APWAL-TR-82-4025

AN EMPIRICAL MODEL FOR LOAD RATIO AND TEST TEMPERATUREEFFECTS ON THE FATIGUE CRACK GROWTH RATE OF ALUMINUMALLOY 2024-T351

University of Dayton

Research Institute300 College Park AvenueDayton, Ohio 45469

APRIL 1982

Interim Report for Period: January - December 3.981

Approved for public release; distribution unlimited.

(I

'KT

MATERIALS LABORATORY ,. i7

AIR FORCE WRIGHT AERONAUTICAL LABORATORIESAIR FORCE SYSTEMS COMANDWRIGHT-PATTERSON AIR FORCE BASE, OHIO 45433

82~ Uk 6"

NOTICE

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AFWAL-TR-8 2-4025 U ~ _____________

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AN EMPIRICAL MODEL FOR LOAD RATIO AND TEST interim Technical ReportTEMPERATURE EFFECTS ON T1AE FATIGUE CRACK lanuary-Deceinber 1981GROWTH RATE OF ALUMINUM ALLOY 2024-T351 6 PERFORMING ORO. REPORT wuMflER

__________________ UDR-TR- B2-4 27. AUTHORý1) S. CONTRACT OR GRANT NUMEER(a)

Ru.asell R. Cervay F33615-80-C-5011

S. PERFORMING ORGANIZATION' NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASK-R h AREA & WORK UNIT NUMBERSUniversity of Dayton ReerhInstitute300 College Park AvenueDayton, Ohio 45469 2421-03-15

ii. CONTROLLING OFFICE NAMjE AND ADDRESS t2. REPROT DATE

Air Force Wright Aeronautical Laboratories April 1982

Materials Laboratory (AFWAL/MLSA) III. NUMBER OF PAGESWright-Patterson ArB, Ohio 45433 50_______14. MONItORING AGENCY NAME & AOORESS(If differen~t Irani Conttalllng Os fle#) IS. SECURITY CLASS, (of IhIs tejsort)

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Approved for public release; distribution unlimited.

11.I DIST RIU0UT ION ST AT EM ENT (of the abstract enteretd In Block 20, if diffo.,bnl frorm Report) -

Is. SUPPLEMENTARY NOTES-.-f---.

IS. KEY WORDS (Continue orn reveres side If necessary and Identify by blac~k nlumber)

Al~uminum ~ Load Ratio2024-T351 K-ratioFatigue Crack Growth Elevated TemperatureMathematical Modeling

20. ABSTRACT (Continue an reveres aider It nocloe..ry and Identify by block nunqber)

data were generated for aluminum alloy 2024-T351 at 20 test con-ditions: the combination of five load ratips, 0.01, 0.2., 0.3,

* 0.5,,and 0.6 and four test temperatures, 720, 200"', 3000', and 400*F(220', 930', 1490, and 204"C, respectively) . A mathematical modelof the shift in the linear data region with the variation in testtemperature and/or load ratio was formulated. The model,-\,

*DD I AN7 1473 EDITION OF I NOYV05 1S OBSOLETE UNCLASSIFIED

SECURITY CLASSIFICATION Olt THIS PAGE (Aien Dlata Entereudj

UNCLASSIFIEDSECU 'RITY CLASSIFICATION OF THIS PA3,K(V.mn Date neted.)

F0. Abstract (Concluded)

approximates the log-Paris coefficient as a linear relationshipof both the R-ratio and test temperature assuming all other testparameters remain constant.,.-,

Using the model a prediLtive equation was formulated for anunexplored test condition, R=0.35 and a 250OF (121 0 C), prior tothe generation of test data at that test-case test condition.Following the generation of data at the test-case load ratio/test temperature, the best fitting equation to the linear regionof the test-case data set was then calculated; this best fittingequation was found to agree very well with the predictive equationformulated beforehand.

UNCLASS IF IEDSECURITY CLASSIFICATION OF THIS PAOt(Whan Dalt Eunltred)

PREFACE

This interim technical report was submitted by the Uni-versity of Dayton Research Institute, Dayton, Ohio, underContract F3361.5-80-C-5011, "Quick Reaction Evaluation ofMaterials," with the Materials Laboratory of the Air ForceWright Aeronautical Laboratories, Wright-Patterson Air Force

Base, Ohio.

This effort was conducted during the period of January1981 through December 1981. The author, Mr. Russell R. Cervay,would like to extend special recognition to Mr. Donald W.Woleslagle and Mr. Richard Marton of the University of Daytonfor the painstaking care and diligent attention they demon-strated in generating the fatigue crack growth test datapresented herein.

This report was submitted by the author in March 1982.

OTI

¶7 ... , ......

COPY.. j1"OPKOTuI ¶

iii :

~t

TLEOp CONTENTS

SECTION

I INTioDUCTION

II TEST PROGM~M 7AND SPECIMENS9

pX RSULTS A14D DISCUSSION 19

IV CONCLUSIONS

29

ItEpEENCES 2

APPFNDIK

2

?k4OZdCIM FAGI XLAWIENT FILM~

LIST OF ILLUSTRATIONS

FIGURE PAGE

1 Log-Paris Coefficient Versus R-Ratio forAluminum Alloy 7010-T73651 2

2 Tensile Test Specimen 5

3 CT Fatigue Crack Growth Test Specimen 6

4 Loading Ratio Versus Log-Paris Coefficient 12

5 Test Temperature Versus Log-Paris Coefficient 14

6 R=0.35, 250*F (121 0 C) FCGR Test Results 18

A.1 R-0.01, 720F (220C) FCGR Test Results 23

A.2 R=0.1, 720F (220C) FCGR Test Results 24

A.3 R-0.3, 72°F (22 0C) FCGR Test Results 25

4 A.4 R-U.5, 72OF (220C) FCGR Test Results 26

A.5 R-0.6, 720F (22 0 C) FCGR Test Results 27

A.6 R-0.01, 200-F (93 0 C) FCGR Test Results 28

A.7 R-0.1, 200OF (930C) FCGR Test Results 29

A.8 R-0.3, 200OF (930C) FCGR Test Results 30

A.9 R-0.5, 200OF (930C) FCGR Test Results 31

A.10 R=0.6, 200*F (93°C) FCGR Test Results 32

A.11 R=0.01, 300OF (1490C) FCGR Test Results 33

A.12 RO.l, 3000F (1490C) PCGR Test Results 34

A.13 R-0.3, 300OF (149 0 C) FCGR Test Results 35

A.14 R-0.5, 300OF (1490C) FCGR Test Results 36

A.15 R-0.6, 300OF (1490C) FCGR Test Results 37

A.16 R-0.01, 400OF (2040C) FCGR Test Results 38

A.17 R-0.1, 4000F (204 0 C) FCGR Test Results 39

vi

I - -~-,

LIST OF ILLUSTRATIONS (Concluded)

FIGURE PAGE

A.18 R-0.3, 400*F (2040C) FCGR Test Results 40

A.19 R-0.5, 400OF (2040C) FCGR Test Results 41

A.20 R=0.6, 400*F (204 0 C) FCGR Test Results 42

vii

LIST OF TABLES

TABLE PAGE

1 Maximum and Minimum Stress Intensity RangeIncluded as Linear Data Region 8

2 Aluminum Alloy 2024-T351 Tensile Test Results 10

3 Log-Paris Coefficient for Al 2024-T351 11

I

• . .. I j

SECTION IINTRODUCTION

A simple empirically based mathematical model for constantamplitude loading fatigue crack growth rate (F'CGR) test data

is very useful for predicting the crack growth rate for aparticular material at a condition where test data are non-existent. In this manner the necessity for generating dataat a particular unexamined test condition is circumvented.There are several models already in existence that vary intheir degree of complexity and their degree of success in pre-dicting test data results. Reference 1 discusses a simpleempirical model for the shift in the linear region of roomtemperature FCGR data for aluminum alloy 7010-T73651 with achange in load ratio, R-ratio (minimum load/maximum load).The linear data region of FCGR test data is depicted in

Figure 1. The model was based on the Paris equation:

da/dn - CAKm (1)

where da/dn is the crack extension per load cycle, termed the

fatigue crack growth rate, AK is the stress intensity range, andC and m are material dependent constants. The Paris equationis applicable to the linear data region only (assuming the log-stress intensity range, log-AK, is plotted versus the log-crack growth rate); the threshold and rapid growth rate regionsare not considered in this expression (Figure 1). The Reference 1

model represents the log-Paris coefficient, log-C, as linea'rlyrelated to the changing R-ratio at room temperature, assuminga fixed exponent. See Figure 2 . The model was successful

at accurately predicting the best fit straight line to thelinear data region prior to the generation of the data.

This program expands the model developed in Reference 1

to account for variation of the test temperature. To accom-plish this, three issues will be addressed. At elevatedtemperatures does there still exist a linear relationship

I

Pc e*qrý W(m) 3

10-4-

Rapid Growth Regi

1000U-- IB

0t-Jo

-u ~~100

Linear Regionr

0L. 10.eh

0)

0S-T h r e s h o ld R e g io n 10

10-7 .1 10 100

0+rese imemoi4y roange, del+o K, EKSI .c,+(iM.M)

Figure 1. Conventional Presentation of Constant

Amplitude Loading FCGR Test Data.

2

•bJ

00 11

ol

0810

4-4

0

4.

'-I 4i

mV 4-4

H-H

00-0

I.

between the R-ratio and the log-Paris coefficient? If so, is

there a trend in the lines' slopes with a change in test

temperature? Lastly, with the R-ratio held constant can a

simple mathematical relationship be defined to accommodate the

shift in the data's linear region with a change in test

temperature?

I

4t

SECTION 11

TEST PROGRAM AND SPECIMENS

The test material was aluminum alloy 2024, half inch

(12.7 mm) thick, bare, rolled plate. It was produced by theAluminum Company of America. The material was provided inthe T351 condition which is a solution heat treatment followedby cold workinq and natural aging. The results of a chemical

constituent analysis is presented as follows.

Chemical Constituent Composition

Cu Mn Fe Si Ti Al

4.3 1.5 0.58 0.20 0.16 <0.03 Balance

Tensile specimens were machined from the test plate andtriplicate tensile tests were performed at the four testtemperature of interest: 720, 2000, 3000, and 400OF (220,930, 1490, and 204 0 C, respectively) . The specimens were

machined in accord with Figure 3. All tensile specimens were

fabricated with the loading direction parallel to the plate'slongitudinal grain direction. All of these tests were con-ducted in compliance with the applicable ASTM test standard,E-8, "Tensile Testing of Metallic Materials."

Two to six constant amplitude loading FCGR tests werecompleted at each of 20 different test conditions. The testconditions were the combination of five different R-ratios:0.01, 0.1, 0.3, 0.5, and 0.6, and the four different test tem-peratures: 720, 2000, 300Q, and 4001F (220, 930, 1491, and204 0C, respectively). All of the FCGR tests were conducted inaccord with ASTM test procedure E647-78, "Constant-Load-AmplitudeFatigue Crack Growth Rates Above 10-8 m/cycle." Also, all ofthese FCGR tests. (1) were conducted in a laboratory air en-vironment, (2) used a loading frequency equal to 20 Hz, and

(3) used the CT specimen shown in Figure 4 with L-T grainorientation.

5

___ ___ ___ ___2.625 _ _ _ _

--- (66.68)

0501.625 ---- .375 -24UNIF(12.570') (41,28) CLASS 3 THODS

0.125 12.250A(3.18) (251.40 (378 (5)4

(9CH53) m TO CENTE

Figure ~~~3. Tenil Tet--eimn

(6.60)0.12 I.O G - 0.1- C2 1DA

2.500(64)

2.000 .500"(51) ( 03)

1.750"(44)

.100 ..-..

,60 ' 5o1| ..

.125 (28)(.40) .

,_.500 DIA,

Z005 ROOT (3

(.13) RADIUS

DIMENSIONS:INCHES (mm)

Figure 4. CT Fatigue Crack Growth Test Specimen.

17

Only the linear region of the crack growth rate dataas represented on a log-stress intensity range versuslog-crack growth rate pair of axes was considered inthis effort; the threshold and rapid crack growth rate region

immediately preceding failure were not considered and arenot presented herein. The maximuzm and minimum crack growthrates that were used to define the linear region for each ofthe 20 test conditions are listed in Table 1; these limitsrepresent conservative subjective judgementsl generally, thelinear region extends beyond these limits.

For the first 23 tests completed, which represent eachR-ratio in combination with either a 720F (220C) or 200OF

(930C) test temperature, the Paris exponent and coefficientwere allowed to freely vary when calculating the best fittinglinear equation to these individual specimen's data sets.The average value exponent of these 23 individual specimen datasets was 3.36 with the maximum value of 3.50 and a ninimum valueof 3.27 or a range of plus or minus 4 percent. Subsequentlyin calculating the best fitting equation to the 20 multi-

specimen data sets the Paris exponent was fixed equal to-=3.36, and only the Paris coefficient, C, was allowed to

freely vary.

Following the calculation of the best fitting *uationto each of the 20 data sets in accord with the above describedprocedure a mathematical model of the shift in the Pariscoefficient for a change in R-ratio and/or test temperaturewas formulated. The formulated mathematical model was usedto predict the best fitting equation to a test case set ofdata prior to the generation of the test case data. The testcase was arbitrarily selected to be 250OF (1210C)at a load ratio of 0.35.

* L

"A. " ".... . . .. " i ' '

0 -4 0 ~ 0 00 thU') LA LA n L

n LA0 LAW in L

5 ~ C 0o )0

00 0 LM 0 in 0

OH 1c 10 10 1cH0 LAHLiH l H C

LAW LA LAW LA

IN N w

a- r-

UL- - A a- A Ln a-

>4 H W U) Wn WC WH 10 io 10 H0 1 H 1 Cl

Co r-H

H A L HLn HD LAn W~ o- 0 1 . 10 16

10 10 10 00

9 000

44~ 0 00

SECTION IIIRESULTS AND DISCUSSION

Tensile test results are presented in Table 2. Thematerial is a moderate strength and ductile aluminum alloy/heat treatment. For the temperature rise from room temperatureto 4000F (2040C) the average ultimate strength decreases27.0 percent, whereas, the average yield strength only decreases10.5 percent. For the same temperature rise there is littlechange in the percent elongation at failure, however, there isa large increase in the percent reduction of area.

The linear region FCGR test results are presented inAppendix A in Figures A.1 through A.20. Generally, the linearregion shifts down and to the left with an increase in R-ratioand for this material changes very little with an increase intemperature. The best fitting equation that was calculatedfor each data set with the exponent fixed equal to ma-3.36 isalso listed on each of the 20 figures. From this point on inthe discussion of modeling the FCGR data with the Paris equation,the stress intensity range, AK, is in KSI/-n, the crack growthrate, da/dn, is in in./cycle and the temperature is in degreesFahrenheit (OF).

Table 3 lists the logarithm of the Paris coefficient,log-C, for all 20 test conditions of interest. Figure 5 presentsa plot of the loading ratio versus the log-Paris coefficient.Here if the points for a load ratio equal to 0.01 are excludedthe load ratio versus log-Paris coefficient can fairly well berepresented as a straight line, as was done in Reference 1. Thisis true not only of the room temperature tests but is equallyapplicable to the elevated temperature data. The lowest loadratio Paris coefficients do not coordinate well with thecoefficient associated with larger R-ratios. Similarly, inReference 1 the Paris coefficient of some data for load ratiosless than or equal to zero was not linearly related to thosecoefficients for the same material generated at higher R-ratios.

10

* .-~,.

TABLE 2

ALUMINUM ALLOY 2024-T351 TENSILE TEST RESULTS

Test Ultimate 0.2% Yield Elongation in 0.5 in.. ReductionTemparature Strength Strength (12.7 mnm) G.L. of AreaOF (OC)- KSI (Npa) I

72 (22) 66.1(455.7) 50.4(347.5) 27.6 24.866.2(456.4) 50.8(350.3) 26.3 21.765.3(450.2) 53.2(366.8) 23.6 25.5

Avg. 65.9(454.1) 51.5(354.9) 25.B 24.0

200 (93) 62.2(428.9) 49.4(340.6) 23.3 26.162.4(430.2) 49.1(338.5) 26.8 20.762.9(433.7) 49.3(339.9) 26.7 25.7

Avg. 62.5(430.9) 49.3(339.7) 25.6 26.8

300 (149) 56.1(386.8) 45.9(316.5) 27.0 31.855.7(384.0) 47.5(327.5) 30.0 34.856.9(392.3) 46.3(319.2) 29.3 33.0

Avg. 56.2(387.7) 46.6(321.1) 28.8 33.2

400 (204) 47.5(327.5) 45.8(315.8) 22.1 42.0

47.7(328.9) 45.7(315.1) 23.8 43.049.2(339.2) 46.7(322.0) 23.0 44.0

Avg. 48.1(331.9) 46.1(317.6) 23.0 43.0

11

t *".. . .. . . . . . .. -. " '' " 1

TABLE 3

LOG-PARIS COEFFICIENT FOR A12024-T351

Tes tTemperature R- 0.01 0.1 :L3 0.5 0.6

OF (CC)

72 (22) -8.613 -8.447 -8.350 -8.277 -8.231

200 (93) -8.565 -8.409 -8.336 -8.257 -8.212

300 (149) -8.500 -8.402 -8.323 -8.257 -8.178I

400 (204) -8.513 -8.356 -8.275 -8.205 -8.145

12

0011;

0810

pj

440u

*4W 0910

0

LQ

+ *10

0LL LL L

4 W 0010

13

In general, there is very little shift in the data points

in going from the 72 0 F (220C) to the 400OF (204 0 C) data.

This is a very desirable material characteristic but presents

a hurdle in this effort to characterize a material's response

to a change in temperature.

In Figure 5 if lines were drawn through the data points

for each temperature, excluding all of the log-Paris coefficients

for an R-ratio equal to 0.01, the slopes of the four lines (not

shown) would be 0.417, 0.392, 0.424, and 0.418 for the four

test temperatures: 720 F (22*C), 200OF (93 0 C), 300OF (149 0 C),

and 400OF (204 0 C), respectively. Since (1) there is no trend

in the slopes, and (2) the slope for 72*F (221C) and 400OF (2040C),

the minimum and maximum test temperatures, are practically

identical, the slope was assumed to be constant over the tem-

perature range and is approximately equal to the average of

the four values E a 0.413. Assuming the slope of the line

remains constant will accommodate considerable simplification

of the mathematical model for the FCGR test data since

log-C = constant + b.R

is equally applicable for any temperature. Also the Paris

exponent, m, is assumed to be constant, m=3.36, over the entire

R-ratio, temperature, and crack growth rate range (Table 1)included in this program, which represents another convenient

simplification.

Figure 6 presents the log-Paris coefficients listed

in Table 3 along with the temperatures. For all five R-ratios

there is very little change in crack growth data (Figures A.4to A.20) or in log-C with an increase in temperature. Here

again it can be seen that all of the log-C values associatedwith a loading ratio equal to 0.01 plot disproportionately low.

A linear relationship can quite adequately represent the

change in log-C with test temperature for all five of the R-ratios.

14

0054

P4~

* 44

4J

If the best fit lines (not shown) were drawn for each R-ratio,

the slope of each line would be: 0.00031, 0.00026, 0.00021,

* 0.00019, and 0.00027 for loading ratios equal to 0.01, 0.1, 0.3,

0.5, and 0.6, respectively (since the plot for an R-ratio equal

to 0.01 is disproportionally low these log-coefficients data

points will again be disregarded). The average slope for the

four lines associated with the R-ratios larger than 0.01 is

d=0.00023. This average slope is represented as only an

approximate value for the change in log-C with a change in

temperature. Assuming the slope of the lines remains constant

represents another convenient simplification of the mathematical

model for the FCGR data. Consequently,

log-C % constant + U'T

is equally applicable over the R-ratio range from 0.1 to 0.6.

It has been assumed that the trivariant data (R-ratio,

test temperature, and log-C) can be graphically represented by

a series of parallel straight lines. Reference 2 presents

a least squares method for calculating the coefficients for

trivariant linearly related data in the general. form

z = a0 + alx + a 2 Y (2)

for a given set of n data points where

N1 - N2a2 =4 2 2- 2[n Ex -(Exi) 21 [n Eyi-(Eyj)l-[n Exiyi-(zxj) ((y) j 2 (3)

where

N1 [n Zxi-(Exi) 2[n Zyizi.-(Zyi) (zi)] (4)

N2 [n Z-xiyi-(Zxi) (Zyi) I[n Fxizi-(Fxi) ( E zi)] (5)

16

• • • - ... . , .d ' ..

[n Zxizi-(Zxi) (Zzi)] - a2[n Exiyi-(Exi)(Zyi)]a, 2 (6)n x _ (Zxi) 2

Zzi - a2EYi - alTxiand a 0 n (7)

for i 1,2,3...n

For this particular application

x - R-ratio = R

y - Test temperature (OF) = T

and z = log-C.

Since the data for an R-ratio equal to 0.01 appears

to be disproportionately low, only the 16 data points (n=16) forR-ratios greater than or equal to 0.1 were used as input to the

above equations. The results of the calculations were

a0 - -8.503

al - 0.412

and a 2 = 0.00023

or log C = -8.503 + 0.412R + 0.00023T (8)

The two coefficients calculated in this manner are

practically identical to the average values for the lines'

slopes (Figures 3 and 4) presented as approximations earlier.Taking the antilogarithm of equation (8) yields a general

expression for the Paris coefficient., C,

C = 1 0 (-8.503+0.412R+0.00023T) (9)

Therefore, by substituting equation (9) and the average

exponent, mi=3.36, into equation (1) the final mathematical

model for the test material is:

da (-8. 5 0 3 +0.412 R+0. 0 0 0 2 3 T) AK3 . 3 6 (10)

for 720 < T < 400OF and 0.1 < R < 0.6.

17

A test case to verify the general Paris expression (10) wasarbitrarily selected at an R-ratio equal to 0.35 and a testtemperature of 250IF (121'C). Putting the values of these twoparameters into equation (10) a predictive equation for thedata is obtained:

da = 10(-8.503+0.412,0.35+0.00023-250) K 3.36dn

da = (-8. 302) 3 36 (11)dn

da 4.99 10 9 AK3 "3 6 for R=0.35 and T=2500 F (121 0 C)dn

Two specimens were tested for the test case. Test resultsare presented in Figure 7 along with the best fitting linecalculated with the exponent fixed equal to 3.36. (The bestfitting equation calculated for this same data set- with boththe exponent and coefficient free to vary has the same exponent,3.36, and a coefficient equal to 4.76.-9 rather than

4.75.10 .) Also presented in Figure 7 is the predictiveequation (11). The two lines overlap. They were started andended at different stress intensity ranges to facilitate visualdetection of two different lines as opposed to one broad line.

Agreement between the predictive and best fitting equation forthe test case data set is excellent.

18

EMPa eqr+*(m))

04-do/dn- 4. 919* 10 9 AK 33[prodlotive equatiaml

1000 '

4100

-C-

tr))X

0 - -9o - oCn .51L.

"g. -g0 0H

Toot amvitctvnomt-

lob aln

10-7U1110 100

stress Intensity> r-am~g., deltao K, EKSI eqt-t4(irm.)

Figure 7. R-0.35, 250*F (121*C) FCGR Test Results.

19

SECTION IV

CONCLUSIONS

The following conclusions are applicable for the test

conditions used throughout this report; i.e.; 72 0 F (221C) <

Temperature < 400 0 F (204*C), 0.1 < R-ratio < 0.6, and a loading

frequency equal to 20 Hz.

1. The log-Paris coefficient can be modeled as a linear

relationship of the R-ratio and the test temperature

assuming all other test parameters remain constant.

2. In a log-stress intensity range versus the log-crack

growth rate plot the linear region shifts down and to

the left with increasing R-ratio.

3. For a constant loading frequency and load ratio

there is very little acceleration in the crack growth

rate in aluminum alloy 2024-T351 with an increase in

test temperature.

4. The crack growth model derived herein netted a good

fitting predictive equation to the linear region of a

test case data set.

20

- I.

REFERENCES

1. Cervay, Russell R., "An Empirical Model for LoadingRatio Effect on Fatigue Crack Growth Rate Data,"University of Dayton Research Institute, TechnicalReport AFWAL-TR-81-4140, November 1981.

2. Program Manual ST1 Statistical Library, Texas InstrumentIncorporated, Dallas, Texas, 1975.

1 3

2211

.......................................................A

APPENDIX A

22

CMPa eqr+, (m) 3.1I 1.

* Al 2-TO51

ri

X-

, 1i-5 .

00

LN

X

0

a - do/ci- L 8I-N A X.L0 R- LEI1-I

Temp- M2 0 Dog. F

frog. - 20. 0 Hu

lob air

Orienaien- a.-T)

j INS

oIeo ntomlt~y ram!ge, do 1-6 K, rKS I oqr-+(. Im.)3

Figure A.I, R=0.01, 720F (220c) FCGR Test Results.

23

• :u- i i

CMPa oqr4,(m) 3

Al a1WT5

15-4

0

L

do/dia 9.57*16 A KoR 9tn.1I AI

Tampm 72. Oagp Ffraq. m2 1L 8 Ma

lob~ alt-

ot-rooo Inimml+y i-arise, do I1+a K, EKS I oqr-+ (i m.)3

P'igure A.2. R-0.1, 724F (22*C) FCGR Test Results.

24

CMPa eqrt (m)

A t 2124-TOI5

-4.1

tom6~6-

00is-9 a. 9a

Temp M, Dog. .F

frg a2L1Ho11%

Te&4 envromot

10-7 .in

"o.roseoo :ntesy range, delta K, CKSI eqr-I (.)3

Figure A.3. R=0.3, 720F (220C) FCGR Test Results. 2

•2 5 , ,n _

i ~~I I 1 11 I• 3 ' Ia I l I l

CMPa qrc (im) 3

*Al I4--T3I5

116-4-

lii

IN X

LI

U -4

0

9.3

da/dnm 5. 28*11 9 A K

Rd.- . W .i1Tomp- 72.1I DogI. F

Toot mmvironmnk,.lob air

Or tatmkion CL-T)-I 1 -7 I I 1 I I1 I I I III

1 ii 1U

"st.r'ess In!.ne±lty range, deoIa K. EKSI *qr.-. (In.) 3

Figure A.4. R-0.5, 72*F (22 0C) FCGR Test Results.

26

• L~.... . .. . . . . .. . . . . . . . . ..... -... . ... ..- " • 3 . . "1 ' '' i

EMPo oqr-+.(m) 3

* Al ~204-TO81

0X

0

do/dim 5.70010 AK0R-U.86 10

Tinmpm 72.0 Dog. F

21L4m9. a3 HxT..~ iv~remoui

lo6 airOrient.ation CL-T)

1813

s~rss n~hisLyr-ongs, dol1*a K, CKSI wqrAClm.)3

Figure A.5. R=0.6, 72*F (22*C) FCGR Test Results. *27

Ct4P* e.cqr.(m) 3

0 Al 2124-T251

28-I

dI

c~/~w .7010-

R-0 1l

19-7

to 10 0wIr-e lmIIiytc~,dl.cK K1er+(m)

Figue A.. R0,01 200F (3*C)FCGRTes ResltB

28di 2 210 9 ~

10-

di

Xo -9- 9.1

Teapu M.0 Dong. F

LAD AIR

*~rwe n4t.nit~y range, delta K, CKS1 *qr-+.(i.))

FigUre A.7- R=O.lo 200OF (93-C) FCGR Test Results.

29

EMP* eqr-t Wm 3

SAl 5194-TWl

UM-4

1W I

R- 0.

Tap 2M. Do.i£rel- 00H

To4 utrm~ýLA I

1.di 1. Leo~~K~*3

Ot-e RuMat 5.35e C140K S or+(in.

Figure ~ ~ ~ ~ Tap A.B.. R-0.3 20O 90)FG etRsls

30 .~m2.3H

Cmpa osqt (m) I

* Al 2224-T951

ii-m

00

L

IO-a

C./cm a.a* 0816K9

R- 0.50 .1Twf-p 200.0 Dog. F

TmA mnvlrormmmibulob airOr-iaob4bi.,im(LT)

is' .1--Ji-1-U-LJ L4.L Iis tooI

u*.rese int.emoiy range, delta K, tKSI *qr4.(in.)3Figure A.9. R=0.5# 200OF (930C) FCGR Test Results.

31

EMPa eqrt (m) 3II 1in

Al W--5

--

'-i

0X

00

L.4

x

a do/dm6 .14*10 A K 9

0 ~R- 0. NU

Tomp- 206.0 Dong. F

To oir-wimmenjmLAO AIR

*+rse n~n.1.yrang., de1+.c K, EKSI wqr-t(im.)3

Figure A.10. R=0.6, 200OF (930C) FCGR Test Results.

32

CMPc ocqr-4(mt) 3

aAt 2824-TVS1

11000

0 .4

00

-rrL4%O-C

o d./MM" a 318*10 A K0 R" 3.01 j

Tem~p- 333.0 Dog. F

VTmn4 anviv £ onj la1b air I

I to too

"rose.. 4:+.omoit rormg., dmal.c K, EKSZ oqrt lIm.)3

Figure A.11. R=0.01, 300OF (1490C) FCGR Test Results.

33

CMPa egr.(m)3All 111

0 Al 2024-TSOl

10-4-

1000

_ .g

0

0-0

- 3.3

-- R- 0.I0 - 10Temp- 3W9. Deg Ffre•i - 21. 0 No

lab ai-

ii.7 I I I I~ III! I I.!I-LLL

"*!reee lmi.n*1,• y r ange, de.lt K, EKSI eqrtl.(Ln.)3

Figure A.12. R=0.1, 300OF (149 0 C) FCGR Test Results.

34

[MPG eqr4, (m) I

* Al 2024-Tasl

'-4

lu

X

141- 5.U~

0 -0

do/dmo 3. 10*10 t~A K 3

R- 0. 01 isTamp- 801.0 Dog. Pf"q - 21.10 Ha

To 6virom"

106 air

in IIng"sruSe ms r ens1y ramg., de1+.a K, EKSI oqr+,CIn.)3

Figure A.11. R-0.01, 3000F (149 0C) FCGR Test Results.

33

EMPa .qr.; (m) 3

*A I 202t4-TSO I

u--I>g4.

00

LX

-g -0 3.90

S _ ~do/vdm-. 9. 90-10 A K

fxý -9 211 0 Mac

Tee4 envirommnto10-

10tolab atm iSUH

"ereoes lm~msoty range, deltoa K, CKSI[ *tlrT(:n. )3

Figure A.12. R-0.1, 300 0 F (149 0 C) FCGR Test Results.

34

EMPO eqr'4. (m)J10 100i I

€ Al 2024-TIhS

r-U gr 4

1w00

100

a - doa/d- 4. 75*10 ~A K .3L0 R- 0. 90 - 10B

Temp- -300B.0 Dog. Ff'P q, - 20. 0l H m, .

"Tootl onviL om~ment-

lob oil-.

10 10

"--ewe Imtemty Pam•m, delta K, [KSI wIr4 (im.)]

Figure A.13. R-:0.3, 300OF (1490C) lFCGR Test Results.

35

S........ ... ... ..... " . . . • "• "-: .•' • . ' , ' 1• • ,•a .

CMPc eqt-t (m) I

10 190

*Al 2024-T351

10-4.5

~ 0~

Uv-ut I

XI~

L.Xc4)

it

0 ./liun5. 53*10-9 93

Temp- 303.5 0 De. F

freq. a 21.0 a N

loa6 air

l3~~i I Ot ht*i~&on-"CL-T)

*~rsg ehe4~y'-nque del+,o K, CKSI oqr-t(im.)3

Figure A.14, RmO.5, 300*F (1490C) FCGR Test Results.

36

IMPa eq?, (m) 1.10 .10

Al^ 2024-T951

10-4-

.1080 1

.C-

0

-u 10

Sdo/dt•- S. f33I10 -9'A K 3.98

Tepo 300.0 Ong. F'

frt.eq. - 20. 0 Hx

la6 alt-

Ot- omt at Iom- (I.-T)

0-7.10100

im LremwiýLy rang~e, del1•c K, rKSI .r•(•)

Figure A.15. R-0.6, 300OF` (1490C) FCGR Test Results.

37

cia/chrn .. O310~k3 8 1

tMPC3 o.qr+. M)

*Al 2624-T151

1#-4

0 SL-11LI

10-0

T..p- 4M U Do*. F#reowm 251.1 Ho

.'troes i emit~y rong., del+.a K, EKS1 wqr+.(tL.)1

Figure A.16. R-0O.01, 4000 F (204 0C) FCGR Test Results.

38

F'!

EMPa eur'!. (m) 3

* Al 2024-TSOI

10.-4-

I100 L'i

o ID

641

Li

0 ~~do/dn- 4. 41el1-gA K .3

L0 R- 0,.10 _ 10

Tomp- 400.0 Des. F

frc 0q 20. 0 H,.

ToA,• emv ironmmomt

lob cAt-

10-7, S- •, ,I to0 (-T

1 10 .1 1001B.7 t ..t t !!Tt !! 40. I 0m...L iF

e,'.reo, mn.ensl.y rangm, delta K, EKSI sqrLQin.) 3

Figure A.17. R-0.1, 400OF (204 0 C) FCGR Test Results.

39

k - _ _

CMPa qr,. Wm) 3

* Al 2024-TS51

log

.s-S

100 10

L-v 04

SRd=/ , 31*1g A K

RM 0.30-Tamp- 400.0 Dog. Ff'r.eq. 20.0 HK

Teo" %mvirommntol•

lab ait

Or~ietAkatia o- (L-T)

l0-7 I 1 _1 *, I I 1I 114j110 100"roseo im+,emoI+,y ramr~e, demlt€ K(, CKSI oqr4 (in.)]

Figure A.18. R-0.3, 400OF (2040C) FCGR Test Results.

40

EMPc .eqn+ (m) 310 . .10.

* Al 2024-TSBl

li-4-

0

Li

4 -4-0

L

10Tmp, 410. 0 Dug. F

freq. to 20. 0 Ha

lab air

0r- I e1ncaI I oI(LT)-.-..lL.......L L..• tI l ! ! J I_110 100

.tneoeit Intenity Prt-a , del•a K, CKSI oqr,(±ti-.)3

Figure A.19. R-0.5, 400OF (204 0 C) FCGR Test Results.

41

' __.X.T___.ir.I,~~ ~~.4..F • .. __ ,_.TT• ,_

IMPa eqt'- (m) I.10 00

* Al 2024-T351

1000

0

K -U .1000I 0

0 ,

-I I

S01

y

0- r--I

/do/dm- 7.l1*10 6K

L

0 R- 0.80 .10

Tomp,, 400.0 Dm0. F

fraeq. - 20. 0 Hz

10-7 L---L-I L -LL10 100

strseI i.ra+mlOr y range, delic, K, IKSI *qrE (in,.)I

Figure A.20. R=0.6, 4000F (204 0 C) FCGR Test Results.

42

.................................................... /'