Substantiation data for hypersonic cruise vehicle wing structure evaluation - Volume 1, sections 1-10

Section Page

CONTENTS Section Page Volume 1 v Summary vii Introduction 1-i Trajectory Analysis 2-1 2 Vehicle Loads 3-i Aerodynamic Heating Analysis 4-1 Materials Evaluation 5-i Material and Process Development Testing 6-i Structural Analysis Model 7-i A Plane Strain Analysis for Determining Thermal Stresses 8-1 Structural Internal Loads (Air and Thermal) 9-i Internal Temperature Analysis 10-i Optimization Procedure for Panels of Monocoque Structure Volume 2 Optimization Procedure for Panels of Circular-Arc ll-i Corrugation Shear Webs Optimization Procedure for Panels of Semimonocoque 12 -i Structure 13-i Primary Structure Sizing and Weights 14-i 14 Panel Flutter 15-i 15 Vehicle Flutter 16-i Sonic Fatigue 17-i Fatigue 18-1 Creep 19 -i Optimization Procedure for Heat Shields 20-i Heat Shield Sizing and Weights 21-1 Leading Edge Analysis 22- Total Wing Weight Analysis Volume 3 23-i Cost Analysis 24-i Performance Analysis 25-i Reliability Analysis 26-i Interaction Analysis 27-i Structural Element Testing iii SUMMARY An analytical and experimental evaluation was performed for several promising structural concepts to provide the basis of minimum total-system-cost for selection of the best concepts for the design of a hypersonic vehicle wing.

Results, procedures, and principal justification of results are presented in reference 1. Detailed substantiation data are given herein. Each major analysis is presented in a separate section. Vehicle loads and temperatures are given with each structural analysis that influences weight. In addition to the weight analysis, fabrication cost, performance penalties (surface roughness drag), reliability, and total-system-cost analyses are presented.

Reference 1.

Plank, P. P.;Sakata, I. F.;Davis, G. W.;and Richie, C. C. : Hypersonic Cruise Vehicle Wing Structur_e Evaluation, NASA CR-1568, 1970.

V INTRODUC TION The utility of a hypersonic cruise vehicle depends upon a low structural mass fraction in a high-temperature environment. Unfortunately, this requirement exceeds the limits of state-of-the-art structures. The only hypersonic structures flown to date have been the X-15 research airplane and the ASSET unmanned lifting reentry test vehicle, both of which are unsuitable for cruising flight.

For the past several years, the NASA Langley Research Center and other agencies have been investigating promising structural concepts, such as those discussed in references 2, 3, and 4, and the 1967 Conference on Hypersonic Aircraft Technology (ref. 5) was devoted to the subject.

An evaluation was performed of promising wing structure concepts to the same in-depth analyses, including all known environmental structural considerations that could affect the four evaluation factors: weight, cost, performance, and reliability.

These factors were then interacted in a total-system-cost study for a system range- payload capability of 205 billion ton-miles to provide the basis for selecting the best structural concept for the wing structure of minimum total-system-cost.

Results of this structural evaluation are reported in reference 1. This reference also includes the procedures and principal justification of results, whereas this report gives detailed substantiation of the results in reference 1.

Principal analytical and test efforts are presented in separate sections. This report is bound as three separate volumes.

REFERENCES . Heldenfels, R. R. : Structural Prospects for Hypersonic Air Vehicle ICAS paper, 1966.

o Plank, P. P. ; and MacMiller, C. I. : Analytical Investigation of Candidate Thermal-Structural Concepts Applicable to Wing, Fuselage, and Inlet Structure of a Manned Hypersonic Vehicle. AFFDL-TR-66-15, 1966 (conf).

Plank, P. P. : Hypersonic Thermal-Structural Concept Trends. SAE paper 660678, 1966.

o NASA-SP-148 (Conf). Conference on Hypersonic Technology, Ames Research Center, 1967.

vii AC KNOWLE DGE MENT This investigation was conducted under NASA Contract No. NAS1-7573, Research and Development Program for Development and Validation of Structural Concepts for a Hypersonic Cruise Vehicle Wing Structure. The study was originated at the Lockheed-California Company, Burbank, California and completed at Lockheed Missiles & Space Company, Sunnyvale, California.

P. P. Plank was the Program Technical Manager, I. F. Sakata and G. W. Davis the Project Engineers, and C. C. Richie was head of structural concept optimiza- tion. The other contributors to the program are acknowledge at each section.

Four Lockheed-California Company personnel acted in an advisory capacity.

They are L. W. Nelson, Structure Division Engineer, Structures Division; E. J. Himmel, Department Manager, Stress Analysis; W. J. Criehlow, Depart- ment Manager, Advanced Materials and Structural Mechanics; and M. G. Childers, Manager, Physical Sciences Laboratory Development Engineer.

Dr. M. S. Anderson, L. R. Jackson, and J. C. Robinson of the Structures Research Division, NASA Langley Research Center, Hampton, Virginia, were the Program Manager, Technical Representative of the Contracting Officer (TRCO), and Assistant TRCO, respectively, for the project.

Next: Section I →

Section I

Section I TRAJECTORY ANALYSIS by B. C. Wollner, C. F. Ehrlich, R. S. Peyton, J. E. Hames, H. F. Harper 1-± TABLES iPage 1-5 1-1 Time data per mission for various vehicle trajectory phases 1-5 1-2 Number of flights per 10 000 hours of life 1-5 1-..t Time data per 8110 flights for various trajectory phases l-iii ILLUSTRATIONS Page 1-1 Hypersonic cruise vehicle l_ 1-2 Hypersonic cruise airplane design trajectory 1'7 1-.t Forward acceleration of cruise airplane 1-7 1-4 Specific impulse data 1-8 1-5 Trajectory data for cruise airplane --- basic trajectory plus trajectory perturbation 1'9 1-6 Cruise airplane thrust and drag schedule m basic trajectory 1-10 1-7 Cruise airplane weight schedule - basic trajectory 1-10 1-8 Cruise airplane longitudinal acceleration schedule - basic traj ect ory 1-11 1-9 Range and L/D data for cruise airplane - basic trajectory 1-11 1-V SYMBOLS a Acceleration Drag coefficient CD Lift coefficient CL D Drag Gravitational acceleration g H Altitude I Specific impulse sp Lift to drag ratio T'/D M Mach number M Free stream Mach number n ,n ,n Load factors expressed in Cartesian coordinate system x y q Dynamic pressure T Thrust W Weight c_ Angle of attack AC D Incremental drag coefficient ! -vii

Next: Section I →

Section I

TRAJECTORY ANALYSIS The detailed structural concept analyses were conducted for the relatively large wing section of the Mach 8 hypersonic cruise airplane, shown in figure I-1.

The configuration of figure I-I is a discrete wing-body airplane with a low wing that is continuous under the fuselage. A structural arrangement consisting of an integral hot fuselage and hot wing structure with separate liquid hydrogen tanks and pressurized compartments suspended within the fuselage was considered for the structural concept evaluation.

Although only the section of the wing shown in figure 1-I was thoroughly analyzed, load and temperature criteria were determined in a gross sense for the entire airplane. These calculations were required to ensure that representative thermal, aerodynamic and inertia loads were applied to the wing section and to ensure that considerations of rib and spar spacings were included in the wing design.

The following data are used for the hypersonic cruise vehicle: I. Total wing area 10000 ft 2 2. Reference area (rear delta-wing area) 8330 ft 2 3. Vertical tail area 574 ft 2 4. Engine capture area 306 ft 2 5. Zero-lift line (degrees to FRL) 3 dego Masses assigned to the various base-line airplane components are listed below as fractions of the gross takeoff weight, which is 550,000 pounds: Component Mass fraction Fuel 0.40 Structure 0.27 Landing gear 0.03 Propulsion 0.15 Equipment 0.05 Payload 0.10 1-1

The hypersonic cruise airplane utilizes the flight schedule outlined

in figures 1-2 through 1-h. Altitude versus velocity is presented in

figure 1-2, indicating the resulting dynamic pressures. In addition,

acceleration and specific impulse data, figures I-3 and I-4, are required

for determination of time dependent trajectory data.

Forward accelerations for the cruise airplane, as shown in figure I-3,

are for the ascent period. A maximum forward acceleration of 0.2-g is

imposed on the trajectory analysis. At initiation of cruise, a normal

climb at constant Mach8 occurs until maximum L/D is approached, followed

by a 1-g flight attitude at maximum L/D. A constant deceleration of 0.2-g

caused by drag augmentation is used for descent flight. The altitude at

termination of cruise is that which provides the required fuel for descent.

For life analyses, it is assumedthat 90 percent of the flights are with

this trajectory. For determination of limit loads due to pressure, inertial,

and thermal effects, a trajectory perturbation (10 percent of the flights)

is assumedto occur at constant Mach8. This perturbation is a -0.5-g

acceleration normal to the plane of the wing, which is assumedto exist at

the initiation of cruise (Mach 8, q = 1500 psf) resulting from a -1.5-g

(-1.5 + 1.O gravity = -0.5-g) nose-downmaneuver. This -0.5-g condition

is followed by 2.0-g pull-up maneuver(which does not exceed q = 2200 psf)

and is held at constant acceleration until maximum L/D is approached with

a smooth transition to maximum L/D, followed by 1-g nominal flight condition

at maximum L/D for the remainder of the cruise period. Negative limit loads

are the critical combination of temperatures and loads occurring during the

nose-downmaneuver, and positive limit loads are the critical combination of

temperatures and loads occurring during the pull-up maneuver. For life

analyses, this limit load trajectory is used for every tenth flight.

Aerodynamic data were determined in the form of C L = F (M,a) and

CD= F (M, CL). Incremental drag effects (AC D) due to scale effects, engine

cowls and vertical tail were also generated. These data were based on

extensive aerodynamic analysis of a geometrically similar vehicle

(reference I-1). It was necessary to apply the appropriate wing area, engine

capture area, and vertical tail area to obtain the proper C D. The CL data

were used without change.

The aerodynamic data are referenced to the zero-lift line. Negative

lift coefficients, required for the analysis of negative g maneuverat

Mach 8, were obtained.

The flight trajectory characteristics of the vehicle were determined,

utilizing the established aerodynamic data, by using the mission analysis

automated procedure of reference I-2. Given a mathematical model of the

airplane, the program simulates a complete mission within the range of a

given flight profile. A time history of the simulated flight and a final

performance summaryare provided for each mission. The following time-based

trajectory parameters were developed: altitude, velocity, Machnumber,

dynamic pressure, angle of attack, flight path angle, thrust, drag, vehicle

weight, range and L/D.

1-2

Using the aerodynamic data, both a basic cruise mission and maneuver

perturbation trajectory were developed. The resulting time history of the

trajectory parameters of dynamic pressure, angle of attack, altitude and

Mach number is presented in figure I-5. The thrust and drag schedule for

ascent and descent is presented in figure 1-6. The thrust and drag schedule

reflects a power-on descent from end of cruise (q = 470 psf) following a

varying dynamic pressure path to an altitude of 40 000 feet. Drag augmenta-

tion, as indicated, was provided to result in a constant deceleration of

-0.2-g. The baseline vehicle weight schedule is presented in figure 1-7.

Both total vehicle weight including fuel and the fuel consumption schedule

are presented. Figure 1-8 indicates the longitudinal acceleration schedule

during ascent, cruise and descent with resulting load factors of +_0.2-g.

The baseline vehicle's range in the cruise mission and variation of lift to

drag are presented in figure 1-9. The aforementioned vehicle design trajec-

tory data were used to provide time data per mission for the various vehicle

trajectory phases of ascent, maneuver, cruise, and descent. As indicated

in table I-1, I .23 hours are required for the basic trajectory and I .25

hours are required for the basic trajectory plus the maneuverperturbation.

Using the data of table 1-I, 8110 flights were established per 10 000 hours

of life for the basic trajectory and basic trajectory plus perturbation, as

presented in table 1-2. The basic trajectory requires 8978.4 hours and the

basic trajectory plus perturbation requires 1013.75 hours providing an

accumulative total of 9992.15 hours, as shown in table I-2. However, as

indicated in table 1-2, 9000 (basic trajectory), 1000 (basic trajectory

plus perturbation) and 10 000 hours (life) were assumedfor design. There-

fore, using the data of tables I-I and I-2, time data per the 8110 flights

for the various trajectory phases were established, as shown in table 1-3.

Table 1-3 indicates that the maneuverperturblation requires only 16 hours

of a total 10 000 hour vehicle life while the cruise condition requires

4460 hours.

1-3

REFERENCES I--I • Rising, J. J. : Aerodynamic Performance Coefficients for a Proposed Delta Wing - Body, Manned Hypersonic Vehicle, Lockheed-California Company Aerodynamic Memorandum Report No. _0, 1966.

I --2.

Fully Automatic Computer Technique of Sizing for Manned Hypersonic Vehicles. Lockheed California Company Computer Control No. 2802, 1966.

I-4 TABLE I-1 TIME DATA PER MISSION FOR VARIOUS VEHICLE TRAJECTORY PHASES Basic trajectory Trajectory phase Basic trajectory plus perturbation Ascent 21.0 min 21.0 min (0.35 hr) Maneuver -- 0.9 min (O.02 hr) Cruise 33.0 min 33.0 min (0.55 hr) Descent 20.0 min 20.0 min (0.33 hr) Total 74.0 min 74.9 rain (1.23 hr) (1.25 hr) TABLE I-2 NUMBER OF FLIGHTS PER I0 000 HOURS OF LIFE Hours Accumulative Basic trajectory Number of flights Basic trajectory plus perturbation 9992.15 1013.75 8110 8978.4

(iooo) (io ooo)

For design (9000) assume TABLE I-3 TIME DATA PER 8110 FLIGHTS FOR VARIOUS TRAJECTORY PHASES Total Basic trajectory Basic trajectory Trajectory phase plus perturbation

(hr)

2 840 As cent 2560 Maneuver 4020 440 4 46o Cruise 264 2 684 Des cent I0 000 lO00 Total 9000

i-5

(',,m _ _m..I v

V

!,_L.. _ _ soo _s_

_-- _. ._- , _" c.e_ -" eS _" J 1000 psf

/ o_.-

80 _

._e,,,_.._ 2200 psf

e" .'C_f'_'. //" TrajectoryS 4O ,_,/_//_// perturbation 2O I 2 3 4 5 6 7 8 Mach number Figure 1-2. H rpersonic cruise airplane design trajectory 1.O \ 0.8

\

!

-- Full throttle

I

l 0.6

l

I

l

O.4

/

F Throttled 0.2 " _C I 2 3 4 5 6 ?

Zoo Figure 1-3. Forward acceleration of cruise airplane 1-?

6 X 10 3 o _D H o 1 2 3 4 5 6 7 8 Moo Figure 1-4. Specific impulse data 1-8 _ Dynamic _ressuPe Angle of attack Io _-, \ 8 \

\

_ A .u

E a \ c 6 II , I li \ -_I u 4LJ \ II V/_ ._/

!l

II

II II

_, ___ Mach 1 at 40000 ff I I I I • I II i i 30 40 50 60 70 0 10 20 80 Time, mln Figure I-7. Cruise airplane weight schedule - basic trajectory I-I0 +.2 +.I A

)

--° |

J

3 ".2 Climb _. - Cm|se Descent -" (19.90 mln) v-_ (32.82min) - _ (20.15 min) • i i 8O 0 10 2o 3o 4o 5o 6o 70 T|mer mln Figure I-8. Cruise airplane longitudinal acceleration schedule - basic trajectory Cruise w _ Descent- CI i_b _'._ 10 __ Reduced -_ weight cllmb _ 6 L/D Ranger ¶" no ml.

4 _ J J I I I I 0 10 20 30 40 50 60 70 80 Time r min Figure I-9. Range and L/D data for cruise airplane - basic trajectory l-l! _.

Next: Section 2 →

Section 2

Section 2 VEHICLE LOADS by B.C. Wollner, J.L. Benson, and F.L. Falconer 2-i

CONT_NTS

2-i

VEHICLELOADS

2-3

VEHICLE BALANCE

2-5

NETDESIGN LOADS

2 -iii

TABLES

Page 2-8

2-1

Summary of static balance -M8 normal to wing reference line

2-2 2-9

Summary of normal and axial balance at cg - M8 2-i0 Net Vehicle loads -- limit (-0.5g maneuver limit_ rigid)

2-3

2-11

2-4

Net wing loads -- limit (2g maneuver) 2-12 Net wing loads - limit cruise (lg)

2-5

2-13 2-6 Net fuselage loads --limit 2-14 2-7 Wing limit pressure loadings 2-15 2-8 Hypersonic cruise vehicle wing pressures 2-16 2-9 Pressure loadings for entire wing 2-V ILLUSTRATIONS Page 2-i Loads network wing model 2-17, 2-2 Integral engine: hypersonic cruise vehicle 2-17 Static balance: 2-3 2-18 •5g maneuver condition 2-4 Static balance: -2g maneuver condition 2-18 2-5 Static balance: cruise condition (lg nominal) 2-19 2-6 2-20 -0.5g maneuver condition: static balance at cg 2-7 2g maneuver condition: static balance at cg 2-21 2-8 lg cruise condition: static balance at cg 2-22 2-9 Vehicle longitudinal shear distribution (limit) 2-23 2-i0 2-24 Vehicle longitudinal bending moment ( limit ) 2-ii History of wing leading edge pressure variations for cruise mission 2-25 2-12 Wing leading edge pressure (limit) variations during maneuver 2 -26 2-vii

SYMBOLS

Butt line

BL

Center of gravity c.g.

Center of pressure c.p.

D Drag force Engine stream thrust resolved into axial (subscript A) FA_ FN and normal (subscript N) components.

Forces in x, 25 and z axes Fx, Fy_ F z Engine stream thrusts FI_ F2, F3, Fg FS Fuselage station Gravitational acceleration g Lift force L Total airload Lc_ Total elevon load L6 Moments taken about the x, y, and z axes Mx, My, M z Total inertia loads in the x, y, and z axes nxW _ NyW_ nzW Pressure P Dynamic pressure q Radius R T Thrust WRL Wing reference line Angle of attack Pressure differential Ap Vector angle 2_-ix

Next: Section 2 →

Section 2

VEHICLE LOADS

Net vehicle loads, using the airplane configuration and trajectory, were

determined in a general sense for the entire airframe to ensure that represent-

ative net loads were applied to the wing section and that realistic spar and

rib spacings were included in the wing section design.

Unit load distributions were developed for the hypersonic cruise vehicle

to represent the following influence functions: I, Aerod.ynamic loadin_ -- Aerodynamic loadings over the vehicle at the design condition at Mach 8.0 (--5g, 2.0g and cruise conditions) were determined based on oblique shock and Prandtl-Meyer expansion rela- tionships, references 2-1 and 2-2. Newtonian impact theory was used for estimating loadings on the nose of the vehicle, reference 2-3.

Load panel points for application of these theories were established with consideration to vehicle contours. The resultant rigid loading distributions were transformed to a network model for application to the stress analysis and the aeroelastic loads analysis.

. Inertia loading -- Vehicle weights were distributed to provide an inertia loading distribution for use in determining design loads.

Appropriate fuel burn-off was considered in deriving the weights consistent with design loading conditions (-.5g, 2g and cruise).

3. Elevon loading -Ioads due to elevon displacement were concentrated on the control surface. Longitudinal control displacement serves as a trim device to balance vehicle pitching moments.

4. Thrust loading -- To obtain the loads imposed on t_e vehicle by the propulsion system, the following assumptions were made: a. The propulsion system is integral with the vehicle b. The inlet is two-dimensional c. The engine employs a lifting two-dimensional plus nozzle.

The vehicle forebody drag is included in the aerodynamic drag d.

buildup; therefore, the net proFalsive thrust is based upon the change in total momentum from the station at the inlet ramp to the aft vehicle station.

2-1

The network model for application tothe stress analysis and aeroelastic

loads analysis is shown in figure 2-1. In addition to the assumptions pre-

sented, it was also determined that the required net propulsive thrust for the

engine at a q = 2200 psf was 318 000 pounds at Mach8 to provide a vertical

acceleration of 2g. Basedon the assumptions made, the stream thrusts at the

various defined stations (figure 2-2) were computed and are shownbelow: Stream thrust Vector angle, Magnitude F I 1 027 000 lb @ i = 0° F 2 849 000 lb @ 2 = 20 ° F 3 1 017 000 lb @3 = 0 ° Fg, Gross thrust 1 357 000 lb Fg = 2, 7k2° The stream thrust is defined as:

F : + (P- )A = PA (i+ -

The stream thrust vector angle, _ is positive and is measured in the clockwise direction from the wing reference line. Resolution of these engine stream thrust levels into components parallel to and normal to the wing reference line provides the following: Station Location Force i-___2 2-3 3-4 Net FA (lb) -2e9 000 219 000 338 000 328 000 F N (Ib) 290 000 -290 000 64 200 64 200 which result in a net axial force of 328 000 pounds (propulsive) and a net normal force of 64 200 pounds (lifting). From a systems analysis, it was established that the vehicle angle of attack was 7 degrees (freestream flow) direction with respect to the wing reference line) during the 2g maneuver.

Therefore, resolution of the axial and normal propulsive system forces pro- vides a thrust of 318 000 pounds and a contribution of 104 000 pounds to the vehicle lifting force.

2-2

The 2g vehicle trim requirement is 62 676 pounds. Vehicle trim associ-

ated with the cruise condition (q = 750 psf) is 17 635 pounds_as shownin

the tabulation below:

Loads

Conditions 2__gg l__gg -0.5g L_ total airload, ib 831 250 389 372 -236 930 c.p. feet 176.0 176.9 176.9 L6, total elevon load to trim, ib 62 676 17 635 12 160 cp, feet 256 256 256 n W total inertia load, ib -893 926 -407 007 224 770 Z cg, feet 176.8 176.8 176.8 VEHICLE BALANCE Vehicle balance was obtained under the system of forces discussed in the preceding paragraph. Both normal and axial balance were effected with the resultant thrust vector approximately through the vehicle center-of- gravity. (In view of the range of cg motion as fuel is expended, the line of action of the thrust vector is maintained within this region.) Both normal and axial balance requirements were observed. A summary of these forces for all design conditions is contained on figures 2-3 through 2-5. These forces are listed in the body axis systems.

The individual forces contributing to total loads on the vehicle are listed on tables 2-1 and 2-2. These forces are listed in both wind and body axis systems.

The total loads at the cg for the three flight conditions are shown diagrammatically on figures 2-6 through 2-8. Forces are listed in the body axis system. These loadings are distributed, as previously discussed, to pro- vide a loading function for determination of elastic load distributions.

Vehicle balance is inherent in the elastic load solution.

A matrix solution is employed to balance the vehicle under the elastic loadings. The basic representation includes all external forces contributing to vehicle attitude and is as follows:

where

A} = rigid aerodynamic loading

[A_] = aerodynamic influence coefficient matrix

De = differentiating matrix

= structural influence coefficient matrix

V']

= thermal deflection = elevon effectiveness

(_)

= vehicle angle of attack (6e) = elevon deflection Net load is equal to net air z where n = load factor Z IW} = inertia loading T = net thrust

I_I = _ _t _o_n_

Vehicle balance is maintained through the relations

II :o

Ill. Pz net [x]IPzl net = 0 where Ix] represents the distance of each panel load centroid from the cg.

r_ _), In the foregoing solution, the differentiating matrix, [De] , relates vertical deflections at each panel point to the angular deflection of the panel. The aerodynamic influence coefficient matrix was developed considering a one-degree increment in angle-of-attack on each panel using oblique-shock and Prandtl-Meyer expansion relations.

NET DESIGN lOADS Rigid-body load analyses were conducted for the 0.5g, 2g and cruise condi- tions and net panel point loads are presented in tables 2-3 through 2-6.

In addition, aeroelastic analyses were conducted for both the positive maneuver (2g) and cruise conditions. The lower loadings experienced during the negative maneuver condition (-0.5g) were not significantly changed because of flexibility effects.

Net panel point loads (2g and cruise) for both the rigid and elastic wing computations are presented in tables 2-4 and 2-3, which contain wing loads; and table 2-5, which compares loads for the fuselage. As indicated in tables 2-4 and 2-5, elastic loads were obtained for the monocoque, semimonocoque spanwise, semimonocoque chordwise and statically determinant concepts.

The fuselage data of table 2-6 are shown as combined loads on the body at each longitudinal station to indicate that the longitudinal distribution of loading is but little influenced by elastic considerations. Distribution of the net loads between the double panel points at each station was included in the redundant analysis.

Evaluation of the elastic load distribution indicates that the magnitude of the loads at the main wing area does not vary significantly from the rigid load values. The effect of elasticity is to deflect the trailing edge, aft of station 2580, upward, thus inducing a negative angle of attack upon the affected panels. The attendant incremental negative loading necessitates addi- tional trailing edge down elevon deflection (positive load) for trim. Signi- ficant changes in loading due to elastic effects are noted in the area of trailing edge and tip region as well as fuselage nose. Net loads in the tip area decrease in local angle of attack. This loss in lift is made up by additional elevon deflection required for trim which further increases trail- ing edge deflection.

The wide variation evidenced in fuselage loadings (table 2-6) is due in part to the need for trimming the vehicle under the elastic loading; whereas, the chordwise semimonocoque structural concept demonstrates the most flexi- bility in the spanwise direction (table 2-5).

Resultant net shear and bending moment distribution for the specified cruise and maneuver conditions are shown in figures 2-9 and 2-10 as a Ikunc- tion of longitudinal station. Discontinuities evident over the aft portion of the vehicle are due to the concentrated thrust and elevon loads.

2-5 Average pressure loadings over the wing investigation area are listed for upper and lower surfaces for each design condition on table 2-7, where lower surface pressures are further defined in terms of the airload pressure and ramp (propulsion system). The pressure loading for the entire wing is shown in table 2-9. For the detailed evaluation of structural concepts, the pressure loadings of table 2-8 were used. The upper surface shields for aerodynamic smoothness requirements and lower surface heat shield panels were designed for a limit _p of +0.5 psi.

A history of leading edge pressures during the cruise mission is shown on figure 2-11. Variations in these loadings during the defined maneuver excursion are shown on figure 2-12. The lower surface primary load-carrying panels are designed for the calculated aerodynamic pressures. These pres- sures are uniformly distributed over the primary-structure panels (based on complete venting through the heat-shield panels) or with 0.5 psi applied to the heat shield and introduced at the heat-shield support interface, with the balance of the pressure uniformly distributed over the structure panels.

2-6 REFERENCES 2-1 NACA Report 1135; Equations, Tables and Charts for Compressible Flow, 1955.

2-2 NASA Report R-171: The Correlation of Oblique Shock Parameters for Ratios of Specific Heats from i to 5/3 With Application to Real Gas Flows_ 1963.

2-3 Cole, J. D. : Newtonian Flow Theory for Slender Bodies, Journal Aero.

Science, Vol. 24, No. 6, June 1957, PP 448-455.

2-7

TABLE 2-1

SUMMARY OF STATIC BAIANCE -- M8

NORMAL TOWING REFERENCE LINE

Flight condition

Loads, lb

Cruise lg nominal -o.5g

2g (.92g)

.. m

Force

Airload

-258 830 767 150 367 502

cp 174.1 169.3

172.3

Forward ramp 35 4oo

51 9oo 17 700

cp

197.1 197.1 197.1 81 160

Inlet ramp 162 300 238 000

cp 217.O 217.0 217.0 Duct -197 700 -290 000 -98 89o cp 233.0 233.0 233.0 64 200 Aft body 21 90o 21 900 277.0 277.0 cp 277.0 Elevon 12 160 62 676 17 635 256.o 256.0 256.o cp Inertia 224 770 -893 920 -407 010 nzW 176.8 176.8 176.8 cg Note: All loads are limit. All stations in feet.

2-8 TABLE 2-2 SUMMARY OF NORMAL AND AXIAL BALANCE AT CG - M8 Cruise Flight Maneuver Maneuver m n z 1.0 nominal condition n' z = -0.5g n' z = +2.0g =

(.92g)

o _, deg. -2.6 7.0 9.2 ID N ID q, psf 1 500 2 200 -ll4 88O Drag, D -325 55o -iii 520 -24O 88O 860 660 Lift_ L 394 170 ll4 88O Thrust # T 325 550 iii 520 0 0 0

ln'

Inert ia In' W 225 000 -900 630 -412 430 Z D sin_ 18 O2O 39 670 -5 170 L cos_ -241 5oo 367 090 790 050 o 64 200 21 900 21 900 224 770 -407 000 -893 920 nzW D cos_ -113 765 -ii0 050 -323 130 L sins I04 89O 63 700 9 970 I14 000 328 000 113 000 -109 760 _6 65o -10 2O5 Note: All loads are limit.

O-_ L_ j TABLE 2-3 NET VEHICLE LOADS - LIMIT (-0.5G MANEUVER LIMIT, RIGID) Pane i Panel Panel Load 3 Load, Load_ ib number number ib number ib i 16 -i 441 -2 198 32 -i 700 -i 308 1 770 17 33 -i 637 -2 151 -I 194 34 3 572 -3 350 19 -782 35 -227 D 2O 5 -875 -734 36 -381 6 -442 21 37 -595 i 661 22 9 861 38 -730 -9 423 -i 487 5 537 23 39 24 40 -i 611 4 815 -6 878 a 1 484 41 3 244 12 723 25 i io I i II 26 42 -398 -405 -7 685 !

12 43 -693 -35 192 27 -522 28 -468 44 -948 13 -25 123 45 2 908 4 389 29 -592 -I OO8 46 3o -723 15 4 959 -1 520 47 2 255 aIncludes points 48 -- 57 (fig. 2-1) 2-10

TABLE 2-4

(2G I_INER) Elastic_ lb Panel Rigid_ Statically ib Semimonocoque number Semimonocoque Monocoque determinate (chordwise) (sp_nwise) 3 741 16 655 3 494 3 730 3 718 3 409 3 181 3 386 17 3 385 3 31o 3 333 18 3 236 3 085 3 252 3 175 3 224 3 454 3 294 3 281 3 351 2O 2 971 3 ioi 3 199 3 002 3 013 6 656 21 6 311 6 354 6 331 6 519 21 4Ol 22 20 677 20 738 20 778 21 083 -17 145 -17 885 -17 998 -17 961 -17 551 24 -15 154 -15 848 -15 572 -15 315 -15 211 -1 648 -i 629 -i 361 -i 223 -i 698 .....

26 841 860 765 1 288 i i01 1 265 1 211 1 225 i 118 1 088 28 1 038 1 055 935 i 402 1 440 i 51o 1 4A3 l 291 2 640 2 444 2 511 2 234 3o 2 392 4 238 3 841 3 403 31 3 711 3 595 3 461 4 485 3 620 3 898 32 4 131 2 942 2 784 2 577 33 3 891 2 553 12 953 14 375 15 141 34 254 15 415 488 527 478 425 5o6 847 865 701 36 89o 1 513 1 366 1 191 1 407 1 331 1 288 i 822 i 6o8 1 538 38 1 491 3 6Ol 2 948 2 597 3 721 2 951 2 146 2 211 2 382 4o 4 035 2 325 ll 745 41 13 261 14 138 12 238 14 613 8o8 42 649 587 688 453 423 907 43 1 550 44 657 739 2 292 I0 220 ll 818 12 92O ii 869 13 490 481 2 46 215 51o 1 719 lO 306 7 838 9 069 47 9 161 i0 651 --J_.L TABLE 2-5

CR E (la)

Elastic j lb Panel Rigid, ....

Semimonocoque Semimonocoque Statically number lb Monocoque (spanwise) (chordwise) determinate -I 1 875 1 831 1 858 1 796 1 809 1 666 1 681 1 640 1 651 17 1 705 18 1 58o 1 627 1 582 i 581 1 571 1 548 1 545 1 54o 1 551 19 1 592 1 418 2O 1 4o8 1 412 1 455 1 399 21 2 6Zl 2 636 2 679 2 597 2 582 22 7 614 7 544 7 683 7 695 7 569 -6 280 6 467 6 581 6 368 23 6 526 24 -5 724 -5 432 -5 847 -5 797 -5 911 -7OO -706 25 -838 -785 -710 26 461 446 435 62o 648 627 27 631 627 28 528 54o 565 54o 536 7o5 29 739 699 695 1 162 1 124 i 164 30 975 I 191 1 631 i 8o9 31 1 398 1 712 1 721 2 116 1 631 1 908 32 1 774 1 775 1 418 m 428 i 245 1 489 33 2 005 6 Iii 6 358 6 705 34 4 396 6 341 265 247 25O 35 25O 421 410 36 461 423 431 658 645 67o 37 725 38 869 751 729 i 455 1 540 39 1 891 1 532 1 350 1 164 40 1 404 1 368 2 050 1 315 41 4 48o 6 074 6 382 5 795 6 130 42 482 376 373 343 325 43 5o8 398 359 44 631 704 396 525 1 175 5 288 45 5 595 5 907 4 435 5 720 46 345 341 465 388 4 022 4 651 47 3 366 4 467 4 311 2-12

TABLE 2-6

NETFL_ELAGE LOADS -- LIMIT

C

O Elastic, lb Panel Rigid, n Static number 17o Semimonocoque Semimonocoque Monocoque d.

determinate (spanwise) (chordwise) i -2 482 -2 240 -3 021 -2 540 -3 240 2 -12 8oo -12 848 -12 826 -13 128 -12 933 3 -2 754 -3 071 -3 421 -3 775 -3 lO7 447 791 338 695 5+ 48 -2 001 -2 070 -i 785 -I 655 -i 935 -2 126 -2 048 5+ 49 -2 258 -2 069 -1 99o -24o 7 + 50 -518 -441 -361 -317 8+ 51 1 664 6 768 6 938 6 497 6 607 © 6 o82 9+ 52 5 666 5 737 5 9o5 5 9Ol 16 o61 ]_6o81 16 4Ol I0 + 53 15 845 15 875 ii + 54 64 300 64 723 65 330 65 178 65 669 12+55 -81 531 -8o 98o -8o o29 -80 325 -79 799 13 + 56 -68 215 -63 378 -67 521 -67 778 -67 o91 14 + 57 -23 606 -24 231 -23 168 -23 565 -22 596 12 260 ]_2 oo4 15 12 465 12 023 ii 530 i -3 335 -3 o16 -2 981 -2 931 -2 627 -5 382 -5 281 -5 276 -5 305 -5 3Ol -406 3 -127 -71 -307 -125 4 1 660 1 341 1 718 1 138 1 793 -481 -620 5+ 48 -565 -463 -5o5 6+ 49 -694 -698 -698 -763 -725 -165 -165 -167 -167 7+ 50 -132 2 168 2 144 2 160 8+51 2 202 2 155 © 1 383 1 89o 1 921 9+52 1 951 1 9o3 3 208 5 287 i0 + 53 5 341 5 2o4 5 223 o 21 618 2 158 21 639 ii + 54 21 679 21 524 -30 063 12+55 -30 082 -32 275 -30 128 -30 152 -25 969 -25 793 13 + 56 25 65o -26 077 -25 938 -lO 825 -i0 528 14 + 57 -i0 3OO -io 741 -i0 919 1 441 1 483 1 650 15 1 875 1 520 2-13 !

°°°..° °°°°o.

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I L_ I °°°_.l I I II

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"2-i4 TABLE 2-8 HYPERSONIC CRUISE VEHICLE WING PRESSURES Limit pressure Ap, psi a, b, c BL 0-120 BL 120-212 BL 212-350 dition Cruise -0.5-g +2. O-g -0.5-g +2.0-g Cruise -0.5-g +2.0-g Cruise Location Lower surface structural -0.53 -0.97 -0.73 -0.51 -1.46 -0.97 -0.54 -0.98 -0.73 panels All heat shields ±0.50 r & upper surface panels aFor ultimate design pressures, multiply (1.3) (1.5) by limit pressures shown.

bNegative values indicate inward-acting pressures;positive values indicate outward- acting pressures.

CSta. 2274-2366.

2-15

I

I ;-1 -r,-,l r_ Fuselage Station oo O O O O t_ CO O o') f_ O- O @4 @4 @4 @4 I I I I I I 11, I I I I I I I I

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I I

"®4@

-@ @

forebody Coordinates Grid Point FS BL Note: Boxes indicate panels used for rigid - 575 600 0 loads analysis.

(_) 950 0 Circled numbers indicate load (_ 1350 120 grid points for elastic loads analysis and stress analysis.

Figure 2-1. Loads network wing model F-_-_O- _ Wing F?eFeren " 7 Figure 2-2. Integral engine: Hypersonic cruise vehicle 2-ZT Fuselage station, ff

dd " - _"

ev -0.5g maneuver condition Static b_: Figure 2-3.

Fuselage station, ft I Figure 2-4. Static balance: +2.0g maneuver condition 2-18 r-I v .H o._ o & .H CJ _J S'gzl "_"ezl ¢J .1-t I .H 2-19 Z n W _, I0 _5 ib x Wind Ref X Axis Axis Axis ½ n n w = L_4 770 ib z z _= 2.6 ° D cos a = 113 765 ib

/

V X X T = 114 000 lb D sin _ = 5 170 ib L cos_ : 219 600 ib 9 970 Ib L sin _ :

I

Z Figure 2-6. -0.5g maneuver condition: static balance at cg 2 -20 Z

I

L sin _ = 104 890 ib Ref X Axis Wind Axis (V_L) Axis n x O. 244 O. O0 L cos _ = 854 250 ib n i. 987 2 00 z T = 328 000 ib D sin _ = 39 670 ib

xJ

7 ° D cos = 323 130 ib nzW = 893 9_ ib r m,,..

v n W -- 109 760 ib x

I

Z Figure 2-7. 2g maneuver condition: static balance at cg 2-21 L sin _ = 63 700 l.b X Axis Wind Ref Axis (WRL) Axis nx o.15 0.oo L cos _ = 388 990 ib 0.9o 0.92 nz D sin a = 18 020 ib T : 113 000 ib X a= 9.2 ° D cos • = ii0 050 Ib n..W = 407 010 Ib -Z r v nxW = 66 650 ib Figure 2-8. ig cruise condition: static balance at cg 2-22 o c_ !

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ill _ I Upper surface k r_ I I_ ......

I Lower surface I 0 ! 2 16 20 24 28 Time, min Wing leading edge pressure (limit) variations during maneuver Figure 2-12.

2 -26

Next: Section 3 →

Section 3

Section 3 AERODYNAMIC HEATING ANALYSIS by D. A. Brogan, F. L. Guard 3-i CONTENTS Page GENERAL 3-1 Leading Edge Heating 3-1 Wing Lower Surface Heating 3-1 Wing Upper Surface Heating 3-2 Fuselage Heating 3-2 Radiation Equilibrium Temperatures 3-2 Transient Thermal Analysis 3-3 ANALYSIS RESULTS 3-3 3-5 Radiation Equilibrium Temperatures 3-iii ILLUSTRATIONS Page Wing lower surface laminar to turbulent transition 3-1 comparison, cruise condition Wing upper surface view factors to space Radiation and equilibrium temperature distribution 3-I0 for -0.5-g maneuver 3-4 Radiation and equilibrium temperature distribution 3-II for 2.0-g maneuver 3-5 Radiation and equilibrium temperature distribution 3-12 for cruise 3-V SYMBOLS Butt line Configuration factors for determining the radiation heat transfer from lower surface to space, from lower surface to upper surface, and from upper surface to space, respectively g Gravitational acceleration h Local heat transfer coefficient M Local Mach number e Reynolds number evaluated at the boundary layer edge Re e T Temperature Adiabatic wall temperature

%w

£ _nittance Stefan-Bolt zmann constant 3-vii

Next: Section 3 →

Section 3

AERODYNAMIC HEATING ANALYSIS GI_TERAL Accurate prediction of aerodynamic heating and resulting temperatures is required for proper materials selection_ structural design_ and determination of insulation requirements. Theoretical and empirical methods were employed to predict aerodynamic heating rates during this investigation. Also_ predic- tion techniques were required for structural temperature determination using transient structural heating analyses.

Aerodynamic heating requirements were established at various vehicle loca- tions as summarized below. In all cases_ Hansen's equilibrium air properties (ref. 3-1) and 1962 Standard Atmosphere data were used in theory evaluation.

Leading Edge Heating Wingleading edge heating rates were computed by the swept cylinder theory of Beckwith for laminar flow (ref. 3-2) and the Beckwith and Callagher theory for turb_ent flow (refo 3-3).

Leading edge transition from laminar to turbulent flow was based on the criterion proposed by Bushnell (ref. 3-4) and was assumed to occur at a free- stream Reynolds number of 130000 based on leading edge diameter. Circumferential leading edge heating was determined from reference 3-5.

Wing Lower Surface Heating The flow field over the wing lower surface as positive angle of attack (windward surface) was obtained from a real gas computer solution (ref. 3-6) assuming local conditions to be those behind a single oblique shock produced by a flow deflection equal to the local effective angle of attack. Laminar and turbulent heat transfer coefficients were computed from two-dimensional the0ry using Eckert's reference enthalpy method (refo 3-7)_ and the theory of Spalding and Chi (ref. 3-8)_ respectively.

Flow over both the wing lower and upper surfaces was assumed turbulent whenever the leading edge flow was turbulent. For laminar leading edge flow, 3-1

the transition criteria used in analyses resulted from flight heating data

obtained on the ASSET test program (ref. 3-9); however_two other transition

criteria were also evaluated but not used. The second criterion was based on

recent wind tunnel and ballistic range flat plate transition data which were

correlated by Lockheed (ref. 3-10). The third transition criterion evaluated

is by Jillie and Hopkins (ref. 3-11).

Wing Upper Surface Heating

The prediction of heating rates on the leeward wing upper surface is sub-

ject to large unknowns; due to the limited amount of theoretical and experimen-

tal work in this area. For the present study; upper surface flow field and

heating methodswere used which yielded good agreement with data obtained from

theX-15 flight test program (ref. 3-12). For leeward upper surface flow, a

Prandtl-Meyer expansion was assumedto the local expansion angle up to a total

flow deflection angle of 8 degrees. For larger expansion angles; constant flow

properties equal to those for an 8-degree expansion were assumed. Turbulent

flow was assumedfor all flight conditions. For windward flow on the upper

surface; flow field and transition criteria were employedidentical to those

used on the lower surface.

Fuselage Heating

Inviscid flow properties on the fuselage were obtained from a computer

solution of the method of characteristics (ref. 3-13). Pressures along the

upper surface centerline were assumedequal to freestream static_ and heating

rates were determined from the theories discussed previously (vis._ Eckert;

Spalding and Chi). Flow behind the bow shock along the bottom of the fuselage

area was assumedidentical to wedgeflow behind a leading edge oblique shock.

The method of characteristics flow field solution was also used to provide

flow properties upstream of the wing leading edge which were used in evaluating

the freestream Reynolds number for leading edge transition.

Radiation Equilibrium Temperatures

Initial calculations of the vehicle external surface temperature distri-

butions used for the initial struct'_al conce_t and material screening were

madeassuming radiation equilibrium conditions; i.e._ the convective heating

rate to the vehicle surface is balanced by radiation to space. This assump-

tion is reasonable since the various structural concepts are thin metal skins

with little capability for storing heat internally. For the wing_ where

3-2

appreciable heat may be transferred from the lower to upper surface by radiation,

configuration factors were calculated with a formula developed by Hottel

(ref. 3-14). Radiation relief to space was included for all surfaces, with an

appropriate view factor determined by Nusselt's unit sphere method.

Transient Thermal Analysis

Temperatures developed by the radiation equilibrium analysis neglected

thermal capacities of the structure and accounted for radiation within the wing

by a simple two-surface network_ neglecting the effects of intervening struc-

ture. As such_ the analysis defined the general thermal environment and probable

maximum temperatures for the vehicle external surfaces. To aid in the selection

of the optimum structural concepts with the given thermal environment capability,

thermal analyses accounting for transient effects and the necessary structure

detail were used to examine in detail the comparative structural temperature

and thermal gradients for each candidate concept. The analyses were performed

using the Thermal Analyzer IBM-360 (ref. 3-6) computer program_ which affords

direct solution of three-dimensional transient problems involving conduction,

convection_ radiation_ and heat storage under impressed arbitrary boundary con-

ditions (temperatures and/or heating rates). The transient heat transfer solu-

tion is obtained by converting the physical system into one consisting of lumped

thermal capacities (nodes) connected by thermal resistors, and then using the

lumped parameter_ or finite differences 3 approach to solve for the temperature

history of the system. Boundary conditions included the convective heat fluxes

imposed on external surfaces according to the heating theories outlined above_

as well as radiation relief to the surroundings assumedat 0°F. All internal

radiation was assumedto originate from gray diffusely reflecting surfaces of

constant emittance. Reflected radiation was accounted for by using configura-

tion factors determined from the matrix method of Hottel (ref. 3-15). This

method_ in combination with a discrete dissection of the internal structure into

assumedconstant temperature nodes, provides the most sophisticated approach to

the radiation/convection heat transfer problem currently available for solution

on the computer. Conduction heat transfer was accounted for in these analyses

whenever applicable. However_for a thin skinned structure at _ery high tempera-

tures 3 radiation heat transfer within a structure is usually at least an order

of magnitude greater than conduction heat transfer_ and the latter maybe

neglected.

ANALYSIS RESULTS

The laminar-turbulent flow transition criteria were evaluated_ and the

corresponding lower surface temperature computed. The chordwise temperature

distributions during cruise from the leading edge through the t_nsition re-

gion are shown superimposed in figure 3-1 for wing location BL 304.

One criterion was based on recent wind tunnel and ballistic range flat

plate transition data which were correlated by Lockheed (ref. 3-10). The

3-3 following empirical equations were recommended for estimating the locations of the start and end of transition: Ree_z_ start ] : 5.30 + 0.i0 Me

I

/ J

, Ree_ end = 5.95 + o.o8 Me LOGI0 where: Ree/ft = unit Reynolds number per foot Ree3star t = Reynolds number evaluated at start of transition Ree3end = Reynolds number evaluated at end of transition M = local_ch number e Subscript e denotes evaluation at the boundary layer edge. Flow properties on the lower wing surface were computed by wedge theory and also by isentropi- cally expanding leading edge stagnation line properties to the wedge pressure.

The two flow field solutions resulted in transition locations which agreed within seven percent.

The transition criterion proposed by Jillie and Hopkins (ref. 3-11) is based on the assumption that the change in transition location produced by variations in Yach number and sweep angle is associated entirely with changes in local unit Reynolds number. The latter is evaluated assuming an isentropic expansion of leading edge stagnation line properties to the inviscid flat plate pressure. The zero-sweep freestream transition Reynolds number (27 million) was obtained from figure 3 of reference 3-11 and is based on extrapolation of test data obtained at a freestreamYach number of 2.5. Jillie and Hopkins do not present a method for estimating the location of the end of transition.

The temperature distribution shown in figure 3-1 assumes that end of transition Reynolds number is twice the start of transition value.

Comparison of the wing surface temperatures resulting from the three tran- sition criteria_ plotted in figure 3-i_ indicates small differences in transi- tion location compared to the total chord length of 80 feet at this wing loca- tion. For all three criteria_ transition starts within the first i0 feet 3-4 after the leading edge. Peak temperatures at the start of fully turbulent flow fall within a lO0°F range for the three methods_ indicating a flat portion of the curve and good predictability for peak temperatures in this region of the wing.

Radiation Equilibrium Temperatures Initial calculations of the vehicle external surface temperature distribu- tion were made assuming radiation equilibrium conditions. Radiation relief to space was included for all surfaces_ with an appropriate view factor determined by Nusselt's unit sphere method. Computed view factors for the wing upper sur- face are shown in figure 3-2.

A schematic of a typical wing location is shown below: T u Rib / f Spar Sp_ / _ TI An energy balance results in two equations for the two unk_uown surface temperatures: hl (Taw_l - TI) -_£_isTl4 - _£_lu(Tl 4 - Tu 4) = 0 h u (Taw,u - Tu) - o'£SusTu 4 + o'_Zlu(TI 4 - Tu 4) = 0 Methods for computing the local heat transfer coefficients (h) and adia- batic wall temperatures (Taw) were discussed previously. The configuration

3-5

factors_ _is_ _!u_ and_us_ determine the radiation heat transfer from lower surface to space, from lower surface to upper surfac% and from upper surface to space_ respectively.

Results of the radiation equilibrium analysis are shown in figure 3-3_ 3-4_ and 3-5 for the -0.5g_ 2.0g and cruise conditions_ respectively. The tra- jectory perturbations at the end of climb show the effects of peak heating rates on the upper surface (-0.5g condition) and on the lower surface (2.0g condition).

Temperatures for the transient 2.0g condition average 400°F higher than at the cruise condition. For the -0.5g condition, upper wing surface temperatures are hotter than lower surface temperatures because of a negative flight angle of at- tack. However_ expansion of the flow over the upper surface results in decreas- ing temperatures such that at the aft portion of the wing_ upper and lower surface temperatures are almost identical. The effect of radiation heat transfer between the wing surfaces may be seen in the unusual temperature patterns on the lower wing surface_ which reflect the different temperature levels on the differently sloped portions of the upper surface.

3-6 REFERENCES 3-1 Hansen_ C.F. : Approximations for the Thermodynamic and Transport Properties of High Temperature Air. NASA TR R-50_ 1959 3-2 Beckwith_ I.E. : Similar Solutions for the Compressible Boundary Layer on a Yawed Cylinder with Transpiration Cooling. NASA TR R-42, 1959- 3-3 Beckwith_ I.E._ and Gallagher, J. J. : Local Heat Transfer and Recovery Temperatures on a Yawed Cylinder at a Mach Number of 4.15 and High Reynolds Numbers. NASA TR R-I04_ 1961.

B-4 Bushnell_ D. M. : Interference Heating on a Swept Cylinder in Regions of Intersection with a Wedge at Mach Number 8. NASA TN D-3094, December 1965.

3-5 Thomas_ A. C • : Perlbachs, A. ; and Nagel, A.L. : Advanced Reentry System Heat Transfer Handbook for _ Hypersonic Flight. AFFDL-TR-65-195_ June 1966.

3-6 Schultz_ H.D.: Thermal Analyzer Computer Program for the Solution of General Heat Transfer Problems. Lockheed-California Company 3 LR 18902 _ July 1965.

3-7 Ecker% E. R. G.: Survey of Heat Transfer at High Speeds. WADC TR-54-70, April 1954.

3-8 Spalding_ D. B.; and Chi_ S.W.: The Drag of a Compressible Turbulent Boundary Layer on a Smooth Flat Plate With and Without Heat Transfer.

Journal of Fluid Mechanics_ Vol_ 18_ January 1964.

3-9 Pagel_ L.; et al: ASSET_ Correlative Analysis of Heat Transfer Data.

AFFDL-TR-65-31, Vol. IV, April 1966 (Confidential) 3-i0 Schultzj H. D.: Hypersonic Boundary Layer Transition. Lockheed- California Company_ LR 21245_ December 1967.

3-ii Jillie D. W.; and Hopkins_ E. J. : Effects of Mach Number_ Leading-Edge Bluntness_ and Sweep on Boundary-Layer Transition on a Flat Plate. NASA TN D-1071, 1961.

3-12 Personal Communication. F. L. Guard_ Lockheed-California Company and R. D. Banner, NASA Flight Research Center_ Edwards Air Force Base 3 California_ November 1967.

3-13 Benson_ J. L.: Computer Program for the Design and Analysis of Hyper- sonic Inlets. Lockheed-California Company_ LR 18079_ August 1964.

3-7 3 -14 Jakob; M: Heat Transfer. Volume II_ Wiley; New York, 1949.

3-15 _Adams; W. H. : Heat Transmission. McGraw-Hill; New York; 1933.

3-8 200O Transition criteria a Lockheed, LR 21245 b ASSET, AFFDL-TR-65-3 , VOL IV c Jillie and Ho)k;ns, NASA TN D-1071 ii O f J P E u f Laminar _ 8OO 0 2 4 6 8 10 12 14 16 18 20 Chordwise distance from leading edge, ft Figure 3-i. Wing lower surface laminar to turbulent transition comparison_ cruise condition Figure 3-2. Wing upper surface view factors to space 3-9 008_ I c_ I 009_ L ii .H .o a & E .+3 I-- r./] 9£L_ °IS I .rl 000_ .p O08L 009L gt 00_'L ,m -r't -r'-I cf O0_L Sd © 0 • e- G) U o 0 c_ QO '0 u'_ :3 u _ u_ I o c o ..I ::) o 3-i0 oo o oOO o8 o° 8 ° 04 0 _1oo o04 © OOO8 h0 !

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Next: Section 4 →

Section 4

MATERIAL ANALYSIS

by

J. W. Lewis, L. F. Tenn, I. F. Sakata

CONTENTS Page GENERAL 4-I MATERIAL CHARACTERISTICS 4-2 Characteristics of Superalloys 4-2 Characteristics of Refractory Metals 4-2 PARAMETRIC ANALYSIS 4-3 MATERIALS TESTING 4-5 Material Property Tests 4-5 Coating Tests for Leading Edge 4-5 Structural Joint Tests 4-6 Formability Tests 4-6 MINIMUM GAGE SELECTION 4-6 MATERIALS SELECTION 4-7 Primary Structure and Heat Shield 4-7 Leading Edge 4-7 Insulation Materials 4-8 REFERENCES 4-9 4-iii

TABLES

Page

4-1 4-Io

Candidate materials for hypersonic wing structures

4-2 4-Ii

Mechanical properties of Rene z 41 material

4-3 Design parameters for Haynes 25 (L-605) sheet at

4-12 elevated temperatures 4-4 Design parameters for TD NiCr sheet at elevated 4-13 temperature 4-14 4-5 Material minimum gage for structural concepts 4-V ILLUSTRATIONS Page 4-1 Density compensated ultimate tensile stress vs 4-15 temperature of candidate high temperature materials 4-2 Density compensated compressive yield stress vs 4-16 temperature of candidate high temperature materials Compressive loads vs weight index for Ren_41 and 4-3 4-17 Haynes 25 4-4 Coefficient of thermal expansion vs temperature of 4-18 candidate materials 4-5 Thermal conductivity vs temperature of candidate 4-18 materials

4-_9

Specific heat v_ temperature of candidate materials

4-2o

4-7 Emissivity vs temperature of candidate materials 4-8 Compressive modulus of elasticity vs temperature of 4-20 candidate high temperature materials

4-21

Modulus of elasticity (E and E ) -- Reng 41 4-9 c 4-22 4-10 Constant life diagram, Rene 41 (Kt = 4.0) - 1400°F 4-11 Typical isochronous stress-strain diagram for Ren_l 4-23 at 1300°F 4-24 4-12 Creep design data for luconel 625

4-13 Creep design data for Haynes 25 4-24

4-25 4-14 Creep design data for Ren_ 41 4-25 4-15 Creep design data for 90Ta-IOW 4-26 4-16 Creep design data for Cb-752 4-26 4-17 Creep design data for TD NiCr L-vii ILLUSTRATIONS (Cont.)

Page 4-18 Depth of oxidation vs temperature for Renei41, TD NiCr, 4-27 and Haynes 25 4-28

4-19 R412E coating life -- Cb-752

4-2o Effective thermal conductivity vs temperature -- Dyna-Flex 4-28 (atmospheric pressure) 4-viii SYMBOLS C Specific heat P E Modulus of elasticity E Compression modulus of elasticity C Elastic modulus of elasticity Ee_ e Strain F Compression --yield strength cy Ultimate tensile strength Ftu Stress corresponCing to modulus of 0.7 Ee_ FO.?

Alternating and mean stress used when defining cyclic stresses faJfm K Thermal conductivity Stress concentration factor Kt n Shape factor Larson-Miller parameter PL T Temperature t Thickness t Minimum gage thickness m Mean coefficient of thermal expansion P Density 4-ix

Next: Section h →

Section h

Section h MATERIAL ANALYSIS G_TERAL Considering the load-temperature environment and vehicle life charac- teristics, candidate superalloys and refractory metal materials were eval- uated. At elevated temperatures the usefulness of a material system is limited by its strength_ oxidation resistanc% and metallurgical stability. The primary consideration for a candidate alloy_ in this program_ is its ability to maintain strength at its service temperature and perform without serious degradation in properties throughout cyclic exposures.

Superalloys (nickel and cobalt base) were considered for wing primary structure application. Dispersion-strengthened alloys, as well as the nickel and cobalt base superalloys, were considered for heat shield application.

For leading edge requirements, dispersion-strengthened_ and refractory alloys were evaluated. Fibrous quartz materials were considered for the lower sur- face thermal protection aspects.

A ........ _" .................. _11_+_s _rn_p_ _11 available materials.

resulting in a parametric evaluation of several leading candidate alloys. It is important to utilize the correct properties of candidate materials when comparisons are made. Comparing tensile and creep strength alone is often misleading when the failure mode is buckling or minimum gage requirements are imposed. The most significant material property factors were considered in this parametric analysis. These factors are presented as merit indices for the leading candidate alloys. Merit indices_ as listed below_ are devised to relate materials to various design parameters that provide an efficient index for materials comparison.

• Physical properties (_ _ K, Cp, and emissivity) • Mechanical properties (Ftu/P_ Fcy/P_ and creep) • Structural stability during cyclic exposure _ E c • Fabricability t - material minimum gage m Oxidation characteristics • Metallurgical stability In addition to using existing data for the evaluation of leading candidate alloys and final material selection_ 176 material screening, 330 joining _÷_ (oe _ _e_÷_o_ _ technique_ and 576 formabiliby tests were .................... .

h-I

The material screening tests were for oxidation and thermal stability

(tensile properties after exposure to elevated temperatures for various periods

of time and metallurgical examination), and emittance.

The joining technique test evaluation encompassed resistance spotwelding_

spot diffusion bonding_ brazing (spot and continuous)_ TIG welding_ electron

beamwelding and mechanical fasteners for the various leading candidate materials

and a range of gage thicknesses.

The formability evaluation consisted of bend_ flanging-shrink_ flanging-

stretch_ beading-stretch_ and draw form tests for the various leading candidate

materials.

After the final selection of alloys_ design-allowable data were established

and used for the structural concept analyses.

MATERIAL CHARACTERISTICS

M_terials evaluation and selection were heavily influenced by the general

characteristics of superalloys and refractory metals.

_hars.eteristics of SuDeralloys

The term superalloy applies to the nickel a_d cobalt base alloys_ which are

intended for structural use in the temperature range of i000 ° to 2000°F. Gener-

ally_ the cobalt base alloys are more chemically and metallurgically stable at

higher temperatures than are the nickel base alloys. Superalloys display good

weldability with the exception of the thoria-dispersed strengthened alloys_ and

are oxidation resistant except at high temperatures. Oxidation resistance is

dependent not only on velocity_ density_ and composition and flow pattern of

the oxidizing environment but also on structure_ state of stress_ and geometry

of the part. Therefor% alloys designed for strength may not have maximum oxi-

dation resistance. Whenmaximum strength is desired_ protective coatings should

be considered_ usually a light surface oxide for high emittance;however_ inter_

granular oxidation in small amounts can have a serious effect on thin sections.

Intergranular oxidation not only reduces the cross section_ but can act as a

notch in notch-sensitive materials. Of the superalloys_ the precipitation harden-

able nickel base alloys, suchas Ren_ 41_ are the most susceptible to intergran-

ular oxide penetration above 1600°F.

Characteristics of Refractory Metals

For structures to be used at temperatures above 2000°F_ refractory metals

must be considered. For example_ columbiumpossesses several properties that

makeit attractive for high temperature structural applications. This metal

h-2

and most of its alloys possess excellent fabricability_ and its density is less

than that of most of the refractory materials. However_the use of columbiumat

temperatures greater than 1000°F requires an oxidation protective system_ since

unprotected columbiumreacts with oxygen to form a nonadherent oxide at a rate

dependent on alloy composition_ temperature_ and environment. At temperatures

greater than 2700°F_ the rate is great enoughto produce an exothermic reaction_

called autoignition. At lower temperatures_ the diffusion of oxygen causes

embrittlement.

Columbiumretains structural strength up to temperatures approaching 3000°Fj

but the autoignition restricts its maximum useful temperature to approximately

2700°F on a Short time basis. Reuseof coated columbium should be limited to

temperatures up to 2500°F wherein creep is significant. Two fused slurry coat-

ing systems_ R512A(Si-20Cr) and R512E(Si-20Cr-2OFe)_ have been shownto be

effective for high-temperature columbiumapplications.

Tantalum is useful in the greatest temperature range of any metal because

of its high melting poin% retention of ductility at room temperatures_ and ex-

cellent fabricability. Its greatest potential as a structural material lies in

the temperature range greater than that possible with columbium.

However_like columbium_ unprotected tantalum oxidizes at a high rate. For

this reason_ a protective coating must be employed when service temperatures

exceed lO00°F in oxidizing environments. This coating would also inhibit auto-

ignition_ _,_i_h _o_l_ o_1_r at some high temperature (T_3oOO°F).

Two practical coating systems to protect tantalum at 3000°F are Sylcor R512C (So-20Ti-lOMo) and R505 (Sn-25AI).

PARAMETRIC ANALYSIS The materials listed below were evaluated for structural application by parametric analysis based on published property data and were selected for addi- tional screening tests.

Density , ib/i n3) Application Leading candidates / Rene 41 0.298 Primary structure Haynes 25 0.330 / Heat shields Rene 41 0.298 Haynes 25 0.330 NAC r 0.306 Ta-IOW 0.608 Leading edge Cb-752 0.326 TDNiCr 0.306 4-3 Merit indices relating materials to various design parameters provide an efficient index for comparison as shown in figures 4-1 through 4-9. Figures 4-1 and 4-2 show density-compensated tensile and compressive-yield stresses versus temperature for the leading candidate materials. The allowable stresses divided by the density @ show advantages for Ren_ 41 in the temperature ranges 1200 ° to 1600°F of the major portion of the wing structure.

P The compressive buckling weight index, I _ is plotted in figure 4-5

(E c)3

versus the applied compressive stress fc for temperatures of !200°_ 1300°_ and 1400°F. The index P l is an expression of a material's structural

(Ec)

stability characteristic in relation to weight (ref. 4-1). The terms of the ex- pression are: @ is density_ E c is compression modulus _ and _ is the plas- ticity correction factor.

The curves of figure 4-3 indicate that for a given compressive load, panels / would weight considerably less if constructed of Rene 41 rather than Haynes 25_ provided minimum gage does not constrain the results.

OTher factors considered included fabrication, physical properties_ (;_ K_ Cp_ and emissivity)_ creep_ fatigue_ minimum gages_ oxidation characteristics_ and metallurgical stability. Coefficient of thermal expansion_ thermal eonduc- tivity_ specific heat_ emissivity_ and modulus data are given in figures 4-4 through 4-9.

As an example of elevated temperature considerations_ figure 4-10 shows Ren_ 41 constant-life fatigue diagrams at 1400°F for various stress levels.

Variations of mechanical properties of ReneJ41 from room temperature to 1600°F are shown in table 4-2 for both A and B probability values (ref. 4-2). Mechan- ical properties for Haynes 25 and TDNiCr are presented in tables 4-3 and 4-4 (ref. 4-3). _- A typical isochronous stress-strain diagram used for creep analysis is shown in figure 4-11. The temperature environment is 1300°F for the Ren_ 41 sheet ma- terial in the 1400°F aged condition. The 4460 hours corresponds to the cruise condition at the low level of re!iability_ the other 2 curves correspond to nomi- nal and high reliability levels. Fcy (0.2 percent strain) and the 0.5 percent strain for tensile creep are indicated in figure 4-11. Tensile creep data for Inconel 625_ Haynes 25_ Ren_ 41_ 90 Ta-10W, Cb-752 , and TDNiCr are presented in figures 4-12 through 4-17.

Next: section 5). →

section 5).

IWATERIAI_S TESTING Material screening tests were performed in conjunction with parametric analysis. Existing data_ supplemented by data generated under this test inves- tigation_ provided the design allowables used in the structural analysis (see section 5).

Material Property Tests Oxidation and thermal stability_ tensile property_ emittance_ and metallur- gical examination tests were conducted for Ren_ 41_ Haynes 25_ and TD NiCr during the materials screening (176 tests). Emittance tests were conducted for the Cb-752 and Ta-10W alloys.

Tensile test data for Rene/41 and Haynes 25 included room temperature tests of solution heat-treated (annealed) material after exposure to the thermal envi- ronment. The normal aging response to annealed Rene'41 as well as Hayes 25 causes a sharp increase in strength s followed by a drop in strength_ as shown in figure 5-5 of Section 5_indicating an overaged condition. Therefore_ it was found that Rene141 is the most favorable material to satisfy elevated tempera- ture strength requirements_ provided it is aged after fabrication to provide p_ab]e allowables required for design.

Emittance test data obtained over expected temperature ranges for Rene_41_ Hayes 25; TD NiCr; Cb-752 and Ta-IOW, were used in the thermal structural analy- / ses. Rene 41 emlttance test data are shown in figure 5-41 of section 5; and as a result; an emittance of 0.8 was used for designing with Rene'41.

Coating Tests for Leading Edge Initial radiation equilibrium temperature predictions (see_figure 3-4 of section 3) indicated that refractory metals would be required for leading-edge applications. Accordingly, screening tests for coated refractory-metal systems were performed. Two leading-edge material candidates were fabricated and tested in a plasma-arc under simulated flight conditions. The first (porous metal)_ a 50- percent dense porous powder-metallurgy product of Ta-10W, was sintered to a Ta-10W backing sheet. A protective coating of Sylcor R505 (AI-25Sn) was applied to the assembly and vacuum fired at 1900°F for i hour. The second candidate fabricated and tested was a Ta-IOW sheet leading-edge specimen, disilicide_ coated with Sylcor R512C (Si-20Ti-10Mo). This coating was diffused in a vacuum 2580°F for i hour.

The two leading-edge material arrangements (porous and sheet) were tested at 2800% 3000o; and 3100°F for cyclic conditions of temperature to determine the failure point of each. Six-minute cycles were selected to correspond with earlier leading-edge tests; ref. 4-4. The leading-edge test results are shown in figure 5-55 of section 5.

4-5

As shown_ the sheet concept did not fail after 37 six-minute cycles at 2800°F. Although the porous metal failed after 12 six-minute cycles at 2800°F, there were indications of improvements by a factor of 2 over earlier tests with the same type of coating (ref. 4-4). The mode of oxidation that occurs in the porous Ta-IOW/R505 concept produces a considerable number of local hot spots.

Failure is a combination of progressive Ta oxidation and thermal stress. The results indicate that adequate oxidation protection at 3100°F is not practical with either of the concepts tested_ whereas limited oxidation protection is afforded at 3000°F with the monolithic 90 Ta-IOW/R512C concept (37 six-minute cycles ).

Structural Joint Tests Representative structural joints and splices were selected for evaluation (330 tests). Resistance spotwelding and diffusion spot-bonding were evaluated for Ren@ 41. For Haynes 25_ resistance spotwelding was investigated. Diffusion spot-bonding_ brazed-spo% continuous-braze_ and riveted techniques were used for TD NiCr.

The joint technique evaluation results_ shown in table 5-10 of section 5_ indicated that higher joint strengths at elevated temperatures are possible for the resistance spotwelded specimens than for the diffusion-bonded specimens.

/ Y-_y _n_p_e_o_ o_ the Rene 41 s_ots indicated crackfree welds; therefore, re- sistance spotwelding was selected for use in panel fabrication of Ren_ 41. For the TD NiCr materials_ the riveted specimens provided the highest strengths at elevated temperatures_ as shown in table 5-13 of section 5.

Formability Tests Four types of formability tests (bend_ flanging_ stretch bending_ and draw form) were conducted to establish fabrication limits and procedures for the manufacture of the panel-element and structure designs. In the tests of the leading candidate materials_ various gages were considered. Procedures resulting from these tests were defined for design_ manufacturing panels_ and costing exercises (see section 5).

MINIMUM GAGE SELECTION Minimum gage for fabrication of acceptable structural elements_ sheet- thickness availability_ and sheet-thickness variation were considered in the structural concept optimi ...... _ble 4-5 presents _ ...... +_ii_ ma+_al thicknesses that were selected for the concepts evaluation. The basis of se- lection was suitability to fabrication processes involved and to damage resistance• NATERIAIS SELECTION Final selections were Rene/41 for the primary structure and the heat shields (below 1800°F), and TD NiCr for heat shields (above 1800°F) and the leading edge.

Primary Structure and Heat Shield Rene/41 was selected for use in the detailed evaluation of the primary structure and heat shields (below 1800°F) because of its excellent high-temperature buckling strength and acceptable fabricability. As indicated in figures 4-i_ / 4-2_ and 4-3, Rene 41 is the most efficient superalloy at the elevated temper- ature range in which the structure must operate. Because of oxidation_ addi- tional material weight was considered for depth of attack for the operational temperatures and flight times of this program.

Static oxidation behavior at one atmosphere is used for alloy comparison and is shown in figure 4-18 (refs. 4-5, 4-6 and 4-7). Depth of penetration per side for the candidate superalloys is presented, assuming (i) uniform oxide at- tack, (2) depth of penetration, extrapolated from current data, is uniform and linear with respect to time and temperature to the extrapolated points, and (3) at no stress. These published data have been substantiated by static thermal ...... )I and discussed in detail in section 5.

TD NiCr was selected for heat shield application above 1800°F, because it is lower in weight than Rene/41, as discussed in section 20.

Leading Edge For leading edges_ Ta-10W was originally considered the leading candidate on the basis of radiation equilibrium temperatures. However_ the two-dimensional thermal analysis described in the section on leading-edge weight indicated a maximum operating temperature of 2200°F_ allowing use of TD NiCr without the oxidation coating requirement of refractory metals. For service temperatures from 2300°F_ the Cb-752/R512E material was selected_ for service from 2500°F to 3000°F_the Ta-lOW/R512Cmaterialsystem was chosen.

Figure 4-19 shows the predicted coating life of the Cb-752/R512E system under cyclic exposure. These data represent a composite of tests performed at Lockheed and those reported by the supplier, under various reentry conditions of time; temperature, and pressure. The majority of these tests were for a one-hour time-temperature cycle.

4-7 Insulation M_terials Several materials were considered for the insulation required as a part of the lower surface (outboard) thermal-protection system with heat shields. Of the three leading candidate low-density silica fibrous materials_ two (Micro- Quartz and Dyna-Flex) are feltlike materials and one_ Dyna-Quartz, is a block- tile material. The following tabulation shows the leading candidate insulation material characteristics : Vaximum utilization Density_ temperatures

Ins ulat i on OF

lb/et3

16oo Mi cro- Quart z 3.5 (3.0 nominal) 4.5 2750 Dyna-Quartz (hear'stabilized Micro-Quartz) Dyna-Flex 6.0 2800 Dyna-Flex was selected because it was the only insulation material that _s_sf_ed the requirements for the application. Micro-Quartz does not satisfy the maximum temperature requirement for this program (about 2000°F), and Dyna- Quartz is brittle and therefore has doubtful resistance to vibration loads.

Thermal conductivity of Dyna-Flex is shown in figure 4-20.

4-8 REFERENCES 4-1 Plank, P. P. : Hypersonic Thermal-Structural Concept Trends. SAE paper 660678, October 1966.

4-2 Lemco% M. M.,; and Trevin% Jr., A.: Determination of the Effect of Elevated Temperature _terial Properties of Several High Temperature Alloys.

ASD-TDR-61-529, June 1962.

4-3 Lockheed California Company, Advanced Material Handbook, LR 18456, December 1964.

4-4 Stein, B. A.; and Vickorek, G.R.: Results of Current Studies on Coated Alloy Sheet at NASA Langley Research Center, July 1967.

4-5 DMIC Report 153: Physical Metallurgy of Nickel Base Superalloys, Battelle Memorial Institute, Defense Metals Information Center, May 1961.

4-6 DMIC Report 214: Oxidation of Nickel-and Cobalt-base Superalloys, Batelle Memorial Institute, Defense Metals Information Center, March 1965 4-7 TD NiCr Data based on information supplied by E. I. DuPont Nemours & Co., 4-8 MIL-HDBK-5: Metallic _aterials and Elements for Aerospace Vehicle Struc- tures, December 1968.

4-9 High Temperature High Strength Alloys_ American Iron and Steel Institute_ Feb 1968.

4-i0 Tensile and Creep Properties of .010 & .050 in. Ren@ 41 Alloy Sheet from RT to 2000°F, The _rquardt Corp., Report PR 281-IQ-I, AF 33(657)-8706, Sept 1962.

h-9 TABLE 4-1 CANDIDATE MATERIALS FOR HYPERSONIC WING STRUCTURET Wing Leading Temp. structural Candidate candidate material materials Remarks range applicat ion To Cobalt base Annealed material with moder- Wing surfaces_ 1800°F primary alloy: ate tensile properties; good oxidation resistance to structure_ Haynes 25 Haynes 25 heat shield Nickel base i8ooC_ alloy: Inco 625 Inco 718 Hastelloy X Rene p 41 Rene441 Fair weldability_ but excel- lent in all other aspects.

TDNickel Primary structure: 1600°F; heat shields; 1800°F TD NiCr TD NiCr Candidate uncoated material for brat shield application 1800 ° - Lower wing Chrome 30 2500°F surface TD Nickel TD NiCr TD NiCr Candidate uncoated material leading for heat shield and leading edge_ and heat shield edge application to 2200°F Co lumb ium Alloy: Cb-752 Candidate for leading edge application to 2500°F. Moder- D-43 B-66 ately high mechanical proper- FS-85 ties preferred. Coating sys- C- 219Y tem is a fused slurry silicide (Si-20 CR-20 Fe) Cb-752 2500 ° - Leading edge Tantalum 3500°F alloy: Moderate - "_-- _ -" _ 90Ta -10W" 90Ta -10W Lueu_=_±_=_ proper- ties; very good with respect to fabricability. Requires T-222 oxidation protective system h-10

TABLE 4-2

/ MECHANICAL PROPEF_I_ OF REBIE 41 MATERIAL a Rene'41 sheet and strip (1400°F aged); t _ 0.187 inches FO -7 E c n ksi Fcy Temp • u F Basis 106 psi ksi

Grain (b) (b)

L A 75 25 134.5 31.6 135.0 141.0 T A 75 25 i40.7 31.6 140.0 L B 75 25 139 -7 31.6 T B 147.0 75 25 147.0 31.6 24.6 1200 L A 129.6 15 130.7 24.6 1200 T A 15 i37.0 135.4 B 1200 L 24.6 134.4 15 135.9 B 24.6 141.i 1200 T 143.2 A 1400 io8.1 22.8 108.0 L 22.8 112.8 1400 T A 15 i13.3 14oo L B 112.4 22.8 112.0 14oo B 118.4 22.8 117.6 T 15 81.0 L A i0 79 -3 20 "9 84.6 A i0 T 83 -3 20.9 i5oo i0 82.6 84.0 L B 15oo 20.9 B 88.2 T i0 87.2 1500 20.9 16oo L A i0 58.0 55.8 17.7 6o .6 1600 T i0 A 58.5 17.7 60.2 16oo L i0 B 58.1 17.7 i600 T i0 B 61.3 17.7 63.2 aReference 4-3.

bRamberg Osgood Parameters, NACA-TN 902.

h-ll

TABLE 4-3

DESIGN PARAMETERS FORHAYNE_ 25 (L-605) SHEET AT ELEVATED TEMPERATURE a

Material Thickness m n F0. 7, E c, Fcy, Temp ins. F ksi 10epsi ksi O. 020 - Room L B 9 3o.82 34.20 37.o0 Haynes 25 solution 0.187 T B 9 55.09 3LL.20 62.00 treated 1200 21.8_ 24.60 25.40 L B 11 sheet

(5-6o5) T B 34.42 24.6o 38.4o

21.72 23.9o 25.20 1300¸ L B T B 32.o5 23.9o 35.9o 21.08122.6o 2b,.4o, 14oo L B 11 T B 29.28 22.60 32.90 1500 L B lO :6.77 20.9O 20.00 T B i0 26.12 20.90 29.80 1600 13.89 18.80 16.7o L B i0 T B iO 22.72 18.8o 26.0o 27oo L B 8 _.8_ 16.8o 15.0o T B 8 ].9.88 ].6.8o 23.6o 28oo ].o.92 14.00 1_.1o L B 7 T B 7 16.9o 14.00 20.50 aReference 4-3.

4-12

TABLE 4-4

D_IGN PARAMETERS FORTD NiCr SHEET AT ELEVATED TEMPERATURE

Material Condition

Ec_ Fcy_ Temp. ._ ._ n FO •7'

°F 8 ksi ksi

106 psi 21.0 74.0

TDNiCr Long life Room T A i0 71.7

@ 2000°F

dispersion

68.o 5oo T A 1o 65.8 19.5

strengthened exposure

i000 T A i0 49.5 17.3 52.o

DuPont

Ni-2OCr-2ThO 2 24.0 1500 _ A lO 21.7 12.7 16.0 1800 T A i0 14.4 9.0 12.0 2000 T A !0 10.7 7.0 8.0 2200 T A i0 7.0 5.5 6.0 24OO T A i0 5.2 5.0 62.6 T A 21.0 Room lO 59.6 Long life @ 2200°F T A i0 54.6 19.5 57.5 5oo exposure i0 41.0 i000 T A 17.3 43.9 20.1 T A i0 17.8 12.7 18oo T A i0 Ii. 7 9.0 13.3 2000 T A i0 8.7 7.0 9-9 2200 T A 1o 5.6 6.5 5.5 !o 4 .o 4.8 2400 T A 5.0 aEstimated.

h-13 TABLE 4-5 MATERIAL MINIMUM GAGE FOR STRUCTURAL CONCEPTS Min. Thickness_ Element Structural concept in.

Monocoque panels Skin Waffle grid .020 015 _a) Stiffened plate Stiffener 0 ° x 90o and 45 ° x 45 ° Skin (exterior) .o15 Honeycomb-core .010 Sandwich plate Skin (interior) .002 Core Truss-core Skin (exterior) .015 •010 Sandwich Skin (interior) •oo6 Core Semimonocoque panels Skin .O10 Tubular Skin Beaded .o15 Skin .o15 Trapezoidal Corrugation Skin (exterior) .o15 C orrugat ion-st iffened skin .010 Skin (interior) Convex beaded .o15 Skin (exterior) .010 Skin (interior) Ribs & spars .O3O Caps Flanged sheet metal Webs .o15 Corrugation Heat shields ii Skin .010 Corrugation Skin (exterior) .015 Dimpled stiffened .O10 Skin (interior) Skin .O10 Modular aThese gages applicable to bonded construction.

O- E ID I--" r/l .rt ID q,,l

/

L

.r--I m _ CO _ o q,,l

_3 lO

i"-.

°- IO Z !

I 1 ,_Q !

t3 I-- 0', t- .r-t

\

/

',0 0 • u! zd/nl::J 'sseJ.IS _,llSUa.l a4otu!41n pa4osuadtuoo-X4!sua(] 5 x 105 E U . 4 Ren_ 41 -0 °_ o

.%

_ ,,-TD NiCr 1 Cb 752 _F fTa-10W 500 1 000 1500 2000 2500 3000 3500 Temperature _ OF Figure 4-2. Density compensated compressive yield stress vs temperature of candidate high temperature materials k-16 .0005 ! I p "" density, Ib/in 3 q = plasticity reduction factor E c = compression modulus of elasticity, Ib/in 2 .0004 fc = compression stress, Ib/in 2 HAYNES 25 1200°F 1300°F 1400°F Rene" 41 / .0003 W u o.

1400°F / 1300°/ i .0002

//./

.0001 200°F 140 X 103 0 20 40 60 80 1 O0 120 fc ' ps i Figure 4-3. Compression loads vs weight index for Reng 41 and Haynes 25 [_-17 I

I

10 X 10 ..6 -- I f Haynes 25 Rene t 41 . I ..... _162.5 _ _ .__ __._.---Cb -752 J f 90 Ta -10W f I 800 1200 1600 2000 2400 2800 3200 0 4OO Temperature, OF Figure 4-4. Coefficient of thermal expansion vs temperature of candidate materials 5O f 90To- IOW.--_ 4O f I"-" J J "_Cb 752 f I f 3O f £N I'" J TD NiCr 7' ReneW41 Inconel 625

J

E I I I I I I I I I I I 0 400 800 1200 1600 2000 2400 2800 3200 3600 4000 Temperature, OF Thermal conductivity vs temperature of candidate materials Figure 4-5.

L-18 .28 .24 .20 o = J .12

, j

UQ'. ______/ _" TD NiCr J 90Ta - lOW { 0 400 800 1 200 ! 600 2000 2400 2800 3200 3600 4000 Temperature, OF Figure 4-6. Specific heat vs temperature of candidate materials 4-19 [ 1.0 Cb 752 90Ta - 10W J

J

Rene 41 .8

lJ

J Haynes 25 / '_TTD NiCr °6, .4 All specimens pre-_ox[dized .2 prior to test 0 .400 800 1200 1600 2000 2400 2800 Temperature, OF Nmissivity vs tamperature of candidate materials ¥i_o_re 4-7.

I !

40 X 106 _. 32 _/L Rene j41 ' 3200 ' 400 800 1200 1600 2000 2400 2800 Temperature, _F Figure 4-8. Compressive modulus of elasticity vs temperature of candidate high temperature materials 4-20 ...._i .,i --_'_ X ,0 ,-t I o _- +_ Oh 0 ._ !

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N C_ '3 'X!°!_s°13 JO snlnp°w ._'uV91 k-21 ! | n !

Materlal: Rene"41 = 170 ks| min) (FtuRT Specimen: Kt = 4.0 Procedure: Axial loading

IT°140°°FI I I

5O 4O "o 30

20 " __ '0_ ""-

I I 0 10 20 30 40 50 60 70 80 90 100 Mean stress, Fm, % Ftu at room temp Figure 4-10. Constant life diagram, Rene' 41 (Kt = 4.0) - 1400°F 4-22 __ Rene' 41 sheet material - (aged at 1400°F) 40-- -Temperature = 1300°F-

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Rene" 41 at 1300°F 4-23 c_ _0 o "_.,q ! "F o 00_'/.

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C,c,e,o,, a,m_phore/

2100 2200 2300 2400 2500 2600 2700 2800 Temperature, °F _lOn __ l-lf_ -- Ch-7S_ .2O Density = 6 Ib/cu ft Atmospheric pressure • .16

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I I IOO0 2O00 Mean temperature, oF Figure 5,--20. Effective thermal conductivity vs temperature -- Dyna-Flex (atmospheric pressure) 4-28

Next: Section 5 →

Section 5

Section 5 MATERIAL AND PROCESS DEVELOPMENT TESTING by K. A. Wilhelm_ R. C. Dickason_ J. J. Panik_ I. F. Sakataj J. W. Lewis_ R. S. Jusko_ R. Schwartz_ and C. B. Stuhlman 5-i CONTENTS Page MATERIAL SCREENING TESTS 5-1 5-1 Material Screening Test Plan Description of Tensile Specimen 5-1 Tensile Test Setup and Procedure 5-1 5-1 Tensile Properties, Oxidation, and Thermal Stability Test Results Metallurgical Examination 5-2 Emittance Test Results 5-3 5-4 T,_i_g _ _i_ JOINT EVALUATION 5-5 Test Plan 5-6 5-7 Description of Specimens 5-7 Specimen Fabrication and Joining Techniques 5-9 Test Setup Equipment and Procedures FORMABILITYTESTS 5-11 5-ii Room Temperature Bend Tests 5-12 Room Temperature FlangingTests 5-12 Room Temperature Draw Forming Tests 5-13 Room Temperature Stretch Beading Tests 5-iii TABLES Page 5-15 Material screening test plan 5-16 Mechanical properties tests of thermally exposed materials 5-20 Thermal exposure schedule for TD NiCr tensile specimens Thickness of surface oxide on TD NiCr specimens after 5-21 thermal exposure 5-22 5-5 Leading edge test data 5-23 5-6 Leading edge calibration data 5-24 5-7 Leading edge model test data 5-25 5-8 Leading edge temperature-time histories 5-28 5-9 Joint evaluation test plan 5-29 5-1o Summary of lap joint test data lap joint test data for 0.015 Ren_ 41 5-3o 5-11 5-33 5-1e lap joint test data for Haynes 25 5-34 5-13 Summary of TD NiCr lap joint test data 5-35 5-14 lap joint test data for TD NiCr 5-36 Sunmary of spot tension test data 5-15 Spot tension test data for .015 Rene 41 5-37 5-16 5-39 5-17 Formability evaluation plan _-V ILLUSTRATIONS Page 5-_ Standard one-inch gage length tensile specimen 5-41 Room temperature tensile test arrangement showing combined pin and friction clamp specimen attachment Overall view of room temperature tensile test arrangement Typical room temperature tensile stress-strain curves for .016 Haynes 25 5-43 5-5 Typical room temperature tensile stress-strain curves for •015 Reng 41 5-44 5-6 Typical room temperature tensile stress-strain curves for .0i0 _ NiCr 5-45 5-7 Typical room temperature stress-strain curves for •030 TD NiCr Reng 41 "as received" 5-46 5-8 Reng 41 after 500 hours at 1200°F 5-46 ........................ 5-9 5-47 Rene' hl after 1O00 hours at 1200°F 5-Io Ren_ 41 after 250 hours at 1500°F 5-47 5-11 Ren_ 41 after 500 hours at 1500°F 5-48 5-m_ Ren_ 41 after 750 hours at 1500°F 5-48 5-13 5-14 Ren_ 41 after lO00 hours at 1500°F 5-49 5-49 5-15 Haynes 25 "as received" 5-5o 5-16 Haynes 25 after lO00 hours at 1200°F Haynes 25 after 750 hours at 1500°F 5-5o 5-17 Haynes 25 after 1000 hours at 1500°F 5-18 5-51 5- vii ILLUSTRATIONS (Cont.)

Page Photomicrographs showing the longitudinal (upper) and 5-52

5-19

transverse (lower) microstructures of the "as received" TDnickel-chronium specimen 33-1 5-53

5-20 Photomlcrographs showing longitudinal views of TD nickel-

chromium tensile test specimen 33-9, unetched and etched; exposed lO00 hours at 1500°F. Surface oxide measured 0.0002 inch 5-54

5-21 Photomicrographs showing transverse view of TD nickel-

chromium tensile test speclmen 33-9, unetched and etched; exposed lO00 hours at 1500°F. Surface oxide measured 0.0002 inch 5-55

5-22 Photomicrographs showing longitudinal views of TD nickel-

chromium tensile test speclmen 33-B, unetched and etched; exposed 750 hours at 2000°F. Surface oxide measured 0.0002 inch c 09 5-56 _÷_ _n_h_ _hn_ing t_ansverse views of TD nickel- j- _j chromium tensile test speclmen 33-13, unetched and etched; exposed 750 hours at 2000°F. Surface oxide measured 0.0002 inch 5-24 5-57 Photomicrographs showing longitudinal views of TD nickel- chromium tensile test speclmen 33-15, unetched and etched; exposed lO00 hours at 2000°F. Surface oxide measured 0.0002 inch 5-58 5-25 Photomicrographs showing transverse views of TD nickel- chromium tensile test speclmen 33-15, unetched and arched; exposed i000 hours at 2000°F. Surface oxide measured 0.0002 inch 5-26 5-59 Photomicrographs showing longitudinal views of TD nickel- chromium tensile test speclmen 33-16, unetched and etched; exposed 500 hours at 2200°F. Surface oxide measured 0.0003 inch 5-60 5-27 Photomicrographs showing transverse views of TD nickel- chromium tensile test speclmen 33-16, unetched and etched; exposed 500 hours at 2200°F. Surface oxide measured 0.0003 inch %-viii

ILLUSTRATIONS (Cont.)

Page

5-28 5-61 Photomicrographs showing longitudinal views of TD nickel-chromium tensile test specimen 33-19_ unetched and etched; exposed 750 hours at 2200°F. Surface oxide measured 0.0003 inch 5-29 Photomicrographs showing transverse views of TD nickel- 5-62 chromium tensile test specimen 33-19, unetched and etched; exposed 750 hours at 2200°F. Surface oxide measured 0.0003 inch 5-30 Photomicrographs showing transverse views of TD nickel- 5-63 chromium tensile test specimen 33-21_ unetched and etched; exposed 1000 hours at 2200OF. Surface oxide measured 0.0005 inch 5-31 Photomicrographs showing longitudinal views of TD 5-64 nickel-chromium tensile test specimen 33-21, unetched and etched; exposed 1000 hours at 2200°F. Surface oxide measured 0.0005 inch 5-32 Photomicrographs showing the longitudinal (upper) and 5-65 transverse (lower) microstructures of the "as received" TD nickel-chromium specimen 30-1 5-33 Photomicrographs showing longitudinal and transverse 5-66 views of TD nickel-chromium tensile test specimen 30-8j unetched and etched; exposed lO00 hours at 1500°F. No surface oxide was in evidence 5-34 Photomicrographs showing longitudinal and transverse 5-67 views of TD nickel-chromium tensile test specimen 30_14_ unetched and etched; exposed 1000 hours at 2000°F. Sur- face oxide measured 0.00005 inch 5-35 5-68 TD Nickel-chromium specimens and fire brick support after 750 hours at 2200°F. Note the two O.O10-inch thick specimens at lower portion of the photograph 5-36 Sectional photomicrograph through O.010-inch thick 5-68 specimen 33-2 (illustrated in figure 5-35.)

5-37 TD nickel-chromium specimens after I000 hours at 2200°F. 5-69 Upper photograph shows specimens in notched TD nickel- chromium supports held in a grooved high-purity aluminum oxide base. Lower photograph illustrates the extent of the surface oxide on the tensile specimens 5- ix ILLUSTRATIOn, S (Cont.)

Page 5-38 Temperature calibration apparatus 5-70 5-39 Specimens- emittance test 5-71 5-40 Emittance data for Haynes 25 (L605) 5-72 Emittance data for Rene r 41 5-41 5-73 5-42 Emittance data for Co 752 with R512E fused silicide 5-74 coating 5-43 Emittance data for 90Ta-10W/R512C 5-75 5-44 Emittance data for TD NiCr 5-76 5-45 Leading edge test specimens --porous 90Ta-IOW 5-77 (50% density) sintered to .040 in. 90Ta-10W substrate 5-46 5-78 As coated microsection through porous metal leading edge

5-47

90Ta-IOW/R512C sheet leading edge concept 5-79 5-48 Reduced pressure plasma jet facilities 5-79 5-49 Sheet 90Ta-10W/R512C test speclmen (3100°F application) 5-80 5-5o Porous 90Ta-IOW/R505 test speclmen (3100°F application) 5-81 5-51 Porous 90Ta-IOW/R505 test speclmen (2800°F application) 5-82 5-52 Sheet 90Ta-10W/R512C test speclmen (2800°F application) 5-83 5-53 Porous 9OTa-IOW/R505 test specmmen (2800°F application) 5-84 5-54 Sheet 9OTa-IOW/R512C test specmmen (3000°F application) 5-85 5-55 Leading edge plasma arc test results 5-86 5-56 Resistance spotweld and diffusion spot bend lap joint 5-87 specimen configuration 5-57 Riveted lap joint specimen configuration 5-87 5-58 Brazed lap joint specimen configuration 5-88 p-X ILLUSTRATIONS (Cont.)

Page 5-88 5-59 Resistance spotweld and diffusion spot bend tension specimen configuration 5-89 5-60 Electron beam weld tee joint specimen configuration 5-89 5-61 Electron beam butt weld joint specimen configuration 5-90 5-6_ Typical elevated temperature lap joint test arrangement 5-63 5-91 Typical room temperature setup for riveted joint test 5-64 5-9e Typical spot tension test setup 5-93 5-65 Room temperature bend coupons 5-93 5-66 Room temperature flange forming test coupons -- shrink 5-94 5-67 Room temperature flange forming test coupons -- stretch 5-94 5-68 Room temperature draw from test coupons -- cupping 5-95 5-69 Room temperature bead from stretch test coupons -xi

SYMBOLS

Second radiation constant

C2

Apparent modulus of elasticity Ultimate tensile strength

Ftu

Tensile yield strength

Fty

I

Current in Amperes

i

Distance between potential leads Radius

R,r

RT

Room temperature

S

Spectral or apparent

T

Temperature; temperature of blockbody

V

Voltage drop between potential leads Hemispherical total emittance Cht ( Normal spectral emittance at the measured wave length nX X Wave length (y Boltzmann's radiation constant 5- xiii

Next: SECTION 5 →

SECTION 5

MATERIAL AND PROCESS DEVELOPMENT TESTING

MATERIAL SCREENING TESTS

Material Screening Test Plan

Table 5-1 outlines the material screening test program performed in sup-

port of this contract. Existing data_ supplemented by data generated under

this test plan_ were used in establishing the design allowables used in the

final analysis.

Description of Tensile Specimen

Room and elevated temperature tensile properties of exposed Ren_ 413

Haynes 25 and TD NiCr material alloy systems tensile coupons were machined

to obtain mechanic_] prnpprties data in the transverse _rain (or transverse

to the rolling) direction.

Tensile Test Setup and Procedure

Mechanical properties data for the exposed material alloy systems were

determined using accepted standard laboratory testing procedures and equipment.

A 5000-pound capacity Baldwin Universal Testing Machine (in compliance with

ASTM E-4 designation) and a Baldwin B3M Differential Transformer Extensometer

(in compliance with ASTM E-83 and E-21 designations for calibr_tion_ accuracy, and attachment) were used to obtain autographic tensile load-strain curves.

The tensile tests were conducted at a head separation rate equivalent to a

straining rate of 0.000,5 in./in, per minute. Figure 5-1 is a standard one-inch

gage length tensile specimen. A typical tensile test arrangement is shown in

figures 5-2 and 5-3. The method of gripping the tensile specimen shown includes

combined pin and friction clamp attachment at the specimen ends.

Tensile Properties_ 0xidation_ and Thermal Stability Test Results

Tensile test data for Ren_ 41_ Haynes 25_ and TD NiCr, including the

effects of thermal exposure on these materials_ are presented in table 5-2.

5-1

These data reflect room temperature tests of solution heat-treated (annealed)

material after exposure to the environment indicated. The normal aging

response of annealed Ren@ 41 and Haynes 25 is noted with a sharp increase in

strength_ followed by a drop in strength indicating an overaged condition.

The apparent moduli presented are the "best fit" of the autographic load-

deflection curves. It is obvious that Ren@ 41 is the most favorable material

to satisfy the elevated temperature strength requirements of this program.

It is also obvious that Ren4 41 must be aged after fabrication to provide

predictable allowables required for design. Typical tensile stress-strain

curves for Haynes 25 and Ren4 41 after i000 hours static exposure at 1500°F

are shown in figures 5-4 and 5-5.

The tensile test data for TD NiCr, presented in table 5-2_ were determined

at room temperature after exposure to the indicated thermal environments. The

0.2 percent offset yield strengths reported were determined from the autographic

load strain curves using a room-temperature modulus value of 22 x 106 psi.

Typical tensile stress-strain curves for 0.010 and 0.030 gage TD NiCr for

various exposure times and temperatures are shown in figures 5-6 and 5-7.

Metallurgical Examinat ion

Figures 5-8 through 5-18 show microsections of Ren4 41 and Haynes 25

before and after static thermal exposure at ±_uu _ a_,d ±juu • ±_ _=_

times. It is noted that these data agree well with published data (ref. 5-I).

The Ren6 41 specimens exposed at 1200°F did not show any appreciable amount

of oxide penetration. However_ Ren6 41 specimsns exposed at 1500°F for periods

up to i000 hours showed evidence of intergranular oxidation and apparent alloy-

depleted areas. The Haynes 25 specimens showed a negligible effect due to

thermal exposure at 1200°F and 1500°F for periods up to i000 hours.

The TD NiCr tensile coupons were exposed to temperatures of 1500°F,

2000°F_ and 2200°F for 500_ 750 and ]000 hours as indicated in the schedule

shown in table 5-3. After thermal exposure_ the specimens were tested in

tension_ and representative coupons were selected for metallographic section-

ing in both the longitudinal and transverse grain directions. The depth of

the oxide surface contamination due to the thermal exposure was measured.

These data are presented in table 5-4. Photomicrographs depicting the con-

dition of the TD NiCr after exposure at 1500°F_ 2000°F_ and 2200°F are pre-

sented in figures 5-19 through 5-34.

During the thermal exposure of the TD NiCr specimens at 2200°F, a fluxing

reaction between the coupon and the support rack (high temperature fire brick)

was noted (see fig. 5-35)- A chemical analysis (ref. 5-2) was made to deter-

mine the composition of the material at the area of contact between the coupon

and the support rack. The results of the chemical analysis indicated that the

contaminated area of the TD NiCr specimen exhibited a loss of 4 percent

chromium_ whereas the contaminated area of the fire brick exhibited an increase

of 3 percent chromium and a depletion of 5 percent aluminum and 2 percent silicon.

5-2

Metallurgical analyses of specimen sections taken through the areas in contact

with the brick indicated the affected area to be approximately 50 percent of

the original thickness of the material (see fig. 5-36).

An alternate heat treat rack was constructed using high purity aluminum

oxide (A1203) as the base and TD NiCr as the specimen support. This rack was

used to continue the thermal exposure of the 0.010 in. thick TDNiCr specimens

at 2200°F for 750 and i000 hours. Visual examination of the rack and specimens

after thermal exposure disclosed somediscoloration of the rack base and that

a che_calreaction had taken place in the tensile coupon grip area (see fig.

5-37). Note that the contamination in the grip area extended approximately

2 inches b_yond the point of contact between the specimen and support.

Emittance Test Results

Spectral (6500°A) and total hemispherical emittance data were obtained as

a part of this study by Marquardt Corporation over the temperature ranges indi-

cated in table 5-1.

The M_rquardt test apparatus_ figure 5-38, uses the hole-in-tube or

indirect methodof measuring spectral (6500OA)and total hemispherical emit-

tance s_ _orib_ in reference 5-3. The specimen material is formed into a

long, thin walled tube per Marquardt drawing X21182 (figure 5-39). A small

hole is drilled through one wall of the tube near the center for optical

viewing. Water cooled copper electrodes are clamped at each end of the tube

for resistance heating to the desired temperature. Tvo 0.Ol0-inch diameter

wires are spotwelded to the tubej 0.020 inch apart opposite the small hole_

to act as voltage probes. The preoxidized sample is placed inside a bell jar

with optical quality quartz parts for optical temperature measurements. The

bell jar is then evacuated to the indicated partial pressure prior to two

stabilization runs (at maximum temperature) before any optical measurements!!

are recorded. The blackbody temperature is measuredthrough the small hole in

the tube with a calibrated automatic photomatic pyrometer. Sighting the

pyrometer on the outside of the wall of the tube will give the apparent tem, perature_ which is a function of the emittance of the outer wall.

The following relationships were used to obtain the normal spectral

emittance at 6500°A:

in _nk k

where: E

= the normal spectral emittance at the measuring wave length

n k

= the second radiation constant

C2

5-3

the wave length at which the detector measures (in microns)

the blackbody temperature (K)

T =

S =

the spectral or apparent temperature (K)

k

The total hemispherical emittance will be calculated from the

relationship:

= _ _ T 4

IV

ht

2wrl

where :

I = current through the tube (amperes)

V = voltage drop between potential leads (volts)

r = the radius of the tube (cm)

i = the distance between potential leads (cm)

c ht

O- = Boltzmann's radiation constant

T : the blackbody temperature of the tube (K)

The emittance curves for the tested materials are shown in figures 5-40

through 5-44. It should be noted that the emittance curve for 90Ta-IOW/R512C

material system does not reflect the maximum test temperature as indicated in

table 5-1. This was due to an interruption of voltage control through the

attached probes by eutectic melting (alloy formation between free silicon and the

voltage probes). Several runs were mad% using various contact probes

(including Ta). All results were identical. The chemically aggressive free

silicon in the coating reacted with the probes_ resulting in a loss of voltage

control to the specimen.

Figure 5-44 is the total and spectral emittance of preoxidized TD NiCr.

It is well to note that this data is comparable with emittance data published

on TD Ni but does not agree with data published on TD NiCr contained in

reference 5-4.

Leading Edge Testing

Two leading edge concepts were fabricated and tested in a plasma arc

under simulated flight conditions.

5-4

Porous metal concept.- The first concept3 a 50-percent dense porous

powder metallurgy product of 90Ta-!0W was sintered to a O.040-inch thick

90Ta-10W backing sheet to which a 90Ta-IOW tube was electron beam welded to

facilitate attachment to the fixture. A protective coating of Sylcor R505

(AI-25Sn) was applied to the assembly and vacuum fired at 1900°F for one hour.

The coated assemblies are shown in figure 5-45. One additional specimen was

fabricated and sectioned after coating to observe coating penetration by

destructive testing. Figure 5-46 illustrates the general structure of the

impregnated porous leading edge sample. The upper photomicrograph shows the

AI-Sn alloy on the surface with the aluminide below it and the infiltrated

porous 90Ta-IOW below the aluminide. The lower picture shows a portion of the

infiltrated 90Ta-IOW and the substrate.

Sheet concept. - The second concept fabricated and tested was a sheet

leading edge specimen disilicide coated with Sylcor R512C (Si-20Ti-lOMo) coating.

This coating was diffused in vacuum at 2580°F for one hour. A typical example

of this concept is shown in figure 5-47.

Element testing facility°- The plasma arc test facility at Space General

Corporation (fig. 5-28) was selected to evaluate the two leading edge concepts

under simulated flight conditions. The test facility projected a supersonic

(Mach 2.5)_ hyperthermal environment that was accurately controlled. A 3-inch

nozzle was used to input a gas flow of 79-percent nitrogen and 21-percent

oxygen.

Test plan.- The following test plan was formulated for evaluation of the

two leading edge material system concepts (porous and sheet) for cyclic

conditions of temperature to determine the failure point of each material_

coating system at specific levels of temperature. Six-minute cycles were

selected to correspond with earlier work performed at the NASA langley

Research Center (ref. 5-5).

Test I

a. Heat to 3100°F within 30 seconds

b .

Stabilize temperature and hold for 6 minutes

C. Cool for i0 minutes (to approximately 300°F)

Repeat a through c until visual indication of failure

is observed

Test 2

a. Heat to 2800°F within 30 seconds

i ........ _7 "_ 7

b. SLabilize _empera_u±_ _iu_a for 6 minutes

c. Cool for 10 minutes (to approximately 300°F)

d. Repeat a through c until visual indication of failure is

5'5

Test results.- A summary of test results_ identified by model number

coating system_ and pertinent test data_ are given in table 5-5. A detailed

history of all test parameters is given in tables 5-6 through 5-8.

The results indicate that adequate oxidation protection at 3100°F is not

practical with either of the concepts tested, whereas limited oxidation pro-

tection is offered at 3000OF utilizing the sheet 90Ta-IOW/R512C concept (37

six-minute cycles). Although the porous metal concept failed after 12 six-

minute cycles at 2800°F, there were indications of improvements (factor of

two) over previously tested concepts. The mode of oxidation that occurs in

the porous 90Ta-IOW/R505 concept produces considerable local hot spots.

Failure is a combination of progressive Ta oxidation and thermal stress.

The sheet concept did not fail after 37 six-minute cycles at 2800°F.

Figures 5-49 through 5-54 are photographs of the two leading edge concepts

before and after cyclic thermal exposure. A comparison of similar tests con-

ducted by NASA (ref. 5-5) on a modified AI-Sn coating and those completed

under this contract are shown in figure 5-55. Although a direct comparison I

cannot be made due to the difference in stagnation pressures at the specimen-

jet interface_ marked improvements over previously tested concepts are indicated.

(The low pressure tests conducted at Space General are considered more severe

for coatings than those conducted at or near one atmosphere.)

^==_^_7 _÷_=_ ...... _a_ _n en attempt to upgrade the porous metal

concept by the impregnation of the porous material with a disilicide coating.

Results from Sylcor indicated that the R512C disilicide coating system is too

chemically aggressive to be feasible in this proposed application.

JOINTEVALUATION

Test Plan

Four representative joint-type specimens were selected for evaluation

which encompass those joints neededfor the design of subsequent test

components, leading edge test specimens, and representative hypersonic

wing structure components. The joint typesj methodsof joining_ materials, gages3 and test temperatures are outlined in table 5-9.

Description of Specimens

The resistance spotweld and diffusion spot bond specimenconfiguration

is shown in figure 5-56. The riveted lap joint specimen is shown in

figure 5-57- The brazed lap joint specimen is shown in figure 5-58. The

resistance spotweld and diffusion spot bond tension specimen is shown in

figure 5-59. The electron beamweld tee joint and butt joint specimens are

shown in figures 5-60 and 5-61. The fabrication and joining techniques for

these specimensare described below.

SpecimenFabrication and Joining Techniques

Lap joint specimens.- The lap joint specimens were made by shearing

2.0-in. by 4.0-in. coupons and l.O-in, by 2.0-in. doublers (as required)_

deburring_ cleaning#and packaging for joining.

The cleaning procedure consisted of:

Trichlorethylene degrease

Demineralized water rinse

Clean air dry

Chromic-sulfuric acid immersion

Demineralized water rinse

Clean air dry

Seal in polyethylene.

Rene t 41 aged specimens were aged after assembly. All coupons passed

X-ray inspection. Aging treatment consisted of heating in air to 1400°F,

I_-_U±_._.L_ at _i_e_o_r_ .... for 16 _ ...... _ .... _'-- "_ _ _ +_÷_

_..L _ ol_e._ _±±._ _ _._._ o_ room __.

5-7

iii¸ _._i_

Riveted lap joint coupons required O.125-in. and 0.188-in. diameter,

flush head rivets. These rivets were cold headed in plant from TD nickel

wire, due to unavailability of TD NiCr, as follows:

Fini shed

Wire diam., shank diam., Grip length_

Rivet size in. in. in.

i/8 0.123 - 0.1235 0.1245 - 0.1255 0.25

3/16 0.185 - 0.186 0.1870 - 0.1878 0.40

Head configuration - _20426

Rivets were formed from "as-received" wire_ annealed condition_ then

stress relieved after heading (2000°F for 5 minutes). Upsetting was accom-

plished in one-stroke squeeze riveter. Holes were drilled, countersun_ and

reamed before assembly using TI5 high speed steel tools.

Coupons and rivets were cleaned before assembly, white glove handled in

clean room and packaged after assembly in polyethylene bags. The cleaning

procedure used was outlined above.

Spot tension specimens_ - The resistance spotweld _n_ diffusion bond spot

tension joint specimens were made by shearing square coupons 2.0-in. by

2.0-in. and die piercing a 4-hole pattern.

Doublers (0.030 in.) were required to minimize deflection and to verify

tensile spot strength values. Doublers consisted of O.030-in. by 2.0-in.

square coupons with normal 4-hole pattern but with 3/8-in. diameter center

hole. These doublers were resistance spotwelded to the O.Ol5-in. gage coupons.

Aged specimens were made by aging (1400°F for 16 hours) after joining;

solution treated (annealed material) coupons were X-rayed before and after

aging.

Tee and butt joint specimens. - The electron beam welded 90Ta-IOW tee and

butt joint specimens were made by shearing coupons (i.0 in. by 12.0 in. and

4.0 in. by 4.0 in.). The cleaning procedure used was the same as that outlined

for the lap joint specimens. All welds passed X-ray inspection.

5-8

Test Setup Equipment and Procedures

Lap shear tests. - The lap shear joint specimens were tested at room and

elevated temperatures. A typical elevated temperature joint test arrangement is i

shown in figure 5-62. The room temperature setup was essentially the same. i

Both the room and elevated temperature joint specimens were loaded by means of

combined pin and friction gripping. A loading rate of 5000 pounds per minute

was used for these tests. Specimen test temperatures were achieved by means

of radiant heating (Tungsten filament quartz lamps_ type IO00T3/CL/HT_ and

gold plated reflectors_ Research Incorporated Type AU5-212). Power to the heat

lamps was supplied by a lO0-ampere, 4$O-volt Thermac ignitron power controller

unit. Chromel-alumel thermocouples were attached to the test specimens by

the capacitance discharge method. One control thermocouple was used to regu-

late the power to the radiant heat lamps for maintaining specimen test tem-

peratures. The remaining thermocoup!es were used for monitoring and recording

specimen temperature by means of a Brown strip chart recorder.

A typical test arrangement for the riveted joint specimens is shown in

figure 5-63. A Class B-I averaging differential transformer type ex_ensome_er

shown attached to the specimen for the purpose of establishing the joint

yield strength. The yield load for this specimen configuration was determined

by repeatedly loading and unloadingthe specimen to successiveiy greater iuad

levels until a permanent joint deformation of 0.005 in. was obtained. These

data were obtained from the reduction of autographic load-deflection curves

produced by a standard drum type recorder in accordance with the MIL-H-5

committee guidelines.

Spot tension tests.- A typical spot tension test setup is shown in

figure 5-64. The specimen is shown mounted in the compression bay of a

5000-pound capacity Baldwin Universal Testing Machine. The test fixtures_

located on either side of the specimen_ consist of a base and four posts

which apply a bearing load to the specimen face sheet opposite the test

fixture. This arrangement produces a tensile load at the weld located in

the center of the specimen. Test loading was applied at a rate of approxi-

mately 5000 pound per minute.

Joint test results.- A summary of the lap joint test data for Ren@ 41

and Haynes 25 material alloy systems is given in table 5-10. The values

listed in this table are an average of the results of five specimen tests.

A listing of each test specimen result is presented in tables 5-11 and 5-12

which show the scatter in the test data obtained for these two material alloy

systems.

A summary of the lap joint test data for TD NiCr is given in table 5-13,

and represents averaged values for five specimen tests per condition. A

listing of each test specimen result is presented in table 5-16.

I

5-9

The joint technique evaluation resuits_ shown in table 5-i0_ indicated

that higher joint strengths at elevated temperatures are possible for the

resistance spotwelded specimens than for the diffusion-bonded specimens.

X-ray inspection of the Ren_ 41 spots indicated crackfree welds; therefore_

resistance spotwelding was selected for use in panel fabrication of Ren6 41.

For the TD NiCr materials_ the riveted specimens provided the highest strengths

at elevated temperatures_ as shown in table 5-13.

5 -i0

FORMABILITY TESTS

Four types of forming tests were conducted to establish fabrication limits

for the manufacture of the panel element and structure designs. The forming

test schedule is outlined in table 5-17 and lists the materials_ gages_ test

conditions; and total number of tests conducted. A detailed description of

each of the forming tests is given below along with recommended procedures

resulting from these tests.

RoomTemperature Bend Tests

Roomtemperature bend coupons (fig. 5-65) were sheared to l.O-in, by

3.0-in. rectangular blanks. Edgeswere left as-sheared. Half of the coupons

were cut with length parallel to rolling direction of sheet; the other half

of the coupons were cut with length normal to rolling direction of sheet.

Bends were formed in conventional mechanical brake with strain rate control

using radius punch and open channel die. Each coupon was bent in two places

in opposite directions. Minimumbend radius_ effect of grain direction_ edge

and surface effect_ and spring back for each condition of forming were dete_-

mined_ as follows :

Punch radii - 0.010_ 0.015/ 0.031_ 0.045_ 0.061_ 0.O(6_ u.090_ 0.125 imch

Channel die width - punch diameter plus 2-1/2 times metal thickness

Channel die radii - 2-1/2 times metal thickness

Rate - from 0.05 to 1.50 in. per minute

Bend angle - Ii0 ° closed before spring back

Recommended Minimum

Material Gage_ Bend Radius

Alloy in. Lon_it udina ia Transverse b

Haynes 25 0.010 - 0.125 1.0 t 1.0 t

Ren4 41 0.010 - 0.025 1.5 t 1.5 t

Ren4 41 0.030 - 0.i00 2.0 t 2.0 t

TD NiCr 0.010 2.0 t 2.5 t

TD NiCr 0.030 2.5 t 3.0 t

Cb-752 0.010 - 0.060 1.5 t _ 2.0 t

Ta-IOW 0.010 - 0.O60 1.5 t 1.5 t

aNormal to rolling direction of sheet, bparallel to rolling direction of sheet,

All "good" bends were dye penetrant inspected_ sectioned_ and examined

for microscopic cracking at 120 x magnification.

5-II

Room Temperature Flanging Tests

Roomtemperature flanging specimens (figs. 5-66 and 5-67) were prepared

by shearing 3.50-in. wide strips, rough blanking contour_ drilling pin holes_

then trace milling final size shrink and strength flange coupons. All coupons

were cut so that bend would be parallel to rolling direction of sheet (trans-

verse bend). Forming was done on standard flanging tools madeof hardened

steel and with bend radii to match bend radii determined from bend tests.

Edges of coupon blanks were deburred but not polished. Forming was accomplished

using 3/8-in. thick Adipreme LD 167Aurethane elastomer vulcanizate sheet as

a cover, form blocks IC 31-4741-6703-115and -116 for tooling, and in a

41 kiloton, i0 ksi Verson-Wheelonforming press. Forming pressures ranged

from 4500 to 7500 psi. Couponswere photo gridded (0.i00 in. line spacing at

45 deg and 90 deg) before forming and elongations were measuredfrom inner _

mold line to edge of flange. Specimenswere prepared as follows:

Recommended elongation

limits,

Material Gage_ Bend percent

alloy in. radius Shrink Stretch

Ta-10W 0.010 - 0.060 1.5 t 1.5 14.0

_' 1,7 n nln n.np_ 7._ _-. 1.0 22.5

Rene r 41 0.030 - 0.060 2.0 t 1.5 30.0

Haynes 25 0.010 - 0.060 1.0 t 2.0 45.0

TD NiCr 0.010 2.5 t 1.0 10.5

TD NiCr 0.030 3.0 t 1.0 12.5

Room Temperature Draw Forming Tests

Coupons were made by shearing 2.5-in. by 2._-in. squares from sheet stock

(fig. 5-68). Corners were removed as required by hand shearing. Edges of

blanks were deburred. Draw forming results were obtained by L_ckheed Aircaaft

Corporation-modified Ericson cup tests. Previous values were substantiated

for single draw operations.

Summary of draw forming:

Material Gage_ Draw depth to

alloy in. blank diam. ratio_

Ta-IOW 0.010 - 0.030 90

Cb-752 0.010 - 0.0_0 80

RenJ 41 0.010 - 0.020 60

Rene' _i 0.025 - 0.030 80

Haynes 25 0.010 - 0.060 i00

_-!2

Room Temperature Stretch Beading Tests

Roomtemperature stretch beading test coupons were prepared by shearing

3.0-in. by 5.0-in. blanks, deburring edges, and forming by high pressure in

forming tool equipped with positive lock draw ring (fig. 5-69). Limits of

forming in annealed condition were established; parts were then interstage

annealed and second forming, third forming, and fourth forming stage limits

determined. Annealing was accomplished in two different methods. One method

involved encasing blank in a sealed stainless steel envelope so that annealing

in air furnace could be accomplished without oxidation of coupon; the envelope

was removed for final forming stage. A second methodutilized hydrogen

atmosphere bright annealing furnace (not a production facility). No appreci-

able forming differences between the two methodswas noted.

Forming - See room temperature flanging tests above.

Tooling - LC 31-4741-6703-117 (Tungsten carbide facing applied to provide

positive grip at interfaces under draw ring).

Summary of stretch beading:

Recommended total

Material Gage, No. of process max. elong._

anneals a

percent

alloy in.

Haynes 25 0.010 - 0.025 i 50.0

Haynes 25 0.030 - 0.050 i 58.0

Rene' 41 0.0!0 - 0.020 i 17.0

Ren_ 41 0.010 - 0.020 2 25.0

Ren@ 41 0.010 - 0.020 3 30.0

RenJ 41 0.025 - 0.030 i 20.0

Rene' 41 0.025 - 0.030 2 30.0

Rene' 41 0.025 - 0.030 3 36.0

D _

_ene 41 0 025 0.030 4 40.0

a 1950 ° - 1975°F - 15 minutes; cool to 1000°F within 3 seconds.

- ii

5-13

REFERENC_

5-1 Oxidation of Nickel- and Cobalt-base Superalloys, Battele Memorial

Institute, Defense Metals Information Center_ DMICReport 214, M_y 1961.

5-2 Metallurgical Service Lab. Reports 88270-i_ -2 and -3, August 19_ 1968.

Thermal Radiative Properties of Selected _terials. Battelle Memorial

5-3

Institute_ Defense Metals Information Center_ DMIC Report 177_ Volume i_

November 1962.

5-4 Dispersion-Strengthened Metal Structural Development. DAC 60647_

Douglas Missile and Space Systems. Interim Technical Report No. i_

i Feb to i Yay 1967 (Contract F33 615-67-C-1319, BPSN 7 (61136873-

62405334)).

Wichorek, Gregory R; and Stein_ Bland A. : Experimental Investigation of

5-5

Aluminide-Coated Ta-lOw for Heat-Shield Applications. NASA 'ii_ u-pp_._ ±_u_.

i!! i I_ q

5-14

b- 0% rq @

i

rl 0 P4 Oh 0,1 Lp_r_ L_Od 0q o

._ o _ 0

o (kl _4 u-x Od A ,--4 oo r-I E-_ ,,0 OO 0 O0 LP_Od 0 0 _OJ 0 tr-x r--I c_ o o _4 P_ E_ 0 o tr'x 0 o Cvl _0 [q o O0 u_ B b- w O0 H U% _ r-| r, _© (b 0 _l M) 0 0 Od b_ u--, u-, OO -M rf) _q M0 .H o _-I -, O t_ .__ o o -o m _q OO CO h'x E_ 0 r-I _d 0 0 _c; OO b'_ i.gx OJ Od b-- G 4 _

o

I .°

N r_ © ¢) 4o u3 B .H rC_ ,rl O 4_

g

-b_ @ U)

5-15

i pi!ii!!!!iii_

TABLE 5-2

HECHANICAL pROPERTIES TESTS OF THERMALLY EXPOSED MATERIALS

The rmal

E a

Gage _ Heat

exposure Ftu_ Fty_ _o elong.

Material

in. no.

ksi ksi (i in.) psi

hr I °F

29 x lo 6

•015 2490-6- As received 143 72 44

25o 12oo 192 148 is 29

5oo 2o4 158 12 29

750 203 157 14 30

3o

i000 I' 197 159 i0

1500 166 1!4 7 s9

25o

lO8 4 28

152 5oo

143 io5 4 32

75o

1000 102 2 3s

Rene 41

•060 TV361 As received 149 75 38 27

250 1200 188 150 i0 30

500 197 152 9

75o 189 162 4 33

i000 I' 191 162 6 31

134 5

1500 179 25O

131 2 35

5OO

123 3 33

75o

120 2

i000 31

I 157

\ f_

5 -16

TABLE5-2. - Cont inued

MECHANICAL PROPERTIES TESTS OF THERMALLY EXPOSED MATERIALS

Thermal

Heat

Gage_

Ea._ exposure Ftu, Fty _ _ elong.

Material

in.

nO. psm

hr oF ksi ksi (i in.)

36 X lO 6

•016 B16506 As received 139 71 34

114 85 i0 33

25O 1200

5OO 119 97 6 32

132 114 4

75o

i000 'I

133 117 4 31

119 94 9 37

25o 15oo

5OO 113 72 4

121 76 4

75o

i000 "

126 75 5 35

As received

15l 75 36 33

• o3o 51795

250 1200 115 7 35

128 8

5OO 99 33

14o

75O 117 5 37

148 126

i000 I'

3 32

25o 15oo 79 13

154 83 34

5oo

83 33

75o 152

1000 _

15o 89 5 36

As received 69 32

86 18

250 1200 131

5OO 132 98 7 33

124 4

75O 35

1000 143 36

• UOU ±OO-O-

250 15oo 125

132 32

5oo 79

78 31

75o 13o

3i

looo 1 79

13o

5 -17

TABLE5-2.- Continued

MECHANICAL PROPERTIES T_STSOF THERMALLY EXPOSED MATERIALS

Gage_ Heat Ea_ Coupon

Thermal Ftu _ Fty _ ¢ elong.

Material

in. no.

exposure ksi ksi (i in.) psi no.

hr oF

22xi06 33-i

As received 132 87.7 14

I-2

As received 133 88.9 14

I-3

As received 133 88.3 14

I

-4

500 1500 126 87.6 14

500 126 87.3 17 -5

-6

750 122 83.0 16

--7

750 118 81.9 14

i000 122 84.0 15

i000 II 120 83.6 14

I-9

i-lO

500 2000 119 82.9 i0

500 114

82 -5 7

TD NiCr .010 2870

i:-12

66.7 5

75o zo8

73.4 9

75o zu8

-14

i000 102

72.9 5

i000 75.9 71 •2 NA -15

-16

115 71 •i i0

5OO

11.1 72.7 ! 9 a

5oo 113

86.6 48.2 6

X-3

75o

-4

92.1 51.4 12 a

75o

52.6 1o

75o 89.7 -5

!000 47.5 4 .o (z) -13

i000 81.3 43.6 9 I , -14

1 r

48 .o 4"

i000 -15

8o .9

aFailed outside specimen gage length.

5 -18

TABLE 5-2.- Concluded

MECHANICAL PROPERTIES TESTS OF THERMALLY EXPOSED MATERIALS

Thermal

Heat elong.

Ea _ Coupon

Gage_

Material

exposure

Ftu' Fty' (i in.) no.

in. no.

ksi ksi

psi

hr I oF

131 86.2 15 22xi06 30-I

As received

13o 85.o 1T I !-2

As received

132 85.8 16 I -3

-4

125.6 100.9 16

5OO 1500

5oo 124.2 81.3 17 -5

-6

75o 125.2 82.2 17

75o 125.2 81.8 19 ,:_-7

i000

126.8 82.4 19

i000 -9

126.9 83.9 17

-10

TD NiCr 2855 2OOO

5OO •O3O 125.5 79.9 19

-ll

124•7 80.1 18

5OO

I

75o 123.1 80.1 12

-12

7_u 123.8 79.2 17 - ,J-_.)

!

-14

i000

(b) (b) (b)

i000 (b) (b) (b)

:i-15

5oo T8.6 121;1 _-16

121.2 5oo 78.6 -17

-18

75O (c) (o) (o)

75O (c) (o) (c) -19

i000

(c) (c) (c)

It-21

i000 (c)

(o) (o)

bNo data - specimens failed during test.

CNo data - excessive degradation due to thermal exposure; specimens

impossible to test.

5 -19

TABLE5-3

THERMAL EXPOSURE SCHEDULE FORTDNiCr TENSILESPECIMENS

Specimen identification

Exposure time,

Exposure

Thickness,

Alloy

hrs

Temp., code in.

500 750 lO00 OF

0.010 33 33-6, 7 33-8, 9 15oo

33-4, 5

33-14, 15

33-10, ii 33-12, 13

33-16, 17 33-18, 19 33-20, 21

15oo

3o 0.030 30-4, 5 30-6, 7 30-8, 9

30-14, 15

30-10, ii 30-12, 13

22O0

a30-20 , 21

30-16, 17 30-18, 19

a '"

Specimens of O.030-in. thick material that were contaminated from the brick

supporting rack were not exposed at 2200°F for i000 hours.

5 -20

TABLE 5-4

THICKNESS OF SURFACE OXIDE ON TD NiCr SPECIMENS AFTER THERMAL EXPOSURE

Thermal exposure

Surface oxide

Spe_Smen

identiI'zeation thickness_

Time, Temp., in.

hrs oF

As received

33 -I

i000

1500°F 0.0002

33 -9

2000°F 0.0002

33-13

75O

i000 2ooo_ 0.0002

33-15

2200o'£

33-16 5OO

o.ooo3

2200°F

33 -19 Y5O o.ooo3

Iooo PP00°_

0.0005

33-PI

As received

30 -1

3o -8 i000 1500°F NIL

2000°F

i000

30 -14 0.00005

5 -21

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_o C_J (_ (NI

C_ .rt k.O k.O 0 c_ LO '_D

o_ LO

CO CO Cy_ co co co f'-I 0 CO Od C_ c_ (xJ C_ _d P_ 0 0 "d rd .H 4a E_ E_ Z)

5-34

TABLE 5-14

LAP JOINT TEST DATA FOR TD NiCr

Thermal Ult_mate load, ib/spot exposure Specimen Gage, in. Condition Heat No.

Method of joining identification 220_ F hr °F RT 20OO°F 37 33 None None 219 Diffasion •01o /_ealed 31-1 spot bond 285 53 36 31-2 22o 33 31-3 31-h 239 27 31-5 247 38 31 Avg

%3 93

•030 32-i 987 45 57 32 -2 92o 32-3 9o7 32 -4 933 95 32-5 Avg 520 49 35 •01o Brazed 33-i spot h65 63 33 -2 5{3 51 33-3 453 55 33-4 48O 43 36 33 -5 488 52 39 "% Avg 89 47

_5

34-i .o3o 11/2 13o 34-2 i152 131 53 34 -3 1163 27 34 -4 llO0 8_ 34 -5 1098 92 Avg Ult yield 89 7O 596 370 .o3o 35-1 Rivets 89 67 6O( 357 35-2 56( 375 79 35-3 61_ 352 35-h 60] 380 90 35-5 59( 367 73 Avg 1763 916 229 .o6o 38-1 222 167 1700 900 38-2 17c_ 933 169 38-3 209 185 17ce 925 38 -4 1767 900 924 176 38-5 220 176 1730 915 Avg 148 ]3_6 •OlO As 2862-1 Continuous 37-1 rec'd braze 182 lO8 37-9 244 lO4 214o 37-3 L18 37-4 16o 144 37-5 18o 118 Avg

5-35

TABLE 5-15

SUF_AR¥ OF SPOT _NSION TESTDATA

Ult imat e

Thermal exposure

Method of Heat

load_

Condition

no.

joining ib

hr °F

(a)

None

Aged 19o

Annealed None

2490-7-

85!3

25o 15oo

Aged 115

Annealed

25o 1500

Resistance

spot

None

Aged

Annealed None

31o

2490-6-

85Z2

Aged 25o 15o

Annealed

s5o 15oo

None

Aged

Annealed None

Diffusion 2490-7-

spot bond

lO6

25O 1500

Aged

Annealed 112

25O 1500

aAll values are the average of five specimens.

5-36

TABLE 5-16

,0

SPOT TENSION TEST DATA FOR .015 RENE 41

Thermal exposure Ult imat e

Method of Heat

Specimen load_

Condition

no •

id ent if icat ion ib

jo ining

hr °F

Resistance None None

2490-7-

9-1 Aged

9-2 8513

spot

9-3

9-4

9-5

19o

Avg

Annealed 385

i0-i

i0 2 376

io-3

10-4 376

lo-5

Avg

13-1 Aged 25O

z3-s

13 -3

13-4

13-5

Avg

i4-1 120

Annealed

14-2 126

NA

14-3

71, I,

i4-5

Avg

ii-i None None 174

2490-6-

Aged

11-2

11-3

zz-4 163

11-5

Avg

]_2-! Annealed

12 -2

31o

12-3

12-4 3o6

K&

12-5

\ % O-t_

Avg

5-37

TABLE5-16o- Concluded

SPOT T_SION TEST DATAFOR .015 RENE 41

Ult imat e

Thermal exposure

Heat

Method of

Specimen

Condition

load_

ident ificat ion no.

joining

hr °F

ib

25o 15oo 91

15-1 Re s ist ance Aged 2490-6-

15-2 lO5

spot

15-3 93

lO5

15-4

ioo

15-5

Avg

1o4

16-1 Annealed

16-2 98

16-3

lO8

16-4

16-5

Avg

,f I' 'I

'r

6O

None None

Diffusion Aged 2490-7-

17-1

,_nnt bond 8513 49

!7-P I I

17-3

lO9

17-4

17-5

Avg

18-i Anne aled

18-2 194

18-3

18-4 190

18-5

i

Avg

25o z5oo lo3

19 -i Aged

lO3

19-2 I

19-3

19-4 93

19-5

lO6

Avg

8o

20-i Annealed

20-2 115

2o-3

2o-4

2o-5

Avg

5-38

Next: Section 6 →

Section 6

Section 6 STRUCTURAL ANALYSIS MODEL by G. W. Haggenmacher, R. S. Lahey, G. W. Davis, M. J. Blaha, and W. R. Easter 6-± CONTENTS Page 6-1 REDUNDANT NDDEL DESCRIPTION SUMMARY OF REDUNDANT MODEL INPUT DATA 6-3 USES OF REDUNDANT NDDEL OUTPUT 6-3 6-4 REFERENCES 6-iii

TABLES

Page

6-1

EValuation matrix for redundant model loads 6-5 6-6

6-2

Redundant model input data for initial internal loads 6-3 Monocoque waffle redundant model input data for final 6-7 internal loads 6-4 Monocoque honeycomb-core sandwich redundant model 6-8 input data for final internal loads 6-5 Semimonocoque spanwise redundant model input data for final internal loads 6-9 Semimonocoque chordwise _e_11o8_,_t model input data 6 -i0 for intermediate run 6-7 Semimonocoque chordwise redundant model input data 6 -Ii for final internal loads 6-8 Statically determinate redundant model input data for final internal loads 6-13

ILLUSTRATIONS

Page

6-1 6-14

Master model drawing

6-2

6-15 Statically determinate wing structure 6-16 6-3 Loads network model 6 -vii

SYMBOLS

BL Butt line

Gravitational acceleration Forces in Cartesian coordinate system

Px' Py' Pz

T

Temperature Thickness

t

Equivalent extensional thickness e t Equivalent shear thickness S t Web thickness g_ Mean coefficient of thermal expansion _T Temperature differential 6 -ix

Next: Section 6 →

Section 6

STRUCTURAL ANALYSIS NDDEL This section provides a description of the redundant structural analysis model 3 summarizes redundant model input data_ and discusses uses of redundant model output.

REDUNDANT _DDEL DESCRIPTION Internal loads_ displacements_ and influence coefficients for the wing structure were determined by a mechanized redundant-structure analysis solution based on the matrix force method (ref. 6-1). The lumped element model used for this analysis represented one-half of the structure on one side of the symmetry plane of the vehicle. The analysis for influence coefficients and internal loads was necessary only for symmetrical boundary conditions at the symmetrF- plane of the model_ since only symmetrical maneuver loads were evaluated. Fori the analysis of design conditions_ the external loads were transformed into the nodes of the structural model. 0nly loads normal to the wing surface were i!i i consi_er_. A _awing of the model is shown in figure 6-1. It consisted of three parts : i 1. The center wing model was a fairly well-detailed representation of the region of primary interest and was used for the evaluation of structural concepts. This model consisted of cap members and shear panels for both wing cover surfaces_ and had typical spar spacings to satisfy requirements for conducting the stress analysis.

2. The aft wing plate representation (with increasing spacing away from the center area) served to provide realistic restraint and load transfer to the center area and to a number of deflection points sufficient for load computation purposes. Also_ this part of i!

the analysis model consisted of a mesh of spanwise and chordwise bending members and torsion box elements.

o The fuselage model was a highly idealized represen- tation of the fuselage shell and could be coupled to the wing model in _v....... _I ...... ,,_J s +_ ........_u_lyz_ tha @ffect of various fuselage wing attachment methods. The fuselage consisted of a number of longeron_ panel_ and frame elements to represent the bending and shear stiffness of the fuselage.

6-1 The redundant-structure analysis solution determined thermal stresses and thermoelastic deflections due to the average thermal expansion of axial elements.

Stresses due to thermal gradients within elements of the redundant analysis model were computed separately by means of a thermal-stress computer program_ and were superimposed on redundant model stresses. These elements were analyzed for simple boundary conditions (usually no axial restraint and full rotational restraint)_ and their cross sections were subdivided into many small subelements_ for each of which the free thermal expansion was specified in terms of local t emperat ure s.

The wing considered for the Hypersonic Cruise Vehicle was a multispar_ multirib structure. For the purpose of structural analysis_ it was represented by a grid of spanwise and chordwise beams and ribs which consisted of upper and lower cap area and vertical shear web. The grid was completed by cover-shear- panels in each surface. This beam-rib system of the analysis model represented lumped areas of the actual structure_ since model grid distances were different from actual beam and rib spacings.

The beam-rlb gridwork of the analysis model in the investigation region had approximately twice as fine a mesh than fore and aft.

This model was used in analyzing various types of structural panels and two main structural arrangements: 1. Arrangement 1- Full spanwise and chordwise bending continuity for all beams and ribs of the model within the wing was pro- vided. Wing-fuselage connection for both Px and Py loads was located at each spar along the BL 120 rib. This arrangement was analyzed for various sets of section properties represent- Ing lumped values of chordwise, spanwise, and shear-stiffness characteristics of monocoque and semimonocoque structures.

2o Arrangement 2 -Represented the statically determinate wing; a typical configuration is shown in figure 6-2. Its main charac- teristic was the absence of any chordwise bending continuity from one box beam to the next. The same basic model network was used as in arrangement l, each spanwise beam of the model representing lumped beam properties. For this arrangement_ this single model beam represented two adjacent parallel beams which were connected to have the same vertical deflection. The continuity of chordwise cap forces was interrupted at each beam so that no chordwise bending continuity exists in the model.

This was accomplished by a technique of calculating the redun- dant force units in two sets on two sets of alternating box beams (figure 6-2). Each box beam was independently connected to the fuselage --vert- _y-'_1 _. (Pz) at both beams and _^_- _^_+oi i__ __ (Px), only at the top of the front spar of each box. In this fashion no force system was set up which can express continuity of chordwise strains between one box and the next and between wing and fuselage.

6-2

External loads were introduced at node points. Effects of differential

thermal expansion were accounted for by introducing free thermal expansions of

axial elements as initial strains. The load point network for both versions

of the redundant model is presented in figure 6-3. This load point network

was used to introduce air_ inertia_ and ramp loads into the wing structure.

Fuel tank inertia loads were introduced at the wing-fuselage intersection

(BL 120).

SUMMARY OF REDUNDANT MODEL INPUTDATA

The evaluation matrix for redundant model loads is presented in table 6-1.

Initial internal loads were based on a nominal panel configuration representa-

tive of both monocoque and semimonocoque structure concepts. Equivalent ex-

tensional and shear thicknesses of the primary structural panels used for

determining initial loads are shownin table 6-2. Thermal data (sAT) were

input for each flight condition_ and temperatures were from preliminary iso _

therm data. These isotherms were constructed from radiation equilibrium

temperature data at five stations and approximately twenty discrete points

per wing surface. _

Final and intermediate internal loads were based on the panel dimension

_I_v_i_+_ and actual thermal in_t a8_8 a_gc_bed _n tables 6-3 through 6-8:

respectively, for the monocoque(waffle and honeycomb), semimonocoque (spanwise

and chordwise), and statically determinate primary structure concepts. The

element flexibility matrix for the waffle version of the redundant model was

adjusted to account for Poisson's effect. Tworedundant analyses were required

for the chordwise concept (intermediate and final).

USES OF REDUNDANT MODEL OUTPUT

For this program, the redundant model output data were us_l in the follow-

ing areas:

i. Internal load distributions, particularly in the main area of

interest, as a basis for the stress analysis and evaluation of

the various structural concepts. Initial redundant model loads

are presented in the evaluation results section of this docu-

ment as well as the final redundant model internal loads for

the monocoque,semimonocoque (spanwise and chordwise), and stat-

ically determinate primary structure concepts.

2. Structural influence coefficients for vehicle flutter evaluation.

3. Vehicle deflections for evaluating aeroelastic effects on panel

pressure distributions and cruise performance (drag change).

6-3 REFERENCES 6-1 Haggenmacher_ G. W. : Preparation of Data for the Redundant Structures S Analysis Programs. Lockheed-California Company_ LR 13091_ February 1964.

iii_ 6-4 o .H do 40 _.H • H 4 ° ._ hO ,H u_ O tq ,H

oa

-p

o

O.H

g

._ +_ _3 40 .,-I E-_ O -_ • r-t _ • H _ h0 (1) O o o e..t _d _d _.

I o 0 0 _ o_ kO o o 4o 4o o f_ X ® o

H t

E-4

_ o_

uJ h0 • r-t .H .H .r--I ba H •H ,H ,H •H .H .H .H • H 0 _ 0 ID .H •H ,H .H H p_ oH k-_ H H Or'- O ca • H -IO 0 .H .H O4o _ % b-4 r/1 "--_ .el ,-I % .H _ _ 0 _-_ • HID _ % o 4_ O m O._ o _ o _ O _ 0 0 o _ _ _ _o_0 .HOD 40 O'H 6-5 TABLE 6-2 REDUNDANT MODEL INPUT DATA FOR INITIAL _ERNAL LOADS Panel concept: nominal panel configuration representative of both monocoque and semimonocoque concepts.

Panel orientation: chordwise Material: a. primary structural panels - Ren_ 41 b. rib and spar webs - Haynes 25 Thermal protection system: no heat shields or insulation Rib and spar webs: 60 ° circular-arc corrugation, minimum gage web thickness, t = 0.015 in.

w Equivalent extensional (te) and shear (ts) thickness of the primary t t .e .$ Location in, in, 0.038 0.020 Upper Surface 0.038 0.020 Lower Surface Panel size: spanwise direction = 46 in.

chordwise direction = 92 in.

Rib spacing: 46 in.

Spar spacing: 92 in.

Effective cap areas (includes closeout effects): spar caps = 0 rib caps = 0 Thermal data: (mAT) input for each flight condition Modulus: extensional and shear modulus based on average temperatures for the 2g maneuver con_Itmon.

6-6 TABLE 6-3 MONOCOQUE WAFFLE REDUNDANT MODEL INPUT DATA FOR FINAL INTERNAL LOADS Panel concept: -45 ° x 45 ° unflanged waffle grid plate Panel orientation: chordwise Material: Panels, ribs, ans spars material RenJ 41, solution treated and aged at 1400°F Thermal protection system: partial heat shields at outboard area lower surface Rib and spar webs: 60 ° circular-arc corrugation, minimum gage web thickness, t = 0.015 in.

Equivalent extensional (te) and shear (t s) thicknesses of the primary structural panels: t e , t s , Location in___, in.

0.020 O.040 Upper Surface Lower Surface BL 0-120 0.025 0.046 BL 120-212 0.025 0.046 BL 212-350 0.030 0.053 Panel size: spanwise direction = 20 in.

chordwise direction = 43 in.

Rib spacing - 23 in.

from cap _, to cap Spar spacing - 46 in.

Effective cap areas (includes closeout effects): spar caps = 0.16 in.

rib caps = 0.12 in.

Thermal data: (aAT) input for each flight condition Modulus: extensional and shear modulus based on temperatures for the 2g maneuver condition 6-'7 TABLE 6-4 MONOCOQUE HONEYCOMB-CORE SANDWICH REDUNDANT MODEL INPUT DATA FOR FINAL INTERNAL LOADS Panel concept : Honeycomb-core sandwich Panel orientation : chordwise M_terial: Ren6 41_ solution-treated and aged at 140OOF Thermal protection system: partial heat shields at outboard area lower surface Rib and spar webs: 60 ° circular-arc corrugation_ minimum gage web thickness_ t w = 0.015 in.

Equivalent extensional (te) and shear (ts) thicknesses of the primary structural panels: te_ ts_ Location in. in.

UDDer Surface 0.029 0.029 Lower Surface BL 0-120 0.033 0.033 BL 120-212 o.o42 o.o42 BL 212-350 0.027 0.027 Panel size : Sl_nwise direction = 40 in.

chordwise direction = 80 in.

Rib spacirg: 40 in.

Spar spacing: 80 in.

Effective cap areas (includes closeout effects): spar caps = 0.315 in. 2 rib caps = 0.315 in. 2 Thermal data: (_AT) input for each flight condition • ,,udu_: extensional and _o_o_ _i_o__ based _ tempe_+u_e_ ..... for the 2g maneuver condition J 6-8 TABLE 6-5 SHMIMONOCOQUE SPANWISE REDUNDANT MODEL INPUT DATA FOR FINAL INTERNAL LOADS Panel concept: Tubular panels (upper and lower surfaces) Panel orientation: spanwise Material: Panels, ribs, and spars material Ren_ 41, solution treated and aged at l_O0°F.

Thermal protection system: heat shields, both upper and lower, with par- tial insulation (1/4 inch Dyna-Flex) on the lower surface outboard area Rib and spar webs: 60 ° circular-arc corrugation configuration with minimum gage thickness_ t = 0.015 in.

W Equivalent extensional (te) and shear (ts) thicknesses of the primary structural panels : Location t t e s in, in, TT ........ -n_ N AoP. O N]_ Lower surface BL 0-120 0. 026 0.0] 5 BL 120-212 0. 030 0. 018 BL 212-350 O. 028 O. 016 Panel size: spanwise direction = 43.0 in.

chord_ise direction = 89.0 in.

Rib 46.0 in.

spacing: from cap _ to cap Spar spacing: 92.0 in.

Effective cap areas (includes closeout effects): spar caps = 0.22 in, rib caps = 0.34 in.

Thermal data: (_AT) input for each flight condition Modulus: extensional and shear modulus based on temperatures for the 2g maneuver condition.

.... h 6-9 TABLE 6-6 Sm_ONOCqUE CHORDWlS_ REDUNDANT MODEL INPUT DATA FOR !qYfERMEDIATE RUN Panel concept: Convex beaded panels for exposed upper surfaces; tubular lower surface panels Panel orientation: chordwise Material: Panels, ribs, and spars material Ren@ 41, solution-treated and aged at 1400°F Thermal protection system: heat shield lower surface with partial insulation of the outboard lower surface Rib and spar webs: 60 ° circular-arc corrugation configuration with minimum gage thickness_ t w = 0.015 in.

Equivalent extensional t e and shear t s thicknesses of the primary structural panels: t e _X t s Location in. in. _ Upper Surface 0.029 O. 022 Lower Surface 0.044 O. 028 Panel size: spanwise direction = 89.0 in.

chordwise direction = 43.0 in.

Rib spacing: 92.0 in.

from cap _ to cap GL Spar spacing: 46.0 in, Effective cap areas (including eloseout effects): spar caps = 0.34 in. 2 rib caps = 0.24 in.2 Thermal data: (aAT) input for each flight condition Modulus: extensional and shear modulus based on temperatures for the 2g maneuver condition 6 -i0

TABLE 6-7

S_MIMONOCOQUE CHORDWISE REDUNDANT MODEL

INPUTDATA FORFINAL INTERNAL LOADS

Panel concept: Convexbeaded panels for upper exposed

surfaces;tubular lower surface panels

Panel orientation: ehordwise

I

Material: Panels, ribs, and spars material Rene 41,

solution-treated and aged at 1400°F

Thermal protection system: heat shield lower surface with partial insulation

on outboard lower surface.

Rib and spar webs: 60° circular-arc corrugation configuration with minimum

gage thickness, t = 0.015 in.

w Equivalent extensional t and shear t thicknesses of the primary structural e s t t e,X s Location in. in.

Upper surface - BL 120 0.025 0.016 BL 120 - OUTBOARD 0.031 0.025 Lower surface % - BL 120 0.026 0.015 BL 120 - BL 212 0.033 .... 0.020 BL 212 - BL 350 0.028 0.017 Panel size: 57 x 21 in. (span x chord), _ - BL 120 75 x 21 in., BL 120 - OUTBOARD Rib spacing: 60 in., _ - BL 120 Ifrom cap (_ to cap_ I 78 in., BL 120 - OUTBOARD Spar spacing: 24.0 in.

6-ii

TABLE6-7 - Concluded

SHMIMONOCOQUE CHORDWISE REDUNDANT MODEL

INPUTDATAFORFINALINTERNAL LOADS

Effective cap areas (includes closeout effects): spar caps:

Location

Upper Lower

_L - BL 120 0.34 O. 25

BL 120 - BL 212 O.4O 0.21

BL 212 - OUTBOARD

O. 31 0.20 rib caps: 0.19 in.

Thermal data: (_&T) for each flight condition Modulus: extensional and shear modulus based on temperatures for the 2g maneuver condition 6-12

TABLE 6-8

STATICALLY DETERMINATE REDUNDANT MODEL INPUT DATA FOR FINAL INTERNAL LOADS Panel concept: Beaded both surfaces Panel orientation: spanwise Material: Panels, ribs, and spars material Ren_ 41, solution treated and aged at 1400°F Thermal protection system: heat shield both surfaces no insulation Rib and spar webs: 60 ° circular-arc corrugation configuration with minimum gage thickness, t = 0.015 in.

w Equivalent extensional (te) and shear (ts) thicknesses of the primary structural panels: t t in. in.

Location Upper Surface 0.028 0.016 Lower Surface BL 0 - 120 0.026 0.015 BL 120 - 212 0.030 0.018 BL 212 - 350 0.028 0.016 Panel size: 43 x 89 in. (span x chord) Rib spacing: 46 in.

cap _Lto cap _I from Spar spacing: 92 in.

Effective cap areas (includes closeout effects): spar caps = 0.15 in.

rib caps = 0.12 in.

Thermal data: _ T) input for each flight condition Modulus: extensional and shear modulus based on temperatures for the 2g maneuver condition 6-13 io ii m )N i< i0 < )I- 0£0£ V.L hO in m iN A" ;; gt 99E_ V±$ _'L.ZZ V.L$ ZBI.Z V.I.S

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Next: Section 7 →

Section 7

A PLANE STRAIN ANALYSIS FOR

DETERMINING THERMAL STRESSES

by C. C. Richie CONTENTS Page 7-1 A PLANE-STRAIN ANALYSIS FOR DETERMINING THERMAL STRESSES 7-1 ANALYSIS 7-5 SUMMARY OF EQUATIONS 7-iii SYMBOLS

A

Area of lumped element, _st

a,b,c Rectangular Cartesian coordinates

E

Modulus of elasticity

L

Length

M

Bending moment

N

Extensional force in xy coordinates

T

Temperature

t

Average thickness of lumped element U Axial displacement Mean coefficient of thermal expansion As Average width of lumped element Strain Stress Subscripts a,b,c Denotes relationship to a,b, and c axes J Denotes number of lumped element Denotes first and last number of lumped elements, respectively; m,n also, m denotes mean value Denotes temperature at which the thermal stress of all elements is zero 7-V

Next: Section 7 →

Section 7

Section 7 A PLANE-STRAIN ANALYSIS FOR DETERMINING THERMAL STRESSES A plane-strain analysis of thermal stresses is presented in this section.

For many applications_ the procedure provides an adequate estimate of stresses due to temperature gradients• It is especially useful for determining approxi- mate stresses of high-temperature structures during the preliminary phase of design• ANALYSIS Consider the lumped structural model shown in figure 7-1• When the structure is subjected to external loading of Na_ Mb_ and Mc_ and to transient heating_ a plane located originally at a' = 0 is translated parallel to the a' axis and rotated about the b" and c" axes. This analysis was conducted using the methods of references (7-1) and (7-2). The Bernoulli-Euler assumption was used for the axial displacement equation• This requires the axial displacement component be a linear function of Lhe c_hlat_ in the plane of the cross section• Denoting the axial coordinat@ by a'_ and letting b' and c' be the centroidal cross section. The axial displacement u may be written as

(7-1)

u. -- ;o (a') ÷ c: Fl (a') ÷ bi F2 (a')

3 3 3 where = linear functions of the axial coordinate FO_ FI and F 2 = coordinates measured from centroidal axes of cross a'_ b' and c' section = subscript denotes number of lumped elements The corresponding strain can be written as _U • • • (7-2) Ej : _, = F0 + c3tF1 + b j:F2 where dots indicate differentiation with respect to a'.

7-1 The stress component is + c'j F I + bLj F2) -amj Ej (Tj - To ) aj = Ej [Ej-amj (Tj - To) ] = Ej (F 0

(7-3)

where mm = mean coefficient of thermal expansion based on To, in./in.

T = temperature at which the thenual stress of all elements is zero, OF O The last term on the right-hand side of equation (7-3) is entirely a function of temperature for a given materialj hence, it is convenient to express it simply as

(7-h)

f(T)j = -am.f Ej(Tj - To) J The functions F O _ F I _ and F 2 are determined so as to satisfy the following equations of equilibrium.

j=n

(7-5)

_j_A. = N 3 a j=m j=n (7-6) c: : c • 0"._, Z_j J j=m j=n (7-7) _, aj Z_Aj b: : - + Na_)

j (Mc

j =m in which m b and c = coordinates of centroid, in.

N = axial load acting parallel to a axis, ib a moment about b axis, in.-Ib M = moment about c axis, in.-!b c A = As t = area of lumped element_ in.

7-2 t = average thickness of lumped element As = average width of lumped element m and n = subscripts denoting first and last number of lumped elements, respectively The coordinates of the centroid are j=n Ej AA. b.

J J = j=m (7-8) m EA j=n I Ej AAj cj = j=m __ (7-9) EA where j=n = _ E._A. (7-10) J 3 j=m The coordinates in the b'c' system can now be expressed in terms of the reference coordinate system, b c_ b' : b - b _ (7-ii) c' = c - _ (7-12) Substituting equation (7-3) into equations (7-5), (7-6), and (7-7) and noting that j=n j=n Ej _Aj bT" =J _ E- AA- ct- = Oj _ J j=m j=m yields N a z (7-13) F o - EA 7-3 (7-1h) (_)b F1 + (E-_)bc F2 =

(7-_5)

(_)bo }l + (ET)c}2 = m, C where j j=n N ' = N - > f(T).AA.

(7-16) a a _-_ j j j=m j=n

%' :%-_- _ f(T).AA.o '

(7-17)

j=m Y O 3 j--n M ' = M + N _ + > f(T).AA.b.'

(7-18) c c a _-_ Y Y 0 j=m j=n (7-19) (Z) b : _ E.aA.o ' j=m J J J j--ll (7-20) (_)b : _> _'AA'b'c., c -_-_ J O J O y=m j=n _2 = >+ E.AA.b (7-21) (ET)c __ j J J j=m Solving equations (7-14) and (7-15) for F1 and F2 and then substituting the resulting expressions and equation t. _ _ - _1-±>j into equation (7-3) gives the following final stress equation: r; !

N !

f(T). + aE.

J _ J

(7-22) The stress of all fibers on the principal axes is equal to zero when only the moment loads are considered; hence, the following expression can be obtained from equation (7-22) for the angle between the principal axes, b" and c" coordinate axes, and the centroidal axes_ b' and c' coordinate axes.

c.' Mc'(E-I)b + Mb'(_)bc (7-23) tan_ - J -

b ' _o'(_i) + M '(LT)

j c c bc The above equation is not required to perform a stress analysis with the equations presented herein; however_ for some applications_ it may be desirable to know the position of the principal axes.

SUMMARY OF EQUATIONS The equations thus far presented are spec_fically formulated for the case of complex bending about two axes with axial loading included. For problems of simple bending about two axes with axial loading, bending about one axis with axial loading_ and axial loading only, the equations are of simpler form. A summary of all of the equations is presented.

Case I. Complex bending about two axes and axial loading: N !

o. = f(T). + a E.

J J _ J

(_-i)b . - ' + b '

+ M ' c ' M c Mb'(F-I)bc j c c J +E.

J (E-_)b(_)c- (E--I)2bc j--n Z f(T).AA.

a a j=m J J f-p j=n _m f(T) AAjcj' j= J • .

j=n M' =M +NT+ c c a ._ f(T)jAAjbj, j=m j=n EA= j=rl ,2 (E-I)b = ._ EjAAj c a=m J j=n j=n _m EjAAjbj 'c ' j= O ,2 j=m j=n ._ EjAAjbj J=m EA EA J _A. = tj_sj bj -.- bj - 5 C'-! ---- C. -- o j

M '(#%)b + '

tan _= +_ '(_

_b'(ff)° o )bo

Case 2.

Simple bending about two axes and axial loading: N ' ,Mb, cj , _. = f(T) + _ E + M" 'b '

(%f)b J (_l) J

j=n N ' = N - _ f(T) ZM, a a . .

J=m J J 7-6 j=n

- _ f(T)jAAjcj'

j=m M' =M +N_+ o o a j=n EA = (E-l)b = _ EjAAjcj ,2 j=m j=n j--n Z E.AA.b.'

Z E.AA.b.

c j=m J J J j=m J J J m EA j=n E.AA.c.

c= j=m J J J AA. = t .As.

a J a

b.' =b. -T c.' = e. - c J J J J Case 3. Bending about one axis and axial loading: N ' Mb' c.'

_. = f(T). +---e-as. + J s.

a a s_ a (E)b a

j_n N ' =N - ) f(T).AA.

a a z__ j j j=m 7-7 j=n f(T) .AA.c.'

_' = _ - Na_-

j=m J J J J_ E. AA.

EA = j=m g J j=n E.AA c.

j=m g J J AA. = t.As.

C J J J EA C ! ---- C -- C • ° g J Case 4. Axial loading only: j=n N !

N ' = N _. = f(m). +_a s.

- f(m)j j a a .AA a a s_ a j--n m EA = AA. = t.As.

j_.m E.AA. J J J = J J 7-8 REFERENCE S 7-1 Hubka, R. E. : Effects of Physical Factors and Analytical Procedures on Predicted Temperatures and Thermal Stresses. Lockheed Report 12777, Lockheed-California Company, 1959.

7-2 Boley, B. A., Weiner, J. H.: Theory of Thermal Stresses, John Wiley & Sons, Inc., 1960.

7-9 Lumped element-

\

Principal axes bl!

Centrold b_-e- b I Axes through centrold and parallel to reference axes M Reference axes ap N a j=n i C C !1

\

C i

\

Principal axes

\

Axes through centrold and parallel to reference axes Figure 7-1 Structural Model 7-10

Next: Section 8 →

Section 8

STRUCTURAL INTERNAL lOADS

by

C. C. Richie_ G. W. Dav±s_W. A. Claus_ and D. G. Watson

8-i

Page

STRUCTURAL INTERNAL LOADS 8-1

INITIAL PANEL WEIGHT SCREENING LOADS 8-1

I_ERMEDIATE WEIGHT SCREENING LOADS 8-1

DETAILINTERNAL LOADS (USED FORFURTHER

INTERMEDIATE SCREENING AND FINAL

8-1 STRUCTURAL LOADS) 8-1 MONOCOQUE WAFFLE LOADS S_MIMONOCOQUE SPANWISE LOADS 8-3 8-4 S_4IMONOCOQUE CHORDWISE LOADS 8-6 STATICALLY DETERMINATE LOADS 8-ii{

TABLES

Table

Page

8-1

8-7 Loads used for initial panel weight screening

8_

Preliminary redundant-model loads for wing investigation 8-8 area 8-3 Ultimate thermal strains and stresses_ +2.0-g maneuver condition 8-9 8-1o 8-4 Waffle redundant model loads 8-i0 8-5 Monocoque concept redundant-model loads 8_ Comparison of surface panel equivalent extensional and shear thicknesses for the redundant model and sized 8-12 monocoque primary-structure concept 8-13 Monocoque waffle concept ultimate thermal strains Final redundant-model loads for monocoque-honeycomb-core 8-14 sandwich panels 8-9 Comparison of extensional and shear thicknesses for the honeycomb sandwich redundant model and final honeycomb 8-15 sandwich panel evaluation 8-16 8-i0 Honeycomb sandwich redundant-model thermal strains 8-11 Final semimonocoque spanwise redundant model loads for 8-17 wing investigation section 8-12 Comparison of surface panel equivalent extensional and shear thickness for the redundant model and sized 8-18 semimonocoque spanwise primary structure 8-13 Loads for semimonocoque spanwise-stiffened panel for 8 -19 -0.5-g condition: exposed surfaces shielded 8-14 Loads for semimonocoque spanwise-stiffened panel for 8 -20 +2.0-g condition: exposed surfaces shielded -V _.

Table Page 8-15 Loads for semimonocoque spanwise-stiffened panel for 8-21 cruise condition: exposed surfaces shielded 8-16 Loads for semimonocoque spanwise-stiffened panel for -0.5-g condition: exposed surfaces shielded, 8-22 insulation outboard 8-17 Loads for semimonocoque spanwise-stiffened panel for +2.0-g condition: exposed surfaces shielded, insulat ion outboard 8-23 8-18 Loads for semimonocoque spanwise-stiffened panel for cruise condition: exposed surfaces shielded, insulation outboard Intermediate chordwise design ultimate loads Intermediate redundant model comparison semimonocoque 8 -26 chordwise-stiffened primary structure concept 8-21 Loads for semimonocoque chordwise tubular panels both surfaces; exposed surfaces shielded; no insulation; 8-27 -0.5-g condition 8-22 Loads for semimonocoque chordwise tubular panels both surfaces; exposed surfaces shielded; no insulation_ 8-28 +2.0-g condition 8-23 Loads for semimonocoque chordwise tubular panels both surfaces; exposed surfaces shielded, no insulation;_ 8-29 cruise condition 8-24 Loads for semimonocoque chordwise tubular panels both surfaces; exposed surfaces shielded, partial insulation 8-30 lower outboard; -0.5-g condition 8-25 Loads for semimonocoque chordwise tubular panels both surfaces; exposed surfaces shielded; partial insulation 8-31 lower outboard; +2.0-g condition 8_26 Loads for semimonocoque chordwise tubular panels both surfaces; exposed surfaces shielded, partial insulation 8-32 lower outboard; cruise condition 8-_vi

Table

Page 8-27 Loads for semimonocoque chordwise convex beaded upper, tubular lower; lower exposedsurface shielded; 8-33

-0.5-g condition

8-28

Loads for semimonocoque chordwise-convex beaded upper, tubular lower; lower exposedsurface shielded; 8-34

+2.0-g condition

8-29 Loads for semimonocoque chordwise-convex beaded upper,

tubular lower; lower exposed surface shielded; cruise

condition 8-35

8-30

Loads for semimonocoque chordwise-convex beadedupper,

tubular lower; lower exposed surface shielded, partial

8-36

insulation lower outboard3 -0.5-g condition

8-31 Loads for semimonocoque chordwise for convex beaded

upper, tabular lower; lower exposed surface shielded, 8-37

partial insulation lower outboard; +2.0-g condition

8-32

Loads for semimonocoque chordwise convex beaded upper,

tubular lower; lower exposedsurfaceshielded partial

8-38

insulation lower outboard; cruise condition

8-33 Loads for semimonocoque chordwise convex beaded both

8-39

surfaces; no thermal protection; -0.5-g condition

8-34 Loads for semimonocoque chordwise convex beaded, both

8-40

surfaces; no thermal protection; +2.0-g condition

8-35

Loads for semimonocoque chordwise convex beaded, 8-41

both surfaces; no thermal protection; cruise condition

8-36 Loads for semimonocoque chordwise convex beaded upper

and center lower surfaces, tubular inboard and outboard

lower; partial heat shield lower outboard; -0.5-g

8-42

condition

8-37

Loads for semimonocoque chordwise convex beaded upper and

center lower surfaces, tubular inboard and outboard lower; 8-43

partial heat shield lower outboard; +2oO-g condition

8-38 Loads for semimonocoque chordwise convex beaded upper and

center lower surfaces_ tubular inboard and outboard lower; 8-44

partial heat shield lower outboard; cruise condition

8-v _i

TABLES(COM.)

Table Page 8-39 Loads for semimonocoque chordwise convex beaded upper and center lower surfaces, tubular inboard and outboard lower; partial heat shield and insulation; -0.5-g condition 8-45 8-4o Loads for semimonocoque chordwise convex beaded upper and center lower surfaces, tubular inboard and outboard lower; partial heat shield and insulation; +2.0-g 8-46 condition 8-41 Loads for semimonocoque chordwise convex beaded upper and center lower surfaces, tubular inboard and outboard lower; partial heat shield and insulation; cruise condition Final chordwise ultimate loads Final loads for semimonocoque chordwise concept; convex beaded upper, tubular lower; heat shield and insulation; 8-49 -0.5-g condition 8-44 Final loads for semimonocoque chordwise concept; convex beaded upper, tubular lower; heat shield and insulation; 8-50 +2.0-g condition 8-45 Final loads for semimonocoque chordwise concept; convex beaded upper, tubular lower; heat shield and insulation; 8-51 cruise condition 8-46 Final redundant model comparison, semimonocoque 8-52 chordwise

8-0 8-53

Final statically determinate design ultimate loads 8-48 Final redundant model comparison, statically determinate 8-54 primary-structure concept 8-49 Final loads for statically determinate concept; heat 8-55 shields, no insulation; -0.5-g condition 8-50 Final loads for statically determinate concept; heat 8-56 shields, uo zns_±_±on_ _.0_-_,_±_ 8-51 Final loads for statically determinate concept; heat shields, 8-57 no insulation; cruise condition 8-viii

ILLUSTRATIONS

Fig. Page

8-1

Ultimate chordwise thermal stress distribution at STA. 2320; -0.5-g condition for monocoque waffle concept with partial heat shield at outboard area lower surface 8-58

8-2

Ultimate chordwise thermal stress distribution at STA. 2320, +2.0-g condition for monocoque waffle concept with partial heat shield at outboard area lower surface 8-59 8-3 Ultimate chordwise thermal stress distribution at STA. 2320, cruise condition for monocoque waffle concept with partial 8-60 heat shield at outboard area lower surface 8-4 Spanwise thermal strain distribution for monocoque waffle concept with partial heat shield at outboard area lower 8-61 s urfac e 8-5 Spanwise thermal strain distribution for monocoque waffle concept with partial heat shield at outboard area lower 8-61 surface with insulation 8-6 Spanwise thermal strain distribution for monocoque waffle 8-62 concept with heat shield on entire lower surface 8-7 Spanwise thermal strain distribution for monocoque waffle concept with heat shield on entire lower surface with 8-62 insulation at outboard area 8-8 Spanwise thermal strain distribution for monocoque waffle 8-63 concept with no heat shield and no insulation 8-9 Plane-strain vs redundant force for semimonocoque spanwise 8-64 concept at -0.5-g condition 8-i0 Plane-strain vs redundant force for semimonocoque spanwise 8-65 concept at +2.0-g condition 8-ii Plane-strain vs redundant force for semimonocoque spanwise 8 -66 concept cruise condition 8-12 Limit thermal stress distribution for semimonocoque spanwise 8-67 concept without insulation at 0.5-g condition 8 - ix

TU, mCXONS

Fig • Page 8-13 Limit thermal stress distribution for semimonocoque spanwise 8-68 concept without insulation at +2.0-g condition 8-14 Limit thermal stress distribution for semimonocoque spanwise concept without insulation at cruise condition 8-15 Limit thermal stress distribution for semimonocoque spanwise 8 -70 concept with insulation at -0.5-g condition 8-16 Limit thermal stress distribution for semimonocoque spanwise 8-71 concept with insulation at +2.0-g condition 8-17 Limit thermal stress distribution for semimonocoque spanwise concept with insulation at cruise condition 8-72 8-18 Limit thermal stresses in the chordwise direction at +2.0-g condition for semimonocoque spanwise-stiffened panels with and without insulation 8-73 8-19 Limit thermal stress distribution at Sta. 2320 for semi- monocoque chordwise concept: -0.5-g condition_ both 8-74 surfaces heat shielded 3 no insulation 8 -20 Limit thermal stress distribution at Sta. 2320 for semimonocoque chordwise concept: +2.0-g condition_ 8-75 tubular panel_ both surfaces heat shielded, no insulation 8-21 Limit thermal stress distribution at Sta. 2320 for semi- monocoque chordwise concept: cruise condition, tubular 8 -76 panel_ both surfaces heat shielded_ no insulation 8 -22 Limit thermal stress distribution at Sta. 2320 for semi- monocoque chordwise concept: -0.5-g condition, tubular panel 3 both surfaces heat shielded, partial insulation 8-77 lower outboard 8-23 Limit thermal stress distribution at Sta. 2320 for semi- monocoque chordwise concept: 2.0-g condition_ tubular panel, both surfaces heat shielded_ partial insulation 8-78 lower outboard 8-24 Limit thermal stress distribution at Sta. 2320 for semi- monocoque chordwise concept: cruise condition 3 tubular panel_ both surfaces heat shielded_ partial insulation lower outboard 8-79 _- x ILLUSTRATIONS (CONT.)

Fig. Page 8-25 Limit thermal stress distribution at Sta. 2320 for semi- monocoque chordwise concept: -0.5-g condition, convex beaded (upper) and tubular (lower) panel, lower surface 8-80 heat shielded, no insulation 8 -26 Limit thermal stress distribution at Sta. 2320 for semi- monocoque chordwise concept: +2.0-g condition, convex beaded (upper) and tubular (lower) panel, lower surface 8-81 heat shielded, no insulation 8-27 Limit thermal stress distribution at Sta. 2320 for cruise condition, convex beaded (upper) and tubular (lower) panel, 8-82 lower surface heat shielded, no insulation 8 -28 Limit thermal stress distribution at Sta. 2320 for -0.5-g condition, convex beaded upper and tubular lower panel; lower surface heat shielded, partial insulation lower outboard 8-83 8 -29 Limit thermal stress distribution at Sta. 2320 for +2.0-g condition, convex beaded upper and tubular lower panel, lower surface heat shielded, partial insulation lower 8-84 outboard 8-3o Limit thermal stress distribution at Sta. 2320 for cruise condition, convex beaded upper and tubular lower panel; lower surface heat shielded, partial insulation lower outboard 8-85 8-31 Limit thermal stress distribution at Sta. 2320 for -O_5-g condition, convex beaded panels, no heat shield or 8-86 insulation 8-32 Limit thermal stress distribution at Sta. 2320 for +2.0-g condition, convex beaded panels, no heat shield or insulat ion 8-8y 8-33 Limit thermal stress distribution at Sta. 2320 for cruise condition, convex beaded panels, no heat shield or 8-88 insulation Limit thermal stress distribution at Sta. 2320 for semi- 8-34 monocoque chordwise concept: -0.5-g condition, convex beaded panels, upper and center lower surfaces, tubular lower inboard and outboard_ partial heat shields lower 8-89 outboard_ no insulation 8-xi ILLUSTRATIONS (CONT.)

Page Fig.

8-35 Limit thermal stress distribution at Sta. 2320 for semi- monocoque chordwise concept: +2.0-g condition, convex beaded panels upper and center lower surfaces, tubular lower inboard and outboard, partial heat shields outboard, 8-90 no insulation 8-36 Limit thermal stress distribution at Sta. 2320 for semi- monocoque chordwise concept: cruise condition, convex beaded panels upper and center lower surfaces, tubular lower inboard and outboard; partial heat shields outboard, no insulat ion 8-91 Limit thermal stress distribution at Sta. 2320 for semi- 8-37 monocoque chordwise concept: -0.5-g condition, convex beaded panels, upper and center lower surfaces, tubular inboard and outboard lower, partial heat shields and 8-92 insulation, lower outboard Limit thermal stress distribution at Sta. 2320 for semi- 8-37 monocoque chordwise concept: -0.5-g condition, co_vex beaded panels, upper and center lower surfaces, tubular inboard and outboard lower_ partial heat shields and 8-92 insulation, lower outboard 8-38 Limit thermal stress distribution at Sta. 2320 for semi- monocoque chordwise concept: +2.0-g condition, convex beaded panels, upper and center lower surfaces, tubular inboard and outboard lower 3 partial heat shields and 8-93 insulation, lower outboard Limit thermal stress distribution at Sta. 2320 for semi- 8-39 monocoque chordwise•concept: cruise condition, convex beaded panels, upper and center lower surfaces, tubular inboard and outboard lower 3 partial heat shields and 8-94 insulation, lower outboard 8-xii SYMBOLS x and y distances between simply supported edges of panel

a, b

a/b Panel aspect ratio

Area A Area between _, and BL 120 of wing investigation area Area B Area between BL 120 and BL 212 of wing investigation area Area C Area between BL 212 and BL 350 of wing investigation area BL Butt llne Extensional stresses and shear stress in xy coordinate system fx_ fy_ fxy Gravitational accelerat ion g Extensional forces and shear force in xy coQrdinate system per Nx_ Ny_ Nxy unit length of section Pressure P T Temperature Average panel temperature

(av)

Equivalent extensional thickness t e Equivalent shear thickness ts Mean coefficient of thermal expansion AT Temperature difference Extensional strains and shear strain in xy coordinate system gx _ ey_ £xy 8-xiii

Next: Section 8 →

Section 8

STRUCTURAL INTERNAL lOADS

The structural analysis model discussed in section 6 was used for

determining internal loads for the initial panel weight screening, inter-

mediate weight screeningj and final structural weight evaluation. The plane-

strain analysis of section 7 was used to obtain chordwise thermal stresses for

the various thermal-protection systems.

INITIAL PANEL WEIGHT SCREENING LOADS

Table 8-i shows the loads used for the initial panel weight screening.

The loads resulted from preliminary redundant analyses using an extensional

(bending) stiffness of 0.055 inch and a shear stiffness of .070 inch for the

wing surface panels. These stiffnesses were based on panel geometry for a

typical monocoque waffle wing structure.

INTERMEDIATE WEIGHT SCREENING lOADS

The redundant-model internal loads (based on the data contained in

table 6-20)are shown in table 8-2 and were used for the intermediate screen-

ing. Equivalent extensional and shear thicknesses of the primary structural

panels were based on a nominal panel configuration representative of both

monocoque and semimonocoque prlmary-structure concepts. Poisson's effect was

not included in this redundant model. Thermal data _T) were input for each

flight condition. Temperatures were obtained from preliminary isotherm data.

The isotherms were constructed from radiation-equilibrium temperature data at

five stations and approximately 20 discrete points per wing surface.

A survey of the preliminary transient-temperature data for the three

flight conditions (-0.5-g, +2.0-g_ and cruise) and the loads of table 8-2 led

to the choice of the +2.0-g maneuver condition as the controlling design for

the intermediate screening. The thermal strains of table 8-3 rather than the

thermal loads of table 8-2 were combined with the airloads and the temperatures

of the preliminary transient analysis for each concept.

DETAIL INTERNAL LOADS (USED FOR FURTHER

INTERMEDIATE SCREENING AND FINAL STRUCTURAL LOADS)

_DNOCOQUE WAFFLE lOADS

Redundant-model internal loads and thermal strains for the monocoque

waffle primary-structure concept are shown in tables 8-4 and 8-5. Comparison

of these internal loads with the initial loads shown in tables 8-2 and 8-3

8-1

shows a markedreduction in the final spanwise and chordwise thermal loads

and a considerable increase in the final spanwise airloads.

Comparison of surface panel equivalent extensional and shear thicknesses

for the redundant model and the sized waffle primary-structure concept is

shown in table 8-6. Best correlation is obtained in the inboard and outboard

area lower surface. However, considerable increase in the panel equivalent

shear thickness occurs in the highly loaded inboard area.

A comparison of redundant-model and plane-strain thermal stresses is

presented in figures 8-1, 8-2, and 8-3 for the -O.5-g maneuver, 2-g maneuver, and cruise conditions, respectively. As indicated, good agreement was obtained,

except near the leading edge. In the leadlng-edge area_ the redundant-model

stresses are higher than the plane-strain stresses. These higher stresses are

probably the result of shear lag effect of the leading-edge member resulting

from sweepback and the difference in temperature gradients between the redundant-

model and plane-strain analysis. The plane-strain analysis considers the AT

in the spanwise direction only; whereas, the redundant model considers both

spanwise and chordwise gradients.

Detail internal loads encompass airloads and thermal strains for the

five candidate thermal-protection arrangements that follow:

Heat-shield arrangment

Insulation arrangement

i. Lower surface heat shields No insulation

outboard of one-thlrd wing

chord

2. Lower surface heat shields Insulation

outboard of one-third wing

chord

Heat shields on entire No insulation

lower surface

Insulation outboard of

Heat shields on entire

lower surface

one-third wing chord

No insulation

5. No heat shields

However_ the redundant-model loads were determined only for the first

arrangement. For the remaining four concepts, internal loads were evaluated

by assuming that:

The airloads are constant for all monocoque waffle primary-

structure concepts

8-2

Redundant-modelthermal strains are propore_ional to ehordwise

thermal strains obtained from a plane-strain analysis; i.e.,

6x_ Arrangement i

(61) Arrangement i = (61) Redundant plane-strain

model ex_ Arrangment i analysis

where: i = x, y, xy

The first assumption states that airloads are based mainly on equilibrium

and vary little with perturbations in panel stiffness. The second assumption

is supported by the close correlation (see figs. 8-1, 8-2, and 8-3) of chord-

wise thermal strains obtained from redundant-model and the plane-strain analyses.

Average thermal strains used for final structural sizing of the five

monocoque primary-structure concepts are shown in table 8-7. Average values

for the chordwise thermal strains for each arrangement were obtained from the

plane-strain analyses and are shown in figures 8-4 through 8-8.

MONOCOQUE HONEYCOMB SANDWICH LOADS

The honeycomb sandwich primary structure was evaluated with lower surface

heat shields and insulation outboard of the one-third wing chord, since this

arrangement has the lowest weight for the monocoque waffle concept. Using the

results of the intermediate screening, extensional and shear stiffnesses were

input into the final redundant-model analysis. Thermal data (a_T) for each

flight condition were based on the temperatures obtained from a detailed tran-

sient thermal analysis. Table 8-8 shows the final internal loads, resulting

from the redundant-model analysis, used for the final structural sizing.

Comparison of the surface panel equivalent extensional and shear thick-

nesses for the redundant model and the sized honeycomb sandwich is shown in

table 8-8. Good correlation is obtained in all areas with the exception of

the lower inboard area where a considerable decrease is noted.

Average thermal strains used for the final structural sizing are shown

in table 8- 9 for the three flight conditions.

SEMIMONOCOQUE SPANWISE LOADS

Following the intermediate screening, the equivalent extensional and

shear stiffnesses of the tubular concept (representative of the spanwise

concepts), as shown in section 6_ were input into the final redundant-model

analysis. Thermal data (a_T) for each flight condition were based on the

temperatures obtained from a detailed transient thermal analysis at 30 wing

locations with insulation at the lower surface outboard area. The internal

loads resulting from the spanwise redundant-model analysis are shown in

table 8-10.

8-3

J

A comparison between the surface panel stiffnesses input into the final

redundant model and those obtained by analysis for the two better concepts

using the final redundant model internal loads is shown in table 8-12. Good

agreement in extensional and shear stiffness is obtained. A comparison

between redundant model and plane-strain thermal stresses for identical

stiffnesses and thermal data input is shown in figures 8-11, 8-12, and 8-13.

For all thermal-protection arrangements, except that used in the

redundant model, the thermal strains were calculated by using the mathemat-

ical relationship stated on page 6-2.

The plane-strain limit chordwise thermal stresses for each of the flight

conditions for the two thermal-protection arrangements are shown in figures

8-14 through 8-19. The airloads, which are least susceptible to slight changes

in extensional and shear stiffnesses, were considered to be invariant for all

thermal-protection arrangements. Based on the thermal-strain ratio and constant

airloads, the internal airloads and thermal strains for the various arrange-

ments for each flight condition can be obtained. Tables 8-13 through 8-18

contain the inplane loads (Nx, Ny, and Nxy), the chordwise axial thermal

strains (_x and _y), thermal shear strain (Exy)_ pressure, and average panel

t emperat ure.

Insulation was placed to maintain the 1600°F material limit, to minimize

thermal gradients in the spanwise direction, and to provide a match between the

gradients through the wing and the fuselage. Figure 8-18"shows the reductions

in thermal stresses that result from proper insulation placement.

SEMIMONOCOQUE CHORDWISE LOADS

The results of the initial structural sizing were reviewed, and the

convex beaded upper/tubular lower arrangement was selected for input into the

chordwise redundant-model analyses. This arrangement was considered represent-

ative of the candidates to be carried to the detail sizing analysis. The

extensional and shear stiffnesses, panel dimensions, cap areas_ and basic

description of the model input are presented in section 6.

The temperature data (_T) were input for each flight condition. These

data were based on radiation-equilibrium isotherm temperatures_ obtained from

a detailed gross model thermal analysis performed at 30 wing locations. The

ultimate loads resulting from this chordwise redundant-model run are shown in

table 8-19 for the three flight conditions. A comparison between the stiff-

nesses of the structure sized by using the redundant-model loads is shown in

table 8-20. However, the stiffnesses resulting from the minimum-weight chord-

wise structural arrangement were observed to differ from the stiffenesses used

for the redundant-model analysis. The primary differences encompassed the

shear stiffnesses, the extensional stiff_esses for the upper and lower surface

spanwise direction (effecting spar-cap geomet_)_ and the extensional stiff-

nesses for the lower surface chordwise direction (affecting lower surface panel

shape). Therefore, a new redundant analysis was conducted with the actual

stiffnesses of the minimum-weight chordwise structural arrangement (provided

later in this discussion).

8-4

The following combinations of tubular convex-beaded primary-structure

and thermal-protection arrangements were assessed:

Primary structure and

heat-shield arrangement a

Insulation arrangement

Upper: tubular No

Lower: tubular Yes b

Upper: convex beaded No

b

Lower : tubular Yes

Upper: convex beaded No

Lower: convex beaded No

Upper: convex beaded

Center lower: convex beaded

No tubular Yes b Inboard and Outboard lower: a Tubular upper surface under fuselage for all arrangements.

Convex beaded: no heat shields

Tubular: Heat shields required

b

Insulation on lower surface outboard.

The plane-strain thermal stresses for all flight conditions for the

candidate thermal-protection arrangements are presented in figures 8-19

through 8-39.

Using the same assumption as stated in the semimonocoque spanwise section 3

invariant airloads and the thermal-strain ratio 3 the loads and strains for all

the flight conditions for each candidate arrangement can be determined. Tables

8-21 through 8-41 contain the inplane loads (Nx, Ny, and Nxy ) as well as the

chordwise axial theru_l strains (_x) and the thermal shear strains (_xy). The

pressure and average panel temperature are also listed.

As shown in figure 8-29 and table 8-31, the tubular lower/convex beaded

upper surface arrangement with insulation at the lower surface outboard area

provides the lowest thermal stresses and strains.

The load results of the new and final chordwise redundant analysis for

the three flight conditions_ presented in table 8-40, indicate lower airloads

in the spanwise direction when compared to the loads of table 8-19. For example_

the lower s_face spanwise loads for the inboard area B (BL 120 to 212) were

reduced from -1122 ib/in, to -965 ib/in._ at the +2.0-g flight condition. The

chordwise panel airloads remained approximately the same for both surfaces at

the three flight conditions. In general_ the shear and thermal loads were

reduced.

8-5

Tables 8-43 through 8-45 contain the final airloads_ thermal strains, pressures_ and average panel temperatures for the three flight conditions.

A stiffness comparison between the final sized structure and the

input into the redundant model, shown in table 8-46, shows good correlation

in almost all areas.

STATICALLY DETERMINATE LOADS

Based on the results of the semimonocoque spanwise initial structural

sizing_ the tubular concept was input into the statically determinate redundant

model. The extensional and shear stiffnesses_ panel dimensions_ cap areas_

and basic description of the model input are presented in section 6.

Thermal data (a_T) were input for each flight condition. These data

were based on the final temperature isotherms. The internal loads resulting

from this redundant model run are shown in table 8-48. A comparison between

the final-model internal loads for the selected beaded concept is shown in

table 8-49 .

Good agreement in extensional stiffness is obtained in the center and

inboard regions_ while a variation of approximately 30 percent is recorded

in the outboard region. This same trend is obtained in shear stiffness. The

airloads and thermal strains used for the final sizing were the final redundant-

model loads. These loads are presented in tables 8-49 through 8-51.

8-6

TABLE 8-1

LOADS USED FOR INITIAL PANEL WEIGHT SCREENING

Wing surface

Lower

Upper

i i liJ i i ,

lb/im

-84 -1000 Chordwise

N X

_325

Spanwise

Ny lb/in. -300

, i i i ,

Shear( a )

-32

N y lb/,n. -13_

aused for monocoque only.

.-.g,I • "-'-',-" -'-',-" • I_" T

---_1 5 q 1,4-

-"_1 • j I._l-

.,, _1 I, 'x, I1_

Sponwi se

8-7

L'.- O_ C_ ,.=., I c,I o_ I O,1 O_ v I ¢_ "" b- I c,,I _f_ I v

v

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8-8

TABLE 8-3

ULTIMATE THERMAL STRAINS AND STRESSES_ +2.0-g MANEUVER CONDITION

(Preliminary Redundant-Model Analysis for Intermediate Weight Screening)

Y

I i

+f

x (_x)

Chordwise

I

I-

Stresses, Strains, psi in./in.

Surface Lower Lower

Upper Upper

f =36.3 x 103

Panels

f =-23.7 x i0 _ ¢ =-1.315 x i0

¢x=1.59 x 10 -3

X X X

Between

f= 4.1 ¢ = 0.228

f =-1.89 ¢_ =-0.0831

BL 120-220

y Y Y Y

f =-3.55 7 = 0.672

y =-0. 512

fxy=5.9

xy

Panels

f = -42.1

¢ = -2.02

f = 23.9 ¢ = 1.05

between x X X

BL 220- f = "-6.75 f = 4.45 =-0.412 = 2.13

Y Y Y Y

outboard

f = -4.6

f = -11.25 7 =-0.524 = -1.4

xy xy

a Positive values indicate tension; negative values indicate compression.

8-9

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8- 23

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8-24

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Next: Section 9 →

Section 9

INTERNAL THERMAL ANALYSIS

by

D. A. Brogan, F. R. Mastroly, and F. L. Guard

9-i

CONTENTS Page INTmNAL THERMAL ANALYSIS 9-1 MONOCOQUE WAFFLE CONCEPTS 9-1 HONEYCOMB-CORE SANDWICH CONCEFf 9-6 SEMIMONOCOQUE SPANWISE CONCEPTS 9-6 SEMINONOCOQUE CHORDWISE CONCEFf 9-10 STATICALLY DETERMINATE CONCEPT 9-ii R_ERENCES 9-12 ii, /ii_i • 9-iii ILLUSTRATIONS Figure No.

Page 9-1 Wing-fuselage cross-section temperatures for candidate thermal protection arrangements at +2.0-g condition 9-18 9-2 Temperatures at -0.5-g condition for outboard monocoque waffle panels and heat shield vs insula- tion thickness 9-20 9-3 Temperatures at +2.0-g condition for outboard monocoque waffle panels and heat shield vs insulation thickness 9-20

9-4

Temperatures at cruise condition for outboard monocoque waffle panels and heat shield vs insulation thickness 9-21 Insulation and heat shield location for monocoque waffle primary-structure concept thermal analysis 9-21 Z Wing isotherms at -0,_-g condition for monocoque waffle panels with partial lower heat shield and insulation 9-22 9-?

Wing isotherms at +2.0-g condition for monocoque waffle panels with partial lower heat shield and insulation 9-23 ],> 9-8 Wing isotherms at cruise _ondition for monocoque i iil _ waffle panels with partial lower heat shield insulation 9-23 i 9-9 Panel and beam cap temperatures in OF at fuselage- wing intersection area for monocoque waffle concept 9-24 9-10 Panel and beam cap temperatures in oF at outboard area for monocoque waffle concept 9-2_ 9-ii Waffle panels temperatures (skin and stiffener tip) vs time, inboard location. 9-26 9-12 Waffle panels temperatures (skin and stiffener tip) vs time, outboard location. 9-26 Temperature differentials through m0nocoque waffle cross sections. 9-27 Heat shield isotherms for honeycomb sandwich with heat shield and insulation on lower surface outboard 9-28 Figure No.

Page 9-15 Panel isotherms at -0.5-g condition for exterior skin of honeycomb-core sandwich with heat shield and insulation on lower surface outboard. 9-29 9-16 Panel isotherms at +2.0-g condition for exterior skin of honeycomb-core sandwich with heat shield and insulation on lower surface outboard. 9-30 9-17 Panel isotherms at cruise condition for exterior skin of honeycomb-core sandwich with heat shield and insulation on lower surface outboard. 9-31 9-18 Temperatures at -O.5-g condition for outboard semimonocoque panels with upper and lower heat shields vs insulation thickness. 9-32 i _ _, 9-19 Temperatures at +2.0-g condition for outboard semimonocoque panels with upper and lower heat shields vs insulation thickness. 9-32 9-20 Temperatures at cruise conditions for outboard semimonocoque panels with upper and lower heat hields vs insulation thickness 9-33 9-21 Temperatures at -O.5-g condition for outboard semimonocoque panels with lower heat shield only vs insulation thickness. 9-33 9-22 Temperatures at +2.0-g condition for outboard " semimonocoque panels with lower heat shield only vs insulation thickness. 9-3h 9-23 Temperatures at cruise for outboard semimonocoque panels with lower heat shield only vs insulation / thickness. 9-3h InSulation placement for semimonocoque primary structure-concepts thermal analysis. _ 9-35 Panel isotherms at-0.5-g condition for semimonocoque panels with upper and lower heat shields and no in sul ati on. 9-36 9-26 Heat-shield isotherms at -0.5-g condition for semimonocoque panels with upper and lower heat shields and no insulation. 9-36 9-27 Panel isotherms at +2.0-g condition for semi- monocoque panels with upper and lower heat shields and no _sulation. 9-B7 Y-vi Page Figure No.

9-28 Heat-shield isotherms at +2.0-g condition for semi- monocoque panels with upper and lower heat shields and no insulation. 9-37 Panel isotherms at cruise condition for semimonoco-

9- 9

que panels with upper and lower heat shields and no insulation. 9-38 Panel isotherms at cruise condition for semimono-

9-30

coque panels with upper and lower heat shields and no insulation. 9-38 9-31 Panel isotherms at -0.5-g condition for semimono- coque panels with upper and lower heat shields and Z partial insulation. 9-39 Heat-shield isotherms at -0.5-g condition for semi- 9-32 monocoque panels with upper and lower heat shields • a_d partial insulation. 9-39 9-33 Panel isotherms at +2.0-g condition for semimono- coque panels with upper and lower heat Shields ....

and partial insulation. 9-40 - 9-34 Heat-shield isotherms at +2.0-g condition for _ upper and lower heat shields with semimonocoque _ panels and partial insulation. 9-40 2 Panel isotherms at cruise condition for semimono- •

9-35

coque panels with upper and lower heat shields and partial insulation. 9-41 i[ 9-36 Hear'Shield isotherms at cruise condition for [_ semimomocoque panels with upper and lower heat _-_ shields and parZial insulation_ .... 9-_ _ Panel _isotherms at -0.5-g condition for semimono- 9-37 coque panels with lower heat shield only a_pa_tial insulation. 9-42 Heat-shield isotherms at -0.5-g condition for semi- 9'38 monoeOqUe panels with lower heat shield and partial insulation. 9-42 Panel isotherms at +2.0-g condition for semimono- 9-39 i,_i ii_il : coque panels with lower heat shield oniy and par- tial insulation. 9-43 Heat-shield isotherms at +2.0-g condition for semi- 9-40 monocoque panels wi_u lower heat shield and partial insulation. 9-_.3 9-vii Page .... Figure No.

........ 9-hl Wing isotherms at cruise conditions for semimono- coque panels with lower heat shield only and partial insulation. 9-44 ........ • 9_k2 Wing isotherms at cruise condition for semimonocoque panels with partial insulation and lower heat shield.9-h4 Typical geometries of beam cap studies for semi-

• 9. 3

: :i?............

monocoque primary structure thermal analysis. 9-45 9-44 Temperature difference from middle of panel to adjacent beam cap for upper surface at -0.5-g and for lower surface at +2.0-g for semimonocoque panels. 9-46 Tubular panel vs time at inboard location. 9-47 Tubular panel temperature vs time at outboard location with insulation. 9-47 " 9-h7 Tubular panel temperatures vs time aL outboard location without insulation 9-h8 9-48 Temperature differentials in OF through semimono- coque spanwise tubular stiffened panels. 9-49 9-h.9 Temperature differentials in OF through semimono- coque span_ise trapezoidal-corrugation panels. 9-49 Temperature differentials in °F. through semi- 9-50 monocoque spanwise-beaded panel_. 9-50 .

9-91 Sem_monoooque chordwise-stiffened panel temper- • a%ures vs time as inboard location. 9-50 , 9-52 Semimonocoque chordwise-stiffened panel temperatures vs time at outboard location with insulation. 9-51 ....

Temperature differentials in OF through semimenoco- 9-53 que chordwise-stiffened panel with convex beaded upper surface. 9-51.

_ ii!

ii_i : <ii TABLE S Table No.

Page .

9-1 Temperatures and thermal gradients for monocoque _i _II i< ii _ i _ .....

honeycomb-core sandwich panels with outboard lower surface heat shield and insulation 9-13 _i _ 9-2 Panel temperatures for statically determinate beaded concept, heat shields on exposed surfaces 9-14 no insulation.

9-3 Panel temperatures for statically determinate beaded concept, heat shields on exposed surfaces 1/8 in. insulation on lower surface from _ to BL212 9-15

9-L

Panel temperatures for statically determinate beaded concept, heat shields on exposed surfaces 1/4 in. insulation on lower surfaces from 9-16 to BL212

9-5

Panel temperatures for statically determinate beaded concept, heat shields on exposed surfaces, 1/8 in. insulation on lower surface from BL 304 to outboard. 9-17 9-ix

Next: Section 9 →

Section 9

Section 9 SYMBOLS Area A Area between _ and BL 120 of wing study area Area B Area between BL 120 and BL 212 of wing study area Area C Area between BL 212 and BL 350 of wing study area BL Butt Line FS Fuselage Station Gravitational acceleration g T Temperature TI Honeycomb-core sandwich panel external skin temperature T Honeycomb-core sandwich panel internal skin temperature T(I) Exterior face temperature of upper surface panel of semimonoco- que concepts; waffle skin temperature T(2) Interior face temperature of upper surface panel of semimonoco- que concepts; waffle temperature at base of stiffener T(3) Interior face temperature of lower surface pan_l of semimonoco- que concepts; temperature at tip of stiffener on waffle panel T(4) Exterior face temperature of lower surface panel of semimonocoque concepts Heat shield temperature T HS Equivalent thickness AT Temperature difference between external and internal face sheets of honeycomb-core sandwich panel AT Waffle-panel skin to stiffener-tip temperature differential a Waffle-panel stiffener base to tip temperature differential AT b AT Semimonocoque lower surface panel temperature differential lower Semimonocoque upper surface panel temperature differential AT upper 9-xi

Next: Section 9 →

Section 9

INTERNAL THERMAL ANALYSIS

Detail internal thermal analyses were conducted. The thermal analyses

required for the heat shield and leading edge comparison evaluations are pre-

sented in sections 20 and 21.

MONOCOQUEWAFFLE CONCEPTS

The thermal-protection arrangementswere determined on the basis of

material capability, practicality of design for the given wing cross-section,

and detailed thermal analysis data. The thermal analysis data include tran-

sient effects on structural temperatures and isotherms generated for each

candidate thermal-protection arrangement. The transient effects are based on

a general thermal-model which includes effects of heat-shield placement, lower

surface insulation, and spar/rib size. Typical temperature distributions for

the candidate thermal-protection arrangements at FS 2320 are shown in figure 9-1.

Figure 9-1 presents wing-fuselage temperatures (+2.0-g condition) for the

candidate thermal-protection system arrangements and indicates the temperature

and gradient compatability of the fuselage and wing. The most vertical temper-

ature profiles of figure 9-1 indicates the lowest thermal gradient through the

wing and fuselage cross-section. Whenthese profiles are close together

horizontally, the spanwise wing surface thermal gradients are lowest. Using

these criteria, the arrangement with lower surface heat shields and insulation

outboard of the one-third wing chord provides the lowest spanwise wing thermal

gradients, and the closest match between the fuselage gradient and the gradient

through the wing.

9-1

Thermal analysis of the monocoque (waffle panel) structural concept was

accomplished with three different approaches. All were transient analyses using

the computer program of reference 9-1 for the solution of thermal networks

representing the actual structure with varying degrees of complexity. The

first method, or "gross model" approach, analyzed the section of wing between

FS 2320 and FS 2412 and from vehicle centerline to the wing leading edge, as

shown in the sketch below:

ANALYZED

Primary structures (upper and lower panels and vertical webs) were represented

by flat plates of uniform thickness and temperature. Internal heat transfer

was by radiation only_ with configuration factors determined for diffusely

emitting and reflecting gray surfaces by the Hottel matrix method. The gross

model approach was used to determine meantemperature histories for panels,

webs, and heat shields_ beamcap temperature histories, and the effects on all

temperatures of varying insulation thickness in thermally protected areas.

The second approach was used to develop isotherms for the entire wing structure

and employed the samedegree of thermal network complexity as the gross model

approach. Thirty locations on the wing were examined. This provided an

adequate base from which to draw temperature pattern lines for the entire

upper and lower wing surfaces at specific trajectory times. The third

approach was a detailed analysis of the waffle panel structure, using a

thermal network of five nodes (one for the waffle skin and foDr along the

stiffener) to account for conduction and radiation through the panel. Upper

and lower surface panels were examinedat locations along FS 2366 (under

fuselage, inboard wing_ and outboard wing), accounting for radiation heat

transfer within the panel-web wing box structure by the Hottel matrix method.

The detailed temperatures derived were used to determine local stresses and

deflections due to temperature gradients through the panel structure.

Preliminary temperatures determined from the radiation equilibrium

analyses indicated that thermal protection is required at the outboard wing

areas to limit primary structure temperatures to under 1600°F and to control

thermal gradients. To determine the extent of thermal protection required for

the monocoqueconcept, the variation in structure temperatures with insulation

thickness was examined at one fuselage station (FS 2366) from BL 240 to BL 360.

These temperatures, derived from the gross model analysis, were examinedat the

9-2

-0.5g condition (20.3 minutes in the trajectory) to observe upper surface peaks,

at the +2.0g condition (20.6 minutes) to observe lower surface peaks, and

during cruise (40 minutes) to observe near steady-state effects. The gross

model assumedflat structural panels with an equivalent thickness _ of 0.05

inch and 0.06 inch for the upper and lower surfaces, respectively. A 0.011

inch flat sheet of Rene' 41 was assumedfor the heat shield on the lower sur-

face. The upper surface was unshielded. Insulation material was 6.0 pcf Dyna-

Flex. Figures 9-2, 9-3, and 9-4 showwaffle panel and lower heat shield

temperatures along FS 2366 for the three flight conditions, respectively.

Each figure showsthe temperatures derived for no insulation and for insulation

thicknesses of 0.25 and 0.50 inch attached to the inner surface of the shield.

The general effect of insulation in this area is to lower panel temperatures

and to increase heat shield temperatures. Insulation thickness for the monoco-

que waffle concept was selected to maintain the 1600°F material limit and to

minimize temperature level differences in the spanwise direction to lower

thermal stresses. Accordingly, based on the temperatures at FS 2366 shown in

these figures, an insulation thickness of 0.25 inch is used from the leading

edge to BL 341, a thickness of 0.12 inch is used between BL 341 and BL 268,

and no insulation is used with the heat shield from BL 268 to BL 232. The

remaining inboard lower surface is unshielded. Application of these results

to the entire wing is shownin figure 9-5. The 0.25 inch insulation is used

from the leading edge inboard to a line 34 inches from the edge and running

parallel to it. The 0.12 inch insulation covers from this line to three-

fourths of the distance to the inboard edge of the heat shield. This distance

varies because the inboard heat shield edge follows roughly a line under the

forward upper surface slope break, which does not parallel the leading edge.

The entire lower surface is shielded outboard of BL 442 to protect against

higher surface temperatures due to shorter leading edge distances in this area.

Isotherms for the monocoque waffle primary structure and heat shield are

shown in figures 9-6, 9-7, and 9-8 for the -0.5g, +2.0g, and cruise flight

conditions, respectively. Since the analysis method for the 30 wing locations

used to derive the isotherm temperatures did not account for insulation effects,

temperatures in the shielded area were adjusted for insulation by using the

curves in figures 9-2 through 9-4. Dashedlines shown on the_ower surface

are located under the upper surface slope breaks, shownwith solid lines on

the upper surface diagram. Somelower surface isotherms are located along

these dashed lines, reflecting the influence of sharp temperature differences

between differently sloped sections of the upper surface. _l_eheat shield is

shown displaced from its position covering part of the lower surface for

illustration clarity. The effect of the heat shield on the temperatures of

both surfaces is illustrated particularly at BL 442. Comparisonof the

temperatures of unshielded areas of the monocoque waffle wing with the radi-

ation equilibrium isotherms shownin the aerodynamic heating section, section

3, substantiates the trend to overpredict temperatures when transient effects

are neglected during peak heating. _ne transient analysis of the monocoque

waffle concept predicts temperature for the upper surface at the -0.5g

condition and for the lower surface at the +2.0g condition that are lO0°F to

200°F below the steady-state predictions of the radiation equilibrium analysis.

At cruise, however, both methods predict similar temperatures because of the

9-3 near steady-state heating conditions. The results of the isotherm analysis were used on the redundant model stress program to determine stress levels over the wing.

To aid in the selection of spar and rib cap configurations, an analysis was performed to determine temperature gradients in the fuselage-wing inter- section area of the monocoque waffle structural concept. The thermal model was similar to the gross model approach at this location with the following additional details (see figure 9-9): (1) a small section (15 inches) of the fuselage skin was included in the analysis to determine fuselage temperatures at the intersection corner and their effect on wing temperatures; (2) upper panels and the fuselage section were divided into several nodes to determine panel temperature variations; the effect of the fuel tank inside the fuselage was estimated with an approximate thermal model of an insulated cryogenic tank.

The single shear joint beam caps and the double shear joint upper cap at BL 120 were heated by radiation heat transfer from the internal structure and by aerodynamic heating when applicable. Conduction from panels to caps is of a small order compared to radiation at high temperatures, and was therefore neglected to yield conservative results for panel to cap temperature gradients.

Figure 9-9 shows temperatures for panels, beam caps, and webs at FS 2345 between BL 90 and BL 143 for three flight conditions. The temperatures at the right of the figure are arranged schematically to refer to the circled node locations on the sketch at the left of the figure. Temperature variations on the upper surface panel are lO°F over a distance of approximately 15 inches at the panel center. Panel to beam cap temperature differences at BL 120 are under 70°F for the two transient conditions and at cruise. These temperature variations occur over a distance of about 5 inches across the-panel. Peak temperature differential between the fuselage skin and the upper cap at BL 120 occurs at the +2.0g condition and is 96°F over a distance of about 3 inches.

The panel to cap temperature differences derived at BL 90 and BL 143 are typi- cal for the wing structure under the fuselage and on the "flat" (parallel surface) portion of the wing, respectively.

Panel and rib cap temperatures at the insulated outboard location between BL 321 and BL 365 at FS 2366 are shown in figure 9-10. Insulation thickness is 0.12 inch between BL 321 BL 341 and 0.25 inch outboard. Temperatures derived from the gross model approach are shown for the -0.5g, +2.0g, and cruise flight conditions. Mid-panel to cap temperature differentials are below 50°F for all conditions except for the upper caps at BL 321 and BL 343 during -0.5g (BL 321 cap is 60°F cooler than adjacent panel at BL 332 and BL 343 caps is 75°F cooler than adjacent panel at BL 354) and the upper cap at BL 365 during +2.0g and cruise (60°F hotter than adjacent panel at BL 354). Peak differentials at -0.5g are caused by peak heating on the upper surface and the temperature response lag of the cap due to its greater mass per exposed area. The differ- ential between the upper panel at BL 354 and the upper cap at BL 365 during +2.0g maneuver is also caused by the response lag of the cap as the upper structure cools from its peak temperature condition at -0.5g. This differential is maintained through cruise.

A detailed thermal analysis was performed to determine local stresses and

deflections due to temperature gradients through the panel structure. Typical

results of the transient analysis of detailed waffle panel structure are shown

in figure 9-11 for an inboard location (BL 166) and in figure 9-12 for an out-

board surface waffle skin and stiffener tip are shownfrom take-off (time equal

zero) to mid-cruise (time equal 40minutes). The outboard location temperatures

are based on using a heat shield with 0.25 inch insulation for thermal protec-

tion. During the climb portion of the trajectory (first 20 minutes), temper-

ature increases for both the waffle skin and tip are regular for both surfaces

at the inboard and at the outboard locations. Thermal gradients across any of

the panels are under 70°F. During the trajectory perturbations at the end of

climb, large gradients (over 150°F) are experienced by somepanels, and these

are detailed below. After the perturbations, panel gradients stabilize

rapidly to values under 65°F. Thus, from take-off to mid-cruise the peak

thermal gradients as well as peak temperatures occur at the -0.5g or +2.0g

condition, and these have correctly been defined as the thermally critical

conditions.

Peak panel gradients at the critical conditions and the stabilized values

at cruise are shown in figure 9-13 for four wing locations at FS 2366. Panels

under the fuselage (BL 60), at the inboard location (BL 166), at an outboard

location without insulation (BL 258)_ and at the insulated outboard location

(BL 350), were analyzed. Panel gradients at BL 350 are shownalso for the

case of no insulation. Temperature differences from waffle skin to stiffener

tip and from stiffener base to tip are shown. Becauseof relatively small

mass and large exposure area, the skin portion of the waffle is more sensitive

to peak transient heating than the stiffener. Thus gradients from skin to

stiffener tip are generally higher than those from stiffener base to tip during

the trajectory perturbations. The largest gradients for the upper surface

occur at the outboard (forward wedge) locations during the -0.5g condition,

and for the lower surface at the inboard (unshielded) locations during the

+2.0g condition. The major effects of removing insulation at BL 350 are to

diminish peak upper surface gradients slightly for the -0.5g condition and to

increase all panel gradients at +2.0g and cruise substantially.

9-5

HONEYCOMB-CORE SANDWICH CONCEPT A detailed transient thermal analysis was conducted to determine local stresses and deflections caused by temperature gradients through the panel structure. Figures 9-14 to 9-17 show structure and heat-shield temperatures for the lower surface insulation outboard arrangement. Additional temper- ature and thermal gradient data are shown in table 9-1 for the three flight conditions. During the structural sizing, various combinations of face thicknesses, core densities, and sandwich heights were considered to minimize the panel thermal gradients. As indicated in table 9-1, the largest thermal gradient (323°F) occurs at the +2.0-g maneuver condition on the wing lower surface panel under the fuselage.

S_IMONOCOQUE SPANWISE CONCEPTS Analysis of the semimonoeoque primary structure concepts were conducted with the same procedures outlined for the monocoque waffle structural concept.

A gross model analysis, assuming flat uniform panels, was used to determine mean temperature histories for the primary structure and the effects of vary- ing insulation thickness in thermally protected areas. Isotherms based on analysis at 30 wing locations were developed for both surfaces of the wing for various combinations of heat shields and insulation. Analyses were performed for detailed thermal models of the various semimonocoque panel concepts to determine local stresses and deflections due to temperature gradients through the panel structure. The gross model and isotherm analyses for the semi- monocoque structure are applicable to both the spanwise stiffened and chord- wise stiffened eoneepts_ but are presented only in the spanwise concepts discussion and referenced in the chordwise concepts section.

Preliminary temperatures determined from the radiation equilibrium analysis indicated that tkermal protection is required at the outboard and forward wing areas to limit primary structure temperatures to 1600°F and to control thermal gradients. To determine the extent of thermal protection required for the semimonocoque concepts, the variation in structure temper- atures with insulation thickness and heat shield placement was examined at one fuselage station (FS 2366 ) from BL 240 to BL 360. These temperatures, derived from the gross model analysis, were examined at the -0.5g condition to observe upper surface maximums, at the 2.0g condition to observe lower surface maximums, and at mid-cruise to observe near steady-state effects.

The gross model assumed flat structural panels with an equivalent weight thickness of 0.029 inch for all semimonocoque concepts. Heat shields were assumed to be 0.Oll-inch flat sheets of Rene' 41, and insulation material was 6.0 ib/ft3 Dyna-Flex. Figures 9-18, 9-19, and 9-20, show temperatures along FS 2366 for semimonocoque panels and upper and lower heat shields at the three flight conditions. Figures 9-21, 9-22, and 9-23, show temperatures for the same conditions but with a lower surface heat shield only. Each of the figures shows temperatures derived for no insulation and for insulation thicknesses of 0.25 and 0.50 inch attached to the inner surface of the shield.

9_ The general effect of insulation in this area is to reduce structural panel temperatures and to increase lower surface heat shield temperatures.

The most noticeable effect occurs as insulation is increased from none to a thickness of 0.25 inch. The resulting temperature change is more than twice the additional change caused by increasing the thickness from 0.25 to 0.50 inch.

At the transient conditions (-0.5g and 2.0g), insulation reduces lower panel temperatures more severly than upper panel temperatures, and affects upper heat shield temperatures less than either panel. This non-uniform change in temperatures through the structure may causeitemperature lines to cross, as seen in figures 9118, 9-19,9_21, and 9-22 for-the insulation cases. The un- insulated transient cases and all cases during the steady-state conditions of cruise show a normal temperature progression from one external surface oi' the structure to the other. The effect of deleting the upper heat shield is most noticeable on the upper panel. Upper panel temperatures are hotter by lO0 o to 150°F at the -0.5g condition for the cases without an upper surface shield.

At cruise, upper and lower panel temperatures are cooler by 50 ° to lO0°F with no upper heat shield, due to direct radiation relief to space for the upper panel.

Placement of insulation for the semimonocoque concepts was selected to maintain the 1600°F material limit and to minimize temperature differences in the spanwise direction and to control the gradient through the wing to match the fuselage gradient. Temperatures derived from the insulated semimonocoque structures, either with or without an upper surface heat shield_ were based on the insulation placement shown in figure 9-24. The cross section at FS 2320 in this illustration shows 0.25-inch insulation used from BL 212 to BL 258, and 0.50-inch insulation from BL 258 to the leading edge.

Isotherms for the semimonocoque primary structure concepts were derived for three arrangements of heat shields and insulation. Figures 9-25 through 9-30 show primary structure and heat shield temperatures at the -0.5g, 2.0g, and cruise flight conditions for the case with upper and lower heat shields and no insulation. Figures 9-31 through 9-36 show structure and heat shield temperatures for the same structure configuration and flight conditions but with insulation per figure9-24. Figures 9-37 through 9-42 show temperatures for the arrangement with lower heat shield only and insulation per figure 9-24.

9-7 For each flight condition, structural panel temperatures are shown first and then heat shield temperatures in the figure immediately following. Dashed lines shown on the lower surface in each figure are located under the upper surface slope breaks, shown with solid lines on the upper surface diagram.

Some lower surface isotherms are located along these dashed lines, reflecting the influence of sharp temperature differences between differently sloped sections of the upper surface. The effect of the fuselage on the wing is an increase in upper surface temperatures near the fuselage-wing intersection as radiation relief to space is reduced. General conclusions made upon examin- ation of the isotherms for the different thermal protection arrangements are the following: (a) upper surface (panel and heat shield) temperatures are maximum at the -0.5g flight condition; (b) lower surface temperatures are maximum at the 2.0g flight condition; (c) the effect of insulation at the forward wing area is generally to reduce peak structural temperatures by i00 ° to 250°F and to increase lower heat shield temperatures by 50o to lO0°F; and (d) omitting the upper surface heat shield increases upper panel temperatures at the forward section of the wing by 150°F during the -0.5g maneuver and generally reduces all structure temperatures by 50 ° to lO0°F at the other conditions. The results of the semi-monocoque isotherm analysis were used in the redundant model stress program to determine stress levels over the wing.

To aid in the selection of spar and rib cap configurations, a parametric analysis was conducted to determine the variation in panel-to-cap temperature different with cap mass. Typical geometries for caps examined with the semimonocoque structure are shown in figure 9-43. Cap mass is represented by the cross section area of the channel cap plus the area of the end close- out immediately above the cap. Total cross section area ranged from 0.2 to 0.8 square inch for a range of channel cap thickness from 0.030 to 0.125 inch. Temperature differences from mid-panel to an adjacent cap were examined along FS 2366 from under the fuselage to the leading edge.

Except for surfaces experiencing peak heating conditions (upper surface at -0.5g and lower surface at 2.0g), temperature differentials are under 50°F at all flight conditions for the range of cap areas examimed and a variety of heat shield/insulation arrangements. Temperature differences are smaller with the thinner caps, except that, at the steady-state heating conditions of cruise, beam cap temperatures are independent of mass and depend more on location (i.e., distance from the leading edge). For the transient peak heating conditions on either surface, the differential from panel to cap is generally above 50oF because of the temperature response lag of the cap due to its greater mass per exposed area. Figure 9-24 presents an attempt to correlate temperature differentials during peak heating computed at a number of locations with varying cap areas. Data are shown separately for surfaces with a heat shield and for surfaces without a heat shield. Within a 30OF band (shaded in the figures), temperature differentials seem to be fairly independent of panel location (upper or lower surface, inboard or outboard) and of cap location (outboard, inboard, forward or rearward) relative to the middile of the panel. Surfaces without a heat shield exhibit a greater differential compared to those with a heat shield due to direct exposure to aerodynamic heating.

9-8 _,)_ A detailed thermal analysis was performed to determine local stresses and deflection due to temperature gradients through the spanwise stiffened semi- monocoque panel structure concepts. Typica I results of thetransient analysis for the tubular panel are shown in figure 9-45 for an inboard location (BL166) and in figures 9-46 and 9-47 for an outboard Location (BL 300) with and without insulation_ respectively. Temperature-time histories are shown from takeoff (time zero) to mid-cruise (time = 40 minutes). Both loc- ations assume use of upper and lower heat shields. During cruise, in addition to lowering structure temperatures, insulation reduces the overall temperature gradient from the top of the upper panel to the bottom of the lower panel (point a to point d). This temperature difference is 150°F for the insulated concept (figure 9-46) compared to 260°F for the uninsulated concept (Figure 9-47).

The lower panel with insulation also shows a lower peak temperature (1370°F) at the 2.0g maneuver compared to the sharp peak temperature (1630°F) for the uninsulated panel. During climb_ insulation delays heating of the lower panel and causes a large temperature difference (350°F at time = i0 minutes) from the top of the upper panel to the bottom of the lower panel. For the uninsu- lated cases (inboard and outboard), this difference is under 100°F until about 15 minutes into climb. Peak temperature gradients across the individual panels during climb are about 200°F for all cases except for lower panel of the insul- ated arrangement, which shows practically no temperature difference until the end of climb.

The temperature-time histories shown for the tubular panels are represent- J ative of temperature histories for the other spanwise stiffened panel concepts with both heat shields. The other concepts (beaded and trapezoidal corrugation), however, have a single layer construction and exhibit less of a temperature differential between the outermost and intermost points on the" panel. Thus, curves for temperatures on these panel concepts would lie between the curves shown for the outermost and innermost points of the tubular panel. A comparison between detailed panel temperatures for all three spanwise concepts with temper- atures derived in the isotherm analysis (using the flat, uniform panel assumption) has shown that mean panel temperatures serived from both analysis methods are within 25°F for all flight conditions.

Panel gradients at the critical flight conditions (-0.5g _nd 2.0g) and at cruise are shown in figures 9-48, 9-49, and 9-50 for the tubular trapezoidal corrugated, and beaded panels_ respectively. Temperature d&_fer_ are shown in each case for three locations at FS 2366: under the fuselage (BL 60), inboard win_ (BL 166), and outboard wing (BL 309).

All cases assume upper and lower heat shields, and the outboard location is shown for no insulation and for insulation thicknesses of 0.25 and 0.50 inch.

Panel graidents at the cited flight conditions are 40°F or less for the trapezoidal corrugation and under 20°F for the beaded. These low gradients are the result of the single-layer construction of these panel concepts.

The tubular panel _s of double layer construction and exhibits gradients up to 155°F at the 2.0g condition. The effect of insulation at the outboard location for all the span_ise stiffened concepts is generally to reduce the temperature differential across the outboard panel, except during the -0.5g condition on the upper surface where the differential 9-9 almost doubles for 0.50-inch insulation compared to no insulation. These gradients were used to evaluate local thermal stresses and deflections in the panels and their effect on the overall stress levels of the wing.

SEMIMONOCOQUE CHORDWISE CONCEPT The parametric insulation analysis, panel-to-spar and-rib cap gradient analysis, and the isotherms developed for the semimonocoque primary structure are generally applicable to both the spanwise and chordwise stiffened concepts, and have been shown in the spanwise concepts section. Of particular interest for the chordwise concept are the previous curves which show the effect of insulation on structure temperatures with a lower heat shield only (figures 9-21 to 9-23), and the curves which present isotherms (figures 9-37 to 9-42) for the semimonocoque structure with a lower heat shield only. These curves are appl_cable to the chordwise stiffened concept which utilized an unshielded upper surface convex-beaded panel and shielded lower surface, and were used in the redundant model stress program to determine stress levels over the wing for this concept.

A detailed thermal analysis was conducted for the chordwise stiffened concept to determine local stresses and deflections due to temperature gradients through the panel structure. Figures 9-51 and 9-52 show temperature- time histories for the concept using convex-beaded upper surface panels and tubular lower surface panels with a lower heat shield. Temperatures are j shown from takeoff to mid-cruise for an uninsulated inboard location (FS 2366, BL 166) and an insulated outboard location (FS 2366, BL 300). For both locations, temperatures increase rapidly through the climb portion of the trajectory, peak sharply during the maneuvers at the end of climb_ then settle gradually to cruise values. At the outboard location, lower panel temperature peaks are attenuated at the 2.0g condition by the insulation, but the convex bead on the upper surface undergoes direct peak heating at the -0.5g condition and its temperature peaks sharply. The start of the bead near the leading edge experiences additional high local heating due to the ramp effect of the bead closeout. An estimate of 25 percent increase in the local heat transfer coefficient due to a 3-degree maximum chordwise slope at the closeout yields a local temperature increase of 90°F a{ the -0.5g condition.

Panel gradients at the critical flight conditions (-0.5g and 2.0g) and at cruise are shown in figure 9-53 for chordwise stiffened panels with a con- vex beaded upper surface. Temperature differences across the panels are shown for three locations at FS 2366: under the fuselage (BL 60), inboard wing (BL 166), and outboard wing (BL 300). A lower surface heat shield is assumed, and the temperature for the outboard location is shown for no insulation and for insulation thicknesses of 0.25 and 0.50 inch. Temperature differentials through the lower panel for this comcm_u are _mu_ ±_=_t_ to those for the spanwise tubular concept because of configuration similarity of the lower surface. The convex beaded upper surface, however, is directly {<!i '__ exposed to the airstream and panel gradients for the outboard area are double at -0.5g and 50 percent higher at cruise compared to the shielded tubular / 9 -I0

upper panel. The effect of insulation at the outboard location is generally

to reduce temperature differentials across the panels, except for the upper

surface at the -0. Sg condition where the differential increases from ll5°F

for no insulation to 162°F for 0.50-inch insulation.

STATICALLY DETERMINATE CONCEPT

Heat shields covered all exposed surfaces and three thermal-protection

arrangements were considered: (i) no insulation, (2) insulation on the

lower surface from _ to BL 212 (Areas A and B), and (3) insulation at the

lower surface outboard of the one-third wing chordline.

The second thermal-protection arrangement (inboard) was included to

investigate structural temperatures even lower than 1600°F to provide

minimum-gagepanel designs, since the spanwise loads were low. Becauseof

noncontinuous ribs and the allowable wing rotation at the fuselage, wing-to-

fuselage temperature compatibility is less important in this concept.

Detailed transient thermal analyses were conducted for the thermal-pro-

tection arrangements to determine local stresses and deflections from

temperature gradients through the panel structure. Average panel temperatures

for the candidate thermal protection arrangements are presented in tables 9-2

through 9-5.

Isotherms used for the redundant model input were for the heat shielded

and no insulation arrangement. These isotherms are identical to those shown

for the semimonocoque spanwise in figures 9-25 through 9-30.

9-Ii REFERENCES 9-1 Schultz, H. D.: Thermal Analyzer Computer Program for the Solution of General Heat Transfer Problems, Lockheed-California Company, LR 18902 July 1965. Published under NASA Contract NAS9-3349.

9-12 TABLE 9-1 HONEYCOMB SANDWICH TEMPERATURES AND THERMAL GRADIENTS a,b TABLE 18. - TEMPERATURES a AND THERMAL GRADIENTS FOR MONOCOQUE HONEYCOMB-CORE SANDWICH PANELS WITH OUTBOARD LOWER SURFACE HEAT SHIELD AND INSULATION

oF

Face sheet temperature, Loading Wing panel Item condition location BL 60 BL 166 BL 258 BL 350 980 1312 1588 1661 T 1 1055 1225 1386 1416 Upper T 2 -74 86 201 244

AT

-0.5-g 95 41 21 17 AT' 1166 1286 1396 1403 T 2 Lower 1260 1327 1416 1420 T 1 TH S 1007 1172 1409 T 1 1077 1252 1409 1443 Upper T 2

AT -70 -79 -47 -33

+2.0-g 323 257 122 18 AT 1211 1323 1434 1437 T 2 Lower 1534 1579 1557 1456 T 1 THS 1240 888 946 945 T 1 1276 1107 1137 1085 Upper T 2

AT -35 -219 -139

-191 Cruise AT 28 120 104 84 1298 1215 1241 1149 T 2 Lower 1335 1344 1233 132____6 T 1 1402 1494 THS a. Insulation and heat shield at outboard lower surface.

b. _Symbols: T 1 = external face sheet temperature T 2 = _[nternal face sheet temperature 2% T = T1 - T2 THS = heat-shield temperature Maximum temperatures are underlined.

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BL BL BL BL 120 166 212 304 Typical vehicle crass-section -- -. ,_ Fuselage upper _. temperature -_ ...,dk-,----- Fuselage upper _. temperature " BL 120 120 Q _ Average fuselage gradient __-- Average fuselagelgradlent

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1200 1400 1600 1200 1400 1600 Temperature, OF Thermal-protection arrangement - heat shieJcl Them+at+protection arrangement - heat shield end insulation lower surface outboard of lower surface outboard of one-thirdchordlinez one+third chordline no insulation Wing-f_selage cross-section temperatures for candidate Figure9-1.

thermal protection arrangements at +2.0-g condition 9-18 _ Fuselage u_per _. temperature

\

\_/- Average fuselage gradie.t Fuse/age _Fuselage.wing juncture 1200 1400 1600 Temperatuee, OF Thermal-protection arrangement - no heat shield, no insu[otlon Fuselage upper __ temperature "-_ --'_ _ Fuselage upper _ temperature

\

BL fZO Q Average Fuselage gzadient /_Avetage fuselage gradient Fuselage Fuselage-wing juncture 12_ 1400 1600 1200 _400 1600 Temperature, oF Temperature, OF Thermal-protection arrangement _ heat shields on entire lower ThermQl-protection arrangement - heat shield surface, no insulation on entire lower surface, i.sulatlon 7ower surface outboard of one-third chordline Figure 9-1.

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.50 in. insulation insulation No insulation 25 in 1 I I 320 360 _.uo_ 280 320 _6,,_ n 240 __')Rn_ 240 280 320 360 Butt line at FS 2366 Figure 9-3. Temperatures at +2.0-g condition for outboard monocoque waffle panels and heat shield vs insulation thickness

9-20 -

Upper surface

t

Lower surface _i!_ ¸¸*¸"!_!

Temperatures in OF _ / Figure 9-6.

Wing isotherms at -0.5-g condition for monocoque waffle panels with partial lower heat shield and insulation 9-22 Upper surface

___--- --- -- ,_ - - 7_ - - -7 - _-_----_--

Lower surface Heat shield __ Temperatures in OF _ _ / / Figure 9-7. Wing isotherms at +2.0-g condition for monocoque waffle panels with partial lower heat shield and insulation Upper 1025 ..._.__._ surface |300-- Lower surface Heat shield _ _ (displaced f°r clarity)_ __,_,,..._ o ".vo / Temperatures in F _ / Wing isotherms at cruise condition for monocoque waffle Figure 9-8.

panels with partial lower heat shield and insulation 9-23 ....I C ¢o u .r..I E I ¢....

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Web. _JII

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Heatshieid J _1395 _-- 1410 _-- 1395 _-- 1440 - 1455 + 2.0 g condition _.- 1440 L ii!

-- - - 1440 _ 1465 1485 _ 995 Cruise condition 985 _., "_ _ 980 1 O4O -- 1140 '" 1160 '- 1110 1100

f f t

BL 321 BL 343 BL 365 • 121n. insulation _ .25in. insulation Panel and beam cap temperatures in oF at outboard Figure 9-10.

area for monocoque waffle concept o I;::I .H I.-i -P

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.r-.t 9-28 Upper heat shield Upper panel Lower panel ....... (L) Lower heat shield 18 x 100 I f J f f / (U) _ I I 16 (u) ...- _. " J o 15

i

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0' No insulati_ _" ['

2,0 2_0 320 3_ 2,0 280320 3,0 2,0 2_0320 3,0

Butt line at FS 2366 Figure 9'18. Temperatures at -0.5-g condition for outboard semimonocoque panels with upper and lower heat shields vs insulation thickness (U) Upper heat shield Upper panel Lower panel (L) Lower heat shield 19 ^ 100 I t / / j- J J f CL) . / f I J (L) u. 16 o

i

2 15 /" I J E _ 14 (U) --" " (u)=.,/_'.,_' " ).50 in. insulation

I 0.25 in. insulation

No insulat|o_

f ¢1

I ,- 240 280 320 360 240 280 320 360 240 280 320 360 Butt llne at FS 2366 iFigure 9-19. Temperatures at +2.0-g condition for outboard semimonocoque panels with upper and lower heat shields vs insulation thickness ?-32 Upper heat shield Upper panel Lower panel Lower heat shield / J J I J I" (L) ,....-" _' i (L_ --- s (L) - _ " o u 13 / ..,, -" s / s' t I / /' s (u) -- i _' j I .25 in. insuJation _U)__ ""0-.501 n.

_o insulation I insulation | 240 280 320 360 240 280 320 360 240 280 320 360 Butt line at FS 2366 Temperatures at cruise condition for outboard semimonocoque panels Figure 9-20.

, • _:7 with upper and lower heat shields vs insulation thickness Upper panel Lower panel Heat shield 17 x iuu 16 J / ¢ J J f / / f vJ _ o u- 15 / g

/ J

insulatiOn No insulation 240 280 320 360 240 280 320 360 240 280 320 360 Butt line at FS 2366 Fig. 9-23. Temperatures at cruise for outboard semimonocoque panels with lower heat shield only vs insulation thickness ?

9-3k

/

I (1) 0 m .N 0 (1) 4-_ OJ I .rt _-_' I _ I_OO _12_o _ Temperatures I _ F t _/_\ • \ Figure 9-25. Panel isotherms at -0.5-g condition for s_mimonocoque panels 1 with upper and lower heat shields and no insulation Upper surface _f _// • 1L.__ _. 1250 > --- 1300 < _ _ _ 1250 // .. \ _ 7"- 1350 _'_"_"-'----_ '1300 Low ..... _¢e__"_/_ _. _

•

Figure 9-26. Heat-shield isotherms at -0.5-g condition for semimonocoque panels with upper and lower heat shields and no insulation R-36 Upper surface panels \ Lower surface panels

\

Temperatures :in OF \ Figure 9-27. Panel isotherms at +2.0-g condition for semimonocoque panels with upper and lower heat shields and no insulation Upper surface heat shield 1600 1550 Lower surface \ heat shield \ Temperatures in OF Figure 9-28. Heat-shield isotherms at +2.0-g condition for semimonocoque panels with upper and lower heat shields and no insulation ?-37 Upper surface panels 1300 J Temperatures in OF Panel isotherms at cruise condition for semimonocoque panels Figure 9-29.

/ with upper and lo_er heat shields and no insulation Upper surface heat shield Figure 9-30. Panel isotherms at cruise condition for semimonocoque panels with upper and lower heat shields and no insulation

9-38

-_--__ ..... ,._ _ ,,-----_____-- -

Temperatures in OF _ \ Figure 9-31. Panel isotherms at -0.5-g condition for semimonocoque panels ]y!

with upper and lower heat shields and partial insulation Upper surface _ _ // \ I -- llso_ _ _ 1300 1250 '----'----'_ 7-_o _'_--'-_ I-- \ emperatums |. F - " /\ Figure 9'_2. Heat-shield isotherms at -O.5-g condition for semimonocoque panels with upper and lower heat shields and partial insulation 9-59

i

"i

'_ __a _ _ _ t_o Figure 9-33. Panel isotherms at +2.0-g condition for sem_onocoque panels with upper and lower heat shields and partial insulation

_ _.._._

L_

.__ -.'_L':_-_--- ,_--______-_-_-_

,._,.,_ __!_-._7,_ _\

T_emperatums |n OF Figure 9-34.

Heat-shield isotherms at +2.0-g condition for upper and lower heat shields with semimonocoque panels and partial insulation ?-LO Upper surface " \ Temperatures in °F Figure 9-37. Panel isotherms at -0.5-g condition for semimonocoque panels .... with lower heat shield only and partial insulation ___ _ __ 1250 LOW ..... face _ _/4_20 ,_ _ Figure 9-38.

Heat-shield isotherms at -0.5-g condition for semimonocoque panels with lower heat shield and partial insulation ?-_.2

I

TLbmperol'ures in °r .

Figure 9-39.

Panel isotherms at +2.0-g condition for semimonocoque panels with lower heat shield only and partial insulation

- L__,_-- - _ _ :- _ .... r

_T_mperotures iln o F __ Figure 9-40- Heat-shield isotherms at +2.0-g condition for se_imonocoque panels with lower heat shield and partial insulation Figure 9-41. Wing isotherms at cruise condition for semimonocoque panels with lower heat shield only and partial insulation Lower surFoce __ _ ._. /Q_^ \ heat shield _ _ _. _ -,,u_ _ Temperatures in OF " ___\ Wing isotherms at cruise condition for semimonocoque Figure 9-42.

panels with partial insulation and lower heat shield ?-LL

Next: section area * →

section area *

Beam cap cross

section area *

i _ 3.25 in.

i

0.8 in

t _. .09 in.

{(

Web (typical)

i --_. 3.25 in.

0.5 in

4k-

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, .03 in

II

I

• 04 in.

3.25 in.

I-

i It

0.2 in 2

.04 in.

2.75 in.-- ................ _

* Includes area of end close-out above cap

Figure 9-43. Typical geometries of beam cap studies for semimonoeoque

primary structure thermal analysis

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FS 2366

//

BL 300

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Heat shield t r _ 2 Lower panel _,

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0 lO 20 30 Time, mln Tubular panel temperatures vs time at, Figure 9-47.

outboard location without insulation

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"a 4 _ m

>:_

&

z o o,- o,._ ,_

"6 ,-,"8 ! !

S_

II II I-- v 4-_ O I-- o o -o Z 7 -- !

L g

&

tI)

@ .'-,_

D U l.J .H

.__!

oi_,o 00_

,9, "_

N_ _c_._ 4_4a o° "-I

;o

mo _,o

,, &

o--el ,-!.o -r- D ! i •H I1_ 4-_ m

E_

I- t,- II II

_ m

.H v I--

7 -

4_ O

#_

"6 D I-- I-

.5 ° _ m

I • i¸'" 7_-_.

u o

9-_

FT(I) J Heat sh|eld

/

Upper panel Spanwlse vlew at FS 2366 Inboard Outboard Location BL 60 BL 166 BL 300 Condition Insulation None None None 0.25 in. 0.50 in, ATupper -3 -2 6 9 11 -0.5g ATLowe r 4 4 0 1 0 -3 -7 -7 -2 0 _Tuppe r 2.0g ATkowe r 17 17 14 3 0 0 -15 -16 -11 -8 Cruise &Tupper 0 11 12 8 7 _TLower Figure 9-50.

Temperature differentials in OF through i

samimonocoque spanwise-beaded panels !

16 100

I

/_- d .----____.._

\\

c°

_E_L

\

I0 h- r a _..__._..____.

#-

I"

I Upper panel

6 : ?

,. BL 166

//

I • Lower panel

'///

} Heat shield i I I 1 I 0 10 20 30 40 Time, rain

Figure 9-51. Semimonocoque chordwise-stiffened panel temperatures

vs time at inboard location

9-5;0

Lower panel

16_ mn _ I

Heat shie|d InsulatiOn _lr used) -_d _Tuppe r = T(1) - T(2) -c ATIowe r = T(4) - T(3) _ ! _L._-'_--_ _ o_ J o FS 2366 BL 300 Lower panel 0.50 in. insulation Heat shield I _ d '

I I I I

10 20 30 40 Time, min

Semimonocoque chordvise- Stiff_ed _el temperat_es

ma _re 9- 2

vs time at outboard location with insulation

• T(3) Lower panel U pper pane I Insulation (if used) Heat shield Cross __ect!'c_._ T(4) at FS 2366 ATuppe r = T(1) - T(2) ATLowe r = T(4) - T(3) Inboard Outboard Location BL 60 BL 166 BL 300 Condition Insulation None None None 0.25 in. 0.50 in.

-54 45 115 148 162 ATupper -0.Sg 74 39 3 7 0 ATLower -50 -50 -46 -14 -2 ATupper 2.0g 159 112 86 14 -4 ATLower 0 -151 -157 -99 -75 ATUpFer Cruise ATLower -1 74 82 57 45

Figure 9-53. Temperature differentials in OF through _ semimonocoque

chordwise-stiffened panel with convex beaded upper surface

9-91

Next: Section i0 →

Section i0

OPTIMIZATION PROCEDURE FORPANELS OF

MONOCOQUE STRUCTURE

by

R. E. Hubka

lO-i

I0-i

STRESS ANALYSIS PROCEDURE OF COMPUTER PROGRAM NO. I

LOCALINSTABILITYANALYSIS PROCEDURE OF COMPUTER PROGRAM NO. i 10-5

10-5

0 x 90° Flanged Waffle

0 x 90° Unflanged Waffle lO-lO

45° x 45° Waffle lO-10

10-11

Honeycomb-Core Sandwich

Truss-Core Sandwich

i0-14

GENERAL INSTABILITYPROCEDURE OF COMPUTER PROGRAM NO. 1 lO-16

OPTIMIZATION PROCEDURE 10-18

10-21

ANALYTICAL PROCEDURES OF COMPUTER PROGRAM NO. 2

10-22

Stress and Deflection Analyses of Waffle Plates

10-28

Analytical Procedures for Honeycomb-Core Sandwich Plate

EEFERENCES

I0-29

lO-iii

ILLUSTRATIONS

Page

i0-i

Geometry, applied loading and stress resultants of typical panel 10-31

I0-2 10-31

Typical element of 45 ° x 45 ° waffle plate 10-32

10-3 Typical element of O x 90 ° waffle plate

10-32 10-4 Geometry of honeycomb core sandwich plate 10-33 10-5 Geometry of truss-core sandwich plate 10-6 Procedure for computing utilization factor in analysis of local instability of faces of truss-core sandwich 10-34 10-7 Notation of plate dimensions and loading for general instability analysis 10-35 10-8 Shear buckling coefficients of simply supported, orthotropic plates 10-35 10-9 Sign convention of deflection, moments and pressure loading and expressions of curvatures and twist of waffle plate 10-36 SYMBOLS A Cap area cap X and y distances between simply supported edges of plate a_b Widths of core and skin elements of truss-core sandwich bc,b s Width of flange of flanged waffle bf Pitch b s C.. Stiffness coefficients Stiffness coefficients of governing differential equation of D1,D2,D3 plate d Width of interface _f corm'ribbons of honeycomb-core sandwich E Modulus of elasticity E Compressive Modulus of elasticity C Elastic Modulus of elasticity Eel Extensional tangent and secant moduli Etan,Esec Eccentricity of x and y compressive loading e _ e r F° .

Flexibility coefficients Stress corresponding to modulus of 0.7 Eel FO. 7 Bending_ compressive and shear stresses fb,fc,fs f Cap stress cap intercell (dimpling) and wrinkling stresses of honeycomb-core flB'fWR sandwich f Extensional stress of stiffeners of waffle W _--_-- _- 7 __ ...... _ _h_ _+_s _ _ coordinate system Ix' ±y' fxy Extensional stresses and shear stress of core of truss-core fy, c'_sy, c sandwich vii LOCKHEED MISSILES & SPACE COMPANY Gel _Eel/2(l + u el): elastic shear modulus Moments of inertial per unit length of section associated _x,ly with x-wise and y-wise bending of orthotropic plate Buckling coefficients in analyses of local compressive buckling k,k c Buckling coefficients in analyses of local shear buckling kxy, ks L Length Bending moments and twisting moment in xy coordinate system Mx,My,Mxy per unit length of section.

m Number of half waves in plate buckling equations Extensional forces and shear force in xy coordinate system per N x, Ny, Nxy unit length of section Extensional forces in xy coordinate system per unit length of section of plate.

n Exponent of interaction equation Pressure q R Compressive, stress ratio in general instability analyses C Shear stress ratios in generai instability analyses Rxy, R s Compressive stress ratios in local ouckiing analyses r ,rx,r c y Shear stress ratios in local buckling analyses r s ,rxy T T emp era tur e

IT] Transformation matrix defined by equation 10-6

t Thickness Equivalent panel thickness Effective thickness in expression of shear stiffness S Strain energy; utilization factor w Deflection measured in z direction viii LOCKHEED MISSILES & SPACE COMPANY X_ y_ z Rectangular Cartesian coordinates of panel

z

Location of neutral "surface" of plate Mean coefficient of thermal expansion Curvatures and twist in xy coordinate system

AT

Temperature difference between inner and outer extremities of panel 0.5_xy: shear strain E_tensional strains and shear strain in xy coordinate system Extensional strains and shear strain of reference l'surface" of waffle plates in xy coordinate system Y Poisson' s ratio Elastic Poisson's ratio Vel =- D12/D22_ D 12/Dll: Poisson' s ratios associated with Yxb _'l_yb x and y bending deformations of orthotropic plate Angular dimension of panel cross section Rectangular Cartesian coordinates coinciding with stiffeners of -25 x 25 deg waffle plates f I Column matrix Square matrix

[1

Subscripts Indicates quantity pertains to core of truss-core or honeycomb-core sandwich_ quantities due to compression or coupling cap indicates quantity pertains to cap cr Denotes buckling stress or load f Indicates quantity pertains to flange of flanged waffle GI Denotes quantity associated with general instability ix Number of loading condition General subscript Indicates quantity pertains to skin of waffle plates, faces of honeycomb-core sandwich plate or faces of truss-core sandwich plate T Indicates quantity is due to thermal effects W Indicates quantity pertains to stiffeners of waffle plates or to stiffener web of flanged waffle plate when used with dimensional notation Denotes quantities with respect to x and y directions x_y Denete quantities with respect to _ and 1,2 Denotes lower and upper faces of honeycomb- and truss-core sandwich plate x LOCKHEED MISSILES & SPACE COMPANY

Next: SECTION i0 →

SECTION i0

SECTION i0 OPTIMIZATION PROCEDURE FOR PANELS OF MONOCOQUE STRUCTURE Equations of the two computer programs which were used to design the panels of the monocoque structure are presented in this section. The analyses are formulated for the synthesis concept of structural optimization. A general optimization subroutine is used in the programs to direct a constrained minimization of the weight of the structure. The mathematical procedure of the subroutine, which is not presented_ is based on the maximum gradient method.

STRESS ANALYSIS PROCEDURE OF COMPUTER PROGRAM NO. i A typical panel is shown in figure i0-i. Neglecting coupling betweenl inplane and out-of-plane deformations_ the extensional and shearing strains of the plate are: I N g FII FI2 FI3 x x N (i0 -i) FI2 F22 F23 Y Y -_, /p P /p _ /p N Cx 7 - 13' - - 23' _..t_t' in which E = ¥xy/2 and xy -i = C12 C22 2C23 CII CI 2 2C13 1 C13 C23 2C33 i0-I

O

The stiffness coefficients with plasticity effects included are evaluated with equations of reference i0-i. The subscript i denotes number of loading condition. It is to be noted that the coefficients C13 and C23 are zero for all plates except the 45 ° x 45 ° waffle (fig. 10-2) when an unequal amount of plastic deformation occurs in the _-wise and n-wise stiffeners.

Assuming plane sections before loading remain plane after loading, the cap stresses are

fcap,_,i = m (_ = x,y) (io-2)

see, cap,_,i_,i The extensional stress resultants of the plate are -i ( iO-3a )

i [ 21 A2 i i

where All ,m = L + A E ,x,iFll p,y cap,x sec,cap ,i H E AI2, m = Acap, x sec,cap,x,iFl2,i = E A21, m Acap,y sec,cap,y,iFl2,i

(lO-3b)

= L +A E A22, m p,x cap,y sec ,cap,y,iF22,i = LN -A E BI,m y x,i cap,x sec,cap,x,iFl3,iNxy,i = LN -A E .N B2,m x y,i cap,y sec,cap,y,iF23,m xy,i Expressions of the stiffener and skin stresses of the 0 x 90 ° waffle (fig. 10-3) are

f : _ (_ : x,y) (io-m)

w,_,i sec,w,_,is_,i 10-2

<iiiiiiiiii!)

and f ] "i V s E 4 fX,S I sec ,s ,i

(lO-4b)

• o s 1 y,s I 1 - V s,i 0 0 _fxy, s] .

I or {f}" = tj[Cs] {e}. (i0-4c) 1 i m where the subscripts s and w denote skin and stiffener. The effective Poisson's ratio of the above equations is expressed as follows (ref. 10-2):

-- (o.5 - v 0.5 - rise c

Strains of the 45 ° x 45 ° waffle of figure 10-2 are (ref. 10-3) X ,= O.5 O.5 -I (iO_a) I O.5 O.5 0 gXy .

n .

i or

{e'}. = [T]{e}. (io_b )

I i Expressions of the stiffener and skin stresses are (iO-7a) w,£,i sec,£,iEZ,i

!!<<)

10-9

@

and [" fg,s f = (f'}i = [ Cs ] {_'}.

q_S i m f_n,s i The skin stresses in the xy coordinate system are {f). = IT]-1 {f,).

(lO-8)

1 I The material properties of the faces of the honeycomb core sandwich (fig. 10-4) are assumed to be equal. Hence, the expression of the skin stresses is the same as that of the 0 x 9 0o waffle,iequation (i0-4c).

Expressions of the core stresses of the truss-core sandwich (fig. 10-5) are f = E .g y,c,i sec_c_l y,i (i0-9) ; E f sec ,c ,i - E cos sy,c,i i + v xy,i c,i The face stresses are given by equation (lO-4e).

It is to be noted that Computer Program No. i automstically iterates the stress analysis _ a significant amount of _stic deformat$on occurs.

10-4 LOCAL INSTABILITY ANALYSIS PROCEDURE OF COMPUTER PROGRAMN0. i _ 0 x 90 ° Flanged Waffle The buckling stress of the 0 x 90o biaxially-compressed waffle skin element, which is assumed to be simply supported_ is expressed as follows (ref. 10-4): 2 2 s

(m

t s as + bsJ i Es,i (iO-lO) f£_ s,cr, i = 0.82 i -9 s_i (asbs) i 2 __ + 8_-- Im bs as 1 as s i where as_i = Py - tw,y_ bs_i = Px tw,x, 8i = fy_s,i/fx_s_i ' £ = x if fx_s_i a fy_s_i and as_i = Px - tw_x, bs,i = Py - tw,y_ 8i = fx_s,i/fy, s,i, £ = Y if fy, s_i > fx_s_i The effective modulus is approximated with the expression lO-ii) E = [C 1 _ST + (i - C I) n r] Eel J L in which (ref. 10-5) = ES----_T = 0.5 n [i + 0.5 nST Eel sec i0 -12a )

[

J _ r _ _tan lO-12b ) nr Eel 0.25 nsec + 3 nsec, 10-5

and CI (0 _ C I ! i) is an empirical coefficient, dependent on the loading

and aspect ratio of the plate. Someguidance for evaluating the empirical

coefficient is given in reference i0-i. The effective Poisson's ratio is

definedb_ equation (10-5). The buckling stress of the skin is the minimum

with respect to positive integers of m. Negative or zero values

of f_,s,cr

of the denominator of the buckling equation are not applicable. Note that

f£ is the correct buckling stress only when

,s_cr

maX(fx,s i, f i)- f£

y,s, ,s ,cr

The shear buckling stress of the skin is (ref. 10-4)

(10-13a)

f = 0.82

I i l] ts

2 5.34+ 4

xy,s ,cr,i

l-,o \ s_, \bs/ s,i in which the dimensions of skin are now denoted as follows: as = max (Px-tw,x ' Py- tw,y) (lO-13b) bs = min (Px-tw,x' Py- tw,y) E and w are defined by equations (i0-ii) and (10-5), resDectively.

Using the interaction equation r +r =i c,s xy,s where r = f£ /fz, c,s ,s s,cr l r = f //fxy xy_s xy,s ,s,cr the utilization factor for combined shear and biaxial "compressive loading of the skin is expressed as ) 10-6 0II!_¸_ r + (r_ + 4r 2 )1/2 c,s,i ,s,i xy,s,i (10-14) U = s,i 2 Treating the stiffener web as a plate which is elastically supported along the flange side and simply supported along the other three sides, stable equilibrium of the stiffener web and that of the stiffener as a whole can be expressed by a single transcendental equation (ref. 10-6).

An alternate to using the transcendental equation is to design the stiffener so that (i) the stiffener web can be treated as a simply supported plate, and (2) general instability of the stiffener does not occur. The latter procedure, which is somewhat simpler, is considered to be adequate for the present minimum weight analysis. The two conditions are satisfied if (ref. i0-6):

(_ = x,y) (10-15a)

Yf,z,£ >max (Y£,!' T_,2) in which yf , _ i tf f'_ (£ = x,y) (lO-15b) b 3 ,z £ 12 _f tw,£/ = 1.85 + 2.73 Af,£p£ (£ = x,y) Zftw, £ (iO-i5e)

- o 4 + o 47 + 0.43 A_f,_pp_ w,m

p - t

Y = 1.18 m w,m

_,2 zf " " zft w ,_ zf (£,m = x,y; y,x) where Af,_ = bf_ tf /p_, (4 = x,y) (i0-16) z% = 0.5 (t + tf) + h s 10-7 Note that the subscripting of the expression of I£,2 denotes one equation in which £ = x and m = y and another equation in which £ = y and m = x.

The buckling stresses of the stiffener webs are then expressed as EST,w,_,i w,£

f = 0.82k : x,y) (io-17)

w,£,cr,i w,_

-- _ _\-_-J

i- Vw,_, i where k w,_

[4;(Pro - tw,m)/hw >_ 1

h 2

tw_m)/ wJ _(pm-tm)/h _lww

hw /(Pm- tw,m) +(P m -

(_,m = x,y; y,x) Considering one half of the flange element as a plate with three simply supported edges and one free edge, the local buckling stresses of the flanges are expressed as follows: ff.#..cr.i = 0.82 EST'w'_'i2 [0.61 (i - Vw,_,i) .... i- Vw,_, i [ <i bf'_-tw'_)2]IbPm - tw,m / f,_ _2tftw,_/_

(io-18)

(_,m = x,y; y,x) This equation corresponds to that of reference iO-4_ the formulation of which is based on u = 0.25.

I0-8

In addition to the flexural modesof failure already considered, a

torsional modeof instability of the flanged stiffener is possible. Assuming

simply supported boundary conditions at the ends and unrestrained rotation

about the toe of the stiffener web, the buckling stress is expressed as

(ref. i0-6)

= 9.87 Etan'w'_'i (_ : x,y) (10-19a)

fst,_,cr,i (L/r)_ where Ipc, _ "ll/2 (L/r)_ =(Pm - tw,m) Ist,z,_Z f + F_ + 0.0390Jst,_ Pm- tw,m ( lO-19b ) (_,m : x,y, y,x in which the stiffener properties are defined as follows: %1} = i (t3f 3 + 4t 3 _3) F_ _ bf,£ w,_ f _2 ipc,_ = ist,_ + Ist,z,_ ÷ Ast z ,_ st,_ o _2 + _2 + lw + _6 _ Ist,_ = If,g Af,_zf ,£ Aw,_Zw,_. - Ast,_Zst,. _ (10-19c) I (Af b 2 t2 £) - ,£ f, + Aw,_ w, Ist,z,£ 12 Zst,_ Af,_f + - Ast

- = (

Ast,Z Af,_ + = A w , } 10-9 The properties Af,_ and _f are defined byequation i0-16_ and Aw,£ = hw tw,£/Pz (£ = x,y)

I = h2/12 (z = x,yl

w,_ Aw,_ w (10-20) __ Z _ O, 5 _ / _ts _- hw_ W_Z W A t 2 + 2 w,£ w,& Af,£ tf (£ = x,y) Jst,£ h _.]

!ii_ i t _ 3 ] 0 x 90 ° Unflanged Waffle } The equations for the buckling analysis of the skin element of the un- _ii! _ -?

flanged 0 x 90 ° waffle are the same as those for the flanged waffle, equations (I0-i0), (i0-13) and (10-14). Considering the stiffener as a plate with three simply supported edges and one free edge_ the buckling stress of the stiffeners is expressed with an equation corresponding to equation (10-18) as follows,'.

_i i::i ¸ ,_ = 0 82 ,w,Z,i fw,£,cr,i 1 _ _2 0.61 t - v • w,£,i : - w,g,i[ + .... 2 lhW,£ _ (_,m = x,y; y,x) w,m/j \ w,_/ (10-21) Note that the above equation is written with the provision for h # h w,x w,y which is permissible for some designs in which the stiffener stresses in one direction are small or tensile. The height of the stiffeners in this direction can be larger than that of the stiffeners in the other direction, i 45 ° x 45 ° Waffle A specialized form of equations (i0-i0) through (i0-21) is used for the local instability analysis of the flanged and unflanged 450 x 45 ° waffles.

i0.i0 __moneycom0-uore Sandwich _ J Procedures for the analysis of local instability of honeycomb-core!sandwich pla%_S ) subjected to uniaxial compressive loading are presented in reference 10-7.

• Some_of these analytical methods are adapted herein for the local instabilityi analysis of the honeycomb-core sandwich subjected to combined loading. ....

The basis of the intercell buckling (dimpling) expression of reference 10-7 _<_i!classical buckling equation of a square plate. Using the notation of ! figure i0-4_ the intercell buckling stress of the faces due to biaxial inplane loading is expressed as rain t I i Es, i ,t2 + i ( _0-22 ) _! 6 ;_

( )

flB,i = 0"82CI 2 s 2 i _s,i m.z + 6i where , c iii : 6i = fll,i/fl,i o in which Y f +f .s - fv.sh 2 ]1/2 v,s y_s " i!< fI = 2 ixy_s j 1/2 f + f X,S y_s y,s f2 IIfx's - f 12 1 fll = 2 - - _ + xy,s = il The critical stress is the maximum value of fib with respect to positive t integers of m. Negative or zero values of m + _ are not applicable.

Unequal face thicknesses are considered to provide for different minimum thickness requirements of the faces. Comparing equation (10-22) to that of reference 10-7 for uniaxial ioading_ it is noted that C I _ 0.61. _ i0-Ii The wrinkling stress of the faces due to uniaxial compressive loading is expressed as (ref. 10-7) 0.82C 2 c _imin{tl 't2 E

[_ ] ] 112

E .h r,s,i r,s,l c (i0-23a) fwR,i = i + 0.64K.

I where C_ is a correction factor E is the effective skin modulus expressed by equation (lO-12b), and ' r,s 6Z

K.- o_c,i (lO-23b)

hF c c,i 8 of equation (i0-23b) denotes the amplitude of initial imperfection of the o thinnest face.

The core modulus E and allowable strength F which appear in equations C C' (10-23), are properties which are measured perpendicularly to the sandwich! ii plate. These properties are usually evaluated experimentally. However, when new materials are initially considered, test data, especially for high temperature applications, is not available. Therefore, it is necessary to approximate the properties analytically. Assuming the compressive strength to be critical, the crushing load carried by the core is considered in two _+_ _]_r_l_ ln_a _na _n_f,]mlrklin_ load The bucklin_ stress of the foil (side of a cell) is conservatively expressed by simply supported plate theory as f, = 0.82k EST,c,i I_l 2 c,i 1 - ,2 (lO-24a) c,i where s + ;__ic < i S k _ 4 , h "__c > i S -- I0-12

in which hc = h - t I - t 2. EST_cand Vc are effective properties of the

core material given by equations-(10-12a) and (10-5).

After the foil buckles, additional loading is carried by the material

at the core nodes. The average stress produced by the post-buckling loading

of the effective material is

f" = f - f, (10-24b)

c,i c,max,i c,i = 0.i.

The compressive in which f is the stress corresponding to ntan, c c ,max strength of the core is then expressed as

c +-- f (10-25)

Fc,i - s s where in which C 3 and C 4 are empirical coefficients.

The secant modulus of the core corresponding to the compressive strength is approximated as C sf' + 2beff" E* _. = 2t c_i c_i sec,c,i (10-26) c,i c f 2 c ,max, i s where E* is the secant modulus of the core material which corresponds sec,c to the stress f c ,max The following values of the C coefficients, d and 6 were used in o the design of the honeycomb-core sandwich plates: C I = 0.61, C 2 = i, C 3 = 15_ C 4 = 0.25, d = 0.025 and _ = 0. In ___ ...... _In-l_- a cOmna_son_ __ of o analytical data, which were obtained with the above values, with test data of reference 10-8 indicates that the reported analyses of dimpling and wrinkling stresses are adequate for the present investigation.

lO-13 ] .... Truss-Core Sandwich [ Treating the face and core elements as long_ simply supported plates_ the ,_ .... _ _.{.. .... truss-core sandwich is analyzed for local instability with the theory of ref-i!

"it ih_] {'i _: ..... .... eren'ee 10-9, an analysis of long_ simply supported_ orthotropic plates. The _ face buckling stresses_ when the loading components act individually_ are E s,i f : 0.82 x,s,cr,i i- v 2 s,i s ,i 't2 (i0 -27 ) f = 3.29 y,s,cr,i 1 - v s,i f = 4.40

s i2 [min tl ] l

xy,cr,i 1 - _, s s,i Defining stress ratios as r

(lO-28)

r :f /f

y,s,i y,s,i y,s,cr,i r = f //fxy xy,s ,i xy,s,i ,s,cr,i and specializing the interaction equation of reference 10-9 to an isotropic plate as (10-29' rl'r2'r3'r4 = 2 -}i 8 - 10.14

the utilization factor U of the thinnest face for combinedloading then is

s determined with the procedure of figure 10-6. Note that stable equilibrium of the face exists if @ > 0.

The core is subjected to a compressive loading in the y-direction and a shear loading. Expressions of the corresponding buckling stresses are f y,c,cr,i

(io-3o)

f = 4.40 sy,c,cr,i i - Vc,'\l c / and v are effective material properties of the core element where EST,c c which are expressed by equations (lO-12a) and (10-5), respectively. The inter- action equation for combined loading is r + r = i klu-Ji) C_C sy_c in which r : _y,c ,c cr e,c y ,

(lO-32)

= f /fsy, rsy,c sy,c c,cr It is to be noted that equation (10-31), for the combined loading of the core,i _is_equivalent to equation (10-29). The expression for the factor of utilization or strength ratio for the interaction equation (10-31) is r + + 4r 2

t2 )1/2

c,c,i l_c,c,i sy c,i (10-33) U = c,i 2 The true margin of safety, then_ can be computed from the following equation i M.S. = - -I u lO-l_ ..... ...... .... GENERAL INSTABILITY PROCEDURE OF COMPUTER PROGRAM NO. i i _i: .',_ !_suming simply supported boundary conditions, the compression buckling :__., ...... theory_ of reference I0-i0 and the shear buckling theory of reference i0-i!_ t_g'__@r with an appropriate interaction equmti.on, are used to analyze the waffle, honeycomb-core sandwich and truss-core sandwich plates for general , :,...... . ,:_ instability.

The Compressive buckling load for a biaxially-compressed, simply support?d i orthotropic plate (ref. i0-i0) is i Nl,cr,i = k ,iW2Dl /x 2 c ,i ll,i (i0-34a) <: - i: < where ,,.; ;< Xl,i ,i + mi m. + I 2 D3 21 2 _4 2 DI, i l c,i 2 k = Xll'i Xll'i c,i 2 2 (10-34b) ? ", 2 Xl,i Nll,i Xl,i :. ) m. +_ : :2 z 2 NI, i Xll ,i ,::i?

in which

1/4

ill_ J

(z0-34c)

< c,i The dimensional, loading, and stiffness quantities of equation (lO-34),are defined as follows : _:, Xl, i a, Xll,i = b; NI, i = N i' Nil = _ "" DI = DI ' = D2 = x, ,i y,l' ,i ,i Dll,i ,i 10-16

if

2w2__-7_ + _ - _ > 0 and N >

#D2,i D3 a i 1

y,i x y

Otherwise, = _ ; = D2

Xl, i = b Xll,i = a; N I i = _

' , y,i' Nll,i x,i Dl,i ,i' Dll,i = Dl,i

Their!ate stiffnesses Dl_D2_and D3 are evaluated with equations of reference ii0-i.

Eta n is used for the modulus of the stiffeners of the waffle and the core elements of the truss-core sandwich. The moduli of the faces of the h_neycomb-core and truss-core s_ndwiches are approximated with equation (i0-ii).

The expression E = IC2 nST +(i - C2) _tanl Eel is used to evaluate the moduli of the skins of the 0 x 90 ° and 45 ° x 45 ° waffles. The coefficient C2 10 < C2 < i I is an empirical coefficient dependent on loading and aspect ratio of the plate. Some guidance for evaluating the coefficient is given in reference I0-i.

The buckling load of the plate is the minimum value of N I with _cr respect to positive integers of m. Negative or zero values of the denomin- ator of equation (i0-34b) .... are not applicable. Not that Nl_cr is the correct buckling load only when N I _ Nl,cr.

The shear buckling stress of the plate is _(_e{] i0-ii) N =k .w x

2(DI )I/4/ 2 (i0-36)

xy,cr,i s,i iDll,i ll,i 10-17

!i!!!ii_! ¸_¸)

7 whe re

= b; DI, i = Dl,i, Dll,i = D2,i

Xl, i = a, Xll,i

if

a \D2, i / <--_ DI, i

Otherwise, Xl, i = b, Xll,i = a; DI, i = D2,i, Dll,i = DI, i Values of the shear buckling coefficient which correspond to those given by the theory of reference i0-ii are presented in reference 10-12. Curve_ of !\ t_ii_@fficient are given in figure 10-8 of this section. The stiffness param_ eter, K, of the figure is defined as (i0-37a )

( 1 I/2

<i = D3,i Dl,iD2,i/ _nd bhe ..... " ..............

(i0-37b) s,i The procedure for evaluating the stiffnesses DI, D2_and D 3 is the same as that for compressive loading.

I0-18

Using the interaction equation

R +R 2 = i

c,i xy,i

in which

Rc, i = N!,i/Nl,cr,i R = N //Nxy xy,i xy,i ,cr,i the utilization factor for combined shear and biaxial compressive loading of the plate is c,i ,i ,i (10-38) UGI,i = 2 In evaluating the loading ratios of equation (10-38), one set of stiffnesses in which the effective moduli are based on the stress state due to the com- bined compressive and shear loads is used.

Using a general instability theory_ which neglects shear deformatior_ sig- nificantly llmlts the extent to whlch Computer Program No. i can be applled tO 1 _oneycomb-core plate problems. _._._j ................_ +m_ _s_nt_ investiKation, the sim- plified analysis did not have a significant effect on the plate weight bec_use the compressive loading along the long edges of the panel was considerablei_ith respect to that along the short edges.

OPTIMIZATION PROCEDURE Equations which were used for the stress and stability analysis of the waffle, honeycomb-core sandwich and truss-core sandwich plates have been pre- sented. For each of the structural concepts, these equations, together with constraint functions which remain to be given, define a "region" of permis- sible design within an nth order "design space" in terms of the design variables. The coordinates which make the merit (weight) function assume a minimum value and which fall within the permissible design region are the dimensions of the optimum configuration for a given single or multiple load- ing condition. As already stated, the modification of the structure in • searching for the optimum design is directed by a constrained minimization procedur% which is based on the "maximum gradient" method.

I0-19

The variables which are used in Computer ProgramNo. i are the dimensions

of the plates as follows: 0 x 90 ° Flanged Waffle ,x' bf,y, w s ' w,x w,y bf hl- h + t + t f) Px' Py' tf, ts, t and t 0 x 90 ° Unflanged Waffle hx(- h + t ), hy(_ h + ts)' Px' Py' ts' t and t _sX S Wry W_X w_y -45 ° x 45 ° Flanged Waffle b f, h(= h + t + t ) p, t f, t and t w s f ' s w -45 ° x 45 ° Unflanged Waffle \ + ts| ,/ p, t and t S W H oneycomb-Core Sandwich h, s t t I and t 2 T russ-Core Sandwich h, tc, tl, t 2 and 0 %

}

10-20 ............. _:_ _e constraints of the design space which have been incorporated into i •_ ....... ...... Computer Program No. i can be grouped into two types: (i) behavioral constraihts .... ...... .... and (2) side constraints. The first type limits the design to those configura- .... tion_ which satisfy the failure criteria of the structure. The second type constrains the design_for examples within real space limitations and mamufac- _:, _ _ f_),._-_ ,- . . ° _ ......... t_g'capabmlmtles. As an example of the •system of constraints of Computer ' .... Program No. i_ constraint functions of the unflanged 45 ° x 45 ° waffle program .,, .i 'are: = i - -> 0 GI, i UGI, i _,iii °2,i : l- u >- o ....... s_i t [! < (_ = _ or n)

i::?< %,i -- l- f /% - o

w,_,i ,_,cr,i - ": iil _ _ G_, = ,i ntan,s,i - ntan,min,i >_ 0 £ (£ = _,r or n) . G 5 - 0 ,i = ntan,w,_, ,i ntan,min ,i >- G6=t - t >0 s s ,rain - i:< ,!i!

=t -t >0 G7 w w ,min G8 = (hw/tw) max - hw/tw >-0 It is to be noted that in the design of the 45 ° x 45 ° waffle,only the stiffener with the maximum compressive stress is analyzed for buckling.

!i _ !_ ANALYTICAL PROCEDURES OF COMPUTER PROGRAM NO. 2 i ........... *_ .... _ -_ 45 ° I!5° and O x O0 ° waffle As already ±muluaueu_ um±y o_ _±±_a_5_d x - .

plates and the honeycomb-core sandwich plate are considered in Computer Program No. 2. The program system was developed from the programs of Computer Program No. i. Hence; many of the procedures for designing the unflanged waffle and honeyoomb-core sandwich plates are common in the two program systems_ the basic 10-21 ] _i' • d&ffe_ences being in the analysis of the overall strength and the local failurb .... _ ........ of the waffle plates. The analytical procedures Which are peculiar to Computer .... Program No. 2 are presented on the following pages.

..... ....... .... - Stress and Deflection Analyses of Waffle Plates .. The total in-plane stress resultants acting on the 45 ° x 45 ° waffle panel L Nx,i = N ' + (AE - ) / + (CII_x C12 _ ) P'Y x,i sec,ieT,i cap,x Lc,y ,T,plate + y,T,plate i L c ,y L N = N' + L (AEsec ,i_T ) Y/ y,i ,i cap, c,x y,i + (Cl2Sx,T,plat e + C22Ey,T,plate)i Lc, x ( i0-39 ) m N = N' + xy xy,i C33,i ¥xy,T,i where Nx, N' and N' are stress resultants in which the thermal loading is y xy excluded and the subscript T denotes thermal strain. In the O x 90 ° waffle FI I i F22-1 program, C12 in equations(10-39) is equated to zero_Cll = - and C22 = .

The procedure for evaluating the thermal portion of the loading is consistent with the analyses of the internal loads of the aircraft. Using the loads given by Equations (lO-39)_the total stress resultants of the plate, N._ and _y, are determined with the use of equations (10-3).

Moments due to coupling between in-plane and out-of-plane deformations of the -45 ° x 45 ° and 0 x 90o waffles are -,_

!M{ = x =

(io-4oa )

[o

''c,i I y c,i e21

........ .,_._4. • • _ .._,., ,-,_ ,_ -,-,.,,.,-,_.4 _o of +_ ""_ o+,_o _ where e-- ana e_ 1 are _uc_tlo±_itleo w_ _e _c_ _c_ .... _ _ defined in reference lO-i. The coupling moments occur as force couples (skin forces opposing stiffener forces) in the waff_-e plates. Edge moments of -{M}c are superimposed on the plates to remove the couples from the edges of the plates_ which are assumed to have simply supported boundary conditions.

_- moment sign ...... .r.+4 ,-.-,_ -_{_ Sh_ _n f_ _nre lO-g.

10-22

Momentsdue to eccentric loading at the edges of the plate are

(10-40b)

: \ex1

My ey i e,i were e and e are prescribed eccentricities.

x y Moments due to variation of temperature through the thickness of the plate are determined with the use of superposition of loading. The temperature gra- dient is assumed to be linear, which is considered to be an adequate approxi- mation for the present investigation. Considering the plate first with free boundary conditions, curvatures due to the temperature gradient, which is assumed to be constant along the width and length of the plat_ then are Xx,T = Xy,T = XT. The curvatures, which have sign conventio_ as shown in figure 10-9. are removed with the application of moments along the free edges of the plate. The moments are

: : - (i0-4Oc )

X T

{M)T'i T,i [Dz2 D22J i i

where DII -= D I _ D22 =- D 2 and DI2 =-D x_ D2 = Wyb DI are the bending stiffness coefficients of the waffle plates. The desired plate loading is finally obtained by imposing simply supported boundary_ conditions onto the plate and then super!- imposing the moments - {M}T along the edges.

As already staged_ Computer _ P_gram No. 2_as _implemen_ed for problems/in _i: ii which the plate bows so that the m_.nts at the cent_e_r of the panel are adequate approximations of _he m_ximum m0men_s. Assuming %ha_!_N×v Constigutes a neglfgible • !

portion of the panel loading with respect to general--faiiure, the d-eflection and bending moments at the center of the plate due to the coupling moments, the eccentric loading at the edges, the temperature gradient through the thickness and the "compressive" cu_= ....... ±u_:_- arc _-_- ........ _ .............. A m_ {nlln_^_ (r_f. lO-lq__ and I0-]4] -h.

w_.l= _--_16n MM_ NM_-_Y --Imnl ,i [MX 'i (_)2 M_+ _i (_)2 m=l n=l

io-23

iiiii_ MM NM 16DI ,i M !

x,i m+n M !

(iO-41b)

y,i m+n + + My ,T, i (m = i, 3, . .., _; n = i, 3, • •., NM; M M = N M) where = nkrl

(io-42)

+_,_/_)_- <,_(_)_-T,_(_-_)_]

and <

(io-43)

IMxl I:Ix _IMxl

My i I Ylc,i t yle, i My T,i # Deflection and moments at center of plste due to inplane edge loads and uniform pressure are M N m+n

( !o -_ .__. )

i (-i) a

W ° _ 1 2 k 16qi _ n_l w =i = mn,i I0-2]+ ___nn -i M N i 16qiDl, i q q M"

x,i _ + 12

= =i mn,i M N m+.__n -1 (lO-4_b) Z T!

(_-_)_] ___)_

y,i 16qiD2_i_2 m_: n _ lq=l =lq mnl,i [_xb (_)2 + •., Nq; Mq = Nq) (m = i, 3, • ., Mq; n = i, 3, Deflection and moments at the center of plate due to inplane edge loads and an initial sinusoidal deflection are IT!

1 +-- W. ---- i all ,i

i

M,,,: Dl i[ i )2 i )2]

x,i all'i _ll,i x,1 + _y,i M"' = D--2'--i Nx,i + N

[ (-i) _

y,i all'i Xll,i y,i in which all is the initial deflection and All is expressed by equation (10-42) with m=n=l.

Using the secant modulus, the plate stiffnesses_ which appear in the deflection and moment equations, are evaluated with equations of reference i0-i.

Poisson's ratios u and v of the skin and stiffeners in the stiffness s w equations are approximated with equation (10-5). It is conservatively assumed that the e!astic-p!astie state at the center of the waffle exist over tile entire area of the waffle plate.

The total deflection and the total moments at the center of the plate are W = W! + W'.'+ W'".

i i i i (i0-46a) M = M' + M" + M"' .

x,i x,i x,i X,l 10-25 M = M' + M" . + M"'.

y,i y,i y,l y,l

(tO-L6b)

M : 0

xy, i

The effective curvatures and twist corresponding to the above moments are -i Mx Xx DII DI2 0 M (i0-47a ) DI2 D22 0 'Xy = , 0 0 2D33 i Mxy Xxy f k Strains of the reference surface are -CII C12 0 -i-i [_ CII C12 )('X 0 C14 Ci5 0 i x i

ill

% = io-4?b) C12 C22 0 I_ - C12 C22 0 /c24 c25 0 ' Xy i y N 0 0 J, 0 0 2C 3 i [ xy. i i [Xxy where the stiffness coefficients are evaluated with equations of reference i0-i.

Secant moduli corresponding to the stresses of equations (10-49) are used in computing the stiffnesses.

The C.. stiffness coeffi, cients are formulated with respect_ to the mid- zj plane of the waffle skins. Average strains of the waffle skin then are X ( 10 -48a ) Y ,i °'STxy, O. 5Yxy i0-26 <ii >iii!i!% The stiffener cross section is subdivided into five equal increments for the stress analyses of the waffle plates. For the 0 x 90 ° waffle, the average strains of these increments are Sw,_,k,i = I_£ + [0"5 t s + (0.2k - 0.i)hw,£1X£1i ( lo -48b ) Expressions of the skin and stiffener stresses are f i u 0 x S E sec ;s ,i f • i 0 2 _s Y 1-v ( i0 -49a ) s,i f 0 0 i-_ S i O. 5Yxy]s ,i • xy ,i f = Esec,w,£,k,i SZ,w,k,i w,g,k,i (£ = x,y; k = i, 2, 3, 4, 5) (i0-49b) Stresses of the caps are computed with equations (i0-i) and (10-2) Using strain and curvature components in tie Go-coordinate system_ the _i._._ ___ "_'_ ..... +_oo_o _ +_ h_ ° w h_ ° w_f]_ n.re obtained in the same manner as those of the 0 x 90 ° waffle. The transformation equation for the deformations is X n Y 0.5Vxy

[[j_

(lo-5o)

×< = [[o] X X

X n Xy Xxy X_n i where the submatrix IT ] is the same as that of equation (lO-6b) 1o-27 Local Instability Analyses of Waffle Plates i The skin buckling analyses of Computer Program No. i are used in Computer Program No. 2. As already stated_ a conservative_ simplified procedure is used for the stiffener buckling analyses in Computer Program No. 2. Consider first the 0 x 90 ° waffle. The stiffener buckling stress due to uniform !oading is computed with the same equations as used in Computer Program No. i. The stresses (k = 3,5) fw,y _ max (fw,y,k) i as obtainedin equation(10-49b) are compared with the buckling stresses to deter- mine if stable equilibrium of the stiffeners exists. Effective moduli corre- sponding to the above stresses are used in the computation of the stiffener) buckling stresses.

The stiffener buckling analyses of the 45 ° x 45 ° waffle are the same as those for the 0 x 90o waffle..

Analytical Procedures for Honeycomb-Core Sandwich Plate _ The equations for determining the deflection and moments of the honeycgmb- core sandwich plate are the same as those for the waffle plate_ except the coupling moments due to extensional and bending deformation are not involve_.

The faces of the sandwich are analyzed for local buckling with the procedur_ of Computer Program No. i. _ Constraints The constraints of Computer Program No. 2 are the same as those of Com- puter Program No. i, except that a deflection constraint, _ _hich was not used after initial development of the program system_ replaces the general insta- _i_+_ _+_i_+ Tn _ition the constraints of the honeycomb-core sandwich program were expanded to provide separate load dependent constraints for each of the two faces.

10-28

REFERENCES

i0-i

Hubka, R.E.: Structural Optimization of Six Different Types of

Rectangular Plates Subjected to CombinedShear and Biaxial-

Compressive Loading, LockheedReport 21662, Lockheed-California Co.

1968.

i0 -2 Gerard, George; and Wildhorn, Sorrell: A Study of Poisson's Ratio in the Yield Range. NACA TN 2561 , 1952.

IQ'-3 Wang, Chi-Teh: Applied Elasticity. McGraw-Hill Book Co., Inc., 1955.

I0-4 Timoshenko, Stephen P.; and Gere, James M.: Theory of Elastic Stability. Second ed., McGraw-Hill Book Co., Inc._ 1961.

io -5 Stowell, Elbridge ] A Unified Theory of Plastic Buckling of Columns and Plates. NACA TR 898, 1948.

io_ Bleich, Friedrich: Buckling Strength of Metal Structures. McGraw- Hill Book Co., Inc., 1952.

i0 -7 U.S. Department of Defense: Structural Sandwich Composites_ MIL-HDBK-23. Government Printing Office, Washington, D.C., 1967 (Preliminary is sue ) .

i0 -$ Konishi, Donald Yukio: Optimum Design of a Flat Honeycomb Sandwich Panel Under In-plane Loading. Thesis, College of Engineering, University of California, Los Angeles, 1964.

iO-9 Modlinski, J.; and Uyehara, I.: Buckling of 0rthotropic Plates Under Biaxial Compression and Shear, Lockheed Report 18473, Rev. A, Lockheed- California Co., 1966.

i0-i0 Wittrick, W.H.: Correlation Between Some Stability Problems for Orthotropic and Isotropic Plates Under Biaxial and Uni_ial Direct Stress• Aeronautical Quarterly, Vol. 4, Part I, 1952.

i0-ii Seydel, E.: Uher das Ausbeulen yon rechteckigen, isotropen order orthogonal - anisotropen Platten bei Schubbeanspruchung, Igenieur- Archiv, Vol _, ........

10"12 Contini, R.: Shear Buckling Coefficients for Simply Supported 0rthotropic Rectangular Plates. Lockheed Report 21579, Lockheed- California Co., 1968.

i0-!3 Timoshenko, S._and ................ S. _ ........ _+_ wolnowsiy-_rie_m±-_ : ±llcu±y Shells, McGraw-Hill Book Co., Inc..

,< I / 10-29 REFERENCES (C ont)

iO -14

Theory of Thermal Stresses.

Boley, Bruno A. ; and Weiner, Jerome H. : John Wiley and Sons, Inc., 1960.

i I0-3o !

o _4 o !

%/_<,.;," \ / \/\,__i_

v"-",! \_/\/\,3 "7

0) X z o __ _o E × Z

T

x E "o °_ i

_L_I_ ' °

I 7 >" I c % Q,.

4._ m Z x c t_ _.+._ 15" _,

L:4

o v v

A

>" 11-I---IT #"-T-l

O i .-.i NI _-_ ._.i >_ -- -,4 r_ i0-3i

8_

81¸11:!¸¸ ¸¸ :iiiii!iiii_ ¸_

_::!!iiiiiiiii

e ........

_:i _ i_ "--.-I I.,- \ \\\ x \ "" o

Ixll ____\\ ; x

I \I / _.-_--_',,\IN o..

o I_ II .

-_ 1,, ID O 0

r'T----T_

-- +- -- -e- -l--- o _ _ i __ _ o "_o .'- _ c L. L.

_ . o_ _ o _,.--, • "o o- _ _ + _ ZUU

"i-i-i

o Z 10-:32 Truss core

li!L I I IIM

X b s t2 C _ - " , ..-- 1 J

T

z

t t Figure 10-5. Geometry of truss-core sandwic_ plate i0-33 • I _'l

-'-t

A _i 7--

(_ I<.,I

ll., -0 "'-1 v

l

I I • T T

I r--'i +.__

7, u

,7 _ o-

°-- -,.>- "-T" -,..>" Q.i d- "_ d- ----_ 1: II II II II II.__ £ i,#'l •--, ,_'" ,E 'l i_ _'l ,,.._ I '!

L. × x i., X 0 II II I o II II

°_

I I

[

m E E

;!

E II

E o, " " 2'_

- 10-34 +1 ' J_lausoJod ssouJ++US r-I 0-, o co ,.o '_ _i • . o . .

o "H 40 0

__<_

8 _

')__\\2\\\\\\\ ++ _

x_\\\\\ /t +

1/111

| i i I l i I ii i l i i l; | i i l i i i i ii I i Iii It i f I l | I f Iii I %1'lu_,]:_!.:l.:laoo 6U!l_::,nc I Jo_,HS x" X _Z× Z

++ _k; LI_L

:K c- × Z --_

+-T

0 Z .,14 E

°

O E 0 rt QI |Z >_ .m E _E

p.+_

o_

E O i IZ _ z I, -0 Eo _3 r,- -o ._

oo

X _,--s E

i I-

I v 3.B , ___L ×

__ +p._ p-_+--_ p,.- I1)

-- + b_ ___ IzX _0-35 Right hand rule: Z r -W • -q Y M

/

yx X 0 x 90 ° waffle (shown) or -45 ° x 45 ° waffle _M X ..... __,_s,. M xy xy M

U

x M g M yx Expressions of curvature and twist: g2w c92w g2w X = X - X - x 2 y 2 xy _)x8 y ox ay I J / / / z_ure 10-9. Sign convention of deflection, moments and pressure loadi1_ / and expressions of curvatures and two_st of waffle plate / / / / !0-36

Overview

Section Page View in PDF

Section I View in PDF

Section I View in PDF

Section I

The hypersonic cruise airplane utilizes the flight schedule outlined

in figures 1-2 through 1-h. Altitude versus velocity is presented in

acceleration and specific impulse data, figures I-3 and I-4, are required

are for the ascent period. A maximum forward acceleration of 0.2-g is

imposed on the trajectory analysis. At initiation of cruise, a normal

climb at constant Mach8 occurs until maximum L/D is approached, followed

by a 1-g flight attitude at maximum L/D. A constant deceleration of 0.2-g

caused by drag augmentation is used for descent flight. The altitude at

For life analyses, it is assumedthat 90 percent of the flights are with

and thermal effects, a trajectory perturbation (10 percent of the flights)

is assumedto occur at constant Mach8. This perturbation is a -0.5-g

acceleration normal to the plane of the wing, which is assumedto exist at

the initiation of cruise (Mach 8, q = 1500 psf) resulting from a -1.5-g

(-1.5 + 1.O gravity = -0.5-g) nose-downmaneuver. This -0.5-g condition

is followed by 2.0-g pull-up maneuver(which does not exceed q = 2200 psf)

and is held at constant acceleration until maximum L/D is approached with

a smooth transition to maximum L/D, followed by 1-g nominal flight condition

at maximum L/D for the remainder of the cruise period. Negative limit loads

are the critical combination of temperatures and loads occurring during the

nose-downmaneuver, and positive limit loads are the critical combination of

temperatures and loads occurring during the pull-up maneuver. For life

Aerodynamic data were determined in the form of C L = F (M,a) and

CD= F (M, CL). Incremental drag effects (AC D) due to scale effects, engine

cowls and vertical tail were also generated. These data were based on

extensive aerodynamic analysis of a geometrically similar vehicle

(reference I-1). It was necessary to apply the appropriate wing area, engine

capture area, and vertical tail area to obtain the proper C D. The CL data

The aerodynamic data are referenced to the zero-lift line. Negative

lift coefficients, required for the analysis of negative g maneuverat

utilizing the established aerodynamic data, by using the mission analysis

automated procedure of reference I-2. Given a mathematical model of the

airplane, the program simulates a complete mission within the range of a

given flight profile. A time history of the simulated flight and a final

performance summaryare provided for each mission. The following time-based

dynamic pressure, angle of attack, flight path angle, thrust, drag, vehicle

1-2

Using the aerodynamic data, both a basic cruise mission and maneuver

perturbation trajectory were developed. The resulting time history of the

trajectory parameters of dynamic pressure, angle of attack, altitude and

Mach number is presented in figure I-5. The thrust and drag schedule for

ascent and descent is presented in figure 1-6. The thrust and drag schedule

reflects a power-on descent from end of cruise (q = 470 psf) following a

varying dynamic pressure path to an altitude of 40 000 feet. Drag augmenta-

tion, as indicated, was provided to result in a constant deceleration of

Both total vehicle weight including fuel and the fuel consumption schedule

are presented. Figure 1-8 indicates the longitudinal acceleration schedule

The baseline vehicle's range in the cruise mission and variation of lift to

drag are presented in figure 1-9. The aforementioned vehicle design trajec-

tory data were used to provide time data per mission for the various vehicle

trajectory phases of ascent, maneuver, cruise, and descent. As indicated

in table I-1, I .23 hours are required for the basic trajectory and I .25

Using the data of table 1-I, 8110 flights were established per 10 000 hours

of life for the basic trajectory and basic trajectory plus perturbation, as

presented in table 1-2. The basic trajectory requires 8978.4 hours and the

basic trajectory plus perturbation requires 1013.75 hours providing an

accumulative total of 9992.15 hours, as shown in table I-2. However, as

indicated in table 1-2, 9000 (basic trajectory), 1000 (basic trajectory

plus perturbation) and 10 000 hours (life) were assumedfor design. There-

fore, using the data of tables I-I and I-2, time data per the 8110 flights

Table 1-3 indicates that the maneuverperturblation requires only 16 hours

of a total 10 000 hour vehicle life while the cruise condition requires

1-3

(iooo) (io ooo)

(hr)

i-5

V

!,_L.. _ _ soo _s_

/ o_.-

._e,,,_.._ 2200 psf

\

!

I

l

l

l

Section Page

Section I

Section I

Section 2

Section 2