleetwise. The speed at which the fleet examination takes place, of course, depends upon the severity of the initial defect. In this way the extent of the problem is assessed and the final action will take the form of a modification or repair, which can be raised either by the air line or manufacturer, or by replacement on a lifed basis. In many cases the defect is subsequently monitored by the addition of a specific item to the approved maintenance schedule for inspection at appropriate intervals, or included in the reportable structural inspection pro g ramme.
In the case of a repair, the structure is usually returned to the "as new" condition, but when this is impractical or economically not justified, the fatigue life of the repair must at least match the residual life of the aircraft. In many cases when extensive test- ing or investigation of a fatigue problem is required, it may be necessary to incorporate a temporary repair which satisfies limit loads and thus keeps the aircraft flying. The long-term action which may require a slightly more extensive repair can then be carried out at a later stage, usually at a major overhaul. It has been found from experience that the manufacturer's solution to most light-alloy fatigue failures invariably results in a steel replacement.
Once a defect is found, a repeat inspection of the area is established , which can be extremely frequent in serious cases. The general accessibility and nature of the defect will determine the method of inspection , that is, visual or nondestructive testing tech- niques. In any event the general aim is to implement modification-campaign action to eliminate the defect and its associated inspection.
When a new defect is found , the airline informs the manufacturer, who then advises all operators of similar equipment to inspect for that particular defect. The manufactur- er's notification usually ranges from a newsletter covering general advice, the service bulletin which forms the usual channel of communication , to the service cable for serious problems which require rapid investigation.
Since fatigue failures are generally related to total flying hours or landings , it fol- lows that an airline operating "young" aircraft is less likely to be hit by the nonscheduled problem than an operator with older aircraft of the same type, and has a better chance of carrying out the rectification on a planned basis.
A large number of fatigue problems encountered can be traced to detail design faults, and occasionally the classic "don'ts," such as sharp section changes and stress raisers, still seem to be perpetuated.
It has been found from experience that unnecessary disturbance of an area during maintenance can in fact be detrimental in the long run . For example, abrasion of sur- faces can break down sealants , particularly in integral fuel tanks, and minute scratches are then susceptible to corrosion or crack initiation.
The Corporation is an approved design organisation and designs and incorporates a great deal of repair work, particularly to components. For example, the Corporation has a great deal of experience on the repair of honeycomb structures. Any repair work must maintain the aircraft to airworthiness requirements. This, of course, includes correct heat-treatment techniques , particularly with the high-strength steels , and maintenance of adequate strength reserves after such rework. A copy of the repairs is automatically sent to the manufacturer for his information , but naturally in the event of serious prob- lems the manufacturer is consulted prior to making the repair.
Although the primary airframe structure, critical joints, representative panels, and the like are subj ected to extensive fatigue testing at the design and construction stage to prove the integrity of the basic airframe, secondary structure does not receive the same consideration. Experience shows that defects in secondary structure tend to be repetitive and are both costly and time consuming to repair or replace. For example, certain areas of most aircraft floors require frequent replacement because of corrosion under and adjacent to galley and toilet areas and for damage due to cargo loading and repeated walking traffic . It would seem that the original floor is largely designed by static load requirements on the grounds that a stronger and longer lasting floor, because of the weight penalty incurred, is not justifiable on economic grounds. This, of course, is all good theory , but replacement floor costs are extremely high. Because of the absence of reliable fatigue data on floor materials, various sandwich floor-panel mate- rials were investigated on a cost - effective basis which involved static testing and fatigue testing a large number of samples. In fact, representative panels of various materials have been installed for service evaluation. The airline is, of course, ideally suited to perform actual in-service tests, and new ideas are often subjected to field tests in a true operational environment. Although in the manufacturer's initial fatigue test every attempt is made to represent a true operational condition, it sometimes happens that despite the best efforts of the designer, a part will fail prematurely because of the influ- ence of a secondary unknown or neglected loading system. A case in point recently occurred when a fairly substantial shear angle hidden from immediate view was found to have cracks of considerable length along the bend radius. On investigation the frac- ture face showed that the angle, which had been designed to carry shear loads, was in fact also being subjected to secondary bending loads which tended to open and close the angle. Fortunately, in this case, the cracks were found before a failure occurred.
Another example in which the initial design failed to take complete account of the full loading cycle is the fatigue cracks experienced in top wing skins of some aluminium alloys containing a high percentage of zinc. The alloy is chosen in the first instance because of its mechanical properties and because the normal flight loads give a com- pressive loading. It has been established, however, that the ground loads, which reverse the wing bending system, cause tensile loads of sufficient magnitude to cause fatigue cracks around stress concentrations, fastener holes , for example , in this material.
One interesting case of structural failure occurred when the designer had assumed a certain airspeed for flaps extended for his fatigue analysis within the flaps-out speed range. The pilots , however , were in fact flying the aircraft right up to the flap limit speed, and premature failures occurred. Another problem which occurred was that in - - --- - - -- ~ - - the original design certain assumptions were made with respect to ground turns based upon airports known at that time. Subsequently the Commercial Department decided that a great deal of revenue was forthcoming from lesser known airports, and ground manoeu- vres in excess of the assumptions were made. Airports are very congested places on the ground as well as in the air, and ground turns can be dictated by available ground space.
An aspect of airline usage which is outside the normal operating pattern is crew training. It is quite normal for one aeroplane to spend a considerable time on a training detail, and this operation sometimes results in flying techniques which are not up to nor- mal standards. The number of landings are very considerable over a short period of time and since one of the objects of the exercise is to acquaint flying crews with aircraft- handling characteristics which are seldom met in practice, the airframe is subjected to a great number of loads which are not normally met in passenger service. These facts must be recognized at the design stage. Airframe damage has, in fact, resulted from training details.
Civil aircraft are in service for a considerable period of time, some 15 years or more typically. Airframe lives on the order of 60 000 flying hours are commonplace with the current generation of aircraft, and of course the fatigue problem intensifies as the aircraft get older. The economics of airline operation is such that operators are carrying out life-extension programmes in order to achieve these lives by replacing and/or reworking critical areas at some stage during the service life of the aircraft. It is vital, therefore, that the initial assumptions, analysis, and testing faithfully represent as far as possible the complete loading programme and its environment, and that the effect of new materials is fully examined, particularly where no previous experience is available.
Each new generation of aircraft brings a new challenge both to the operator and manufacturer, and the SST will be no exception. The operator must rely on the manu- facturer to provide a trouble-free product, and to this end, practical airline experience of day-to-day operational problems and practices is freely available. Operational expe- rience should be fed back into new deSigns to ensure long, trouble-free lives, particularly at the detail design stage.
The addition of speed and temperature will bring new complications to the SST. It is to be hoped that the racehorse will not exhibit the temperament of a thoroughbred but will retain the cart-horse stamina for everyday reliability.
SUGGESTED BASIS OF MAJOR STRUCTURE INSPECTION
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PRECEDIN G PAGE BL ANK NOT FILMED FATIGUE FAILURE OF METAL COMPONENTS AS A FACTOR IN CIVIL AIRCRAFT ACCIDENTS By William L. Holshouser and Ruth D. Mayner National Transportation Safety Board Washington, D.C., U.S.A.
SUMMARY A review of records maintained by the National Transportation Safety Board showed that 16 054 civil aviation accidents occurred in the United States during the I 3-year period ending December 31, 1969. Material failure was an important factor in the cause of 942 of these accidents. Fatigue was identified as the mode of the material ~ailures associated with the cause of 155 accidents and in many other accidents the r~cords indicated that fatigue failures might have been involved. There were 27 fatal , accidents and 157 fatalities in accidents in which fatigue failures of metal components were definitely identified.
Fatigue failures associated with accidents occurred most frequently in landing- gear components, followed in order by powerplant, propeller, and structural compo- nents in fixed-wing aircraft and tail-rotor and main-rotor components in rotorcraft.
In a study of 230 laboratory reports on failed components associated with the cause of accidents, fatigue was identified as the mode of failure in more than 60 per- cent of the failed components. The most frequently identified cause of fatigue, as well as most other types of material failures, was improper maintenance (including inade- quate inspection). Fabrication defects, design defiCiencies, defective material , and I abnormal service damage also caused many fatigue failures.
Four case histories of major accidents are included in the paper as illustrations of some of the factors involved in fatigue failures of aircraft components.
INTRODUCTION Civil aviation accidents in the United States were investigated by the Civil Aero- nautics Board from 1940 until 1967, when the National Transportation Safety Board was established as an independent agency within the Department of Transportation. On April 1, 1967, the safety functions of the Civil Aeronautics Board, including the respon- sibility for investigating and determining the cause of civil aviation accidents , were transferred to the new Safety Board. Hence , the information on accidents used in the preparation of this paper was taken from records and files accumulated partly by the Civil Aeronautics Board (CAB) but now maintained by the National Transportation Safety Board (NTSB).
An aircraft accident is defined in NTSB Regulations as "an occurrence associated with the operation of an aircraft which takes place between the time any persons board the aircraft with the intention of flight until such time as all such persons have disem- barked, in which any person suffers death or serious injury as a result of being in or upon the aircraft or by direct contact with the aircraft or anything attached thereto, or the aircraft receives substantial damage." The Board regulations also contain defini- tions of terms , such as "serious injury" and "substantial damage ," that form a part of the definition of an accident. During the last 10 years (1960-1970) the number of civil aircraft accidents per year meeting this definition has ranged from 4709 in 1961 to 6185 in 1967. More than 98 percent of these accidents were in general aviation, which, of course, means that, in general, they involved relatively small aircraft engaged in private flying, business trips, and small commercial operations.
Information on the extent to which fatigue failures in metal components are involved in the cause of accidents was obtained by reviewing accident records and la1;:>oratory reports that are available in Safety Board files. The accident records provided consid- erable data on material failures but did not provide statistically reliable information regarding either the mechanism or cause of failure. Hence, the data presented under the heading of "Accident Records" is included primarily as background information for the results of the study of laboratory reports. Four case histories of maj or accidents are presented as illustrations of some of the factors that are involved in fatigue failures of aircraft components.
ACCIDENT RECORDS There were 16 054 civil aviation accidents in the United States during the 3-year period between January 1, 1967, and December 31, 1969. NTSB records show that mate- rial failure caused, or was a factor in the cause of, 942 of these accidents. Thus, mate- rial failure was involved in the cause of slightly less than 6 percent of the total number of accidents during this period. Only 20 of the 942 material failure accidents occurred in air carrier operations.
Fatigue was identified as the mode of material failure in 155 accidents. There were many other accidents in which fatigue failures might have been involved but the fractures were not identified as fatigue in the record. For example, there were a num- ber of in-flight failures of propeller blades and many cases of connecting rods, connecting rod caps, or connecting rod cap bolts failing in reciprocating engines in which the mode of failure was not identified. It seemed likely that in many ca s es the investigator may have been unable to recognize evidence of fatigue or that such evidence might have been destroyed by subsequent damage to the fracture surfaces.
Information obtained from the accident records is summarized in tables 1 and 2.
The serious nature of fatigue failure accidents is shown by the fact that the 16.4 percent of the material failure accidents in which fatigue failures were identified accounted for 31 percent of the aircraft that were completely destroyed , 46 percent of the fatal acci- dents , and 63 percent of the fatalities.
There may be some inaccuracies in the classification of components in table 2 because the specific part that failed was not always adequately identified in the record.
For example, a few parts listed as landing-gear components might actually be parts of the hydraulic system or some parts listed under powerplants might be more properly identified as electrical system components. However, the general trend of component failures shown in the table indicates that landing gears and powerplants are major prob- lem areas.
The records from which the data in tables 1 and 2 were obtained did not provide any Significant amount of information regarding the basic cause of failure except in one cate- gory. Definite evidence of improper maintenance or inadequate inspection was found in 130 accidents , whereas there were indications that many other accidents might have been prevented by better inspection and maintenance procedures.
The number of accidents listed in the tables, of course , represent only a small per- centage of the total number of material failures in civil aircraft. Most of such failures do not result in accidents and the failed components are replaced or repaired on a more or less routine basis.
LABORATORY REPORTS Additional information regarding the mechanisms and causes of aircraft material failures was obtained from a study of 230 laboratory reports on the examination of failed components . These were reports on work done in the Safety Board ' s laboratory , work done for the CAB and the Safety Board at the National Bureau of Standards , and a few reports from industry laboratories. All the reports were on components from aircraft that had been involved in accidents between 1962 and 1970. Reports on failed components that were not pertinent to the cause of an accident were eliminated from the study insofar as possible.
A summary of the results of the study is given in table 3. In classifying the causes of failure , fabrication defects were listed as such only when they appeared to have been caused by a manufacturing operation. When this kind of deficiency occurred during main- tenance, the cause of the resulting failure was classified as "improper maintenance."
The "abnormal service damage" category includes only failures caused by service dam- age that probably would not have been detected by normal inspection procedures. The cause of failure was listed as improper maintenance if it appeared that the service damage could have been found and repaired prior to failure by ordinary good maintenance practice. As anyone who has been involved in the investigation of service failures will realize, the evidence regarding the cause of failure was not always conclusive. In many of the cases studied, some element of judgment entered into the classification. Stress corrosion and hydrogen embrittlement failures were grouped together in the table because, in some cases, reports of studies of the fracture surfaces with an electron microscope identified the fractures as "stress corrosion or hydrogen embrittlement" but did not attempt to distinguish between the two failure mechanisms.
Fatigue failures accounted for more than 60 percent of the failed components on which laboratory reports were available in NTSB accident files. The distribution of fatigue failures among the causes listed in table 3 illustrates one of the major difficul - ties of preventing such failures in aircraft. So many different kinds of material defects, design errors, mechanical damage, and corrosive attack can contribute to the cause of fatigue failures that it is extremely difficult to guard against all of the possibilities. As in the review of accident records, the results of the study of laboratory reports indicated that improper maintenance is the most frequent cause of fatigue and other types of mate- rial failures that contribute to the cause of aircraft accidents.
Specific causes of failure included in each category in table 3 are as follows. (No attempt was made to list these causes in order of frequency of occurrence. The exact number of failures due to each specific cause could not be determined because in many cases the failure could be placed in one of the broad categories but the cause could not be more specifically defined, mainly because of discrepancies in maintenance records, inconclusive results of laboratory work, and more than one factor being involved in the cause of failure.)
Improper maintenance: Inadequate inspection Failure to replace damaged parts Failure to comply with manufacturer's service bulletins or FAA Airworthiness Directives Inadequate lubrication Failure to service air drying system Unsatisfactory welding Inadequate shot peening Failure to repair damaged protective coating Inadequate or excessive torque applied to fasteners Failure to install fasteners Use of unsatisfactory replacement parts Inadequate cleanup after repairs Foreign material left in gear housing Improper alteration of components Surface damage due to misuse of tools Inadequate control of plating operations Grinding cracks Application of excessive force to press fits not adequately prepared for assembly Improper adjustment of gear engagement Insufficient thread engagement Damage from misuse of inspection equipment DeSign deficiencies: Inaccurate stress analysis (mainly due to insufficient consideration of sources of stress concentration) Inadequate specification of dimensional tolerances Failure to allow for fabrication and assembly variables Selection of unsuitable material or incompatible combinations of material Insufficient consideration of the effect of possible bending loads on parts designed to resist tension or compression loads Insufficient consideration of the direction of grain flow in forgings and extrUSions Insufficient consideration of maintenance problems Failure to specify adequate decarburization limits Fabrication defects: Machining errors Unsatisfactory welding or brazing Unsatisfactory plating Improper drilling of rivet holes Surface damage by defective tools Damage by careless use of tools Failure to remove cleaning solution from a closed cavity Inadequate cleaning after an internal machining operation Inadequate control of bonding operation Defective material: Surface decarburization Heat treating cracks Omitting heat treatment or surface hardening operation Forging flaws Defective extrusion bonding Overheating during heat treatment Casting porosity or cracks Excessive nonmetallic inclusions Gas contamination Failure to use specified material Abnormal service damage: Engine overspeed Excessive vibration Failure of pilot to follow operating instructions Inadequate securing of cargo Unauthorized towing procedures Excessive maneuvering loads Deformation from undetermined source Bird strike Excessive loads resulting from damage to an associated component DISCUSSION The results of the studies summarized in this paper emphasize the importance of fatigue and maintenance problems in the operation of aircraft equipment. By far the most common type of material failure encountered in aircraft accident investigation is in landing-gear and powerplant components of small fixed-wing aircraft. Material failures most frequently cause accidents when they occur while the aircraft is airborne or during landing, although serious accidents may result from failures during any phase of operation.
Opportunities to reduce the number of accidents caused by fatigue failures and other types of material problems exist in almost all phases of aircraft construction, mainte- nance , and operation. The greatest potential for reduction in the number of accidents is in improving the maintenance of general aviation aircraft. However, numerous accidents in both general aviation and air carrier operations could be prevented by improvements in design; better quality control during material proceSSing, fabrication, and assembly; improved inspection and maintenance programs; and more careful handling of aircraft, particularly on the ground during taxiing and towing operations.
Although the air carriers have had relatively few accidents caused by material fail- ure, in the 3-year period included in the review of accident records, 6 of the 20 air car- rier accidents in which material failure contributed to the cause resulted in 138 fatal injuries. Accidents involving fatigue failure accounted for 103 of these air-carrier fatal- ities. In several failures of landing-gear components and jet engine compressor and tur- bine diSks, major disasters were avoided only by fortunate circumstances. Thus , this study indicates that air carrier, as well as general aviation, aircraft have serious material failure problems.
CASE HISTORIES Four case histories of accidents due to fatigue failures of components are presented.
I. Los Angeles Airways, Sikorsky S-61L Helicopter ; Compton, California ; August 14, 1968 This helicopter crashed when a fatigue failure of one of the main rotor blade spin- dles caused the blade to separate from the rotor hub. The drawing of the failed spindle in figure 1 shows the location of the fracture. A fatigue crack had propagated from a single origin (fig. 2) in the journal-bearing fillet through approximately 70 percent of the cross section of the spindle shank prior to complete failure. The spindle was made of quenched and tempered 4340 steel, with a specified hardness of 34 to 38 Rockwell C and a specified minimum ultimate tensile strength of 150 000 pounds per square inch.
This spindle had been reworked in 1966, 2 years before the accident, according to a pro- cedure recommended by the manufacturer. The rework included regrinding, shot peen- ing, and nickel plating the journal bearing surface and fillet where the fatigue crack origi- nated. In June 1968, approximately 2 months before the accident, during a regular peri- odic inspection, the spindle was inspected for cracks by a fluorescent magnetic particle method . No cracks were detected.
A laboratory study after the accident revealed the following factors that were prob- ably involved in the cause of the spindle failure: 1. The fatigue crack was a high cycle, low stress, slowly propagating crack that probably had been present when the spindle was inspected for cracks 2 months before the accident.
2. The fatigue nucleus was in the steel, under the nickel plating, in an area where very small , shallow pits were found in the surface of the fillet.
3. In the area where the fatigue crack originated the steel had a banded microstruc- ture. The overall hardness in this area was 28 Rockwell C, below the specified minimum of 34 Rockwell C, and the fatigue nucleus was in one of the softer bands where the local hardness was well below 28 Rockwell C.
4. Residual tensile stress in the fillet surface as a result of nickel plating might have contributed to the initiation of the fatigue crack although the plating process speci- fied by the manufacturer was selected to minimize residual stresses.
5. The fillet where the fatigue crack originated had not been properly shot peened.
This fact is considered to be an important contributing factor as adequate shot peening would probably have eliminated the effect of the shallow pits and would have reduced the effect of the banded microstructure and low hardness.
II. Lake Central Airlines , Allison Prop-Jet Convair 340; Marseilles , Ohio; March 5, 1967 A fatigue failure of a propeller torque cylinder (fig. 3) precipitated the crash of this two- engine , turboprop aircraft. The fatigue failure , however, was caused by a prior failure in another component of the propeller pitch control system. The initial failure was excessive wear in the splines of the torque piston.
Propeller blade pitch in this aircraft is controlled through torque units (one unit for each of the four propeller blades) operated by hydraulic oil pressure. Through a system of splines , linear movement of the torque piston in the torque cylinder produces changes in propeller pitch. An increase in hydraulic pressure moves the piston outward to increase blade angle and a decrease in pressure permits the normal aerodynamic loads on the propeller to decrease blade angle. The piston has both internal and external splines and after the accident both sets of splines in one piston were found to be severely worn. These splines had not been nitrided as required by the manufacturer's specifica- tion for the piston. The excessive wear in the splines allowed the piston to float free in the cylinder without engaging the splines of the mating parts. This condition did not immediately cause any detectable change in the operation of the propeller because of the redundancy built into the pitch control system . However, each time the oil pressure in the system was increased the free piston was forced hard against the cylinder cap. This force resulted in stresses exceeding the fatigue strength of the cylinder wall and eventu- ally caused a complete fatigue failure of the cylinder.
Examination of the fracture (fig. 4) showed that small fatigue cracks had propagated from the inner surface of the cylinder wall and combined to form a continuous crack completely around the inner circumference of the cylinder. This fatigue crack did not penetrate completely through the wall so that hydraulic pressure was maintained until the cylinder failed completely. When the cylinder failed , loss of hydraulic pressure occun'ed so suddenly that the propeller pitch lock failed and resulted in a severe pro- peller overspeed. All four propeller blades were thrown off the propeller hub; and one of them went through the fuselage and caused the airplane to break up in the air and crash.
The series of events that led to this accident started with the omission of the nitrid- ing of the torque piston splines. As a result of investigations associated with the acci- dent , changes were made in the quality control system of the propeller manufacturer and several design modifications were made in the propeller pitch control system. These changes appear to be adequate to prevent a similar set of circumstances causing another accident.
lIT. Wein Consolidated Airlines, Fairchild F-27B; Pedro Bay, Alaska; December 2, 1968 This aircraft encountered severe to extreme . clear-air turbulence and crashed dur- ing a flight from Anchorage to Iliamna in Alaska. Investigation of the accident showed that an in-flight structural failure of the right wing had occurred through an area where fatigue cracks had weakened the structure on both sides of an access door in the bottom surface of the wing.
The piece of wreckage in which the fatigue fractures were found is shown in fig- ure 5. Fatigue cracks had originated at four fastener holes, two on each side of the access door, that were alined in a chordwise direction. These initial cracks had prop- agated and joined to form a crack about 31 inches long on the aft side of the access open-
ing and about 2~ inches long on the forwaid side. No evidence of fatigue cracking was
found in the access door cover. Adjacent to the fastener holes, the fracture surfaces were flat and smooth, as shown in figure 6, but as the cracks progressed away from the holes, they showed an increasing tendency to propagate as slant fractures. Numerous crack jump marks (small regions of ductile rupture) were found in both the flat and slant fracture areas. An example of the appearance of these jump marks is shown in figure 7.
Fatigue and fail-safe tests of an F-27 wing made several years before the accident gave some indication that a load equal to about 77 percent of limit load might have been required to break the wing with cracks about 3 inches long on both sides of the No.1 access door. However, the numerous indications of high stress intensity found on the fatigue fracture surfaces suggested the possibility that high gust loads might have caused a rapid tearing extension of the cracks shortly before the wing failed completely. Such a rapid crack extension would not have left any visible evidence on the fracture surface.
If it included rupture of the access door cover, it would have connected the two fatigue cracks; thus the crack length was increased to more than 17 inches and the load required for final failure was reduced.
A Federal Aviation Administration (FAA) Airworthiness Directive requires u.S.
operators to make periodic inspections for cracks at many locations in the F-27 wings.
For several years before the accident, X-ray inspections at 1200-hour service time inter- vals had been made in the area of the No.1 access door in both wings of the plane that crashed. There was nothing in the aircraft maintenance records to indicate that cracks had been detected. Reexamination of the inspection radiographs after the accident, how- ever, revealed evidence that cracks had been present in the vicinity of the access doors in both wings for more than a year before the accident. Crack indications were found in three sets of radiographs made during this period. If the cracks had been detected and reported, the operator would have been required by the Airworthiness Directive to make an approved modification of the wing structure which would have increased the strength of the access door area where the wing failed.
As soon as the crack indications were found in the radiographs, the FAA was noti- fied and a special inspection was recommended by the Safety Board. The FAA issued a telegraphic Airworthiness Directive requiring an immediate inspection for cracks in the wings of all F-27 aircraft with 5000 hours or more time in service. Sixty-seven aircraft were inspected in compliance with the Airworthiness Directive and 13 cracks were found in eight aircraft.
IV. TAG Airlines DeHavilland Dove; Lake Erie near Cleveland, Ohio; January 28, 1970 A TAG Airlines DeHavilland Dove crashed through the ice into Lake Erie in January 1970, after a fatigue failure of a wing attachment fitting. The appearance of the failed fitting is shown in figure 8 and the surfaces of the fatigue fracture in figure 9. Fatigue cracks had originated at the edge of the hole for the main wing-to-fuselage attachment bolt and had propagated through approximately 75 percent of the cross-sectional area at that point before the fitting failed completely.
The fitting was made of steel that had been heat treated to an ultimate tensile strength of approximately 175 000 pounds per square inch, and the bore of the hole where the failure occurred had been chromium plated. No chromium plating had been used in the original design, but some fittings with chromium plating in the attachment bolt hole were installed prior to 1961. The National Transportation Safety Board report on this accident stated: "The manufacturer had long been aware of the problem caused by the chro- mium plating process and had reduced the 'safe life' of this fitting to 10 000 fly- ing hours in July 1961 (Technical News Sheet 178). At this time, it was recom- mended that an inspection for the chromium plating of the root-joint attach fitting be carried out at the next convenient opportunity and, in any case, prior to the accumulation of 10 000 flying hours. It was recommended that any fitting found to have the chromium plating be changed at the next removal of the wing or before 10 000 hours, whichever came first. This recommendation had the approval and concurrence of the United Kingdom's Air Registration Board. These requirements became mandatory for aircraft registered in the United Kingdom but not for those registered in the United States.
"Based upon this recommendation by the manufacturer, the Federal Aviation Administration issued Airworthiness Directive 61-18-3, effective September 1, 1961.
This directive repeated the opening preamble of the Technical News Sheet 178 but adopted only the requirement to inspect the fitting for chromium plating and to ~~-- - -- - replace it, if so plated, prior to the accumulation of 10 000 flying hours. The recommendation to replace any chromium plated fittings at the next wing removal was not made a part of the requirement by the FAA on the U.S. registered aircraft."
In November 1965 the wings of the aircraft had been removed for certain required modifications. At that time, the fitting that eventually failed had been in service for 4998 hours. It was inspected for cracks, but was not replaced, and failed after 9383 hours of service time. A factor in the failure of the fitting before it reached the 10 OOO-hour mandatory removal time was the severe operating conditions at TAG Airlines. TAG flights were considerably shorter and were flown at higher speeds and lower altitudes than the standard flight profile for Dove aircraft.
TABLE 1.- U.S. CIVIL AVIATION ACCIDENTS INVOLVING MATERIAL FAILURE AS A CAUSE OR CONTRIBUTING FACTOR @anuary 1, 1967 to December 31, 196~ Air General Total carrier aviation All material failure accidents: Number of accidents . . .
922 942 Number of fatal accidents 6 53 59 Number of fatalities . . .
138 110 248 Material failure accidents involving fatigue failure: Number of accidents . . .
12 143 155 Number of fatal accidents 23 27 Number of fatalities . . . .
103 54 TABLE 2.- U.S. CIVIL AVIATION ACCIDENTS INVOLVING MATERIAL FAILURE AS A CAUSE OR CONTRIBUTING FACTOR @anuary 1, 1967 to December 31 , 196~ .
Number of accidents in Number of which fatigue failures accidents were identified Type of aircraft: Small fixed wing 814 107 Large fixed wing Turboprop .. 16 Reciprocating engine 11 5 Turbojet and turbofan 5 2 Helicopters . . . 96 34 Phase of operation : In-flight.
416 76 Landing .. .. . .
352 45 Take-off .... .
145 28 Taxiing or towing 28 Parked ..... .
Extent of damage to aircraft: Substantial . .
818 117 Destroyed 122 38 Minor or none Type of component that failed: Landing gear . . . .
Powerplant . . . . .
333 23 Propeller assembly Flight controls 25 5 structural 24 10 Fue I system .
24 1 Hydraulic system Electrical system Tail rotor assembly Main rotor assembly .
Instruments .....
Auxiliary components 0:> ~
"'"
TABLE 3.- SUMMARY OF DATA FROM 230 LABORATORY REPORTS ON FAILED COMPONENTS Number of failures due to - Classification Totals High Stress corrosion Stress of causes Excessive wear temperature Overload or hydrogen Corrosion Fatigue rupture or deformation oxidation em brittlement I 2 102 11 15 4 Improper maintenance 52 18 1 39 31 6 1 Fabrication defects 1 1 37 5 4 1 1 Design deficiencies 24 1 1 Defective material 10 3 1 2 23 Abnormal service 13 damage Undeterminetl 11 2 1 18 17 6 3 4 230 141 41 Totals CO\J , 'ECTS TO ROTOR HUB CONNECTS TO MAIN ROTOR BLAOE FATIGUE '1
o I A > 4.5
Figure 1.- Drawing of the failed main rotor spindle, showing the location of the fracture.
Figure 2.- Appearance of the spindle fracture in the vicinity of the fatigue origin (arrowl. X 6.
--- --- - - - -- , Figure 3.- Failed torque cylinder. Arrows indicate the mating surfaces of the fracture in the two pieces. Approximately X 1/2.
I nsile shear Figure 4.- A portion of the fracture in the torque cylinder shown in figure 3. The remainder of the fracture was similar in appearance. X 3.
Figure 5.- Piece of the lower surface of the right wing, including the inboard end of the No.1 access door. Arrows "a" and "b" indicate the location of fatigue fractures . X 1/ 8.
62 7 Figure 6.- A portion of the fatigue fracture indicated by arrow "a", figure 5. Arrows "c" indicate flat fracture areas; arrows "d" and "e," slant fractures. X 2.
Figure 7.- Appearance of one of the fatigue fracture areas that showed numerous small regions of ductile rupture between fatigue striations. X 8.
Fracture
Failed Fitting
Intact Fitting
Figure 8.- Fai l ed wing attachment fitting with an intact fitting to show the shape of the end where the fracture occurred. X V3.
Figure 9. - Appearance of the fracture in the failed fitting shown in figure 8. X 2.
FATIGUE TESTS ON BIG STRUCTURE ASSEMBLIES OF CONCORDE AIRCRAFT By V. P. N'Guyen Societe Nationale Industrielle Aerospatiale Toulouse, France and J. P. Perrais Centre d'Essais Aeronautiques Toulouse, France INTRODUCTION The Concorde, a delta-shaped-wing aircraft, has been submitted to numerous mate- rial, attachment and protection tests since, with its structural design, it is capable of reaching supersonic speeds (Mach number, 2.05). In addition, this aircraft has been tested in the scope of structural engineering tests performed on substructures. In this paper, only development tests on large structure assemblies and airworthiness substan- tiation full-scale tests are considered.
This paper is limited to the tests performed at the Centre d' Essais Aeronautiques of Toulouse (C.E.A.T.), France. The tests carried out in the United Kingdom are to be presented by the Royal Aircraft Establishment (R.A.E .). As a rule, the development tests achieved both in France and in the United Kingdom are usually performed on struc- tures for which Aerospatiale and British Aircraft Corporation are responsible. All certi- fication static tests are to be carried out in France and all certification fatigue tests are to be performed in the United Kingdom.
EXPERIENCE FROM STATIC TESTS
/
Two main sections have been submitted to pressure, mechanical load, and thermal static tests and are shown in figure l.
I I Fuselage Section 1 bis.
I The structure, named fuselage section 1 bis. or 1(a), consisted of a 4.68-meter-Iong twin-looped cylindrical fuselage section including six standard frames and two main frrmes. On both sides of the lower part of the fuselage, rectangular structural boxes represented the wing assembly and its fuselage junction section. The purpose of this operation was to create the same thermal stresses over this area as those encountered , in flight. The skin panels (A - U2GN sheet) were attached in a classical way to the stringers and frames.
The aim of the tests was to observe the structural behaviour under the most severe flight conditions such as combined pressurization, fuselage torsion and loads on floor, and thermal stresses. Test measurements of temperatures and mechanical strains were also compared with calculated values of thermal stresses in order to (1) justify design methods, (2) make an analysis of the role played by thermal stresses among total stresses (to manage a test program of structures which will be tested in the future), and (3) perfect new test methods, especially in the scope of infrared heating and air-cooling units injecting liquid nitrogen. The tests started at the end of 1964 and ended in the spring of 1966.
This testing enabled the manufacturer to check for the thermal stress level in the fuselage areas hidden by the wing assembly and in the longitudinal stringers located at the bottom of the fuselage. (Fig. 2 shows the results of comparative tests on the heated lower part and the unheated lower part to simulate the presence of a fuel tank.) It was necessary to carry out tests, especially fatigue tests, by representing in a most accurate way thermal stresses where they are significant.
Section 2.8.b The test structure, section 2.8.b, was composed of a fuselage section (first defini- tion of the aircraft, 10 m ;:::: 35 ft long) and of main adjacent wing elements having an over- all span of 44 ft. (Refer to fig. 1.) This structure is a genuine aircraft element. The purpose of the test was (1) To check in a more exact way the aircraft design methods. Therefore, the test structure itself with its proposed end effects has been calculated by means of the same network as an aircraft (analog electrical network for internal load computation).
(2) To compare thermal stress distributions obtained from different aircraft mis- sions. These distributions are not easily obtained by computation.
(3) To evaluate fuel influence in the tanks on these thermal stresses.
(4) To study the superimposition of cabin and tank pressure, of air and inertia loads, and thermal effects.
(5) To prove the "fail-safe" characteristics of this structure by making some cuts to simulate cracks in the main spars, ribs, and frames, and then performing residual- strength tests.
(6) To familiarize test laboratories with exceedingly complex installations in order to proceed with the certification static tests on a full-scale aircraft structure (fig. 3) under satisfactory conditions.
These tests commenced in the autumn of 1966 and ended in the summer of 1969.
Results are too extensive to be presented in this paper. Therefore, only tests which made it possible to perfect the fatigue test programs are presented.
It was shown by the design calculations that the maximum thermal stress values highly depended upon the aircraft acceleration laws. This dependence was verified when a few wing panels buckled locally during tests simulating missions with high acceleration and low take-off weight. (See fig. 4.) (It was a case of a flight corresponding to a pre- vious definition of the aircraft.) The purely thermal stresses remain moderate in abso- lute value but are reversed, and their peak-to-peak values are significant. The presence of fuel causes the stresses in heavy parts of spars and ribs to be reduced. On the other hand, the internal skin surface is subjected to tensile thermal stresses when the fuel tank is empty. These tensile stresses add to the internal tensile stresses due to flight loads. The following conclusion may be drawn from this program. For tests on partial structures, great care should be exercised in Simulating the temperature distributions over the fuselage internal areas (especially those areas hidden by wing assemblies). (The parasite end effects are very strong.)
Because of the high strength of the fuselage in the presence of large cuts (as required in the FAA fail-safe tests), fatigue tests can be safely conducted by using air to cyclically pressurize the fuselage.
A few "dynamic-cut" tests which were performed on the fuselage throughout frames ended the fail-safe tests; the data from these tests will be used for certification substantiation.
STATIC TESTS FOR AmWORTffiNESS SUBSTANTIATION The test structure is a full-scale aircraft. The test program consists of a sequence of tests to be performed under room-temperature conditions and including five different tests with loads on a part of the aircraft. All tests were conducted at least up to ultimate design load of the structure and some of them even beyond. The latter sequence of tests will be made under thermal conditions about July 1971 and will start with thermal tests only, during which several aircraft missions will be achieved under realistic conditions. In a first stage, to investigate ovens and cooling problems, C.E .A.T.
will use calculated temperatures which are being verified by means of flight measure- ments on the prototype. The test temperatures will be submitted to the Airworthiness Authorities for approval. Figures 5 and 6 illustrate different static-test sequences.
- - - - - - - - - - ---- FATIGUE TESTS These tests have been performed on many structural components, but the test pro- grams achieved by use of big substructures 2.3.2 and 2.6/2.7 (fig. 1) are by far the most significant.
Preliminary static tests showed that it was necessary to reproduce the temperature distributions during acceleration and deceleration sequences. When the fatigue test pro- grams were initiated, it was found that this operation would require a test of long dura- tion; the time cycle in the laboratory was almost equal to the time required for an actual flight. It was absolutely necessary to compromise some part of the test program in order to obtain some desired results for the structural behaviour within a reasonable period of time.
Two changes were made in the test program to compensate for accelerating the thermal tests: (1) To compensate for creep, normal structural temperature has been 0 0 0 increased by 20 C (from 100 C to 120 C), (2) To compensate for deteriorations due to thermal stresses , the heating rate d 8 /dt has been increased during acceleration and deceleration sequences in order to increase the stresses by 15 to 20 percent, depending upon particular components.
In order to a ccelerate testing, the time during which the external wall temperatures were constant was decreased. Figure 7 shows that this decrease was feasible since (a) the same maximum temperatures were achieved as in actual flight for both external wall and internal structure, (b) the wall and structure returned to room temperature at the end of the programed time cycle, and (c) the heating sequence during the time of con- stant temperature produced satisfactory thermal gradients during the deceleration sequence.
On the test section 2.3.2, this requirement was met by blowing hot or cold air onto fuselage areas hidden by the wing assembly. On test section 2.6/2.7, the same result was obtained by injecting hot and cold liquid into the fuel tanks, as required. These pro- cedures are called "complementary means."
Determination of Cycle Random maneuver and gust loads were applied by lever jigs. For these develop- ment tests to be performed, it was preferable to reduce the typical loading spectrum to its simplest terms to investigate more easily the possible crack propagation rates. Pres- sure loads, since they are actually known, have been used at their flight true values; that is, p = 736 mb inside the cabin compartment, and p = 250 mb inside the fuel tanks.
Thermal stresses were increased 10 to 20 percent, depending upon the area , to accelerate the observance of the deteriorations due to thermal stresses. By using this increase, an attempt was made to double the damage value due to thermal stresses.
Three mechanical and three pressure cycles were superposed on each thermal stress cycle. In one instance (A), the mechanical and the pressure cycles were applied simultaneously while the thermal stresses were high. In two other instances (2B), the mechanical and pressure cycles were applied simultaneously while the thermal stresses were small or nil (corresponding to a slow return to room temperature). This sequence of loading produced a threefold increase in damage due to the usual loads. Cycles C = A + 2B are performed one after the other.
Final Test Conditions Final test conditions were based on and perfected from typical tests. During these typical tests, the actual flight real time requirements were met in order to accurately determine the required heating rates and thermal stresses during a flight. Based on the results of these typical tests, several short time cycles were tested and complementary means were used to obtain the desired temperature and stress evolution (especially peak-to-peak) at all significant measurement points. The complete time cycle of test 2.3.2 is shown in figure 8; whereas the complete time cycle of test 2.6/2.7 is shown in figure 9. It is easily noticed that with 1 hour'S cycle (of which 40 minutes is thermal) for 2.6/2.7 tests and that with a 34 minutes' cycle (of which 26 minutes is thermal) twice the thermal damage and three times the mechanical damage of a 3 hr 15 min flight is produced.
Results Obtained on Test Structure 2.6/2.7 By March 10, 1971, 9900 cycles (A + 2B) and 10 900 additional B cycles (repre- senting purely subsonic flights) were applied. This stress history corresponds to the damage caused by 40 600 flights under mechanical fatigue conditions and about 19 800 flights under thermal fatigue conditions. The deteriorations that were noticed occurred on the (current) fuselage frames at the level of the cabin floor. They were due to a combination of pressurization and thermal cycles. As a result of these deteriora- tions, design improvements were made on partial assemblies representing the damaged area (fig. 10). In tests on these partial assemblies, a special fixture was used to simulate the frame warping due to thermal stresses. The results of these tests were very satis- factory, and enabled an excellent behaviour of the frames to be foreseen on series aircraft.
Results Obtained on Test Structure 2.3.2 By March 1, 1971, 14 000 complete cycles (A + 2B) and 4000 purely subsonic flights were applied. This stress history corresponds to the damage caused by 46 000 flights under mechanical fatigue conditions and about 28 000 flights under thermal fatigue condi- tions. The deteriorations that were noticed confirm those which were obtained with the substructure 2.6/2.7 , and indicated that the same design improvements were required.
Some minor deteriorations were found in the door and emergency exit lOCking devices.
These deteriorations very likely come from local bending effects due to thermal stresses, and to defects in the door. A few cracks on metal sheets were detected and the investi- gation of the crack propagation rate is being made. Inside the wing fuel tanks, the orig- inal rods fitted with clevis welded by an electron bombardment process did not have a suitable fatigue life and have been replaced by conventional design rods.
Residual Strength Mter Deteriorations Deteriorations, especially those concerning fuselage frames, were always found during the systematic inspection of the structures, that is, following completion of a pro- gram block including 1000 cycles (A + 2B) . The damaged structure exhibited satisfactory residual strength during the last cycles of the program block.
A flight limit load test upon occurrence of deteriorations has just been made on structure 2.6/2.7; this test will be used for certification purposes. Figures 11 and 12 illustrate the test rigs 2.3.2 and 2.6/2.7.
CONCLUSIONS FROM DEVELOPMENT TESTS The main conclusions are as follows: 1. On a supersonic aircraft whose structure weight is a Significant part of the weight analysis, many fatigue and static strength development tests should be made.
2. Fatigue thermal tests are absolutely necessary. Temperature and thermal stress calculations, although they are very developed, cannot foresee any fatigue failures caused by distortion incompatibilities which are not easily evaluated.
2.6/2.7
2.8. b
FATIGUE TEST
2.3.2
STATIC TEST
FATIGUE TEST
FRENCH TEST SUBSTRUCTURES FOR
CONCORDE DEVELOPMENT TESTS
Fi gu re 1.
STRINGER TEMPERATURE ) STRINGER TEMPERATURE STRESS )
°C
WITHOUT FUEL daN/mm ksi STRINGER
z 6 TEMPERATURE 60
o WITH FUEL ,-,
~ 4 "\. 40
z w __ "\.
~2 -~- "-
o ~~--~~--~--~--~----~~~--~~~ o
"
3,000 4,000 s,doo 6,000 7,000
-2 \ STRINGER THERMAL I TIME) seconds -20
z -4 \ '
o \ STRESS WITH FUEL I
~ -6 :10\ I
w -)
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--
2 I
--
-- - -- - - - --- --, / STRINGER THERMAL 0-10 I ./ U \ ,," STRESS WITHOUT FUEL -12 '
\ "
-20 -" STRUCTURE 1 bis -EFFECT OF THE FUEL ON LONGITUDINAL THERMAL STRESSES ON A BOTTOM STRINGER OF A FUSELAGE FUEL TANK Figu re 2.
2. S.b THERMAL TEST - COOLING BY LIQUID NITROGEN 2.8.b THERMAL TEST - WING OVENS Figu re 3.
---- - -- --- - - - -- TEMPERATURE J 8 } 0 C SKIN TEMPERATURE STRESS
2/000
a
TIME )
z
stlconds
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0: -10 -8 a..
1: -15
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TEMPERATURE ) e) 0 c
120 -
STRE55
1,000
2,000
o
O~------------~------------~I-------+
____ -_=========::;::;. TIME)
-2
stlconds
-5 -4
GAGE B
-6
-10
LOW ACCELERATION
ksi
daN/mm 2.8. b STRUCTURE - THERMAL TESTS.
Figure 4.
MAJOR
STATIC TEST-
GENERAL
VIEWS.
Figure 5.
THERMAL STATIC TEST.
INFRA-RED OVENS ARE BEING INSTALLED AROUND THE FUSELAGE.
Figure 6.
-- - ------ - ---- - -- --
TYPICAL CHANGE IN TEMPERATURES
e °c
J
OURI NG AN ACTUAL FLIGHT
EXTERNAL WALL TIME
o 1500
12,600 5 t 3~ hr
TEST SHORTENING ACHIEVED DURfNG
e °C
,
A THERMAL FATIGUE TEST
OJNTROLLED HEATING OF INTERNAL AREAS CONTROLLED COOLING OF INTERNAL AREAS TI ME
o ' 1,500
PHASE AI PHASE ~ FOR A AND 8 PHASES THE TENPERATURES CHANGE AS IN THE ACTUAL FLIGHT.
THE PRINCIPLE USED TO SHORTEN
THE THERMAL CYCLE DUR.ATION
Figure 7.
TEMPERATURE,
e, °C 10 GUSTS 10 GUSTS 6 GUSTS
4 GUSTS r, r, \ I \
I I
I e HIDDEN
._, I ' TANK
l PRESSURE
I \
j
\
o
TIME) SECONDS NOTE GUST LOADS AND PRESSURE LOADS ARE NOT SCHEDULED IN THIS PLATE.
TEMPERATURE AND FATIGUE CYCLE OF THE
CONCORDE 2.3.2 DEVELOPMENT FATIGUE TEST.
Figu re 8.
6 44 ~------------- ---- - -- TEMPERATURE
e °C
) TWO SUBSONIC FLIGH TS SUPERSON Ie FLIGHT °C ·· ---- -- ----- --~ ------ -- ~ -----~------ I
e ENGINE AREA
\
e EXTERNAL
GUSTS I \ I \ I \ -- -- ~ . .
\ \ " I I { \1
o
1,000 3~000 3,400 TIME, SECO N DS
2.6/2.7 CONCORDE TEST STRUCTURE-
TEMPERATURE AND FATIGUE CYCLE.
Figure 9.
NOTE: T HE LOAD L WAS DETERMINED TO OBTAIN BETWEEN B- AND E- SECTIONS THE STRESS DISTRIBUTIONS THAT WERE MEASURED ON FRAMES OF THE 2. 6/ 2. 7 STRUCTURE DURING THERMAL AND MECHANICA L FATIGUE TEST.
L VIEW FROM F
,
FRAME SKETCH
, r - -"r'--
F
/ /
--- _/
E
, 1\ I, I I 'I I I I I ,II I "- -' I ,
SECTION
1 -1
, ' L _________ 1
. ,-
EMBEDMENT JIG
DEVELOPMENT SPECIMEN TO APPRAISE IN A SHORT
TIME IMPROVEMENTS OF THE FUSELAGE FRAME DESIGN.
Figure 10 .
GENERAL VIEW OF THE 2.6/2.7 TEST RIG.
CONTROL ROOM OF THE 2.6/2.7 FATIGUE TEST.
Figure 11.
2.3.2 FATIGUE TEST RIG.
T HE WING PART IS VISIBLE BETWEEN TOP AND BOTTOM WALLS OF THE OPEN OVEN.
GENERAL VIEW OF THE 2.3.2 FATIGUE TEST RIG.
Figure 12 .
STRUCTURAL TESTING OF CONCORDE AIRCRAFT - FURTHER REPORT ON UNITED KINGDOM TESTS By Norman Harpur British Aircraft Corporation Limited Filton, United Kingdom SUMMARY This section of the United Kingdom review of structural testing for the period 1969 to 1971 gives a summary of the tests being carried out on Concorde nacelle structure as part of the structural development and certification progr a mme. It attempts to complete the overall picture provided by other papers which primarily deal with testing of the remainder of the Concorde airframe.
INTRODUCTION During this symposium , much information has been presented on the structural testing of Concorde. In particular, paper no. 1 by E . L. Ripley, given as the Third Frederick J. Plantema Memorial Lecture, deals extensively with the Concorde air- frame major fatigue test and similar development tests on fuselage components.
Paper no. 20 by V. P. N'Guyen and J. P. Perrais gives a summary of the Concorde major airframe static test and other large fuselage " -wing component tests at the Cen- tre d'Essais Aeronautiques de Toulouse (C.E.A.T.) in France.
To complete the picture, the present paper gives an account in general terms of a series of tests being carried out in the United Kingdom (U.K.) on Concorde nacelle components. These components are relatively large structural elements (e.g., the intake is 3.5 by 7 by 17 feet) subject to unique types of loading and involving novel forms of design and construction. They are designed to meet the full static strength , fail-safe, and fatigue requirements of the basic airframe and, thus, have to be the subject of a complete certification test programme. In this sense, they must be con- sidered as a complementary part of the major static and major fatigue test programmes.
SYMBOLS M Mach number n manoeuvering load factor ---- -----~~ design cruiSing speed design diving speed DESCRIPTION OF NACELLE STRUCTURAL SPECIMENS A supersonic aircraft, such as Concorde, requires a sophisticated power-plant installation, including a variable-geometry intake with its own automatic-control system, an engine bay providing full accessibility, and a variable - geometry nozzle incorporating thrust reversers. A general view of the complete Concorde nacelle is shown in figure 1, and a more detailed description of the specimens is given in the appendix.
Part of the basic philosophy for the production nacelle structure has been to design the three main components - intake, engine bay, and nozzle - as separate units linked together in a statically determinate manner to minimise redundant interaction forces arising because of wing distortions. For the same reason, the engine bay itself has been designed in two halves - a forward bay and a rear bay - simply spigoted together at the joint.
Advantage has been taken of this design philosophy to reduce the complexity of testing; thus, the air intake was tested separately from the engine bay and nozzle, and the forward engine... bay was tested independently of the rear engine bay.
A summary of the nacelle structural test specimens either tested or to be tested as part of the Concorde development and certification programme is given in table 1 for the intake and in table 2 for the engine bay and nozzle.
An additional production nozzle specimen is also being provided, and will be tested under operating environmental conditions behind a pair of Olympus engines installed in a test bed at Societe Nationale d 'Etude et de Construction de Moteur d'Aviation (SNECMA) in France.
PROBLEMS ASSOCIATED WITH INTAKE TESTING Summary of Loading Actions The primary loading action on the intake results from internal pressures due to the airflow through the ducts. The internal pressures due to two typical operating conditions are shown in figure 2. Since part of the top of the intake is closed by the lower surface of the wing, these pressures produce significant loads in the wing-nacelle attachment links, as well as designing the intake shell. Additional loading in intake and links is due to the interaction forces at the links due to wing distortions.
During supersonic cruise conditions, the intake is also subjected to elevated tem- peratures with the internal temperature reaching a maximum of 125 to 130 C and the external temperature a value of 100 C. Because both inside and outside surfaces are subjected to similar forcing conditions, thermal stresses during acceleration and decel- eration are, in general, less than those produced by the cruise temperature gradients quoted previously.
Test Realisation For all three intake test specimens, the approach to the problem of simulating wing interaction loads and pressure loads is the same. To represent Wing-nacelle interaction loads, the specimens are mounted from a rigid test frame by links at the points A, C, E, and G shown in figure 1. Each link is then calibrated to enable the link-reaction load to be measured. Three remaining links (points B, D, and F) are attached to hydraulic jacks which are controlled to apply specified displacements.
The representation of the varying pressure distributions within the ducts has been a major difficulty. The interior of the specimen was divided into four main zones, with a fifth zone representing the boundary-layer bleed between the wing and the forward part of the intake. (See fig. 2.). Between adjacent zones a pressure seal has had to be developed in such a way that while maintaining the interzone pressure differentials, local loading and restraint to specimen movement have been avoided. The final solution, following exten- sive development, has led to the design of flexible suction seals mounted off a central core rigidly supported by the test frame. The assembly of one such core for the room- temperature tests on specimen 2.9B is shown in figure 3.
For the thermal testing on specimen 2.9.4, the specimen has to be heated cyclically inside and outside. Each internal zone is thus supplied with pressurized air through a separate closed-circuit system of ducts with outlets into the specimen through the central core. The heating of this air is controlled through a heat exchanger. For cooling, the circuit is depressurized and switched to open circuit; ambient air is then blown through the specimen. The exterior of the specimen is surrounded by a duct through which unpressurized air is blown at the requisite temperatures. This system, which is dupli- cated for each intake duct, results in an extremely complex facility. A scale model of this facility is shown in figure 4.
With this facility it is possible to simulate adequately the major loading actions. In the fatigue test, advantage is taken of the absence of Significant climb and descent thermal stresses by shortening the thermal cycle to simulate only cruise gradients and imposing a test cruise time of 12 minutes compared with an average aircraft cruise time of 75 min- utes. To compensate for this shorter test time at temperature, creep rate is increased by a factor of approximately 5 by increasing maximum test temperatures 15 C. The proposed test cycle is shown in figure 5. The aim is to achieve a rate of testing compar- able with the major airframe fatigue test (where each 1-hour test cycle simulates the damage done in two typical aircraft supersonic flights).
PROBLEMS ASSOCIATED WITH ENGINE-BAY AND NOZZLE TESTING Summary of Loading Actions The loading actions on the engine bay and nozzle are similar to those on the intake, but there are some significant differences which are summarized below: (1) The distribution of pressure in the engine bay and nozzle is essentially constant; thus, only one internal-pressure zone is required in each duct.
(2) The concentrated system of hydraulic jacks required to represent reverse- thrust bucket loads, bucket operating jack loads, and engine jet pipes leads to local com- plications in the heating, cooling, and pressurisation system.
(3) The maximum operating temperatures in the rear engine bay and nozzle are 0 0 high, reaching about 240 C in the engine bay and between 320 and 410 C in the nozzle ; as in the intake, a steady gradient is present during cruise causing Significant thermal stresses. In addition, large transient thermal gradients arise in the nozzle centre-wall structure during descent and due to reheat in the climb and result in another thermal- stress cycle. These temperatures are shown diagrammatically in figure 6.
Test Realisation Two of the engine-bay specimens (specimen 1.11.2.2 and specimen 2.9.4.2) are relatively simple; tests on these specimens involve static pressure and mechanical loading at room temperature. Specimen 2.9.4.3 is subjected to a pressure fatigue test at elevated temperature. This test poses no serious problems apart from the control and monitoring of temperature and the timing of the pressure cycle to ensure a consistent accumulation of creep and fatigue damage.
The fourth specimen, specimen 2.9.6, is subjected to both static and fatigue testing with representation of thermal conditions. This testing requires a complex test facility similar to that for the intake shown in figure 4. The simulation of wing distortions and bay pressures is done in a similar manner to that for the intake; the number of pressure zones is less, but seal design is complicated by the higher temperatures required.
In order to limit the test temperatures, advantage is taken of the fact that thermal stress due to temperature gradient is the most Significant requirement since creep and material degradation at the aircraft temperature levels are unimportant for the stainless steel materials of the nozzle bay and the titanium and inconel alloys of the engine bay.
The required temper . rr radients of about 250 C maximum through the nozzle side- . by blowing air at room temperature over the outside of the walls are therefore o.
specimen and blowing hot ~ from the rear to the front through the inside. A special problem arises in simulati r.; t1 temperature gradients through the centre wall of the nozzle during descent and duf' ' , reheat in the climb.
To achieve these in as -, nort a time as possible, a special system is provided to blow alternately hot and cold air into the centre wall void. This system is switched on at appropriate times in the cycle, thus enabling the required cruise and recovery equilib- rium conditions to be rapidly achieved. (See fig. 7.) A diagram of the fatigue cycle achieved with this forcing system is shown in figure 8; the target, as in the case of the intake, is to achieve a rate of testing comparable with the major airframe fatigue test.
TEST CONTROL Both the intake (specimen 2.9.4) fatigue test and the engine-bay and nozzle (speci- men 2.9.6) fatigue test are to be controlled and monitored by a single IBM 1800 computer, which will also provide data logging and both on-line and off-line data analysis and display.
The monitoring facility checks the applied values of all control variables with the required values against a set of inner and outer limits; the inner limit exceedances are printed-out and the outer limit exceedances cause shutdown of the test.
A general view of this installation is shown in figure 9, and a flow diagram illus- trating the control logic of the test facility is shown in figure 10.
APPENDIX
APPENDIX DESCRIPTION OF PRODUCTION NACELLE STRUCTURE Air - Intake Structure A structural breakdown of the intake is shown in figure 11. The operating temper- ature during Mach 2.0 cruise is approximately 120 C, and aluminium alloy is used for all the structure with the exception of the rear frame (frame 204), which is made from titanium alloy to provide a fireproof bulkhead. The forward lip, the forward- and centre- duct skins, and the intake frames are mostly machined from thick plate. The moveable ramps are made from aluminium alloy honeycomb.
The intake is suspended from the wing at six points, with a forward and rear attach- ment on each of the three walls. Five of the attachments are simple links taking vertical loads only; the sixth, at the centre of the rear frame, is a fixed-point attachment taking loads in all planes. A secondary horizontal link is also provided on the forward centre wall to provide yawing restraints.
Engine - Bay Structure The general arrangement of the engine bay can be seen from figure 1. Since the engines are mounted directly from the wing, engine-bay loads derive predominantly from internal pressures. The bay consists of a forward and rear section, simply spigotted together; each section consists of a fixed centre wall with an L-shaped door forming the side and bottom walls of each bay. The front and rear bulkheads of the bay are formed by the rear frame of the intake and the front frame of the nozzle-fixed structure, respectively.
The centre wall (see fig. 12) has a maximum operating temperature of 250 C and must resist flame temperatures of up to 1100 C for 5 minutes. Thus, both front and rear sections are made from a nickel alloy (Inconel 718) honeycomb-sandwich panel.
The forward doors (see fig. 13) have a maximum operating temperature of 150 C and are made from aluminium alloy. Inner and outer skins are riveted and spot-welded, respectively, to close-pitched frames of the extruded I-section. The rear doors (shown in fig. 14), where maximum operating temperatures are about 200 C, are of similar con- struction but made of titanium alloy with the frames either machined from bar or fabri- cated from welded plate. Both sets of doors are provided with fore and aft sliding free- dom of about 30 mm along a line near the door corner. This freedom has been provided to eliminate large interaction forces between the wing and door which would otherwise arise because of wing distortions in flight. The slide also incorporates a hinge, so that
APPENDIX
APPENDIX it is possible to open the bottom part of the door independently for simple servicing.
Also to avoid interaction forces due to distortion, the doors are supported from two hinges, at the front and rear of the top edge only. Intermediate hinges are provided but are designed to only restrain the door against lateral pressure forces.
Nozzle structure The general arrangement of the nozzle fixed structure is shown in figure 15. The maximum operating temperature of the structure is in the region of 450 C, and for this region stainless steel is the basic structural material.
The basic structure is made up of a pair of barrels forming the main ducts , sup- ported by spectacle frames and enclosed by an outer fairing. These components are mainly fabricated from stainless steel stresskin honeycomb. Upper and lower fore and aft longerons run between the inner barrels and outer fairings in the sidewalls and centre walls. These form the primary load path for the reverser bucket loads; these buckets are attached to hinge fittings which connect with the aft end of these longerons.
This fixed structure is attached to the engine-bay-wing interface at three non- redundant fittings, one on each sidewall and one on the centre wall. A fourth attachment at the centre wall is provided as a fail-safe standby. The main centre-wall attachment connects with the engine-bay centre wall, the two sidewall attachments connecting with a pair of triangulated frames attached to the wing undersurface.
Provision in the fixed structure is made for attaching the engine primary nozzle by means of three spigot fittings projecting into the main ducts. Additional attachments are provided for the reverser-bucket operating jacks, four in each duct.
0) 0) TABLE 1.- INTAKE MAJOR STRUCTURAL TEST SPECIMENS Summary of test requirements Description Remarks Static Fail-safe Fatigue Specimen 2.9B A twin left-hand intake Static design cases at room (prototype air to prototype standard.
temperature up to 85 % ultimate intake) load to clear prototype flying .
Rig applies internal pressure in four zones per Test cases include duct with wing distortions.
(1) Symmetric and asymmetric surge cases (2) Ground running manoeuvre cases at YD.
Specimen 2.9.4 A twin right-hand Static design cases for Certification fatigue (production intake to preproduction certification at elevated tempera- test. CycliC temperature, air-intake standard.
ture as appropriate up to 50% pressures, and wing fatigue ultimate load in or der not to distortions.
Rig applies internal and specimen) invalidate fatigue test.
external heating in association Temperatures increased with internal pressure in four Test cases include by 15 C to give a factor of 5 internal zones . Wing distor- (1) Ground running single engine on creep, resulting in a shorter tion can be simulated .
surge test cycle.
(2) Single engine surges at V C, Static-strength certifica- M; 0.66 tion of the intake is based on (3) Double engine surges at hot tests to limited loads V ' M; 2.0 C (4) Supersonic wing distortion, M; 2.13 at V , n; 2.5.
D Specimen 2.9.5 Basically a twin right- Static d esig n cases for Crack propagation and (production hand intake to production certification up to 1 00 % ultimate residual tests to meet FAA air-intake standard.
load. All tests were at room fail -safe requirements for fail-safe temperature; for hot cases, loads intake structure.
Rig similar to that for and static- and pressures are adjusted to specimen 2.9.4 but at room All tests will be done at strength allow for thermal stresses, temperature only.
rOom temperature.
specimen) adjustment based on r esults Static-strength certifica- from specimen 2.9.4.
tion of the intake is based on Test cases were the same cold tests to 100% ultimate load.
as those for speCimen 2.9.4.
TABLE 2.- ENGrNE-BAY AND NOZZLE MAJOR STRUCTURAL TEST SPECIMENS Summary of test requirements Description Remarks Static Fail-sale Fatigue Specimen 1.11.2.2 Rig applies lateral pressures, Static design cases at room (prototype engine- engine mounting loads, and nozzle temperature to clear prototype bay centre-wall loads.
flying.
specimen) Design cases include (1) Ground running (2) Symmetric reverse thrust (3) One engine windmilling (4) Manoeuvre at V (with and D without nacelle twist) Specimen 2.9.4.2 Test to provide Mach 2.0 A single design case to (preproducUon flight clearance for 01 aircralt 100% ultimate load. Outboard engine-bay centre- flying .
engine, windmilling at V C, wall specimen) M = 2.0 (inboard engine, normal Test at room temperature runnin g).
since temperature not critical for this component.
SpeCimen 2.9.4 .3 Fatigue and creep test for Certification fatigue (forward engine- certification.
test: cyclic pressure and bay door) wing distortion, at constant Static certification of this elevated temperature.
com ponent is being based on cal- culation plus detail tests.
A temperature gra- dient is maintained through the door, temperature levels being increased to accelerate creep.
Specimen 2.9.6 A twin left -hand rear engine Static design cases for certi- Nozzle loads only applied Certification fatigue (rear engine bay bay and type 28 nozzle to produc- fication with thermal stresses. with various members discon- test: cyclic temperatures and type 28 nozzle) tion standard.
Where appropriate, loads and pres- nected in turn.
and pressures with dis- sures are limited in the right-hand tortions and nozzle loads.
Rig applies internal heating Redistribution of stresses duct in order not to invalidate and pressurisation in association measured.
fatigue test ; thus, symmetric cases with primary nozzle and reverser Load levels limited to are taken to 50% ultimate load; bucket loads.
avoid invalidation of fatigue asymmetric cases to 85 % ultimate Heating represents internal test.
load in the left-hand duct.
to external temperature g radients Design cases include only; absolute temperature judged (1) Reverse thrust on ground to be not critical .
(2) Ground running, maximum take-off power (3) Manoeuvre at V , M = 2.2 D (4) One engine wind milling, V C, M= 2.0 (5) Single-engine surge, V C, 0:.
C]l M = 2.0
""
CENTRE WALL ( AFT) FRAME 204
> _ ~GINE~
/ NTAKE ~
FORWARD SIDEWALL Figure 1.- General . view of complete nacelle.
1- 2.351 , 4.2 ' __ ...J MAIN DIFFUSER-- ~
-- --'
_--==--1
- 2 . 17 , 8 . 08' - 2 67 ---r=I;::~=jL- I
~
__ ...J -3 . 70
L __ ~ L . 80' .-.J
L1JJ FIG. 2 ( b ) TEST PRESSURE ZONES RAMP VOID ENGINE BAY MAIN DIFFUS ER ~
--
THROAT PRESSURE SEALS
-----------
FigU ~ re ~ 2 ~ . = _I = t ==~=====7.=====I==jl - -.J
n ake pressures and pressure test zones.
Figure 3.- Internal core for one intake duct (specimen 2. 9BI.
Figure 4. - Model of intake test rig .
GROUND RUNNING AND TAKE · OFF ...
CLIMB - CRUISE - DESCENT
LANDING AND I
• GROUND RUNNiNG
I
TYPICAL
I
ZONE PRESSURE MECHANICAL LOADING ( ENGINe-BAY IN TERACTION ) TYPICAL WING DISTORTION INTERNAL
FORCING ,-- - ---- -- ---"
;I EXTERNAL , AIR ~ , TEMPERATURE SUPERSONIC CYCLE (x 4) SUBSONIC CYCLE (x 1) Figure 5.- Diagrammatic representation of intake fatigue cycle.
ALL TEMPERATURES 0 C SECTION' B B' SECTION' AA ' Figure 6.- Engine-bay and nozzle temperature distribution.
,..
'" -
><~
i '\
L_--- "'- __ --, VERTICAL SECTION THROUGH NOZZLE CENTRE LINE Figure 7.- Internal forced heating and cooling of nozzle centre wall.
NOZZLE LOADING PRESSURE SIDEWALL TEMPERATURE GRADIENTS CENTRE- WALL TEMPERATURE GRA DIENTS ON GROUND
ON GROUND I TAKE OFF I CLIMB CRUISE I DESCENT I GROUND
REVERSE ENGINES OFF
I ENGINES OFF
THRUST Figure 8.- Diagrammatic representat ion of engine-bay and nozzle fatigue cycle.
Figure 9.- IBM 1800 computer installation.
ENGINE & NOZZ LE l iNT AKE SPECIMEN ~ ___ _ BAY SPECIMEN TWIN DUCTS EACH TWIN DUCTS EACH DIVIDED INTERN- DIVIDED INTO 4 ALL Y INTO TWO PRESSURIZED AND BAYS PRESSURISED HEA T ED COM PART - AND HEATE~ 1 MENTS - ONE HEATED DUL I PRESSURISED AND AROUND HEATED DUCT ON TOP, ' 1 HEATED DUCT AROUND
~~~~
DATA ACQUISITION SYSTEM PRINTER ENGINE SYSTEM ALARM PLOTTER MESSAGES ACTION AND LOGGING NON PROCESS ALARM ANALYSES MESSAGES MESSAGES ALARM DATA ALARM DATA DATA DATA LOGGING LOGGING Figure 10.- Nacelle test-control flow diagram.
~
SIDEWALL ,...- _____ LOWER LIP BASIC MATERIAL : AL. ALLOY Figure 11.- Structural breakdown of the intake.
LOADS ) FAIL · SAFE LINK Y BRACING ( Y. Z. LOADS ) REAR CENTREIVALL FORWARD CENTREIVALL BASIC MATERIAL : INCONEL Figure 12.- Engine-bay centre wall.
6 63 EXTERIOR ALUM . ALLOY ROLLED DOUBLER 'Y' RESTRAINT HI NGE __ STEEL H EAT SHIELD - APPROX 8" AIR CONDITIONING CHANGE - OVER VALVE ~ ,~~ ::;,
l
--- ' ~ / SLIDE HINGE BUTT STRAP I S SK IN AIR STARTER . AIR PANEL AND --7'-~c-----_ MANUAL STARTER FLAP OPERATION BUTT STRAP lIS OF OUTER SKIN RESTRA INT BOLT LATCH ACCESS GROUND RUNNING FLAP BASIC MATERIAL : AL. ALLOY Figure 13.- Engine-bay forwa rd doo r (sl.
REINFORCING PLATES STRUT ATTACHMENT FITTING TYPICAL WIGGLE WEB FRAMES ENGAGEMENT SPIGOT STRUT ATTACHMENT SLIDE ASSEMBLY .A.~---- BUTT STRAP TRUNNION MOUNTING ~---- ENGAGEMENT SPIGOT ' G' LAB AIRVEN.T AND TURBINE BEARING AIRVENT HOOK LATCH HOUSING SPAR 72 STRUT ATTACHMENT TRUNNION MOUNTING --~~"-2~ ~~~ ::::::::~ ~ ST AGE BLOIV OFF AIR STARTER DOOR BASIC MATERIAL : - TITANIUM ALLOY FORWARD LATCH HOUSING Figure 14.- Engine-bay rear door(sl.
ARY NOZZLE ENGINE PRIM SP IG OTS ENT ATTACHM BASIC MATERIAL :- S STEEL STRESSKIN t of nozzle structure.
angemen - General arr Figure 15.
1'l:EDlNG PAGE BLANK NOT FILMED ;,) 'YJ. - ;;?q q {7
A COMPARISON OF RELIABILITY AND CONVENTIONAL ESTIMATION OF SAFE FATIGUE LIFE AND SAFE INSPECTION INTERVALS By F. H. Hooke Aeronautical Research Laboratories Department of Supply Commonwealth of Australia SUMMARY Both the conventional and reliability analyses for determining safe fatigue life are predicated on a population having a specified (usually log normal) distribution of life to collapse under a fatigue test load.
Under a random service load spectrum, random occurrences of load larger than the fatigue test load may confront and cause collapse of structures which are weakened, though not yet to the fatigue test load. These collapses are included in reliability but excluded in conventional analysis.
The theory of risk determination by each method is given, and several reasonably typical examples have been worked out, in which it transpires that if one excludes collapse through exceedance of the uncracked strength, the reliability and conventional analyses gave virtually identical probabilities of failure or survival.
INTRODUCTION The conventional approach to safe-life estimation envisages a fatigue test which imposes on at least one full-scale structure the equivalent fatigue damaging effect of service loading, according to some regular pattern which restricts, however, the largest load , regularly applied, to some fraction of the virgin strength. Life to .
collapse is regarded as a statistical variable, of whose population mean the test failure is treated as an estimator. Variability is estimated from other representative experi- ments in which each member's strength falls to a single lower value (in different life- times), which is accounted failure, and the probability density function of life to failure is usually assumed log normal.
Determination of the safe life as a function of desired or acceptable probability of failure requires merely the estimation of the desired percentile of the population, that is, the desired percentile of the distribution of fatigue lives, measured to the point at which each member ' s strength has fallen to the largest applied load in the test sequence.
Reliability theory, applied to this problem attributes the same strength properties to the population as before, including the decay of strength as fatigue crack growth occurs, but does not assume that collapse occurs when each member's strength has fallen to a common value. Collapse occurs rather when a member of the population meets a load larger than its current strength, and this event would correspond to a conventionally assessed life for that member if the service spectrum were modified or truncated so that all load peaks larger than the fatigue test load were reduced to that value.
The purpose of this study was to present the theory of risk determination for each method and to ascertain by the working of several reasonably typical examples whether the conventional method significantly underestimated the failure risk through ignoring service loads higher than the fatigue test load.
SYMBOLS ratio of maximum fatigue test load to virgin strength or strength at critical b crack length g ratio of crack propagation time (from detectable to critical size) to total life H population life in hours; a log normal random variable H population geometric mean life in hours H crack length l "critical" crack length at which strength U has fallen to bU o crack length detectable with certainty frequency of occurrence, per hour, of applied load >V m{V) number of load cycles applied n p{U) probability density function of strength for population p{V) probability density function for applied load V for some arbitrary time interval P(t) probability of collapse before time t P(n) probability of collapse before nth applied load Pc probability of collapse in arbitrary time interval oP c probability of collapse in arbitrary time interval of small element of popula- tion characterised by its value of H r(t) risk or risk rate or risk of failure at time t of survivors at time t r(n) risk or rate of failure at the nth applied load of survivors of (n-l)th load R(t) reliability at time t or probability of survival to time t R(n) reliability at nth applied load or probability of survival from first to (n-l)th load t time, hours
Tb safe inspection period for probability of failure p = p percent of gH
U strength U virgin strength o V applied load a standard deviation of log H 1> strength decay function of crack size tJ; crack propagation (time function) STATISTICAL MODEL AND SAFE-LIFE ANALYSES The statistical model used herein is the one used in references 1 and 2, as shown in figure 1 in both normal and logarithmic coordinates, and has the following features: (1) The population life H is log normally distributed with geometric mean H and variance a , H being the hours in which the strength U is reduced from U to o bUo which corresponds to the largest load in the test spectrum.
(2) Crack propagation in each member is scaled to the member'S potential life to failure H under the specified test history and follows the expression
_l = lj;(!:..)
lcr \II
(3) Strength is related to crack size; thus, and the condition (1) gives <1>(1) = b.
(4) Whereas crack propagation is governed by condition (2), failure is governed by the frequency of occurrence m(V) per hour, of service loads exceeding V, or in non- dimensional terms, the frequency m(V /U ) of service loads greater than V / U ' o o In conventional analYSiS, a safe life for a probability of failure p is merely the p percentile of the variable H. Insofar as H is the time at which U falls to Uo, it is independent of the shape of the crack propagation curve and is only dependent on the time H at which l = lcr.
The calculation of failure by the reliability approach requires the following defini- tions (refs. 4 and 5): P{t) probability of fracture before time t R{t) reliability at time t or probability of survival to time t _1_ dP{t) r{t) risk or rate of failure at time t of survivors to time t, R{t) dt and the expression -It r{t)dt R{t) = e 0 (1) Or, alternatively, the probability of failure before a given time, the reliability and the risk (hazard rate or force of mortality) may be expressed as a function of number of cycles n, as P{n), R{n), and r{n). In this case r{n) dn is the probability of failure in dn cycles of members surviving at n cycles, so that (With dn = 1), r(n) is the probability of failure per cycle of members which survive to the nth cycle.
If the probability density functions of strength and of load occurring in some arbi- trary time are p(U) and p(V), respectively, as shown in the following diagram,
Probability
p(U)
density
Strength U ~
Appl ied load V
then the probability of collapse in this arbitrary time is the probability that a load V falls on a structure of strength U less than V. For a load lying between V and V + dV, occurring with probability p(V) dV, its contribution to the probability of collapse is U=V (2) p(V) dV Su=o p(U) dU and the total probability of collapse is V=oo U=V (3)
Pc = S p(V) 1 p(U) dU dV
V=O U=O Or , alternately, if there is considered an element of the population of structures lying between U and U + dU, the probability of a structure having a strength in this interval being p(U) dU, its contribution to the probability of collapse is V=oo (4) p(U) dU Sv=u p(V) dV so that the total probability of collapse is also oo V Pc = rU= oo p(U) r : p(V) dV dU (5) JU=O JV=U In the example of concern, in which strength U is distributed as a function of Hand also decreases with time, the calculation is most readily made by taking small elements p(H) dH of the population characterised by their values of H and using equation (4) to find the contribution to the probability of failure by each element; that is, V=oo
oP c = p(H) dH r p(V) dV
JV=U
= p(H) dH ~r(V > UD (6)
It will be noted that U is a function of time U(t) = Uoep {lft(t/H)) so that oP = p(H) dH [!>r(V > U(t)B c
-S, r(t)dt
t }
= p(H) dH 1 - e 0
f
from equation (1), r(t) being the risk function for this element, [ -s,\n(v> U(t))dt;
oP c = p(H) dH - e 0
(7)
l
where m(V> U(t)) is the frequency per hour with which the applied load exceeds the element's strength U(t).
The total probability of collapse is
H=oo f - S,t m(V > U(t))dj
Pc = S, p(H) 1 - e 0 dH
(8) H=O which is identical, allowing for a difference in notation, with the expression
F(U)=l - S, n(U)dt
t }
P(t) = S 1 - e 0 dF(U)
{ F(U)=O of reference 2 (p. 29).
INSPECTION INTERVAL ANALYSIS Safety may be achieved in an inspectable structure if the critical crack length lcr, at which strength falls to a selected unsafe value , is larger than the crack length detect- able with certainty ld' The time remaining in which a crack propagates from ld to lcr (and strength to U = bUo) is some fraction of the life H, say gH, and with this model g is a constant for all members of the population. Thus gH is log normally 2.
distributed with median gH and variance 0- In conventional analysis, the critical length lcr is the same for all members of the population, and the unsafe value of strength is equated to b U , the highest load in the o fatigue test programme. A safe operating period after inspection Tb for a probability of failure p in the interval is the p percentile of the variable crack propagation time gH, since it can readily be seen that only p percent of cracks can propagate from ld to lcr in a time less than Tb' This result assumes that all structures are cracked to just below ld at the inspection date, and it is seen to be independent of the shape of the crack propagation curve for cracks smaller than ld' In reliability analysis, structures may be conSidered to be cracked to just below ld at the beginning of the propagation time but to reach a failure state governed by load exceeding strength. Where the safe lives, as calculated by reliability and conventional methods, coincide it is concluded that this will imply a coincidence of the values of safe inspection intervals.
APPLICATION OF THE THEORY TO TYPICAL EXAMPLES Example A(l) represents a military aircraft situation where the structures are sub- jected to the manoeuvre load spectrum (curve A of fig. 2) in which limit load is exceeded once per 100 hours, crack size l / lcr is a power function of t / H, the decay of strength with crack size conforms to the laws of fracture mechaniCS , and the standard deviation 0- is 0.167.
Example A(2) represents the same situation as example A(l) except that the stan- dard deviation a is 0.16712.
Example B(l) represents a civil aircraft situation where the structures are sub- jected to the gust spectrum (curve B of fig. 2) in which three-fourths of limit load is exceeded once in 5000 hours, crack propagation follows figure 28 of reference 3, the decay of strength is a linear function of crack length, and the standard deviation is 0.17.
Example B(2) represents the same situation as example B(l) except that (perhaps unrealistically) crack growth is assumed linear from zero time up to failure.
Constants used in the various calculations are listed in table I, and the results of the calculations are shown in figure 3 where probability of failure or survival is plotted against life in hours. Calculations for the conventional analysis have been made with the same computer programme by truncating the load spectra at b U ' o DISCUSSION OF RESULTS OF THE ANALYSIS Examination of figure 3 shows that for the Civil example B(l) both methods of
analysis gave virtually identical results within the computed range from p = 0.001 to
p = 0.999. In the computations the distribution of H was divided into its 0.1 percentile.
If results are desired for p < 0.001 these can readily be obtained by computing with smaller elements of the distribution of H. For example A(l), both methods gave virtu- ally identical probabilities of failure for lifetimes longer than 3000 hours, but for shorter lifetimes the reliability method gave higher probabilities than the conventional method.
It is appreciated that the reliability method of analysis included, whereas the conventional method excluded , the risk of failure from loads exceeding the virgin strength (whether of uncracked structure or of cracked but yet unweakened structure).
The probability of such overload failures can readily be derived from the frequency of exceedance of U for example A, namely once per million hours. This probability of o overload failures is plotted as a dashed line in figure 3; the reliability calculation closely approximates this curve at low probabilities of failure.
The result for example A(2) is similar to that for example A(l), except that, because of the larger scatter, the reliability calculation assessed a given probability to have been reached in a slightly shorter lifetime; for example, a probability of failure of 0.002 was reached in 1500 hours by reliability analysis and in 1750 hours by conventional analysis
with the corresponding scatter factors being . ~ and 4, respectively. Again, at a prob-
ability of failure of 0.001, the major contribution was overload failure through loads greater than the virgin strength.
Reliability analysis provides a rigorous method for validating the conventional methods of safe life and inspection interval analyses which are based upon a seemingly arbitrary choice of the value of unsafe strength, this choice having been made by choosing what is to be the highest load in the fatigue test programme on the representative struc- ture to estimate mean life. The conventional analysis is vastly less time consuming than the reliability analysis, since it involves a simple slide-rule calculation rather than a complex digital computer programme run.
Examples A(l), A(2), and B(l) were constructed to represent closely conditions existing in military and civil aircraft situations. For the most part the reliability analy- sis validates the Simpler conventional analysiS. For the military type of spectrum and at short lives, the probability of failure is dominated by loads exceeding the uncracked strength; when these are added to the conventional analysis, the result agrees closely with the reliability methods.
Example B(2) represents an artificial extreme example of a structure assumed to have linearly decaying strength from zero time up to failure. Nevertheless, here again, at probabilities of failure less than 20 percent, the corresponding lifetimes were virtually identical with those for a more usual strength-decay curve , or, indeed, for the step- function strength decay curve which is implicit in the conventional analysis.
The examples that have been discussed have not considered the case of a long period of detectable crack propagation during which the strength does not decay below virgin strength. Here inspection will not prevent failures from exceedance of the virgin strength, but will weed out cracked structures before they become weakened.
CONC L USIONS For a range of conditions which are typical of military and civil aircraft structures and load histories, reliability analysis validates the much simpler conventional methods of safe life and inspection interval analysis.
The reliability method, ipso facto, includes the probability of failure through loads exceeding the virgin strength - a factor which is inevitable by any fatigue analYSiS, inspection schedule, or safe-life determination.
Where there is a long detectable crack propagation time without diminution of the structural strength, inspection will weed out cracked structures before they become weakened but will not prevent failures from loads exceeding the virgin strength.
ACKNOWLEDGEMENT The author desires to g ratefully acknowled ge the assistance of Mr. M. R. Thomson in performing the computations.
REFERENCES 1. Hooke, F. H.: Consideration of the Rationale of the Use of Half Critical Crack Length as a Failure Criterion. A.R.L. Internal Paper, Oct. 1969.
2. Hooke, F. H.: The Fatigue Life of Safe-Life Structures - An Australian Approach.
Report from Laboratorium fur Betriebsfestigkeit (Darmstadt), Apr. 1970.
3. Payne, A. 0.: Determination of the Fatigue Resistance of Aircraft Wings by Full Scale Testing. Proceedings of Symposium on Full-Scale Fatigue Testing of Aircraft Structures, F. J. Plantema and J. Schijve, eds., Pergamon Press, 1961, pp. 76-132.
4. Myers, R. H.; Wong, K. L.; and Gordy, H. M.: Reliability Engineering in Electronic Systems. John Wiley & Sons, Inc., 1964.
5. Bazovsky, 1.: Reliability Theory and Practice. Prentice-Hall, Inc., 1962.
TABLE I CONSTANTS USED IN EXAMPLES A(1) AND A(2) (MILITARY) AND EXAMPLES B(1) AND B(2) (CIVIL) SAFE-LIFE ANALYSIS Example A Example B Constant in calculation (military aircraft) (civil aircraft) H = Median population life 8000 hours 25000 hours a = Standard deviation 0.167 for A(1) 0.17 0.1671/2 for A(2) b Uo = Highest test load 0.67U 0.5U o o (t/ H)9.0 B(1): l/l cr = 1fi(h / H)
o for t/H<0.6
t/H-0.6 for 0.6 <t/H< 0.97 -20 + 2lt /H for t / H > 0.97 B(2) : l / lcr =t / H 1 -l / 2l U/ Uo = ¢(l/lcr) 1 for l / lcr <0.44 cr 0.67Vl cr/l for l / lcr >0.44 U / Uo = ¢{1fi(t/H)} 1 for t/H<0.91 B(1) : O.67(H/ t)4.5 for t/H>0.91
o for t/H < 0.6
1. 3 - O. 5t/H for 0.6<t / H<0.97 11 -10.5t / H for t/H >0.97 B(2): 1- 0.5t / H
m(V /u 10 -12V /U 104. - 15V / U
o) o o
~t
p (H) :-=>- .o . ~ CU \I) .oc o Q) L..~ ~ H .."
H -- hrs. to failure L..
() .......,
t
crack growth .-..)
for population ..x U Q) median cu N L..'- U III ~ .-..)
t hours of service >-
P (log H)
~~1 cu·-
.0 III o C L.. Q) a.~
log H
L.. log hrs . to failure = log H -- U (]l log H-~ log t- o ~ crack growth Q) for any member N \/I ...x: u cu L..
U ......., (]l o O\~ ~ II Figure 1.- Crack growth and failure distribution model.
100---- ---- ~---- r- ~ ------_.------_.--------r_-- --~ ct!
:::> x a:: I.U I:L III I.U Z r-- ~ 0 => I.U I.U ~ '-../ >< MANOEUVRE LOAD I.U
lE
SPECTRUM L&- (8) (MEAN LIFE ·1 GUST LOAD
= 8000 HR )
z SPECTRUM I.U (,!)
~ (MEAN LIFE a:: I.U =25,000 HR > ~ '01 FOR RELIABILITY \ LIFE ASSESSMENT ·001 ~---- --~------ +---\r----+--+---F- +---===;:::": ~-- ------i TRUNCATION FOR CONVENTIONA L LIFE ASSESSMENT ·0001 L- ____ __ L- ______ L- __ L- ...l-L-----1..- ____ ...L...l. __ ____ ....!... f ______ ---J
o '2
'8 V APPLIED LOAD
- =
Uo VIRGIN STRENGTH Figure 2.- Typical load exceedance curves.
61 9 99·99999 '0000001 -000001 99·9999 dVIL I I AIRCRAFT _ 99·999 ·00001 EXAMPLES 99'99 ·0001
I I It
B (Z) RELIABILITY _ 99-9 '001 CALCULATION - 99-8 :002 1\ 1 99-5 -ODS
}T
99 ·01
}/1
1 L
98 -02 rJ
0 V
j ~ -OS ,..
li Vi
90 -I w a: :I
IL lL
80 • 2 >- MILITARY cs:
=
YI ~ I-
L0- '3 AIRCRAFT ..J ~
A
lA. 60 ·4 CD EXAMPLES II cs:
II
·5 ..J V >- UJ '6 t::: a::
vfi(1)
A (I) lI.
'7 CD
=
RELIABILITY
cs: 0' =-167 --"", j
VV
20 CD -8 AND a: A(Z)
VI I CONVENTIONAL
CL
l .~
J
'9 CALCULATIONS
"'" i' "-
(1' = '167.12
b(1
C-."
I
j- 5 t-- ·95 ~
II II
I
'98 t-OVERLOAD FAILURES 1/
ti 1
I '99 t- ONLY, I. E. FAILURES
V
-5 -995
t- FROM LOADS GREATER L
- THAN VIRGIN STRENGTH Uo 1 IL
·2 -998
\ ,--L~
-I - j- ' -999
1 I
\ -Ii""'''~~ V ~ I ',
_ _ ~~ CONVENTIONAL
I
.. .
-01 CALCULATION
IJ
RELIABILITY ·001 CALCULATION '99999 '0001 '999999 .
·00001 2 9999999 10 2 3 4 6 8 10 2 3 4 6 8 10 2 3 4 6 6 TIME IN SERVICE, HOURS Figure 3.- Probabilities of failure and survival calculated by reliability and conventional anal yses.
NASA- L ang l ey. 1972 - 32