Advances in Fatigue and Fracture Mechanics Analyses for Metallic Aircraft Structures

NASA/TM-2000-210084

Advances in Fatigue and Fracture

Mechanics Analyses for Metallic Aircraft

Structures

J. C. Newman, Jr.

Langley Research Center, Hampton, Virginia

April 2000

The NASA STI Program Office ... in Profile Since its founding, NASA has been dedicated to CONFERENCE PUBLICATION. Collected the advancement of aeronautics and space papers from scientific and technical science. The NASA Scientific and Technical conferences, symposia, seminars, or other Information (STI) Program Office plays a key meetings sponsored or co-sponsored by part in helping NASA maintain this important NASA.

role.

SPECIAL PUBLICATION. Scientific, The NASA STI Program Office is operated by technical, or historical information from Langley Research Center, the lead center for NASA programs, projects, and missions, NASA's scientific and technical information. The often concerned with subjects having NASA STI Program Office provides access to the substantial public interest.

NASA STI Database, the largest collection of aeronautical and space science STI in the world.

TECHNICAL TRANSLATION. English- The Program Office is also NASA's institutional language translations of foreign scientific mechanism for disseminating the results of its and technical material pertinent to NASA's research and development activities. These mission.

results are published by NASA in the NASA STI Report Series, which includes the following Specialized services that complement the STI report types: Program Office's diverse offerings include creating custom thesauri, building customized TECHNICAL PUBLICATION. Reports of databases, organizing and publishing research completed research or a major significant results ... even providing videos.

phase of research that present the results of NASA programs and include extensive For more information about the NASA STI data or theoretical analysis. Includes Program Office, see the following: compilations of significant scientific and technical data and information deemed to • Access the NASA STI Program Home Page be of continuing reference value. NASA at http'//www.sti.nasa.gov counterpart of peer-reviewed formal professional papers, but having less • E-mail your question via the Internet to stringent limitations on manuscript length help@sti.nasa.gov and extent of graphic presentations.

• Fax your question to the NASA STI Help TECHNICAL MEMORANDUM. Scientific Desk at (301) 621-0134 and technical findings that are preliminary or of specialized interest, e.g., quick release • Phone the NASA STI Help Desk at reports, working papers, and (301) 621-0390 bibliographies that contain minimal annotation. Does not contain extensive Write to: analysis.

NASA STI Help Desk NASA Center for AeroSpace Information CONTRACTOR REPORT. Scientific and 7121 Standard Drive technical findings by NASA-sponsored Hanover, MD 21076-1320 contractors and grantees.

NASA/TM-2000-210084

Advances in Fatigue and Fracture

Mechanics Analyses for Metallic Aircraft

Structures

J. C. Newman, Jr.

Langley Research Center, Hampton, Virginia National Aeronautics and Space Administration Langley Research Center Hampton, Virginia 23681-2199

April 2000

Available from: NASA Center for AeroSpace Information (CASI) National Technical Information Service (NTIS) 7121 Standard Drive 5285 Port Royal Road Hanover, MD 21076-1320 Springfield, VA 22161-2171 (301) 621-0390 (703) 605-6000 ADVANCES IN FATIGUE AND FRACTURE MECHANICS ANALYSES FOR METALLIC AIRCRAFT STRUCTURES J. C. Newman, Jr.* This paper reviews some of the advances that have been made in stress analyses of cracked aircraft components, in the understanding of the fatigue and fatigue-crack growth process, and in the prediction of residual strength of complex aircraft structures with widespread fatigue damage. Finite-element analyses of cracked metallic structures are now used to determine accurate stress-intensity factors for cracks at structural details. Observations of small-crack behavior at open and rivet-loaded holes and the development of small-crack theory has lead to the prediction of stress-life behavior for components with stress concentrations under aircraft spectrum loading. Fatigue-crack growth under simulated aircraft spectra can now be predicted with the crack- closure concept. Residual strength of cracked panels with severe out- of-plane deformations (buckling) in the presence of stiffeners and multiple-site damage can be predicted with advanced elastic-plastic finite-element analyses and the critical crack-tip-opening angle (CTOA) fracture criterion. These advances are helping to assure continued safety of aircraft structures.

INTRODUCTION In 1969, Schijve in the Second Frederik J. Plantema Memorial Lecture [1] stated that "fatigue in aircraft structures is a problem for which quantitative and generally accepted solutions are not available." During the past 30 years, many advances have been made in the stress analyses of cracked aircraft components, in understanding the fatigue and fatigue-crack growth behavior in metallic materials, and in the prediction of residual strength of complex built-up aircraft structures with widespread fatigue damage. Although the failure rate in aircraft structures due to fatigue and structural failure has dropped significantly [2] from the mid-1950's, the fatigue and fracture community must stay alert. The technical community should continue to improve the understanding of the fatigue and fracture process and to use the advanced analysis tools to safeguard the public against unexpected failure modes, such as the Aloha Airlines fuselage failure in 1988 due to widespread fatigue damage. Swift, in the Eleventh Plantema Lecture [3], discussed how multiple-site damage cracking could reduce the residual strength of fuselage structures.

The Seventeenth Plantema Memorial Lecture is a review of some of the technical developments and concepts that have led to a better understanding of the fatigue and fracture process in metallic materials. Advances in computer technology has allowed more accurate stress analyses to be conducted on three-dimensional crack configurations, more realistic simulations of fatigue and Mechanics and Durability Branch, NASA Langley Research Center, Hampton, VA, USA 23681

fatiguecrackingin structuralcomponents, andthe useof moreadvanced elastic-plastic fracture

mechanics concepts to assess the residualstrengthandfail-safecapabilityof aircraft structures.

This reviewis limited in scopeandwill not be ableto fully coverthe vastamountof research that

hasbeenconductedoverthe past30 yearsin the fieldsof fatigueandfracturemechanics.The

authorrequests thereaders'indulgence andforgiveness if somemajoreventshavebeenomitted, or if reference is not madeto all of thosewhohavemadesignificantcontributions to the subject.

In particular,this paperwill review someof the advances thathavebeenmadein the areaof stress

analyses of crackedbodies,fatigue(crack-initiationandsmall-crack behavior),fatigue-crack

growth, andfractureof complexfuselage structure.The paperwill discuss the globalstress

analyses of crackedfuselage lap-jointstructureto determine local fastenerstresses. Theselocal

stresses arethenusedto developstress-intensity factorsfor surfaceandcornercracksat openand

fastener-loaded holesusingthree-dimensional codes. Observations of small-crack behaviorat

openandrivet-loaded holesandthe development of small-crack theoryhaveledto theprediction

of stress-life behaviorfor components underconstant-andvariable-amplitude loading. Someof

thesepredictionsareshownfor materials commonlyusedin aircraftconstruction.Fatiguecrack

growth underaircraft spectrum loadingcanbepredictedwith the crack-closure concept. The

importanceof constraint(three-dimensional stressstatearoundthe crackfront) onfatigue-crack

growth underspectrum loadingwill be discussed. The ability of the advanced finite-element

codesto predictthe severe out-of-planedeformations of crackedsheets is demonstrated.

Predictionsof residualstrengthof crackedpanelswith severe out-of-planedeformations in the

presence of stiffeners andmultiple-sitedamage crackingwill bedemonstrated with advanced

finite-element codesandthe criticalcrack-tip-opening angle(CTOA) fracturecriterion. In the

last decade, the international conferences on agingaircraft [4-6] haveintensified the development

of theseadvanced methodologies andtoolsfor fatigueandfracturemechanics analyses, seefor

exampleHarriset al. [7]. Theseadvances arehelpingto insurethe continuedairworthiness of

aircraftstructures.

STRESSANALYSES OF CRACKEDBODIES

Duringthe past30 years,the stress-analysis communityhasdeveloped a largenumberof finite-

element codesto conductlinearandnon-linearstress analyses of complexaircraftstructural

components.Many aircraftcompanies determine stressanddeformationstatesin aircraft

structures usingcodes,suchasABAQUS [8], ANSYS [9], MSC/NASTRAN [10] andSTAGS

[11,12]. Manyof thesecodeshavespecialfeaturesto analyze crackproblemsanddetermine the

stress-intensity factor or the non-linearequivalent, the J-integral. Someof thesecodes,suchas

ABAQUS andSTAGS,haveincorporated the critical crack-tip-opening angle(or displacement)

fracturecriterionfor conductingmaterialandgeometric non-linearfractureanalyses of complex

structures.Thedevelopers of STAGShavealsoincorporated the "plane-strain"shellelement

[12] for moreaccurate fracturesimulations of crackedshellstructures.

At NASA Langley,somespecialty codeshavebeendeveloped to conductfatigueandfracture

mechanics analyses of crackedspecimens andstructuralcomponents.Thesecodeswere

developed to calculatecrack-tipparameters or to studynewfatigueandfracturecriteria. The

ZIP2D code[13] wasoneof the first to be usedfor fatigue-crack growthsimulations to studythe

crack-closure mechanism. This codewasalsousedto studythe critical crack-tip-opening

displacement (CTOD)fracturecriterion. Later, SURF3D[14] andZIP3D [15] weredeveloped

to calculatestress-intensity factorsfor surfaceandcornercracksin platesor at holes. The ZIP3D

codealsoincorporated materialnon-linear(smallstrain)effectsto studythe J-integralandthree-

dimensional fatigue-crack growthandclosure.

A numberof theuniversities andcompanies involvedin the NASA AirframeStructuralIntegrity

Program[7] havealsodeveloped codesto conductstressanddeformationanalyses of cracked

specimens andstructuralcomponents.ChangandMear [16] developed the FADD2D codeto

determine mixed-mode stress-intensity factorsfor almostanytwo-dimensional crackconfiguration

subjected to eitherstress or displacement boundaryconditions.The FADD2D codeis based on a

boundary-element methodwith somespecial dislocationformulationsto modelarbitrarilyshaped

cracks. Ingraffeaandhis colleagues [17,18] havedeveloped a seriesof codes,FRANC2D and

FRANC3D,to conductlinearandnon-linearstress analyses of two- andthree-dimensional bodies

with arbitrarilyshaped cracks.The FRANC2Dcodeis basedon a finite-element approach,

whereas the FRANC3Dcodeis based on theboundary-element formulation. Doddsandhis

students[19] havealsodeveloped anadvanced materialandgeometricnon-linearcode,

WARP3D,basedonthe three-dimensional finite-element method. This codehassomespecial

featuresto studyfracturesimulations usingeithera void-growthmodelor the critical CTOA.

Later, someresultsfrom thesecodeswill be presented to demonstrate their capabilities.

In the NASA agingaircraftprogram,a uniquecapabilityhasbeendeveloped thatintegrates the

fracturetopologymodelingcapabilities of FRANC3D with the generalshellanalysis capabilities

of STAGSinto anintegratedFRANC3D/STAGSanalysis procedure[18]. The automatic

adaptive remeshing capabilityof FRANC3D andthe geometric non-linearstress analysis capability

of STAGSprovidethe analysis basisrequiredto predictthe crackgrowth, crackturning,and

crackarrestbehaviorexhibitedby pressurized shellstructures in damage tolerancetests. The

integratedFRANC3D/STAGSanalysis procedurecurrentlyoperates on high-levelworkstations

or on mainframe computers.This capabilityis described in a greaterdetailin References 7 and 18.

AnalysisMethodologyfor RivetedLap Joints

The generalstrategyfor developing the structuralanalysis methodology for predictingthe stress

anddeformationstatesin stiffenedshellsis shownin Figure1. Large-scale globalmodelsof a

stiffenedfuselageshellof interestaredevelopedandanalyses areconductedto determine the

internalstress distributionsandgeneral response of the shell. A hierarchical modelingapproach is

usedto providehighlyrefinedlocal models,which aredeveloped basedonthe globalmodel

results. Thelocal modelprovidesthe higherfidelity solutionsthat arenecessary to calculatethe local stresses andrivet loadingin the lap-jointregion. To determineaccurate rivet-loadtransfer, the rivet is modeledwith rigid links (stiff springs)andsheets areconnected by a rivet springwith 6 degrees of freedom(3 translational and3 rotational). Examples of theseanalysis capabilities are demonstrated in References 20 and21.

Overthe last 30 years,several laboratories havetestedlap-jointspecimens to determine the

influenceof manufacturing processes andenvironment on fatiguelife. An extensive test program

wasconducted by Hartman[22], at theNationalAerospace Laboratory(NLR), to assess the

effectsof manymanufacturing variablesonthe fatiguebehaviorof thin-sheet rivetedlapjoints, as shownin Figure2(a). Manufacturing variables suchasthejoint configuration, type of fastener,

surface treatmentof the metalprior to riveting,andseveral differentrivetingtechniques were

investigated.All specimens hadstraight-shank button-head rivets andweretestedunderambient

conditionswith constant-amplitude tension-tension fatigueloadingor avariable-amplitude block-

programloading. Furtherdetailsof the testprogramandananalysis of thetest resultsaregivenby

Newmanet al. [23]. Later, Furutaet al [24], atthe KawasakiHeavyIndustries(KHI) andthe

NationalAerospace Laboratory(NAL), testedsimilarlap-jointspecimens with two- or three-rivet

rows using100-degree countersunk rivets. Thesetestswereconducted undereitherambient

conditionsor immersed in a 3.5 % salt-watersolution. An analysis of thesetestdatais givenby

Harriset al. [25]. Herein,the testandanalysis resultsunderambient conditionswill alsobe

presented to demonstrate the applicationof small-crack theoryto lap-jointspecimens. Fatigue testingon a full-scaleaircraftindicatedthatafterabout66,000pressure cyclesextensive cracking haddeveloped at a lapjoint [26] with 4-rivet rows, likethat shownin Figure2(b). An analysis of thesedata[27] indicated that the rivetedjoint mightbeconsidered asa "neat-fit" joint with very little rivet-holeinterference andminimalclamp-upeffects. A crack-growthanalysis usingonlythe

rivet load,by-passstress,andlocalbendingstresswassufficientto matchthe crack-growthrates

measured from the fuselage panel.

The fatigueanalyses of theriveted lap-joint specimens, presented in References 23 and 25, were based on stress-intensity factors for through cracks and corner cracks at a rivet-loaded hole, as shown in Figure 3. From the global-local finite-element stress analyses (Fig. 1), the rivet loading (P), by-pass stress (Sb), and local bending moment (M) were determined. The rivet interference (A) and stresses due to local clamp-up effects are unknown parameters that are very difficult to determine. Thus, an "effective" interference level was used to estimate interference and clamp-up effects in the NLR specimens [23]. But for the KHI-NAL lap-joint specimens with the 100 degree countersunk rivets, no rivet-hole interference was required to fit the test data [25].

Stress-Intensity Factor Analyses Two of the codes from the NASA toolbox [7] were used to determine stress-intensity factors for through cracks at a rivet-loaded hole in a lap joint. The FRANC2D/L code (FRANC2D code with layering capability [17]) and the FADD2D code [16] were used to analyze two symmetric cracks emanating from a rivet-loaded hole in a segment from a lap-joint specimen. The insert in Figure 4 shows the configuration analyzed. This configuration models the lap-joint specimen shown in Figure 2(a) with a 50% by-pass load. The FRANC2D/L code was used to analyze the rivet and rivet-hole contact and the stress-intensity factors are shown as circular symbols. In the FADD2D analysis, the rivet was not modeled but the rivet-contact stresses were used to load the hole boundary. The square symbols show the FADD2D results, which agreed well with the FRANC2D/L results. The solid curve is an equation [23] that was fit to these results.

The analysis toolsfor determination of stress-intensity factors(K) for three-dimensional cracks,

suchasa surfaceandcornercrackin a plateor at a hole,havegreatlyimprovedin the last 20

years. In 1979,Newman[28] reviewedthe stress-intensity factorsfor a surface crack in aplate.

A comparison of the K solutionsfrom the literaturefor a semi-elliptical surface crackin a plate

subjected to remotetensionis shownin Figure5(a). Thenormalized stress-intensity factoris

plottedagainst the crack-depth-to-plate-thickness (a/t) ratio. Thedashed curvesarefrom tabular

resultsandthe solidcurvesarefrom equations.SeeReference 28 for detailsonthe various

methodsusedto obtaintheseK solutions. Thisplot demonstrated thatthe K solutionfrom

variousresearchers variedby almost100%for the same crackconfiguration.The dark solid

curveis the equationdeveloped by NewmanandRajuthat wasfit to their finite-element results

[29]. After twenty years, the Raju-Newman solutionshavebeenshownby otherinvestigators to

be within about5% of the accepted solution.

In 1999,Bakuckas[30] conducted annumericalroundrobin to assess the capabilityof stress

analysts, usingsomeof the neweradvanced codes,to determine the stress-intensity factorsfor a

cornercrackemanating from anopenholeunderremotetension.Theseresultsareshownin

Figure5(b) asa functionof theparametricangle,_),aroundthe crackfront. The hole-radius-to-

plate-thickness (fit) ratio was2 andthe hole-radius-to-plate-half-width (r/w) was0.2. Thecrack- shape ratio (a/c)was0.8 andthe crack-depth-to-plate-thickness (a/t)ratio was0.2. Six analysts

tried eitherfinite-element (FEM, FEAM), boundary-element (BEM, FADD) or weight-function

(WFM) methods to solvethe crackproblem. The dark solidcurveis,again,generated usingthe

Newman-Raju equations (alsofit to their finite-element results[31]) for this crack configuration.

SeeReference 30 for detailson the varioussolutionsmethods.All of the resultswerewithin

about5% of eachother. Theseresultsdemonstrate that three-dimensional stress-analysis codes

cannowbeusedto obtainaccuratestress-intensity factorsatthe structuraldetaillevel.

SoftwareValidation

Oneof the objectivesin the NASA agingaircraftprogram[7] wasto developandvalidate

advanced stressanalysis codesor validateexistingcodesfor analyzing the stress anddeformation states in a crackedfuselage structure. A crackin a pressurized cylinder,like a fuselage, will bulge dueto the internalpressure.Because of crack-tipyieldingandlargeout-of-planedeformations,

ananalysis codewith non-linearmaterialandgeometriccapabilitywasrequired. Both the

STAGSandthe WARP3Dcodeshadthepotentialto predictthe out-of-planedeformations.To

verify thesecodes,a largetensionpanelwith a centralslot of 102mmlength(2c) wastestedto

measure the out-of-planedeformations (seethe insertin Fig. 6). The endsof the slot hada drilled

circularhole of 2.4mmradius. Theholeswereusedto preventa crackfrom developing and

extendinguntil a very high loadwasreached.The measured out-of-plane displacements are

shownas symbols in Figure6 at an appliedstressof 240MPa. The displacements weremeasured

alongthe dashed line shownin the insertat a y/w valueof 0.125. The solidcurveshowsthe

WARP3Danalysis results[32]. The three-dimensional, elastic-plastic, large-deformation analysis agreed well with the testmeasurements obtained usinga digital-imagingmethod[33].

In summary, stress-analysis codesandmethodsareavailable to determine the stress and

deformationstatesof aircraftstructuralcomponents with andwithoutcracks. Accuratestress-

intensityfactorscannow bedetermined for two- andthree-dimensional crackconfigurations for

usein durabilityanddamage toleranceanalyses. Materialandgeometricnon-linearanalyses

codescanbeusedto predictthe stressanddeformationstatesfor complexstructures.Someof

thesecodeshavebeenvalidatedby comparing the analysis resultswith experimental test data.

FATIGUE OF METALLIC MATERIALS

Thefatiguelifeof ametallic material isdividedinto several phases: cracknucleation, micro-crack

growth,macro-crack growth,andfailure.Cracknucleation is associated withcyclicslipandis

controlled bythelocalstress andstrainconcentrations. Althoughthe slip-band mechanism of crack

formationmaybenecessary in puremetals, the presence of inclusions or voidsin engineering

metalswill greatlyaffectthe crack-nucleation process.Micro-crack growth,atermnowreferred to asthe"small-crack growth"regime, is thegrowthof cracks frominclusions, voids,or slipbands, inthe

rangeof 1to 20gm in length.Schijve[34] hasshownthat for polishedsurfaces of puremetalsand

for commercialalloys,the formationof a smallcrackto about100-ginin lengthcanconsume 60

to 80 % of the fatiguelife. The AGARD [35,36] andNASA]CAE [37] studies on small-crack

behaviorshowedthat about90%of the fatiguelife wereconsumed for crackgrowth from about

10 gm to failure on a varietyof materials.Thisis thereasonthatthereis somuchinterestin the

growth behaviorof smallcracks. Macro-crack growthandfailureareregions wherefracture-

mechanics parameters havebeen successful in correlating andin predicting fatigue-crack growthand fracture.Thisreviewwill highlight the advances thathavebeen made in theuseof the same fracture- mechanics parameters in thetreatment of micro-or small-crack growthusingcontinuum-mechanics approaches.

Small-Crack Behavior

AluminumAlloy 7075-T6--Earlier work by Pearson [38] onfatigue-crack initiation andgrowth

of smallcracksfrominclusionparticlesin two aluminumalloys(BSL65 andDTD 5050) setthe

stagefor the development of small-crack theory. His resultsareshownin Figure7 asthe dotted

curve,alongwith additionalsmall-crack data(light solidcurves)from Lankford [39] on 7075-T6

aluminum alloy usingun-notched (KT= 1) specimens. Thesetestswereconducted at a stress

ratio (R = SmiJSmax) of 0.05. Lankford'sdatawentdown to AK values that areaslow as 1.5

MPa_/m.Theyboth concluded thatcracksof aboutthe average grainsizegrew several times

fasterthanlargecracksat nominallyidenticalAK values.The opensymbolsanddash-dot curve

showthe large-crackdataandthe development of the large-crackthresholdat about3 to 4

MPa_/m.Somegeneralobservations from Lankfordwerethatthe minimumin dc/dNoccurred

whenthe cracklength,c, wasaboutthe minimumdimension of the grain sizeandthat the

magnitude of the lower rateswascontrolledby the degreeof micro-plasticityin the nextgrain

penetrated by the crack. If thenext grainis orientedlike the first, thenno deceleration will occur, asindicatedby theuppermostsmall-crack curves.

At this stage, it wouldbe of interestto compare the testresultsfrom Pearson andLankford with

the small-crack growthpredictions madefrom the continuum-mechanics modelbased on crack

closure[40,41]. The baseline AK_rate relation used in the FASTRAN closure model [42,43]

was obtained from Reference 44. The constraint factor (_) used in the analysis was 1.8 for rates less than 7E-4 ram/cycle. The constraint factor accounts for the effects of stress state on crack- growth rate behavior (plane stress or plane strain) and was used to correlate the large-crack growth rate data for various stress ratios (R). The AK_rate results were generated from large- crack data for rates greater than about 2E-6 ram/cycle. The lower section of the AK_rate relation (below 2E-6 ram/cycle) was estimated on the basis of small-crack data [37]. Because small cracks are assumed to be fully open on the first cycle, the AK_rate relation is the starting point for small-crack analysis. The results of an analysis of the test specimen used by Lankford are shown by the heavy solid curve. The initial defect was selected as a 10-_m radius semi- circular surface crack. As the small crack grew, the closure level increased much faster than the AK level and a rapid decrease in rates was calculated. The rapid drop is a combination of the closure transient and the sharp change in slope of the AK_rate relation (at about 1E-6 ram/cycle). At about 30 _m, the crack-opening stresses had nearly stabilized. The predicted small-crack results are in excellent agreement with Pearson's data and agree with some of Lankford's data, which did not exhibit a grain-boundary influence. But interestingly, the small- crack analysis showed a single dip in the small-crack curve, similar to the "single" dip observed in some of Lankford's small-crack data. Would the grain-boundary interaction always occur at the same crack length (40 _m)? Why aren't there other dips, or small indications of a dip, in the rate curve at 80 or 120 _m? Similarly, a shift in the AK_rate relation to higher AK_ values in the near-threshold regime and a larger initial defect would also shift the analysis "dip" to higher AK values, closer to the test data. Further study is needed to help resolve these issues.

The results shown in Figure 7 demonstrate that small-crack data is the "typical" data and that the large-crack data, approaching the large-crack threshold, is the "anomaly." There are no models that can predict the development of the large-crack threshold but the growth of small cracks (30 gm or greater in this alloy) are growing under steady state conditions (constant crack-opening stresses). In the 1980's, it was thought that the small-crack effect was the anomaly and that the large-crack data approaching the threshold was the correct data. During the last decade, research on the large-crack threshold behavior has demonstrated that the threshold is being caused by a rise in crack-closure behavior (due to plasticity-, roughness-, and/or oxide-induced closure).

Aluminum Alloy 2024-T3--Small-crack data [35] have been generated on single-edge-notch tension specimens made of 2024-T3 aluminum alloy (B = sheet thickness = 2.3 mm); and some of these data at R = 0 are shown in Figure 8. Specimens had a notch radius of 3.18 mm and a width (w) of 50 mm.

The small-crack data was obtained by using the plastic-replica method. The small-crack data, shown by the symbols, is only a small part of the overall database on this alloy. These results were taken from one laboratory and at an applied stress level of 110 MPa. In the calculation of AK for small surface cracks at the notch root, the crack-half-depth-to-crack-length (a/c) ratio was assumed to be 1.0 (see Ref. 35). (Note that for a surface crack at a notch root, the crack depth, 2a, is measured in the sheet thickness, B, direction, andc is measured in thespecimen width,w, direction.)This alloy

showeda very largedifference between the large-crackthreshold(about3 MPa_/m)[45] and

small-crack growthbehavior. Smallcracksgrewat AK valuesaslow as0.75MPa_/m.But for

AK valuesgreaterthanabout3 MPa_/m, the small-andlarge-crack dataagreed quitewell. The

dashed curveistheAKe_-rate (da/dN) relation;andthedashed-dot curveshows theAK-rate(dc/dN)

relationfor largecracks [44]. Althoughthetestdatashowed alargeamount of scatter, thecrack-

growthanalysis (solidcurve)fromFASTRANagreed reasonably well withthetrendsin thetestdata.

Theinitial6-gmsemi-circular surface defect wasverycloseto theinclusion particle(or void)sizes that initiatedcracks atthenotchroot [35].

Steel 4340_Swain et al. [46] conducted small- and large-crack tests on 4340 steel. The large-crack results were obtained on middle-crack tension specimens (B = 5.1 mm) tested at various stress ratios (R = -1, 0 and 0.5). The small-crack data were obtained from single-edge-notch tension (SENT) specimens with a notch radius of 3.2 mm and width w = 25.4 mm (Kw = 3.3) at the same stress ratios.

Again, the plastic-replica method was used to measure the growth of small cracks (see Ref. 36).

Examination of the initiation sites for 35 fatigue cracks gave information on the distribution of crack- initiation site dimensions. Two types of crack-initiation particles were observed: a spherical particle and a stringer particle, as shown in the SEM photographs in Figures 9(a) and 9(b), respectively. The spherical (calcium-aluminate) particle was by far the most dominant crack-initiation site particle. The cumulative distribution function for these defects is plotted against an equivalent semi-circular defect radius based on the actual area of the defect in Figure 9(c). The mean defect was about 13-gm in radius. Selecting defects of 8- and 30-gm radius covered over 80% of all defects.

A comparison of some of the small- and large-crack data on the 4340 steel is shown in Figure 10 at the R = 0 condition. The symbols show small surface-crack data from the SENT specimens. The dashed- dot curve is the large-crack data obtained from M(T) specimens [46]. Note that the small cracks were measured in the a-direction and large cracks were measured in the c-direction. Here the small- and large-crack data agreed quite well. The small-crack effect appears to be less dominant at the positive stress-ratio conditions for a variety of materials [35,36]. Again, the dashed curve is the AKe_-rate curve determined from the M(T) specimen data. The constraint factor (o0 was 2.5 for rates less than 5E-4 mm/cycle [44]. The solid curves show the predicted results from the FASTRAN closure model with either an initial semi-circular surface crack of 8- or 30-gm with S_x = 360 MPa. Again, all predictions start on the AKeff-rate curve because the initial crack is assumed to be fully open on the first cycle. Because the effective stress-intensity factor curve is near to the large-crack curve, small-crack effects are weak. The predicted results for the largest defect size rapidly approaches the large-crack behavior. But the predicted results for the smallest defect size showed a very rapidly drop and then a very rapid rise to large-crack behavior. Again, this behavior is due to the crack-closure transient and the shape of the AKeff-rate curve at low rates.

Predictionof FatigueLife usingSmall-Crack Theory

Newmanandhisco-workers [35-37,41,44,46] haveusedcontinuum-mechanics concepts with initial

defectsizes, likethosewhichinitiatedcracks atinclusion particles, voidsor slip-bands, andthe effective stress-intensity factorrangeagainst raterelations to predictthefatiguelivesfor manyengineering materials.Thebaseline crack-growth ratedatafor these materials wereobtained fromlarge-crack data,in mostcases ignoringthelarge-crack threshold, andusingsmall-crack growthratesatextremely low rates.Small-crack thresholds wereestimated fromsmall-crack dataand/or theendurance limitsfor these materials.In thefollowing,some typicalexamples of usingsmall-crack theoryto predictfatigue behavior will bepresented.

Steel 4340_Everett [47,48] conducted fatigue tests on 4340 steel using three types of specimens.

The first specimen was an un-notched (KiT = 1) specimen (B = 8.9 mm). The second specimen was the same KT = 1 specimen but the specimen had a sharp scratch (51-gm deep) machined across the width of the specimen. The last specimen had a single open hole with a radius of 3.2 mm (B = 3.2 mm) that had a stress concentration (KT) of 3.23. Tests were conducted under both constant-amplitude and spectrum loading. The material used in this study had the same strength level as the material tested in Reference 46 (see Fig. 10), but the specimens had a different thickness and were taken from a different batch of material. However, it was assumed that the large-crack data and inclusion-particle sizes would be the same. A small-crack effective threshold, (AKeff)th, of 3.2 MPa_/m was used to predict the endurance limits or the applied stress level where the initial defect would not grow.

Constant-Amplitude Loading: Figure 11 shows test data obtained from un-notched specimens with and without the machined scratch (solid and open symbols, respectively). All specimens were tested at a stress ratio R = -1. The baseline AKeft_rate curve for the steel is shown in Figure 10 (dashed curve).

Using the mean defect size from Figure 9, the 13-gin initial semi-circular surface crack, fatigue-life predictions were made on the pristine specimens. The analysis (solid curve) fit the test data quite well.

For the specimens with the scratch, an edge-crack configuration was assumed with a crack depth of 51 gin. Using the same baseline data, FASTRAN predicted the influence of the scratch on fatigue life extremely well. These results demonstrate that small-crack theory and the crack-closure model can be used to predict either the influence of either material or manufacturing defects on fatigue life.

Felix-28 Spectrum Loading: Results of fatigue tests conducted under the Felix-28 [49] load sequence are shown in Figure 12 as symbols. The maximum stress in the spectrum is plotted against the cycles to failure. Predictions of total fatigue life under the Felix-28 load spectrum were made using the FASTRAN code [43] by calculating the number of cycles necessary to grow a crack from the assumed initial defect size, located at the center of the open hole, to failure. The predicted results for the two initial defect sizes (8- and 30-gm) bounded the test data quite well.

Aluminum Alloy 2024-T3--In the following, small-crack theory will be used to predict the fatigue life of un-notched laboratory specimens and several types of riveted lap joints with countersunk rivets. The initial cracksizewill be selected to bestfit the experimental testdata,like the "equivalentinitial flaw size"concept[50].

Laboratory specimens: Grover et al. [51] conducted fatigue tests on flat (Kw = 1) dog-bone specimens made of 2024-T3 aluminum alloy under R = 0 and -1 loading. The specimens were electro-polished but no information on crack-initiation sites was available. Thus, in the analyses it was assumed that cracks initiated as quarter-circular corner cracks. A comparison of experimental and calculated fatigue lives is shown in Figure 13. Various initial crack sizes were selected by trial-and-error to find the best value to fit the test data. Analyses with a 20- gm initial crack size fit the test data quite well for both R ratios. Results for each R ratio approached the flow stress Oo (average of the yield stress and ultimate tensile strength) for the high-applied stress levels. Some discrepancies were observed for both R = 0 and -1 analyses at applied stress levels above the yield stress. These discrepancies were expected because the closure model does not account for strain-hardening effects but uses an average flow stress. To fit fatigue limits, a value of (AKeff)th of 0.8 MPa_/m was needed for the 20-gm initial crack.

Riveted-lap joints: A series of lap-joint tests were conducted by Furuta, Terada and Sashikuma [24] to study the fatigue behavior of countersink riveted lap-joint panels exposed to laboratory air or to a corrosive salt water environment. Figure 14 shows the configuration of the four types of 2024-T3 (Aclad) panels tested: Type 1 - two rivet row, Type 2 - three rivet row, Type 3 - three rivet row with thin-straight tear straps, and Type 4 - three rivet row with non-uniform thick tear straps. The rivet spacing was 20 man on all joint types, see Figure 2(a) for details on the Type 1 joint. Testing was conducted at constant-amplitude loading which simulated the fuselage skin stress. Tests were conducted under ambient (laboratory air and room temperature) conditions and under a corrosive environment. For the corrosive environment, the lap-joint panels were immersed in circulating 3.5% NaC1 solution. Only the results tested in the laboratory air will be considered here (see Ref. 25 for results under the salt solution).

In the FASTRAN code, the riveted-lap-joint analysis used the remote stress due to rivet load (Sp), the by-pass stress (Sb) and the remote bending stresses (SM) in calculating the stress-intensity factors for a corner crack and through crack emanating from the rivet hole. An interference level (A) was not used in the calculations for these panels. Further discussions on why an interference level was not used will be made later. See Figure 3 for illustration of the various rivet loadings.

The applied stress, S, was 96 MPa (= Sp + Sb) at a stress ratio (R) of 0.125. The two-rivet row (Type 1) panels had a 50% rivet and by-pass stress; whereas, the three-rivet row (Types 2-4) had 37% rivet stress and 63% by-pass stress. Only Type 1 was considered with and without bending, corresponding to panels tested with and without edge clamps to help prevent bending. It was assumed that the tear straps would also help prevent joint bending. Schijve's [52] bending equations (1-degree rivet-rotation correction) were used to estimate the bending stresses for Type 1. Based on 3-D stress analyses presented in Reference 23, the applied stress level of 96 MPa should have yielding the rivet hole and greatly reduced the bending effects.

Furutaet al. measured multiple-sitecrackingonthe Type 1 panels.Sometypicalresultson a

singlepaneltestedwith the edgeclampsto preventjoint bendingareshownin Figure15. They

usedboth opticalanda SEM examination on the brokenspecimen to generate the cracklength

against cycles(opensymbols).Cracksinitiatedandgrewat several rivet holeslocatedin the mid-

bayof the panel,linkedup at about10mmhalf-cracklengths,andcaused panelfailure. The solid

curveis the predictedresultsfromFASTRANusingthebaseline AKeft_rate curve(Fig. 8) andan

initial 6-gm semi-circular flaw. Bendingstresses werenot considered in thesecalculations

because thepanelswererestrained from bending usingedgeclamps. An interference level (A)

wasnot includedin thesecalculations. The 6-gmflaw is the initial defectsizeneeded to predict the fatiguelife of pristinecircularhole specimens madeof this alloy [44]. It wassurprisingthat no interference or clamp-upstresses wereneeded to predictthe life of thesepanels. In retrospect,

if a largerinitial flaw size,saya 10-gmflaw, hadbeenassumed, thenthe fatiguelife wouldhave

beenshortof thetest data. Thena non-zerointerference level wouldhavebeenrequiredto fit the

test data. Thus,it canonlybe assumed that the 6-gm flaw is an"equivalentinitial flaw size"

(EIFS)to fit the data. TheEIFS accounts for manufacturing defects,rivet interference, clamp-up stresses, andmanyotherfeaturesin a lap-jointspecimen (seeRef.25).

Figure16 showsthatthe fatiguelife of Type 1,3 and4 panelstestedunderambient(laboratory

air androom temperature) conditions(opensymbols).Somepanels haveedgeclampsto prevent

joint bendingandothershadtear straps(seeFig. 14). The FASTRANpredictions(solid symbols)

agreed well with the paneltestresults. Here,the fracturemechanics based calculations assumed a

6-gmradiuscornercrackin a neat-fitrivet-loadedstraightshankhole (rivet fit-up and

interference fit stresses wereassumed small). But at this stage, the 6-gm radiusflaw mustbe considered asanEIFS to accountfor the manyunknownsin a lap-jointpanel.

FATIGUE CRACK GROWTHIN METALLIC MATERIALS

Events in thenaval, nuclear, andaircraftindustries havefostered thedevelopment of thefieldof fracture mechanics andtheapplication of stress-intensity factoranalyses to fatigue-crack growth. The failureof theComettransport jet aircraft[53]fromfatiguecracks gaveriseto treatments of crack propagation using the stress-intensity factorconcept of Irwin [54]andPariset al.[55]. Thesimplicity ofthe stress-intensity factorconcept rapidlydeveloped into thedurability anddamage-tolerance concepts currently usedtodayto design fatigue- andfracture-critical components. Thediscovery of fatigue-crack closure by Elber[56]ushered in anewrationalmethod to treatfatigue-crack growth.

Thecrack-closure concept put crack-propagation theories ona firmfoundation andallowed the

development ofpractical life-prediction methods forvariable-amplitude andspectrum loading,suchas experienced by modem-day commercial aircraft.

In 1968,Elber [56,57] observed that fatigue-crack surfaces contactwith eachotherevenduring

tension-tension cyclicloading. This contactis dueto residualplasticdeformationthatis left in the

wakeof anadvancing crack,asillustratedin Figure17(a). Thisdeformedmaterialcontacts

duringunloading.It is surprising that this observation appeared so manyyearsaftercrackgrowth was first studied. But this simple observation and the explanation of the crack-closure mechanism (or more properly crack-opening) began to explain many crack-growth characteristics almost immediately. Since the discovery of plasticity-induced closure, several other closure mechanisms, such as roughness- and oxide/corrosion/fretting product-induced closure, have been identified.

The roughness mechanism, discovered by Walker and Beevers [58], appears to be most prevalent in the near-threshold regime of large-crack growth where the maximum plastic-zone sizes are typically less than the grain size. At these low stress levels, crack extension is primarily along a single slip system resulting in a Stage I-like mechanism and a serrated or zig-zag (+ 0 deg.) crack- growth path, as shown in Figure 17(b). These cracks will have mixed-mode (Mode I and II) crack-surface deformations, which provide the mechanism for contact between the surfaces during cyclic loading. Suresh and Ritchie [59] have developed a model of roughness-induced closure. Cracks growing along a non-planar path, such as during overloads in aluminum alloys, will develop surface contact and create debris due to fretting and the growth of oxides from the newly created crack surfaces (see Fig. 17(c)). This debris will cause premature contact, as discussed by Paris et al. [60]. These new closure mechanisms, and the influence of the plastic wake on local crack-tip strain field, have greatly advanced the understanding of the fatigue-crack growth process. In the future, models will be developed which will include these three mechanisms of closure, but presently, the majority of the crack-growth models for retardation and acceleration (see Ref. 61 for details) are based on only the plasticity-induced closure concept.

To make life predictions using Elber's crack-closure concept, AKeff as a function of the crack- growth rate must be obtained for the material of interest. Fatigue crack-growth rate data should be obtained over the widest possible range in rates (from threshold to fracture), especially if spectrum load predictions are required. Data obtained on the crack configuration of interest would be helpful but it is not essential. The use of the nonlinear crack-tip parameters is only necessary if severe loading (such as low cycle fatigue conditions) is of interest. Most damage- tolerant life calculations can be performed using the linear elastic stress-intensity factor analysis with crack-closure modifications.

Middle-Crack Specimens under Constant-Amplitude Loading Under constant-amplitude loading, the only unknown in the plasticity-induced crack-closure analysis [42] is the constraint factor, o_. The constraint factor accounts for the effects of state-of- stress on crack-tip yielding and crack-surface displacements. The constraint factor is determined by finding (by trial-and-error) a value of o_ that will correlate the constant-amplitude fatigue- crack-growth-rate data over a wide range in stress ratios, as shown by Newman [62]. This correlation should produce a unique relationship between AKeff and crack-growth rate. In the large-crack-growth threshold regime for some materials, the plasticity-induced closure model may not be able to collapse the threshold (AK-rate) data onto a unique AKeff -rate relation because of other forms of closure. Roughness- and oxide-induced closure (see Ritchie and Lankford [63]) appears to be more relevant in the threshold regime than plasticity-induced closure. This may help explain why the constraint factors needed to correlate crack-growth rate data in the near thresholdregimearelower thanplane-strain (o_ = 3) conditions. Theconstraintfactorsare 1.7to

2 for aluminum alloys,1.9to 2.2 for titaniumalloysand2.5 for steel. Several references

[35,37,40and41] haveshownthat large-crack thresholddata(determined from the load-

reductionprocedure)arenot applicable for smallcracks. However,further studyis needed to

assess the interactions betweenplasticity-,roughness- andoxide-induced closurein this regime.

If the plasticity-induced closuremodelis not ableto give auniqueAKeff-raterelationin the

thresholdregime,thenhigh stress ratio (R > 0.7) data may be used to help establish the AKeff - rate relation in the near-threshold regime. But small-crack test data should be used to establish the proper AKeff -rate relation in the near-threshold regime.

In the following, an illustration of the AKeff -rate relation for an aluminum alloy will be presented but similar procedures may be used to establish the relationship for other materials. The large- crack results for 2024-T3 aluminum alloy are shown in Figure 18 for data generated by Hudson [64], Phillips [45] and Dubensky [65]. This figure shows the elastic AKeff plotted against crack- growth rate. The data collapsed into a narrow band with several transitions in slope occurring at about the same rate for all stress ratios. Some large differences were observed at high R-ratios in the high-rate regime. These tests were conducted at extremely high remote stress levels (0.75 and 0.95 of the yield stress). Even elastic-plastic crack-tip parameters were unable to collapse the data along a unique curve in this regime. From a high-cycle fatigue standpoint, however, this discrepancy has very little influence on total life. The elastic-plastic fracture criterion (Two- Parameter Fracture Criterion, TPFC; see Ref. 66) used in the analysis (KF = 267 MPa_/m; m = 1) predicted failure very near to the vertical asymptotes of the test data, see the vertical dashed and dotted lines for R = 0.7 and 0.5 (at 0.75 and 0.95 of yield), respectively. Similar vertical lines (not shown) would also indicate failure at the other R ratios. Lower R ratios would fail at higher values of AKeff. For these calculations, a constraint factor (o0 of 2.0 was used for rates less than 1E-07 m/cycle (start of transition from flat-to-slant crack growth) and o_ equal to 1.0 was used for rates greater than 2.5E-06 m/cycle (end of transition from flat-to-slant crack growth). For intermediate rates, o_ was varied linearly with the logarithm of crack-growth rate (see Ref. 43).

The values of o_ and rate were selected by trial-and-error and from analyses of crack growth under spectrum loading (see Ref. 67). The constraint-loss regime (o_ = 2 to 1) has also been associated with the flat-to-slant crack-growth behavior. Reference 67 developed an expression to predict the location of the flat-to-slant crack-growth regime and the effective stress-intensity factor at transition is by (AKeff)T = 0.5 C_o_/B

(1)

For the 2024-T3 alloy sheet, (AKeff)T = 10.2 MPa_/m. The width of the constraint-loss regime, in terms of rate or AKeff, is a function of thickness but this relationship has yet to be developed. In the low crack-growth rate regime, near and at threshold, tests and analyses ]40,68] have indicated that the threshold develops because of a rise in the crack-opening-stress-to-maximum-stress ratio due to the load-shedding procedure. In the threshold regime then, the actual AKeff -rate data would lie at lower values of AKeff because the rise in crack-opening stress was not accounted for in the current analysis. For the present study, an estimate was made for this behavior on the basis of small-crack data [35] and it is shown by the solid line below rates of about 2E-09 m/cycle.

The baseline relation shown by the solid line was used to predict fatigue lives under constant- amplitude results shown in Figures 13, 15 and 16.

Middle-Crack Specimens under Spectrum Loading Wanhill [69] conducted spectrum crack-growth tests on middle-crack tension specimens made of 2024-T3 Alclad material (B = 3.1 mm). Tests were conducted under the TWIST (transport wing spectrum) [70] clipped at Level III with a mean flight stress of Smf = 70 MPa. Figure 19 shows a comparison of test results and calculated results from Newman's closure model [42,43] with the constraint-loss regime (o_ = 2 to 1) estimated from equation (1). The model used AKeft_rate data like that shown in Figure 18, but for the 2024-T3 Alclad alloy. To illustrate why the constraint- loss regime is necessary, example calculations were made for constant constraint conditions of either o_ = 1 or 2 (dashed curves). The model with a low constraint condition (o_ = 1) predicted much longer lives than the tests, whereas the model with the high constraint predicted much shorter lives than the tests. Thus, the correct constraint-loss regime is required to predict fatigue- crack growth under aircraft spectrum loading in thin-sheet materials.

Stiffened Panels under Constant-Amplitude Loading In 1971, Poe [71] conducted fatigue-crack growth tests on riveted-stiffened panels made of 2024- T3 sheet material with either aluminum or steel stiffeners. The dimensions of the panel are shown in Figure 20. The total width (2w) of the panel was 915 mm. The panel had five intact stiffeners with a single crack located under the central stiffener. The stringers were placed symmetrical about the sheet, so that sheet bending would be minimized. Poe had also developed a stress- analysis code to determine the stress-intensity factors for a crack in an infinite sheet with stiffeners attached with rigid fasteners. The normalized stress-intensity factor against crack-length-to-half- width (c/w) ratio is shown in Figure 21, as the solid curve. These results were for a stiffened panel that had a stringer-area-to-total-area (g) ratio of 0.41. These results showed that the normalized stress-intensity factor dropped rapidly as the crack approaches a stringer (located at c/w = 0.33 and 0.66). In 1999, Chen [72] conducted a stress analysis of Poe's panel but assumed that the fasteners were flexible using Swift's fastener-flexibility model [3]. Because of the more flexible fasteners and lower fastener loads, Chen's stress-intensity factors (dashed curve) were 10 to 20% higher than Poe's solution.

The experimental results obtained from two panels tested by Poe [71] under constant-amplitude fatigue loading with a remote applied stress of 103 MPa at R = 0.1 are shown in Figure 22. This figure shows crack length against crack-growth rate measured (symbols) from two panels with = 0.41. These results show higher rates for large crack lengths until the crack approaches the first stiffener. Here the rates show a rapid drop and then rise after the crack grows pass the stiffener.

FASTRAN and the AKeft_rate curve shown Figure 18 were used to make several predictions.

First, the dottedcurveshowsthe predictions madefor anun-stiffened panel. Theseresultspredict

muchhigherratesthanthe tests. UsingPoe's stress-intensity factor solution(Fig.21), the

predictionsareshownasthe dashed curve. Herethepredictedratesagreedfor cracklengthsless

that about25 mmbut the predictedrateswere20 to 40%lower thanthemeasured ratesfor larger

cracklengths.Using Chen'sstress-intensity factorsolution(Fig. 21), thepredictionsareshown

asthe solidcurve. The predictedresultsagreed quitewell with the measured ratesexceptfor the largestcracklengths(c > 150mm). It is suspected that rivet yieldingor fastener-hole yielding, which wasnot accounted for in the eitheranalysis, wouldhavecaused lower rivet loadsand, consequently, highercrack-growthrates. Theseresultsdemonstrate that rivet flexibility is an

importantparameter to considerwhenpredictingthe fatiguecrackgrowthor fracturebehaviorof

stiffenedpanels.

FRACTUREOF METALLIC MATERIALS

Oneof the objectivesof the NASA AirframeStructuralIntegrityProgram[7] wasto developthe

methodology to predictthe residualstrengthof fuselage structures with largetwo-baycracksin

the presence of multiple-sitedamage (MSD) crackingat adjacent rivet holes. Thepredictionof

the residualstrengthof a complexbuilt-upshellstructure,suchasa fuselage with frames,tear-

straps,andlap-splice joints, requiredthe integrationof a ductilefracturecriterionanda detailed

nonlinearstress analysis of the crackedstructure.The criticalcrack-tipopening-angle (CTOA)

fracturecriterion [73-75]hasbeenexperimentally verifiedto be a valid fracturecriterion for mode

I stressstates in thin andmoderately thick (13-mmor less)aluminumalloys[76-78]. The CTOA

criterionhasbeendemonstrated to bevalid for predictingthe link-up of a largeleadcrackwith

smallfatiguecracksahead of the advancing leadcrack [79]. This fracturecriterionhasbeen

implemented into the STAGSgeometricandmaterialnonlinearfinite-element-based shellanalysis

code[12] to provideanintegratedstructural-integrity analysis methodology.The capabilityto

modela growingcrackthatmayextendin a non-self-similar directionhasbeenaddedto the

FRANC3D/STAGScode[80] alongwith anautomated meshrefinement andadaptiveremeshing

procedure.Thetopologicaldescriptionof the growingcrackis providedby theFRANC3D

fracturemechanics code. The geometric nonlinearbehaviorof a stiffenedfuselageshellis

currentlyunderstudyfor internalpressure loadscombined with fuselage bodyloadsthat produce

tension,compression andshearloadsin the shell.

In the following sections, the CTOA fracturecriterion will bereviewedandsomeexperimental

measurements will bepresented on a fuselage material. Theapplicationof two-dimensional finite-

elementanalyses to simulate the fractureprocessusingthe critical CTOA will be presented to

illustratehow the state-of-stress (plane-stress or plane-strain conditions)aroundthe crackfront affectsthe fractureanalysis.In practice,widepanelfracturetestsareusuallyconducted with anti- bucklingguideplatesto preventthe out-of-planedeformations of the crack. But restraining the

out-of-planedeformations havebeenfoundto bevery difficult, especially for wide panelswith

stringersor tear-straps.Because large2-baycracksin fuselage structureexhibitlargeout-of-plane

deformations (bulgingfrom internalpressure), the analysis toolsmustbeableto predictthe

influenceof bulgingor bucklingon the fractureprocess.Thus,the useof anti-bucklingguideplate

systems shouldbeusedonly in limited cases andthe wide panelsshouldbe allowedto buckle,so

that experimental testdatacanbe obtainedwith bothin-planeandout-of-planedeformations.The

useof the STAGS shellcodeto predictthe fracturebehaviorundertheseconditionswill be

illustrated. The applicationof the STAGS/CTOAanalysis will bepresented on someof the

FAA/NASA wide panelfracturetests[81]. Thesetestscombined the influenceof a largelead

crackwith varioussizesof multiple-sitedamage (MSD) cracking(simulatinga rivet-row

cracking),with intact or brokenstiffeners, andsevere out-of-planedeformations duringstable

tearing,cracklink-up, andfracture.

CTOA FractureCriterion

The criticalcrack-tip-opening-angle (CTOA) fracturecriterionis a "local" approach to

characterizing fracture. An extensive testprogram[82] hasbeenconductedto experimentally

studythe characteristics of the CTOA criterionandto establish its validity asa fracturecriterion

for thin-sheet 2024-T3. Several laboratory-type specimens havebeenusedto measure the CTOA

duringthe fractureprocess.A high-resolution long-focal-length microscope wasusedto record

the stable-tearing results. The tearingeventwasthenanalyzed on a frame-by-frame basisand

CTOA wasmeasured, as shownin Figure23. Measurements madeon compactC(T) andvarious

sizemiddle-crack tensionM(T) specimens areshownin Figure24. The criticalCTOA was

relativelyinsensitive to crackextensionafteraninitial transitionregion. The initial transition

regionhasbeentracedto 3D effectsthat occurasthe cracktunnelsandtransitionsfrom flat-to-

slantcrackgrowth [78]. Three-dimensional fracturesimulations with stabletearingandtunneling

havedemonstrated thatthe CTOA is high at the free surfaceandrapidlydropsduringcrack

extension[83]. But the CTOA in the interior is low andrisesduring stable tearing. After a small amountof stable tearing(aboutequalto sheet thickness),the criticalCTOA in the interior andat

the free surfaceapproach nearlythe same value. Over50 manof stabletearingwasrecordedand

the CTOA valueswerenearlyconstant(5.8degs.).

Two-Dimensional Finite-Element Analyses with Plane-Strain Core

In the past[74-75], two-dimensional (2D) elastic-plastic finite-element analyses, underplane-

stress conditions,wereusedto studystabletearingin analuminumalloy (6-mmthick). But the

resultsindicatedthat CTOA washigh at crackinitiationanddroppedwith crackextension.The

drop wasnot asrapidasthat shownin Figure24. Theresultswerediscouraging andindicated

that CTOA wasnot a constant.However,Newmanet al [77] foundthatneitherplane-stress nor

plane-strain conditionswereableto fit experimental testdata(25-mmthick steel)usingthe critical CTODfracturecriterion (equivalent to the CTOA criterion). But a hybrid analysis with a coreof plane-strain elements aroundthe cracktip andplane-stress elements elsewhere wasableto fit the test dataquitewell.

The influenceof the state-of-stress on fractureis illustratedin Figure25. Fractureresultsfrom

variouswidth middle-crack tensionspecimens (restrained from buckling)areshownassymbols

[84]. The failurestress is plottedagainst specimen width for 2c/W = 1/3. By trial-and-errorand usingthe 2D elastic-plastic finite-element analysis, a critical angle(gtc)of 4.7 degrees with a

plane-strain coreof 1.9manwasdetermined to bestfit the data(solidcurve). Theplane-strain

corehalf-height(he)is measured from the crackplaneto the heightof the core. Elements within

this corehadplane-strain conditions. Theupperdash-dotcurveshowsthe calculations madewith

allplane-stress elements andgtc= 4.7 degrees.The shape of the curveis suchthat it would not be ableto fit the failurestresses on all of the specimens. Likewise,the dashed curveis theresults of plane-strain analyses. Herethe analyses fit the smallerspecimens but underpredictsthe failure

stresses on the largespecimens. Thus,the fractureprocess is a 3D problemandtheuseto the

"plane-strain core" conceptallows2D analyses to accurately simulate thefractureprocess.The

plane-strain core(heaboutequalto the thickness) modelsthe high constraintarounda cracktip

but allowsfor the widespread plasticyieldingunderplane-stress conditionsawayfromthe crack

tip.

Effectsof BucklingandVariousAnti-BucklingGuideSystems

The useof guideplatesis intendedto decouple the crack-growthprocessfrombucklingbehavior.

The intentis to determine the load-crack-extension behaviorunderrestrained conditions. A series

of wide paneltests(1000-ram wide) wereconducted by Dawickeet al [85] to determine the

effectsof variousguideplatesystems on residualstrength.The first two testswereconducted

without guideplates,Figure26(a),andthe average failurestresswas166MPa. The appliedstress

against crackextension for thesetwo testsareshownin Figure27 asthe lowestsymbols.The

initial 1000-ram wide guideplatesconsisted of four 12.7-ram-thick sheets of aluminum alloy that

sandwiched the specimen.Teflon sheets wereplacedbetweenthe guideplatesandthe specimen

to reducethe friction betweenthe specimen andguides. The 1000-ram wide specimen testedwith

theseguideplatesexperienced a 24%increase in failurestressoverthe unconstrained test, as

shownin Figure26(a)andthe square symbols in Figure27. The guideplatesystem shownin

Figure26(b)hadbeensufficientto preventbucklingin smaller width specimens, but the guide

platesalonedidnot preventbucklingin the 1000-ram wide panel. The guideplateswereobserved

to deformout-of-planeabout3 ram,indicatingthatthe stiffness of the guideplateswasnot

sufficientto preventbuckling. The out-of-planestiffness of the guideplateswasincreased by

attaching six pairsof I-beamsto the outsideof the plates,as shownin Figure26(c). A third,

identicalspecimen wastestedwith the modifiedguideplatesystem andthemeasured failure stress

was46%higherthanthe unconstrained test. A comparison of the appliedstressagainst crack

extensionfor the unrestrained testsandthe othertestsconducted with the two guideplatesystems areshownin Figure27.

The STAGS shellcode[12] andthe critical CTOA fracturecriterionhasbeenusedto studythe

behaviorof crackedpanels that wereeitherrestrained from bucklingor allowto buckle[86]. It

hasbeenfoundthatthe sameCTOA canbeusedto predictthe effectsof bucklingon stable

tearing. An illustrationof the STAGS/CTOAcapabilityis shownin Figure28. Two middle-crack

tensionpanels(W = 610mmwide) weretestedwith anti-buckling guides[87] andtheseresults

areshownasthe uppermost symbols.Thentwo identicalcrackpanelsweretestedwithout the

guides[87] andtheseresultsareshownasthe lower symbols.Bucklinghada largeinfluence

(about25%) on theresidualstrength. Thecritical CTOA (_tc)of 5 degrees wasdetermined from

a ZIP3D fractureanalysis andthe plane-strain coreheight(he)of 1 mmwasdetermined from a

ZIP2D fractureanalysis(to fit the ZIP3D results)from 152-ram wide compacttensionspecimen

tests[88]. The_tc andhevalueswerethenusedin the STAGScode(with the plane-strain core

option [12]) to predictstabletearingon the panelrestrained from buckling(dashed curve)andthe

panelallowedto buckle(solidcurve). Thepredictedresultsagreedquitewell with the test data

anddemonstrate thatthe fracturemethodology canaccountfor severe out-of-planedeformations.

This methodology hasbeensuccessful usedto predictstable tearingandresidualstrengthin large

curvedpressured fuselage testarticleswithin about10%[88].

FAA/NASA WidePanelFractureTests

NASA andthe FAA jointly designed andconducted fracturetestson 1016-mm wide sheets made

of 1.6-mmthick 2024-T3aluminum alloy with andwithout stiffeners [81]. Someof the specimens

hadfive 7075-T6aluminumalloy stiffeners (2.2-mmthick) rivetedon eachsideof the sheet,as

shownin Figure29. The centralstiffeners werecut alongthe crackline. Openholeswere

machined into the sheetatthe requiredrivet spacingalongthe cracklinebut rivetswerenot

installed. Fivedifferentcrackconfigurations weretested:a singlecentercrack,a singlecenter

crackwith an arrayof 12holeson eithersideof the leadcrack,anda singlecentercrack with

threedifferentequalMSD cracking(0.25,0.76 and1.3-mm)at the edgeof eachhole,see

Reference 89. For eachcrackconfiguration,identicalspecimens weretestedwith andwithout

rivetedstringers.All testswereconducted understrokecontrol. Measurements weremadeof

load against crackextension.

Comparisons of measured andpredictedload against crackextension for a stiffenedpaneltest

with a singlecrack anda test with a singlecrackandMSD areshownin Figures30(a)and30(b),

respectively.The CTOA (gtc= 5.4 deg.)wasdetermined from laboratoryspecimens restrained

from buckling[89]. The stiffenedpanelswereallowedto buckle. The STAGSanalyses with the

plane-strain core(he= 2 mm)compared extremelywell with thetest data(symbols).Theseresults

demonstrate thatthe residual-strength analysis methodcanpredictstablecrackgrowthandfailure

loadsfor complexstructure.

CONCLUDINGREMARKS

The Seventeenth FrederikJ. Plantema MemorialLecturepresented a review of someof the

technicaldevelopments andconcepts that haveledto a betterunderstanding of the fatigueand

fractureprocessin metallicmaterials.Advances in computertechnologyhasallowedmore

accurate stressanalyses to be conductedonthree-dimensional crackconfigurations, morerealistic simulations of the fatigueprocessandfatigue-crack growth in structuralcomponents, andthe use of moreadvanced elastic-plastic fracturemechanics concepts to assess the residualstrengthand fail-safecapabilityof aircraftstructures.The following conclusions weredrawnfromthis review: (1) Finite-element andboundary-element analyses areableto determine accuratestress-intensity factorsfor crackedstructuralcomponents.

(2) "Fatigue"is "crackpropagation"from micro-structural features, suchasinclusionparticles,

voids,andslipbands,for manyengineering materials; andfatiguelivescanbepredictedunder

constant-andvariable-amplitude loadingwith Small-CrackTheory.

(3) Fatigue-crack growth canbepredictedunderaircraft spectrum loadingwith the Crack-

ClosureConceptandconsideration of constrainteffectson plasticyieldingaroundthe crack.

(4) Fractureof "thin-sheet"materials underthe influenceof rivetedstringers, buckling,and

multiple-sitedamage crackingcanbepredictedwith the critical crack-tip-opening-angle (CTOA)

fracturecriterion.

REFERENCES

[1] Schijve,J., "FatigueLife of StructuralComponents underRandomLoading," 2 nd Plantema

Memorial Lecture, International Committee on Aeronautical Fatigue (ICAF), Stockholm, Sweden, 1969.

[2] Goranson, U. G, "Damage Tolerance - Facts and Fiction," 14 'h Plantema Memorial Lecture, 17 'h Symposium of the International Committee on Aeronautical Fatigue (ICAF), Stockholm, Sweden, June 9, 1993.

[3] Swift, T., "Damage Tolerance in Pressurized Fuselage," 11 'h Plantema Memorial Lecture, 14 'h Symposium of the International Committee on Aeronautical Fatigue (ICAF), New Materials and Fatigue Resistant Aircraft Design, Ottawa, Canada, June 8-12, 1987.

[4] Structural Integrity of Aging Airplanes, S. N. Atluri; S. G. Sampath and P. Tong, eds., Springer-Verlag, 1991.

[5] FAA-NASA Symposium on the Continued Airworthiness of Aircraft Structures, C. A.

Bigelow, ed., DOT/FAA/AR-97/2, July 1997.

[6] The Second Joint NASA/FAA/DoD Conference on Aging Aircraft, C. E. Harris, ed., NASA CP-208982, January 1999.

[7] Harris, C. E.; Newman, J. C., Jr.; Piascik, R. and Starnes, J. H., Jr., "Analytical Methodology for Predicting the Onset of Widespread Fatigue Damage in Fuselage Structure," Journal of Aircraft, Vol. 35, No. 2, 1998, pp. 307-317.

[8] ABAQUS User's Manuals, Version 5.5, Hibbitt, Karlsson and Sorensen, Inc., 1995.

[9] ANSYS User's Manuals, Version 5.4, Swanson Analysis Systems, Inc., 1998.

[10] MSC/NASTRAN User's Manuals, Version 70.5, MacNeal-Schwendler Corp., 1999.

[11] Almroth, B; Brogan, F. and Stanley, G., "User's Manual for STAGS," NASA CR-165670, 1978.

[12] Rankin, C. C.; Brogan, F. A.; Loden, W. A. and Cabiness, H. D., "STAGS User Manual- Version 2.4," Lockheed Martin Advanced Technology Center, Report LMSC P032594, 1997.

[13] Newman,J. C., Jr., "Finite-Element Analysisof FatigueCrackPropagation- Includingthe

Effectsof CrackClosure,"Ph.D. Thesis,VirginiaPolytechnicInstituteandState

University,Blacksburg, VA, May 1974.

[14] Raju,I. S. andNewman,J. C., Jr., "surf3d:A 3-D Finite-Element Programfor the Analysis

of SurfaceandCornerCracksin Solidssubjected to Mode-I Loadings,"NASA TM-

107710,February1993.

[15] Shivakumar, K. N. andNewman,J. C., Jr., "ZIP3D - An ElasticandElastic-Plastic Finite-

ElementAnalysis Programfor CrackedBodies,"NASA TM-102753,November1990.

[16] Chang, C. C. andMear,M. E., "A BoundaryElementMethodfor Two-Dimensional Linear

ElasticFractureAnalysis,"InternationalJournalof Fracture,Vol. 74, 1996,pp. 219-251.

[17] Wawrzynek, P. andIngraffea,A., "FRANC2D: A Two-Dimensional CrackPropagation

Simulator,"NASA CR-4572,March 1994.

[18] Potyondy,D. O.; Wawrzynek,P. A. andIngraffea,A. R., "DiscreteCrackGrowth Analysis

Methodologyfor ThroughCracksin Pressurized Fuselage Structures,"NASA CP-3274,C.

E. Harris,ed.,September 1994,pp. 581-602.

[19] Koppenhoefer, K. C., Gullerud,A. S., Ruggieri,C. andDodds,R. H., Jr., "WARP3D:

DynamicNonlinearAnalysisof Solidsusinga Preconditioned Conjugate GradientSoftware

Architecture,"StructuralResearch Series(SRS)596, UILU-ENG-94-2017,Universityof

Illinois at Urbana-Champaign, 1994.

[20] Young,R. D.; Rouse,M.; Ambur,D. R. andStarnes, J. H., Jr., "ResidualStrengthPressure

TestsandNonlinearAnalyses of Stringer-andFrame-Stiffened AluminumFuselage Panels

with LongitudinalCracks,"TheSecondJointNASA]FAA/DoD Conference on Aging

Aircraft, C. E. Harris,ed.,NASA CP-208982, 1999,pp. 408-426.

[21] Chen,C. S.; Wawrzynek,P. A. andIngraffea,A. R., "Crack Growth SimulationandResidual

StrengthPredictionin AirplaneFuselage s," NASA/CR-1999-209115, March 1999.

[22] Hartman,A., "The Influenceof Manufacturing Procedures onthe Fatigueof 2024-T3

AlcladRivetedSingleLapJoints,"NLR TR 68072U, July 1968.

[23] Newman,J. C., Jr.; Harris,C. E.; James, M. A. andShivakumar, K. N., "Fatigue-Life

Predictionof RivetedLap-SpliceJointsusingSmall-Crack Theory," Fatigue in New and

Ageing Aircraft, R. Cook and P. Poole, eds., EMAS, Ltd., 1997, pp. 523-552.

[24] Furuta, S.; Terada, H. and Sashikuma, H., "Fatigue Strength of Fuselage Joint Structures under Ambient and Corrosive Environment," Fatigue in New and Ageing Aircraft, R. Cook and P. Poole, eds., EMAS, Ltd., 1997, pp. 231-249.

[25] Harris, C. E.; Newman, J. C., Jr. and Piascik, R. S., "A Practical Engineering Approach to Predicting Fatigue Crack Growth in Riveted Lap Joints," 20 'h Symposium of the International Committee on Aeronautical Fatigue (ICAF), Bellevue, WA, July 14-16, 1999.

[26] Piascik, R. S.; Willard, S. A. and Miller, M., "The Characterization of Widespread Fatigue Damage in Fuselage Structure," FAA/NASA International Symposium on Advanced Structural Integrity Methods for Airframe Durability and Damage Tolerance, NASA CP- 3274, 1994, pp. 563-580.

[27] Piascik, R. S. and Willard, S. A., "The Characteristics of Multi-Site Fatigue Damage in the Fuselage Riveted Lap Splice Joint," Fatigue in New and Ageing Aircraft, R. Cook and P.

Poole, eds., EMAS, Ltd., 1997, pp. 93-114.

[28] Newman,J. C., Jr., "A ReviewandAssessment of the Stress-Intensity Factorsfor Surface

Cracks,"Part-ThroughCrackFatigueLife Prediction,ASTM STP687,J. B. Chang,ed., AmericanSocietyfor TestingandMaterials,Philadelphia, PA, 1979,pp. 16-42.

[29] Raju,I. S. andNewman,J. C., Jr., "Stress-Intensity Factorsfor a WideRangeof Semi-

Elliptical SurfaceCracksin Finite-Thickness Plates,"Engineering FractureMechanics, Vol.

11, No. 4, 1979,pp. 817-829.

[30] Bakuckas, J. G., Jr., "Comparison of BoundaryCorrectionFactorSolutionsfor Two

Symmetric Cracksin a Straight-Shank Hole," DOT/FAA/AR-98/36,April 1999.

[31] Raju,I. S. andNewman,J. C., Jr., "Stress-Intensity Factorsfor Two SymmetricCorner

Cracks,"FractureMechanics, ASTM STP677,C. W. Smith,eds.,AmericanSocietyfor

TestingandMaterials,1979,pp. 411-430.

[32] Gullerud,A. S.; Dodds,R. H., Jr.; Hampton,R. W. andDawicke,D. S., "3-D Finite

ElementModelingof Ductile CrackGrowth in Thin AluminumMaterials," Fatigue and

Fracture Mechanics: 30 th Volume, K. L. Jerina and P. C. Paris, eds., American Society for Testing and Materials, 1998.

[33] Hell, J. D., "Use of Three-Dimensional Digital Image Correlation for the Experimental Characterization of Buckling in Large, Thin, 2024-T3 Aluminum, Middle-Crack Tension Specimens," Ph.D. Thesis, University of South Carolina, 1999.

[34] Schijve, J., "Four Lectures on Fatigue Crack Growth," Engineering Fracture Mechanics, Vol. 11, 1979, pp. 167-221.

[35] Newman, J. C., Jr. and Edwards, P. R., "Short-Crack Growth Behaviour in an Aluminum Alloy- and AGARD Cooperative Test Programme," AGARD R-732, 1988.

[36] Short-Crack Growth Behaviour in Various Aircraft Materials, P. R. Edwards and J. C.

Newman, Jr., eds., AGARD R-767, 1990.

[37] Newman, J. C., Jr., Wu, X. R., Venneri, S. and Li, C., "Small-Crack Effects in High- Strength Aluminum Alloys," NASA RP- 1309, 1994.

[38] Pearson, S., "Initiation of Fatigue Cracks in Commercial Aluminum Alloys and the Subsequent Propagation of Very Short Cracks," Engineering Fracture Mechanics, Vol. 7, No. 2, 1975, pp. 235-247.

[39] Lankford, J., "The Growth of Small Fatigue Cracks in 7075-T6 Aluminum," Fatigue of Engineering Materials and Structures, Vol. 5, 1982, pp. 233-248.

[40] Newman, J. C, Jr., "A Nonlinear Fracture Mechanics Approach to the Growth of Small Cracks," Behaviour of Short Cracks in Airframe Components, H. Zocher, ed., AGARD CP- 328, 1983, pp. 6.1-6.26.

[41] Newman, J. C., Jr., Swain, M. H. and Phillips, E. P., "An Assessment of the Small-Crack Effect for 2024-T3 Aluminum Alloy," Small Fatigue Cracks, The Metallurgical Society, Inc., Warrendale, PA, 1986, pp. 427-452.

[42] Newman, J. C., Jr., "A Crack Closure Model for Predicting Fatigue Crack Growth under Aircraft Spectrum Loading," Methods and Models for Predicting Fatigue Crack Growth under Random Loading, J. B. Chang and C. M. Hudson, eds., ASTM STP 748, 1981, pp.

53-84.

[43] Newman, J. C., Jr., "FASTRAN II - A Fatigue Crack Growth Structural Analysis Program," NASA TM 104159, 1992.

[44] Newman, J. C., Jr.; Phillips, E. P. and Swain, M. H., "Fatigue-Life Prediction Methodology using Small-Crack Theory," International Journal of Fatigue, Vol. 21, 1999, pp. 109-119.

[45] Phillips,E. P., "The Influenceof CrackClosureonFatigueCrackGrowth Thresholds in

2024-T3AluminumAlloy," Mechanics of Fatigue Crack Closure, ASTM STP 982, J. C.

Newman, Jr. and W. Elber, eds., American Society for Testing and Materials, Philadelphia, PA, 1988, pp. 505-515.

[46] Swain, M. H.; Everett, R. A.; Newman, J. C., Jr. and Phillips, E. P., "The Growth of Short Cracks in 4340 Steel and Aluminum-Lithium 2090," AGARD R-767, 1990, pp. 7.1-7.30.

[47] Everett, R. A., Jr.; Newman, J. C., Jr. and Phillips, E. P., "The Effects of Machining-Like Scratch on the Fatigue Life of 4340 Steel", Proceedings of the American Helicopter Society, 55 'h Annual Forum, Montreal, Quebec, Canada, May 25-27, 1999.

[48] Everett, R. A., Jr., "A Comparison of Fatigue Life Prediction Methodologies for Rotorcraft," NASA TM 102759, 1990.

[49] Edwards, P. R. and Darts, J., "Standardised Fatigue Loading Sequences for Helicopter Rotors (Helix and Felix)," Royal Aircraft Establishment, Technical Report 84084, August 1984.

[50] Rudd, J. L., Yang, J. N., Manning, S. D. and Garver, W. R., "Durability Design Requirements and Analysis for Metallic Structures," Design of Fatigue and Fracture Resistant Structures, ASTM STP 761, P.R. Abelkis and C.M. Hudson, eds., 1982, pp. 133- 151.

[51] Grover, H. J.; Hyler, W. S.; Kuhn, P.; Landers, C. B. and Howell, F. M., "Axial-Load Fatigue Properties of 24S-T and 75S-T Aluminum Alloy as Determined in Several Laboratories,""NACA TN-2928, 1953.

[52] Schijve, J., "Some Elementary Calculations on Secondary Bending in Simple Lap Joints," NLR TR 72036 U, 1972.

[53] Cohen, B, Fatten, W., Duncan, W. and Wheeler, A., "Report of the Court of Inquiry into the Accidents to Comet G-ALYP on 10 January 1954 and Comet G-ALYY on 8 April 1954," HMSO, London, 1955.

[54] Irwin, G. R., "Analysis of Stresses and Strains near the End of a Crack Tranversing a Plate," Journal of Applied Mechanics, Vol. 24, 1957, pp. 361-364.

[55] Paris, P., Gomez, M. and Anderson, W. A., "A Rational Analytic Theory of Fatigue," Trend in Engineering, Vol. 13, 1961, pp. 9-14.

[56] Elber, W., "Fatigue Crack Propagation," Ph.D. Thesis, University of New South Wales, 1968.

[57] Elber, W., "The Significance of Fatigue Crack Closure," Damage Tolerance in Aircraft Structures, ASTM STP 486, 1971, pp. 230-242.

[58] Walker, N. and Beevers, C. J., "A Fatigue Crack Closure Mechanism in Titanium," Fatigue of Engineering Materials and Structures, Vol. 1, No. 1, 1979, pp. 135-148.

[59] Suresh, S. and Ritchie, R. O., "A Geometric Model for Fatigue Crack Closure Induced by Fracture Surface Roughness," Metal Transactions, Vol. A13, 1982, pp. 1627-1631.

[60] Paris, P. C., Bucci, R. J., Wessel, E. T., Clark, W. G. and Mager, T. R., "Extensive Study of Low Fatigue Crack Growth Rates in A533 and A508 Steels," ASTM STP 513, 1972, pp.

141-176.

[61] Newman, J. C., Jr., "The Merging of Fatigue and Fracture Mechanics Concepts: A Historical Perspective," Progress in Aerospace Sciences, Vol. 34, No. 5-6, 1998, pp. 345- 388.

[62] Newman,J. C., Jr., "A Crack-Opening StressEquationfor FatigueCrackGrowth,"

International Journalof Fracture,Vol. 24, 1984,pp. R13l-R135.

[63] Small Fatigue Cracks, Ritchie, R. O. and Lankford, J., eds., The Metallurgical Society, Inc., Warrendale, PA, 1986.

[64] Hudson, C. M., "Effect of Stress Ratio on Fatigue-Crack Growth in 7075-T6 and 2024-T3 Aluminum Alloy Specimens," NASA TN D-5390, 1969.

[65] Dubensky, R. G., "Fatigue Crack Propagation in 2024-T3 and 7075-T6 Aluminum Alloys at High Stress," NASA CR-1732, March 1971.

[66] Newman, J. C., Jr., "Fracture Analysis of Various Cracked Configurations in Sheet and Plate Materials," ASTM STP 605, 1976, pp. 104-123.

[67] Newman, J. C., Jr., "Effects of Constraint on Crack Growth under Aircraft Spectrum Loading," Fatigue of Aircraft Materials, A. Beukers et al, eds., Delft University Press, 1992, pp. 83-109.

[68] Minakawa, K. and McEvily, A. J., "On Near-Threshold Fatigue Crack Growth in Steels and Aluminum Alloys," Proceedings of the International Conference on Fatigue Thresholds, Vol. 2, 1981, pp. 373-390.

[69] Wanhill, R. J. H., "Fright Simulation Fatigue Crack Propagation Evaluation of Candidate Lower Wing Skin Materials with Particular Consideration of Spectrum Truncation," NLR TR 77092 U, July 1977.

[70] deJonge, J. B., Schutz, D., Lowak, H. and Schijve, J., "A Standard Load Sequence for Fright Simulation Tests on Transport Aircraft Wing Structures (TWIST)," NLR TR-73029 U, Nationaal Lucht-en Ruimtevaartlaborium, Netherlands, 1973.

[71] Poe, C. C., Jr., "Stress-Intensity Factor for a Cracked Sheet with Riveted and Uniformly Spaced Stringers," NASA TR R-358, May 1971.

[72] Chen, C., Private communication, The Boeing Company, Long Beach, CA., February 1999.

[73] deKoning, A. U., "A Contribution to the Analysis of Slow Stable Crack Growth," National Aerospace Laboratory Report NLR MP 75035U, The Netherlands, 1975.

[74] Kanninen, M. F.; Rybicki, E. F.; Stonesifer, R. B., Broek, D.; Rosenfield, A. R.; Marschall, C. W. and Hahn, G. T., "Elastic-Plastic Fracture Mechanics for Two-Dimensional Stable Crack Growth and Instability Problems", Elastic-Plastic Fracture, ASTM STP 668, American Society for Testing and Materials, Philadelphia, PA, 1979, pp. 121-150.

[75] Shih, C. F.; de Lorenzi, H. G. and Andrews, W. R., "Studies on Crack Initiation and Stable Crack Growth", Elastic-Plastic Fracture, ASTM STP 668, American Society for Testing and Materials, Philadelphia, PA, 1979, pp. 65-120.

[76] Newman, J. C., Jr., "An Elastic-Plastic Finite-Element Analysis of Crack Initiation, Stable Crack Growth and Instability," ASTM STP 833, American Society for Testing and Materials, Philadelphia, PA, 1984, pp. 93-117.

[77] Newman, J. C., Jr.; Booth, B. C. and Shivakumar, K. N., "An Elastic-Plastic Finite-Element Analysis of the J-Resistance Curve using a CTOD Criterion," Fracture Mechanics: Eighteenth Symposium, ASTM STP 945, D. T. Read and R. P. Reed, eds., American Society for Testing and Materials, Philadelphia, PA, 1988, pp. 665-685.

[78] Newman, J. C., Jr.; Bigelow, C. A. and Dawicke, D. S., "Finite-Element Analyses and Fracture Simulation in Thin-Sheet Aluminum Alloy," Durability of Metal Aircraft Structures, S. N. Atluri et al, eds., W. H. Wolfe Associates, Alpharetta, GA., 1992, pp. 167- 186.

[79] Newman,J. C., Jr.; Dawicke,D. S.; Sutton,M. A.; andBigelow, C. A., "A Fracture

Criterionfor Widespread Crackingin Thin-Sheet AluminumAlloys", Durabilityand

StructuralIntegrity of Airplanes,Vol. I, A. F. Blom, ed.,EMAS Ltd., 1993,pp. 443-468.

[80] Potyondy,D. O.; Wawrzynek,P. A.; andIngraffea,A. R., "DiscreteCrackGrowth Analysis

Methodologyfor ThroughCracksin Pressurized Fuselage Structures,"NASA CP 3274,C.

E. Harris,ed., 1994,pp. 581-602.

[81] Dawicke,D. S.;Newman,J. C., Jr. andTan,P. W., "FAA/NASA WidePanelFracture

Tests- PartI ExecutiveSummary," NASA TP (in progress),1999.

[82] Dawicke,D. S.; Sutton,M. A.; Newman,J. C, Jr. andBigelow,C. A., "Measurement and

Analysisof Critical CTOA for anAluminumAlloy Sheet," Fracture Mechanics: Twenty-

Fifth Volume, ASTM STP 1220, F. Erdogan, ed., 1995, pp. 358-379.

[83] Dawicke, D. S.; Newman, J. C.; and Bigelow, C. A., "Three-Dimensional CTOA and Constraint Effects during Stable Tearing in a Thin-Sheet Material," Fracture Mechanics: 26 'h Volume, ASTM STP 1256, W. G. Reuter, J. H. Underwood and J. C. Newman, Jr., eds., 1995, pp. 223-242.

[84] Eichenberger, T. W., "Fracture Resistance Data Summary," Report DA-20947, The Boeing Company, June 1992.

[85] Dawicke, D. S.; Gullerud, A. S.; Dodds, R. H., Jr.; and Hampton, R. W., "Residual Strength Predictions with Crack Buckling," The Second Joint NASA/FAA/DoD Conference on Aging Aircraft, C. E. Harris, ed., NASA CP-208982, 1999, pp. 565-574.

[86] Seshadri, B. R. and Newman, J. C., Jr., "Analysis of Buckling and Stable Tearing in Thin- Sheet Materials," Fatigue and Fracture Mechanics: 29 'h Volume, ASTM STP 1332, T. L.

Panontin and S. D. Sheppard, eds., American Society for Testing and Materials, 1998, pp.

114-134.

[87] Johnston, W. M., "Fracture Tests on Thin-Sheet 2024-T3 Aluminum Alloy for Panels with and without Buckling," NASA/CR (in progress), 1999.

[88] Young, R. D.; Rouse, M.; Ambur, D. R.; and Starnes, J. H., "Residual Strength Pressure Tests and Nonlinear Analyses of Stringer- and Frame-Stiffened Aluminum Fuselage Panels with Longitudinal Cracks," The Second Joint NASA/FAA/DoD Conference on Aging Aircraft, C. E. Harris, ed., NASA CP-208982, 1999, pp. 408-426.

[89] Seshadri, B. R.; Newman, J. C., Jr.; Dawicke, D. S. and Young, R. D., "Fracture Analysis of the FAA/NASA Wide Stiffened Panels," The Second Joint NASA/FAA/DoD Conference on Aging Aircraft, C. E. Harris, ed., NASA CP-208982, 1999, pp. 513-524.

Rivet simulation for Global Model lap-joint load transfer Frame

I

Rivet Model (spring)

Stringer

Rivet Shank _ Rivet Head (spring) Figure 1. - Finite-element models from global to local stress analyses of fuselage structures.

___1111 _O -- " / ;oo o I ° ,, mm 0 0 0 0 0 ', , o

oo°°°

',o / o " S S "['-/ ', o S ,,o ,, Rivet S II 0 0 0 I 0

" ) ioo

,, o o iRivet ', o " 01 _ Ioo o ,,o

',o o ) ioo°o

rl I I I_ 1020 10 mm (a) NLR and KHI-NAL lap-joint specimens (b) Full-scale aircraft fuselage lap joint Figure 2. - Typical lap-splice joints specimens and joints in full-scale test article.

Sb

,. 2r, F q

(a) Through crack

(b) Corner crack

Sp+ S b

Figure 3. - Crack configuration and loading for rivet-loaded hole.

S b o FRANC2D/L [] FADD2D

#

-- Equation [23] ) K 2w r S Edge of rivet 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

(c + r) / wr

Figure 4. - Stress-intensity factors for through crack at rivet-loaded hole.

2.4 Newman 2.2 a/c=0.2 Smith _=_/2 %._/ 2.0 I

/

/

Raju-Newman /

/

1.8 Rice-Levy _ K Smith-Sorensen 1.6

s q-_-E6

Kobayashi-Moss 1.4 Kobayashi Shah-Kobayashi 1.2 Anderson et al.

Paris-Sih 1.0 Irwin 0.8 0.0 0.2 0.4 0.6 0.8 1.0 a/t (a) Semi-elliptical surface cracks 3.5

r/t= 21 r/w= 02 \

a/c = 0.8; a/t = 0.2 FEM(GIL,J) ]_ _" !

FADD(3D) ] . _./"_ 3.0 BEN FEAM _ ,_zx_ K S *,/_a/Q 2.5 FEM(DIM) WFM(3D) / Plate surface Hole surface I I I 2.0 0 30 60 90 Parametric angle, O, degrees (b) Quarter-elliptical corner crack at hole Figure 5. - Comparison of normalized stress-intensity factors for three-dimensional cracks.

S S = 240 M Pa B = 1.6 mm i0 c= 102 mm w = 305 mm y/w = 0.125 =X Out-of-Plane Displacement, WARP3D mm 2w S I I -2 i i -0.5 0.0 -i .0 0.5 1.0 Distance from centerline (x/w) Figure 6. - Measured and calculated out-of-plane deformations in middle-crack tension specimen.

1e-3 7075-T6 r KT = 1 AKeff J j- I [ Smax/<J°=075 '_../CS 18-4_ R=0.05 Y _....

i_ -- FASTRAN(o_=I.8)// /-"

le-5 L Lankford / in:. -__o

dc/dN, jJ o

mm,c ce F

le-6 t //_"_'t \ _ --Large cracks 18_7[/// V /\'_ Pears°n I I I I F 20 40 80 160 I- 2c, _m le_8 / , I I I I I I I I 1 2 3 4 5 6 7 8 910 AKorAKef f, MPa_/m Figure 7. - Small- and large-crack data on 7075-T6 aluminum alloy from un-notched specimens.

le-3 le-4 da/dN le-5 or dc/dN, mm/cycle le-6 le-7 le-8 0.5 1 2 5 10 20 AK or AKef f, M Pa_/m Figure 8. - Small- and large-crack data on 2024-T3 aluminum alloy from notched specimens.

1.0 Swain et al 4340 Steel • B = 5.1 mm 0.8 w = 25.4 mm • r = 3.2 mm Z KT = 3.3 ....................................... F ....

0.6 Cumulative (a) Calcium particle distribution function 0.4 i 0.2 A I I _ I I I I II I I I I I I III 0.0 10 100 Equivalent semi-circular defect radius, lam (b) MnS particle (c) Cumulative distribution function for 4340 steel Figure 9. - Crack initiation sites and cumulative distribution function for 4340 steel.

1e-3 1e-4 da/dN le-5 or dc/dN, mm/cycle le-6 le-7 le-8 1 10 100 AK or AKef f, M Pa_Jm Figure 10. - Small- and large-crack data on 4340 steel from notched specimens.

1000 4340 Steel B = 8.9 mm; w = 25.4 mm 800 ¢}_ KT= 1.03; R =-1 Surface crack a i = c i = 13 pm 600 \ \ Smax, • \ _ o_&..O......_ MPa _ uu cb 400 \ FASTRAN _ • a i = 51 pm • 200 (scratch) 10 3 10 4 105 10 6 10 7 Nf, cycles Figure 11. - Prediction of fatigue life on pristine and scratched specimens of 4340 steel.

8OO _,_ Felix-28 4340 Steel B = 3.2 mm w = 12.7 mm , 8pm r = 3.2 mm 6OO _ _,'/ KT = 3.23 \ o _ Test (Everett) Smax, MPa FASTRAN a i = c i = 30 pm 10 4 105 10 6 10 7 108 Nf, cycles Figure 12. - Prediction of fatigue life on circular-hole specimens under Felix-28 spectrum.

5OO - _u Groveret al.

2024-T3 OO B = 2.3 mm _---'__ __o w = 25.4 mmKT= 1 - _ys N_ Smax, MPa FASTRAN a i = c i = 20 #m 0 I I I I I I 1 0 2 10 3 10 4 105 106 10 7 108 Nf, cycles Figure 13. -Prediction of fatigue life on 2024-T3 for un-notched specimens at two stress ratios.

L

:::::::!:::::::]-

!

_1 ÷÷÷+÷4.4.÷++++÷" 4-*÷st 4-++4.+++++++ r-- *'*'°'°_ ...... "1 ....... ! j__, 7 j SO0 Type-1 Type-2 L ------.

_I °°*°** .... **°°

>&2&

).L i ].L ..o°,°°*...*°°° ..... oo/ .......

]1

, j alo Type-3 Type-4 Figure 14. - Riveted lap-joint panels tested by Furuta, Terada and Sashikuma [24].

Furuta et al. (1997) 2024-T3 | Sma x=96Mpa; R=0.125 / 100 ° Countersunk rivets L_ Laboratory air Test oo_"_o'6"o 8 o__ ° 6 Crack _-_ Ooe'/^u o length, FASTRAN o_° °/o " o° c, mm a i=c i=6pm oO°°O_/ o (No bending and o / o 0.1 no interference) 0.01 i i i i i i i i i i i i I 0 1 e+5 2e+5 3e+5 Nf, cycles Figure 15. - Measured and calculated crack length against cycles for Type 1 lap joint under ambient conditions.

2024-T3 Lab Air o Tests (Furuta et al.)

le+6 • FASTRAN (a i = 6gm) O N f, cycles 1e+5 O 1e+4 _ _ _ Type: 1 1 3 4 Edge clamps: No Yes No No Tear strap: No No Yes Yes Figure 16. - Comparison of measured and calculated fatigue lives for various lap joints under ambient conditions.

e

T

(a) Plasticity-induced (b) Roughness-induced (c) Oxide/corrosion product- closure closure induced closure Figure 17. - Various forms of fatigue-crack-closure mechanisms.

1 e+l Hudson, Phillips and Dubensky 2024-T3 Middle crack tension 1 e+O B = 2.3 mm I 1 e-1 -- Baseline cl ---- Failure (R = 0.7) 1 e-2 /_ ........ Failure (R = 0.5) _L c_ 1 1 e-3 dc/dN, R mm/cycle o 0.7 [] 0.5 le-4 T c_=2 0.3 1 e-5 <> 0 v -1 le-6 • -2 le-7 [] 1 e-8 1 10 100 AKef f, MPa,,/m Figure 18. - Effective stress-intensity factor against crack-growth rate for 2024-T3 aluminum alloy over a wide range in rates and applied stress levels.

2024-T3 Alclad 50 8 B=3.1 mm TWIST (Level III)

I

Smf = 70 MPa 40 (Z=I I

/

I Crack 30 I (z = 2 I Tests // length, I (Wanhill)// c, mm

20 / /

/ /

J FASTRAN 10 J / _ (z= 2to 1 --- (z=lor2 0 5 10 15 20 25 30 Flights x 103 Figure 19. - Measured and predicted crack length against flights for thin-sheet 2024-T3 alloy under TWIST (Level III) loading.

--_ W=915 mm {iiiiiiiiiiiiiiii_iiiiiiiiiiiiiii_iiiiiiiiiiiiiiii_iiiiiiiiiiiiiiiQiiiiiiiiiiiiiiiiiQiiiiiiiiiiiiiii_iiiiiiiiiiiiiiii_iiiiiiiiiiiiiii_iiiiii

\

+ + + Bonded + + + + + + + + + ++ ++ ++,_.

t t _ 6 t

\

t t t : !5! Iml; Riveted + + , + ++ ++ ++ E E + + + t t i.o + + + + i 7 +- +, II

\

T ÷ ++ 2024-T3 ÷ ÷ ÷ ++ 2 _.______.

++ ++ i 152 mm 4\ ++ ; : ++ Aluminum ÷ ÷ ÷ or Steel 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Figure 20. - Stiffened panel tested by Poe [71] to determine fatiguelcrack-growth rates.

1.0 Chen - 1999 0.8 _,_......__" (Fastener flexibility) \ 0.6 Poe- 1971 \\ K (Rigid fasteners)\_ j/__\ 0.4 Width (W) = 915 mm 0.2 Stringer spacing (b) = 152 mm Stringer area to total area (_) = 0.41 0.0 I I I I I I I 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 C/W Figure 21. - Stress-intensity factors for cracked stiffened panel with rigid and flexible rivets.

Poe (1971 ) Unstiffened ....

le-1 Sma x = 103 MPa I 2024-T3 panel ..........

R=0.1 .....-" ......... " .-'" ?O O _ n []

..."oo _ -_

le-2 . .''" dc/dN, mm/cycle le-3

r t

1e-4 FASTRAN (Chen - flexible fasteners) I FASTRAN (Poe - rigid fasteners) I I I I I I I I le-5 0 25 50 75 100 125 150 175 200 Crack length, c, mm Figure 22. - Measured and predicted crack-growth rates for Poe's stiffened panel.

1 mm :_

Figure 23. - Photograph of tearing crack and measurement of critical crack-tip-opening angle (CTOA).

[] C(T) W = 152 mm ,# z_ M(T) W=76 mm O M(T) W=305 mm • M(T) W=610mm Z& _c, degs. 6 CTOA, __ 58 degs

o 4-T3

B = 2.3 mm B 0 I I I I I I 0 10 20 30 40 50 Crack extension, Ac, mm Figure 24. - Measured critical CTOA values for compact and middle-crack tension specimens.

200 _..__ Plane stress \\'_j..-.........._ Plane-strain core Failure 2219-T87 _ stress, Boeing (1962) _ Plane strain MPa Middle-crack tension _ B = 254 mm (restrained) Tests (2c/W = 1/3) --- Plane stress: _c = 47deg Plane strain: _c = 47 deg -- _c =47deg;h c=19mm 0 200 400 600 800 1000 1200 Width, W, mm Figure 25. - Measured and calculated failure stresses for middle-crack tension specimens as a function of specimen width.

)k Steel t- _l"

- k--

CRACK 75 mm

/

203 mm 7075-T6 2024-T3 B = 1.6 mm <--_ W = 1 m -_->

/

I,,-- 4-4 12.7 mm W S Sf = 166 MPa 206 243 24% 46% (a) No guides (b) Guide plates (c) Guide plates and I-beams Figure 26. - Two anti-buckling guide plate systems to restrain middle-crack tension specimens.

250 - Guides plus I-beams 200 - 150 - S, MPa (buckling) 100 - 2024-T3 B = 1.6 mm W = 1016 mm 50- 2a = 203 mm 0 I I I 0 20 40 60 Crack extension, Ac, mm Figure 27. - Stable crack extension on wide middle-crack tension specimens with various anti- buckling guide systems.

B Tests (guides) i--d_-5 _ _/ Tests (no guides) S, MPa 100 - i_ 2024-T3 (TL) B = 1.6 mm W = 610 mm 2c = 203 mm 5O 0 10 20 30 40 50 Crack extension, Ac, mm Figure 28. - Measured and predicted stable tearing in buckling-restrained and buckling panels.

I" W = 1016 mm 't iiiii_iiiiiiiiiiiiiiiiCiiiiiiiiiiiiiiii_iiiiiiiiiiiiiii_iiiiiiiiiiiiiii_iiiiiiiiiiiiiii_iiiiiiiiiiiiiiiCiiiiiiiiiiiiiiiii_iiiiiiiiiiiiii_iiii iiiiiiiiiiiiiiiiii_iiiiiiiiiiiiii_iiiiiiiiiiiiiiii_iiiiiiiiiiiiii_iiiiiiiiiiiiiii_iiiiiiiiiiiiiii_iiiiiiiiiiiiiii_iiiiiiiiiiiiii_iiiiiii

\

+ + Bonded ++ + ++ + + + t t ll_ll. _l I t \

r]m_ + \

+ + + Riveted ++ + t

Lead crack l

E E OJ eel O 4 OJ ++ ++ ++ H I

I Rivet hole and MSD I \

++ ++ + + 2024-T3 ++ ++ ',++ ++ ;++ ++ ++

\

+ + ++ ++ ++ ;++ 7075-T6 + + + + J _ _IJ+L _......j ÷÷_ _.......j +÷_ _.._ 0 0 0 O 0 O 0 O 0 0 O O 0 O 0 O 0 _[_ _6mm Figure 29. - FAA/NASA wide stiffened panel crack configuration.

7OO 2024-T3 / 7075-T6 B = 1.6/2.2 mm W = 1016 mm 2c i = 203 mm Unrestrained _ - . ©._ / Panel "_S t j._l_ Stiffener failed Load, 400 .O__ failed (analysis) kN STAGS - t Analysis: Stiffener _c = 5.4 deg.

h c = 2 mm I I I I I I I I 0 20 40 60 80 100 120 140 160 Crack extension, Ac, mm (a) Wide stiffened panel with a single crack 2024-T3 / 7075-T6 STAGS B = 1.6/2.2 mm '£c = 5.4 deg.

W = 1016 mm h c = 2 mm 2c i = 203 mm Unrestrained 3OO O ----------4 Load, Sheet kN failure Q) 2OO (3) (3) 13] Stiffener O 1.3-mm MSD 100 o Crack • O O / -O- -O -O- .O- -O- I I I I I I I 0-_o 0 20 40 60 80 100 120 140 160 Crack extension, Ac, mm (b) Wide stiffened panel with a single crack and multiple-site damage cracks Figure 30. - Comparison of measured and predicted stable tearing on the FAA/NASA panels.

4O REPORT DOCUMENTATION PAGE Form Approved OMB NO. 0704-0188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.

1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED April 2000 Technical Memorandum 4. TITLE AND SUBTITLE 5. FUNDING NUMBERS Advances in Fatigue and Fracture Mechanics Analyses for Metallic Aircraft Structures WU 706-11-11-01 6. AUTHOR(S) J. C. Newman, Jr.

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER NASA Langley Research Center Hampton, VA 23681-2199 L-17955 10. SPONSORING/MONITORING 9.SPONSORING/MONITORING AGENCY NAME(S) ANDADDRESS(ES) AGENCYREPORTNUMBER National Aeronautics and Space Administration NASA/TM-2000-210084 Washington, DC 20546-0001 11. SUPPLEMENTARY NOTES Invited paper presented at the International Conference on Aeronautical Fatigue (ICAF), Seventeenth Frederik J.

Plantema Memorial Lecture, Seattle, WA., July 12-16, 1999.

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE Unclassified-Unlimited Subject Category 26 Distribution: Standard Availability: NASA CASI (301) 621-0390 13. ABSTRACT (Maximum 200 words) This paper reviews some of the advances that have been made in stress analyses of cracked aircraft components, in the understanding of the fatigue and fatigue-crack growth process, and in the prediction of residual strength of complex aircraft structures with widespread fatigue damage. Finite-element analyses of cracked metallic structures are now used to determine accurate stress-intensity factors for cracks at structural details.

Observations of small-crack behavior at open and rivet-loaded holes and the development of small-crack theory has lead to the prediction of stress-life behavior for components with stress concentrations under aircraft spectrum loading. Fatigue-crack growth under simulated aircraft spectra can now be predicted with the crack- closure concept. Residual strength of cracked panels with severe out-of-plane deformations (buckling) in the presence of stiffeners and multiple-site damage can be predicted with advanced elastic-plastic finite-element analyses and the critical crack-tip-opening angle (CTOA) fracture criterion. These advances are helping to assure continued safety of aircraft structures.

14. SUBJECT TERMS 15. NUMBER OF PAGES Fatigue, Fracture, Metals, Cracks, Crack growth, Stress-intensity factor, Crack 16. PRICE CODE Closure, Plasticity, Buckling, Multiple-site damage, CTOA A03 20. LIMITATION 17. SECURITY CLASSIFICATION 15. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION OF ABSTRACT OF REPORT OF THIS PAGE OF ABSTRACT UL Unclassified Unclassified Unclassified NSN 7540-01-250-5500 Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std. Z-39-18 298-102