Static and fatigue strength of FM-123-2 adhasive in double strap joints of various lengths of overlap

(1)

vu

•

April, 1971.

1 n . ,..

"

~'J71

STATIC AND FATIGUE STRENGTH OF FM-l~3-2 ADHESIVE

IN DOUBLE STRAP JOINTS OF V ARIOUS LENGTHS OF OVERLAP

by

V.Niranjan, D. R. Hamel and C. A. Yang

(2)

STATIC AND FATIGUE STRENGTH OF FM-123-2 ADHESIVE

IN DOUBLE STRAF JOINTS OF VARIOUS LENGTHS OF OVERLAP

by

V. Niranjan, D. R. Hamel and C. A. Yang

Manuscript submitted August, 1970.

(3)

ACKNOWLEDGEMENT

The authors wish to thank Dr. G. N. Patterson and Dr. G. K. Korbacher for providing the opportunity to write this technical note.

Thanks are due to Mrs. Dorothy Finlay and Mrs. Barbara Waddell for patiently typing the manuscript; to Mr. Ralph Magid for doing most of the drawings; to Mr. John McCormack, Mrs. Margaret Stewart and Mr. David Hynes for their help in the publication of this technical note; and to Mrs. Asta Luik and Miss Nora Burnett for the library services.

The financial support of Fleet Manufacturing Limited, Fort Erie, and the National Research Council, ottawa, is gratefully acknowledged.

(4)

SUMMARY

Statie and fatigue test resu1ts on 160 doub1e-strap joints of 2024-T3 c1ad a1uminum bonded with FM-123-2, a modified nitri1e epoxy adhesive manufactured by the Bloomingda1e Department of the American Cyanamid Company are reported. The results are statistica11y ana1yzed. S-N curves are presented with 95 per cent confidence 1imits. A computer program for the statistical analysis of fatigue resu1ts is appended.

(5)

TABLE OF CONTENTS PAGE Summary Notation I. INTROD,UCTION 1 t, 11. EQUIPMENT 1

lIL TEST SPECIMENS l~

IV. ANALYSIS OF RES~TS AND STATISTICAL BACKGROUND 2

V. COMPurER PROGRAM 3 VI. DISCUSSION

4

REFERENCES 5 APPENDIX TABLES FIGURES iv

(6)

, J

"

... cv

m N. ~ n P P. ~ R r

x.

~ ~l NarATION Coefficient of variation

=

rr/~

Fatigue strength reduction factor = Fatigue strength of

plain metal at a given endurance~a~igUe strength of a

joint specimen that failed in tne metal at the same

endurance

Length of overlap Order number

Life of the ith specimen Sample size

Probability of failure or cumulative frequency

=

m/~'n + 1)

Load at failure of the ith specimen in statie testing

Stress ratio

=

rr. /rr

~n max

Coefficient of correlation

Probability in linear units on the probability scale of

a normal probab~ity paper

Log N. ~ True mean n

I

N/n or i=l n

I

p/n i=l n

[

'\

'

Logarithmic mean = Antilog ~

i=l replace N. by P.

~ ~ n

' \' (Log Nol)

/~

,

Mean of logarithmic life, ~ ~ '

i=l

True standard deviation

[ I

i=l or replace N. by P.

1. 1.

Standard deviation of logarithmic life =

n

[

I

i=l

(7)

o-max

0- •

InJ.n

Stress level, maximum stress in a sinusoidal fatigue cycle

Mînimum stress in a sinusoidal fatigue cycle

vi

(8)

I. INTRODUCTION

, T~e subject of adhesive bonded joints has made rapid strides in recent years (Ref.

9').

One of the very basic joint concepts is the double-st,rap joint

(Fig. 1). A 'lap joint has a characteristic design parameter known as the

opti-. mum lebgth of overlap. A very elementary definition of the optimum length of overlap would be as follows: an optimum length of over~ap is that length of over-lap beyond which an increase in overover-lap does not produce a worthwhile iIlcrease inthe joint strength. A more detailed description of this quantity may be

~ found in Refb 4. Semi-experimental methods for determining the load carrying

. capac;j.-ty of a joint at any length of overlap were first discussed by Szepe (Refs. 3 and)(!. Szepe's approach can be used to determine the optimum length of over-lap w~ th a minimum number of test specimens. ' .

Statie and fatigue test results on 160 double-strap joint specimens (Fig. 1) are repdlrted in this technica): note. These test results· have been analyzed

s~atistically, assuming lognormal distributions for the specimens. A least

squares analysis was performed and the coefficient of correlation calculated to determine t~e goodness of fit of a lognormal distribution to the .experimental data. The various statistical parameters of interest like the mean, standard deviation, coefficient of variation, etc., have been computed. The results of the statisti-cal analysis are presented in both tabular and graphistatisti-cal form~ The fatigue test results are presented as S-N curves and the 95% confidence limits are also given.

The results of this technical note are utilized in a sèmi-experimental analysis of bonded joints. Since the level of mathematical cornpiexity involved in this analysis is higher than in the subweet matter discussed in this technical note, it is published elsewhere (Ref. ~).

11. EQUIPMENT

All fatigue tests were carried out on a model SF-l-U Sonntag Fatigue Machine with static load maintainer. A short description of this machine may be found in Ref. 1.

Statie ~ensilè tests were carried out at Fleet Manufacturing Ltd. on a model NST-l Detroit Testing Machine.

111. TEST SPECIMENS "

A total of 205 specimens were tested under statie and fatigue loadi~g

conditions. Out of these specimens, 166 were tested in fatigue at a stress ratio of R ~ 0.1. The remaining were tested under static loading. Out of the 166

fatigue specimens, 126 were double strap joints of the type shown in Fig. land 40were plain 2024-T3 clad specimens. The results for the 2024-T3 clad specimens, already reported in Ref. 1 are reproduced in this report for cOmParative

pur-poses. out of the 126 double strap joints tested in fatigue 15 had an overlap length of.i = 0.125",18 had.i = 0.25",18 had.i = 0.375",40 had.i

=

0.5",17 had.i = 0.625" and 18 had.i = 0.75". Out of the 39 statie test specimens, 5 were

p~ain 2024-T3 clad and the rest were double strap joint specimens of the type

èhQwn in Fig. 1. From the 34 double strap joint statie test specimens five each were tested at lengths of overlap of .i = 0.125", 0.25", 0.375", 0.625" anel 0.75". Nine specimens had .i;;;:; 0.5".

(9)

for the program of Ref. 1. As the program was extended to cover tests with

various lengths of overlap, specimens witht = 0.1:25",0.25",0.375",0.625"

and 0.75" were manufactured in a second batch. Both batches of specimens were subjected to identical surface treatments and adhesive curing procedures. It is believed that the principal difference in the two batches of specimens was in using two different batches of adhesive. At the time of manufacture of the

speci-mens it was assumed that the batch-to-batch variations in the specimens would be

insignificant. Test resut ts (Fig. 19) showed that the specimens with t

=

0.5"

were stronger than the specimens with "

=

0.625" by a smal1 amount for a fatigue

life greater than 104 cycles. This difference in strength is believed to be neg-ligible from the point of view of production bonding. However, for purposes of

theoretical analysis, it would be good practice not to mix the results of the

two batches of specimens. As an afterthought, it was felt that all the specimens should have been manufactured in one batch.

All the double strap joint specimens were manufactured by Fleet

Manufacturing Ltd., Fort Erie, using FM-123-2, a modified nitrile epoxy adhesive

manufactured by the Bloomingdale Department of the American Cyanamid Company.

This adhesive was cured at 2500F and about 50 psi for approximately an hour. The

aluminum surfaces received the standard sodium dichromate-su1phuric acid surface

preparation (Ref. 2).

Dl • ANALYSIS OF RESULTS AND STATISTICAL BACKGROUND

The various symbols used in the foblowing discussion are defined in the

notation.

The distribution function for the fatigue lives N of a sample of n specimens is assumed to be log-normal. The goodness of this assumption is deter-mined by the coefficienn ,of corre1ation. The median and the 95% confidence limits are determined under the log-norma1 assumption. S-N curves are presented for the fatigue results using the media~ and the 95% confidence limits. The goodness of

fit of a log-normal distribution to the static strengths is also determined and

the median and 95% confidence limits computed. The details of the statistical ana1ysis:

The statistical parameters ~,~, CV and ~ are co~puted according to the

following formulas. n mean life,

₌

L

N./n l i=l standard deivation, ~ Coefficient of variation, CV

=

~/~

[ f-

'

Logarithmic mean, ~ = Antilog ~ i=l

n

[

I

(~-Ni)2/(n-l)J

1/2 i=l

(10)

..

The raw fatigue data is initially arranged in increasing order of fatigue life.

Then, a probability value is assigned to each specimen according to P = m/(n+l).

The values of P for sample sizes ranging from

4

to 15 are given in Table

40.

The corresponding values of X. (see notation) are given in Table

41.

If

Y. = Log N. ~ then the ~ives ot the specimens'are distributed log-nonmal if all

tTIe points1(X., Y.) from a sample fall on a single straight line on an ordinary

1 1

graph paper 0

If y.l = MX. + B is the regression line of Y on X (Ref.

~),

then

1 1

n ' n

(Ï

Y_i)

n

I

X.Y.

-

CI

X. )

1 1 1

M= i=l i=l i=l

n n 2 n

C

I

Xi 2 ) -

CI

xiy

i=l i=l and B i=l

Thi coefficient of correlation r is a measure of the goodness of fit of the line Y. MX. + B to the experiment al points (X., Y.) 0 It is given by (Ref. 6') ,

1 1 1 1 n., r

=

1 from Y. 1 bilities n \ ' X.Y.

L

1 1 i=l

Having computed Mand B, the 95% confidence limits can be determined

=

MX. + B, by substituting for X. the values corresponding to

proba-1 1

of 9705% and 205%0 The median corresponds to a probability of 50%.

The test results have been analyzed as described above. The raw data

and the comput~d statistical parameters are presented in Tables 1 to

38.

Tables 1 to 23 have to be read in conjunction with Table 24. The results of the

statistical analysis are presented in graphicá~ form in Figs. 2 to

8.

V. COMPUTER PROGRAM

A program to do all of the statistical analysis described in Section

IV has been written in Fortran for the UTIAS IBM 1130 Computer. The listing

(11)

and graphic form. Tables 1 to 23 and Figs. 2 to 8 form the output of the IBM 1l30.

VI. DISCUSSION

The results of the statistical analysis of fatigue results are presented in Figs. 2 to 8. In Ref. l,the statistical analysis to determine the goodness of fit of a log-normal distribution to the experimental data was done in an approximate

manner by making use of the fact that 68% of the population lies between ~l + rr

l and ~1 - rr

l in a normal distribu~ion. The more rigorous anarysis of the present technlcal note was applied tOvthe results of Ref. 1. It was found that the diff-erence between the approximate and rigorous analyses was negligible for the

re-sults of Ref.l. This comparison is shown in Fig. 9. The approximate and

rig-orous analyses were applied to the results of the present technical note. The

agreement between the two analyses was good in those cases where the coefficient

of variation was small as shown in Fig. 10. The agreement was poor in cases where

the coefficient of variation was large as may be seen from Fig. 11.

In Fig. 10, for rr

=

40.0 ISI and r

=

0.94, the straight 1ine fits the experimenta1 points ver~~e11. In Fig. 11, for the same coefficient of

correlation of r = 0.94, the straight line dOeS1Jllot fit the experimental points

so weU. This is due "tio the fact that the éoefficient of variation in Fig. I I

is larger than in Fig. 10. Thus the appearance of the goodness of fit on a graph

depends very much on the scale used. On a smaller scale, the fit would appear

better. The coefficient of correlation is independent of the scale used ( Ref.

6) and hence a better indicator of the gocxiness of fit than the graphs.

S-N curves are presented in Figs. 12 to 18 for the various specimens

uested. A summary graph of all the tests done is given in Fig. 19. The fatigue

strength reduction factor K~(see Notation) vs. life is presented in Fig. 20.

The value of Kt is seen to 5e below 1.2 in the whole range.

There were two main objectives for this report. First, as an aid to

ot her researchers working in the field of fatigue, a complete computer program for statistically analyzing fatigue gest results has been presented (Appendix).

Second, the fatigue properties for a double strap joint with varying lengths of

overlap have been determined. These fatigue properties should be helpful to anyone who plans to use a 2024-T3/FM-+23-2 bonded joint in their own research.

Also, the data in this report may be of use to design engineers.

4

(12)

1. Hamel, D. R. 2. 3. Szepe, F.

4.

Niranjan, V. 5. Niranjan, V. 6. Freund, J. E. • REFERENCEE

Bonded Joints - Increasing Fatigue Strength by Bevelling. UTIAS Tech.Note NO.159, June 1970. Handbook for Adhesives. American Cyanamid Company, Bloomingdale Dept., Havre de Grace, Maryland.

Strength of Adhesive-Bonded Lap Joints with Respect to Change of Temperature and Fatigue. Experimeni;.al Mechanics. May 1966.

Bonded Structgres and tpe Optimum Design of a Joint. (to be published as a UTIAS Tech.Note) Bonded Joints - A Review for Engineers. UTIAS Review No.28, May 1970.

Modern Elementary Statistics. Prentice-Hall Inc, New York 1952 •

(13)

APPENDIX

// FOR

*LIST SOURCE PROGRA~

SLJP,ROUTINE POUT

C T I-' I S S U f-\ ROU TIN ETA K ESA SITS I fW U T H l E V A LUl SOF T H i:: V A I~ I AD L Co S X, Y , N , i', ~ ,

C XSTR,R FRO~ TH~ MAlM PROGRA~ A~D PRESE~T~ TH~ k~~UlTS OF THl STATISTICAL

C ANAL Y SIS j,'~ GRAP H I CAL FOq,\j. SEE:. Hit:: :>1A I i~ PROGRM-: FûR A Dt:.SCR I PT ION OF

C THE VARIARLE NA~ES. DI\~ENSI(JN X(lOO) ,Y(lOO) CO~YON X,y,~,N2,XSTR,R IF (~;2-111tl,2 1 CALL SCALF(O.BO,G.2e,-14.U,O.U) (ALL FGRID(O,o.c,o.n,1.o,5) Xl=-O.13 X2=3.0 00 100 1=1, I) CALL FCHAR(Xl,-1.1,O.13,0.13,O.l .,IR I TE ( 7 013 ) X 2 13 FORMAT (F3.1) Xl=Xl+l.0 X2=X2+ 1. 0 100 CO\!TINUE CALL FCHAR(2.5,-2.2,O.2,u.?,O.) viRITE(7d2)

12 FORMAT( 'LOG CYCLES')

CALL FGRlf)( 1 ,o.c: ,(l.O,3.10t! l CALL FGRID(1,O.ü,3.1U,3.ü3,1) CALL FGRID(1,O.O,6.13,2.14,1) (ALL FGRID(1,O.0,B.27,2.14,ll (ALL FGRID(1,O.O,lO.41,3.03,1) (ALL FGRID(1,O.O,13.44,3.10,1) (ALL FCHAR(-.75,0.,n.13,Q.13,O.) \"R IT E ( 7 , lil) 14 FORrvAT('02.0') (ALL FCHAR(-.75.03.10,O.13,O.13,0.) ~.!R IT E ( 7 , 1 5 ) 1 5 FOR~A T ( , 10.0 ' l (ALL FCHAR(-.75,05.83,O.13,O.13,0.) I,!R IT E ( 7 • 16 ) 16 FORl\iAT ( '30.0') CALL FCHAR(-.75,ü8.ü7,O.13,ü.13,0.) ':IR I T E ( 7.17 ) 17 FOR,"1AT('50.0') (ALL FCHAR(~.75,lü.21,O.13,O.13.0.) 'tiRITE(7,18), 18 FOR~Y1AT ('7ü.0') (ALL FCHAR(-.75,13.22,0.13,O.13,0.) WRITE(7tl9) 19 FORI'IAT('90.0') (ALL FCHAR(-.75,16.29,0.13,O.13,ü.) I:iR IT E ( 7,20 ) 20 FORMAT('98.0')

(14)

\·.;r~ I TE ( 7, 11 )

11 FORVtAT( 'PROHAHILITY')

CAL L F C HAR ( 5 • 1 , 1 6 • 54 , 0 • 1 u ,

°

.

1 () , o. ) I/RITE(7,21)

21 FOR~AT( 'SY~AOL ~AX.STRESS SA~PLE SIZE COR.COEFF.')

CALL FPLOT(-l,O.,O.)

C N2 IS ASSU~ED NOT MORE THAN 6 2 D O 200 I=l,N CALL FPLOT(-2,Y(I)-3.0,X(I)) CALL PO r,'H (N2-l) CALL FPLOT(l,Y(I)-3.0,X(I)) 200 COt.,;T If\WE CALL FPLOT(-2,Y(N+11-3.0,0.) CALL FPLOT(-1,Y(N+2)-3.0,16.541 RN2=!\)2 CALL FPLOT(-2,5.35,16.54-RN2) CALL POINT(I~2-1) CALL FCHAR(6.47,16.54-RN2,0.lO,O.10,O.) \·IR ITE (7,22 I XSTR 22 FORMAT(F5.21 CALL FCHAR(8.22,16.54-RN2,O.lO,O.10,O.) 'dRITE(7,23)N 23 FORrlAT(I21 CALL FCHAR(9.6,16.54-RN2,O.10,Ü.lO,O.1 ItIR!TE ( 7,24) R 24 FORMAT(F4.2) CALL FPLOT(-l,O.,O.) RETURN END

CORE REQUIREMENTS FOR POUT

CO~~ON 408 VARIABLES END OF COMPILATION I I DUP *DELETE _POUT CArH ID 0001 DA A[)Dr~ 54H6 *STORE WS UA PUUT CART ID 0001 DH ADDR 54~6 I I FOR

*LIST SOURCE PROGRA~

14 PROGRA."i DU2t) DB c.'\ T 002LJ 6?8 *NAt"'E :\'.l!, I '\I *IOCS(CARD,1132PRINTEk,PLOTTERI

C v.'nRMUAN,lJTIrIS,STATISTICAL Ä,\ALYSIS OF I-'ATIGUE DATA C TESTING THE GOODNESS OF FIT OF A LOG NOR~AL DISTRI~UTION

C LINEAR REGqESSIU~ ANALISIS,LEAST SQUARES FIT,CORRELATIUN CUEFFIC1ENT DIMENSION RL(100),Y(100) ,X(lOJ)

COMMON X,Y,N,N2,XSTR,R C RL=LIFE IN CYCLES,Y=LOG RL

C X=PROBARILITY I~ U~ITS THAT LI~EA~ISE A NOR~AL DISTkIBUTIUN

C N=SAMPLE SIZE,~l=~U~HER UF STkESS LEV~LS AT WHICH THE GIVEN TYPE U~

C SPECI~EN IS TESTED IN FATIGUE,N2=ORDEk ~UMHER OF STKESS LEVtL U~t)E~

C CONSIDERATION 1\ A DECREASING SEUUl~C~ 999 READ(2,199\Nl

(15)

"

17 1 11 2 12 3 13 C 4 5 15 90 IF(N1)9,9,77 N2=1 DO 888 L=l,Nl READ(2,11)N FORMAT(I2) REI\D(2,12) (RUI) tl=l,N) FOR~AT(8F9.0) RE t,D ( 2 ,13 ) ( X ( I ) , 1=1 ,N ) FOR,'v1AT (14F5. 0)

K=TA~LE NU~BER,XSTR=MAX.STRESS IN KSI

RE AD ( 2 011 ) K

READ(2tl5)XSTI~ FORMAT(F6.0) DO 90 I=l,N

Y( I )=ALOG(RU I)) IALOG( 10.0) CONTINUE SU~l=O.O 00 100 I=l,N SUM1=SU,\11+X ( I ) 100 CONTINUE A=SUMl SUf'v':2=0.0 DO 200 l=l,N SUM2=SU~2+Y(I) 200 CONTINUE B=SUM2 SUM3=0.0 DO 300 1=1, N SUM3=SUM3+(X(1 )**2) 300 CONTINUE C=Surv13 SUM4=0.0 DO 400 I=l,N SUM4=SU~4+(Y(I)**2) 400 CONTlt'WE D=SUtv!4 SU~15=0. 0 DO 500 I=l,N SU~5=SUM5+(X(i)*Y(I) ) 500 COI\;TINUE E=SUV,5 RI\J=N F=(RN*C)-(A**2) G=(RN*D)-(R**2) H=(RN*E)-(A*R)

C L INE WITH LEAST SUUARE DEVIATION IS Y=(RM*X)+RH R,"1=H/F

c

R~c(C*B-A*E)/F

R=CORRELATION COEFFICIENT

R=H/SQRT(F*G)

Y97=LOG N AT 97.5 PRORABILITY Y2=LOG N AT 2.5 PROBAHILITY

Y50=LOG N AT 50.0 PROHABILITY

Y(N+1)=LOG i\I AT 2.0 PROBARIL1TY,Y(f~+2)=L(;(, i~ AT 'Jd.1.J ~RûI'3AlHLITY Y97=RM*16.15+RB

Y?' =R"HOO. 40+I~B Y50=RM*08.27+RB

Y(N+1)=RR

(16)

CALL POUT

C RL97 AND RL2 ARE 95 CONFIDENCE LIMITS IN CYCLES

C RL50=MEOIAN(50. PROBARILITY)OF LOGNORMAL D1STRIBUTI0~ IN CY(Ll~

RL<i7=lO.O**Y97 RL2=lO.O**Y2 RL50=lO.0**Y50

C COMPUTATION OF MEAN,STD.DEVIATION,CO~FF.OF VARIATIUN AN~ LU~ARITH~IC MEA~

SU~6=O.0

DO 600 I=1,N

SU"'6=SUM6+RL(I) 600 CONTINUE

C RMEA~=~EAN,SD=STD.DEVIATION ,CV=(OEFF. OF VARIATION,~LM=LU~ARITHMIC ~EA~ Rrv;EAN=SUrv16 IN

SUrv,7=0.O DO 700 I=l,N

SU~7=SUM7+( RL(I)-RMEAN)**2

700 CO rIlT I NUE

SD=SQRT(SUM7/(N-l» CV=(SD/RMEAN)*100.0

RL~=10.0**(B/N)

21 WRITE(3,31)K,XSTR,N

31 FORMAT(1H1,10X,6HTABLE ,1211121H FATIGUE TEST RESULTSII

1 17H MAXI~UM STRESS =,F6.2,5H KSI/17H SAMPLE SIlE =,121/)

22 WRITE(3,32) RL(1)

32 FORMAT(22H RAW DATA,LIFE(CYCLES)116H .E14.4) 2 3 \<1 RIT E ( 3 , 3 3 ) ( RL ( I ) , I = 2 , N )

33 FORMAT(6H ,E14.4) 24 WRITE(3,34)

34 FORMAT(lHO)

25 \l/RITE(3,35)r~MEAI~,SD,CV,RL[v1,R

35 FORMAT(lH ,31HCOMPUTED STATISTICAL PARAMET~k511

1 27H MEAN LIFE,CYCLES = ,Ell.41 2 27H STD.DEVIATION,CYCLES = ,E11.41 3 27H COEFF.OF VARIATION = ,F4.11

4 27H LOGARITH~IC ~EAN,CYCLES = ,Ell.41

5 27H CORRfLATION CO~FFICIENT ,F5.2) 26 WRITE(3,36)RL97,RL2,RL50

36 FOR~AT(25H LIFE AT 97.5 PROAAHILITYI

1 27H (CYCLES)= ,Ell.41

2 25H LIFE AT 02.5 PRORAHILITYI

3 27H (CYCLES)= ,El1.41

4 25H LIFE AT 50.0 PRORABILITYI

5 27H (CYCLES)= ,El1.4)

N2=N2+1

8H8 CONTINUE

C RY rv;EANS OF THE FULLC\':U,j(j STATtYE(\;T THE Al\J\LYSIS CI\,~ UE LJlk:L 0.\ AS

C ,\~ANY SETS OF DATA AS F(Et~UIf~ED.THE Efm UF n-.t: i,)ATA IS l.\JDICAT~D tlY 1\ bLAI~K

C CARD

GO TO 999 9 CALL EX IT

(17)

TABLE 1 FATIGUE TEST RESULTS

I'I,AX H1U."1 STRESS

SA1v_l_{PLE SIZE} = 15.50 = 5 KSI RAW DATA,LIFE(CYCLES) 0.2490E 04 0.4670E 04 0.5R20E 04 0.6000E 04 0.7030E 04

CO~PUTED STATISTICAL PARAMETERS

MEAN LIFE,CYCLFS :: _0.5202E

STD.DEVIATION,CYCLES = Ool731E

COEFF.OF VARIATJON :: _33.2

LOGARITHMIC "IEAN, CYCLES = 0.49101:

CORRELATION COEFFICIENT = 0.91 LIFE AT 97.5 PROBAB I LI TY (CYCLES)= 0.1291E LIFE AT 02.5 PROBI\R I LI TY (CYCLES)= O.lB65E LIFE AT 50.0 PROAARILITY (CYCLES)= 0.L+904E TABLE 3

FATIGUE TEST RESULTS

MAXIMUM STRESS = 11.00 KSI

SAMPLE SIZE = 5 RAW DATA,LIFE(CYCLES) 0.6979E 05 0.4891E 06 0.2416E 07 0.3254E 07 0.5460E 07

COMPUTED STATISTICAL PARAMETERS

MEAN LIFE,CYCLES = 0.2338E

STD.DEVIATION,CYCLES :: _0.2188E

COEFF.OF VARlATION = 93.6

LOGAR ITHM I C MEAN,CYCLES = 0.lU79E

CORRELATION COEFFICIENT = 0.94 LIFE AT 97.5 PROHABILITY

«(YCLES)= 0.8584E

LIFE AT 02.5 PROBAB I U TY

(CYCLES)= 0.135:)E LIFE AT 50.0 P~OBABILITY

(CYCLES):: O.1073E 04 04 04 05 04 04 07 07 07 oe 05 07 TARLE ? F A TI ei lJ F T F. S T 1< E SULT S 'v'AX I 1-1 U ,\1 STRESS SAvPLF. SIZE = 13.50 = 5 KSI RAW DATA,LIFE(CYCLES) Cl.3040E OS O.3540E 05 0.4121E 05 O.4550E 05 0.1770E 06

COMPUTED STATISTICAL PARA~~TERS

.'-'lEAN LIFE,CYCLES = O.6?YOE

STD.DEVIATION,CYCLES = O.6236E

COEFF.OF VARIATIü;~ = <74.6 LOGAR I TWq C \.iEAN,(YCLES = 0.5135E

CORRELI\TlON COF.FFICIE!\.T :: ₀_._H5 1I FE AT ,7.5 PRORABIlI TY (CYCLES)= O.2506E LIFE AT 02.5 PROBARILI TY (CYCLES)= O.1:l49E LIFE AT 50.,0 PRORAB I LI T Y (CYCLES)= 0.5125E TARLE 4

~AXIMUM STRESS = 25.50 KSI

SAMPLE SIZE = 6 RAW DATA,LIFE(CYCLES) Cl.5420E 04 O.9490E 04 0.9R80E 04 O.1139E 05 O.1203E 05 Ool284E os

COMPUTED STATISTICAL PARA~ETERS

.'v1EI\N LIFE,CYCLES = 0.10171::

STD.DEVIATIO~,CYCLES = 0.2652E

COEFF.OF VAR It,T IO,'! :: _26.0

LOCiARITHv;IC "":FAI\,CYCLFS = Q.9815E

corH~ELAT ION COEFFICIU!T = O.H9

UH AT 97.5 PRORAB I U TV ICYCLES):: o ol 'J9BI: LIFE AT 02.5 ·PRORAFlILITY (CYCLES):: O.4820E LIFE AT 50.0 PROBAIlILITY u5 J~ O!J 06 Q!J 05 05 Ll4 04 05 04

(18)

T MSLE 5

FATIGUE TEST RFSIJLTS

~AXI~U~ STRESS = 21.00 KSI

SA~PLE SIZE = 6 RAW DATA,LIFE(CYCLES) O.6730E 04 0.3863E 05 0.4163E 05 0.4751E 05 O.9';67E 05 O.2003E 06

CO~PUTED STATISTICAL PARA~ETERS

MEAN LI FE ,CYCLES = O.7174E STD.DEVIATION,CYCLES = 0.6916E COEFF.OF VARIATION = 96.3 LOGAR JTH'''' I C :':EAN, CYCLES = 0.4630E CCRRELATION COEFFICIENT = 0.94 LIFE I\T 97.5 PRORARILITY

(CYCLES)= 0.7147E L1FE AT 02.5 P!WBAB I L I TY (CYCLES)= 0.2999E L1FE AT 50.0 PRORABILITY (CYCLES)= 0.4622 E TABLE 7

FATIGl.IF TEST RESlJLTS

~AXIMU~ STRESS = 38.UO KSI SAvPLE SIZE = 6 RA~ DATA.LIFE(CYCLES) O.38i101:: 04 0.90GOE 04 0.1l54E 05 O.1212E 05 O.1518E 05 O.1639E 05

CO~PlJTED STATISTICAl PARAvETERS

~EAr-J _LIFE,CYCLfS ₌ _0.1l35E

STD.DEVIATIO~,CYClES ₌ ₀_.45171::

(üEFF.OF VARIATION = 39.7 LOGARITHVrC '1F.AN .(YCU:S = 0.1033E CCJRRElATIOf\; COEFFICII::.'\T = 0.90 LlFE AT 97.5 PROBARILITY (CYCLES)= O.3473E LIFE AT 02.5 PRORAR I L I TV (CYCL[S)= O.3072E LIFE AT 50.0 P~ORAR I L I TV (CYCLES)= OolO32E. 05 05 05 06 04 05 O? 04 05 05 04 05 TABLE 6 FATIGUE TEST RFSULJS

~AXIMUM STRESS = 18.00 KSI SAYPlF SIZE = 6 RA~ DATA,LIFl((YCLES) 0.2791E 05 O.3142E 06 0.7349E 06 0.7408E 06 0.7817E n6 ·0.10R5E 07

COUPUTFD STATISTICAl PARAM~TERS

V,EAN LIFE,CYCLES = O.6140E. STD.DEVIATION,CYClES = O.3778E COEFF.OF VARIATIO:\! = 61.5 LOGARITHvIC '·~EAN, CYClES = 0.3992E

COr~I~ELAT I

o

"-i COEFFICIENT = 0.R3

LI FE AT 97.5 PROflAR I LI TV ((YClES)= O07337E LIF[ AT 02.5 pr~ORAR I LI TV ((YClES)= O.?172E LIFE AT 50.0 PROPABILI TY (CYCUS) = O.3't!14E TARLF. 8

FATIGUF. TEST RESULTS

~AXIMlJ~ STRESS = 31.00 KSI

SA~PLF SIZE = 6 RAW DATA.LIFE(CYClES) 0.5667E 05 O.1096E 06 Ool172E 06 Ool338E 06 Ool378E 06 Ool610E 06

CO~PUTED STATISTICAl PARAMETfRS

:"EAN LI FE ,CYClES = Ool193L

STn.DEVIATION,CYCLES = 0.35531::: COEFF.OF VARIATIOj\J 29.7 LOGARITHiVIC vEAN.CYClES = 0.1l37E

COR~E:lATIO/\! COFFFICI[NT = 0.89 LI FF. AT 97.5 PR()RAf~ I l I TV (CYClES)= O.?ólHE LIFE AT 02.5 PROPAEl I LI TV ((Y(lES)= O.4936E LIFt: AT 50.0 prWRAK I LI TY (CYClES)= 0.1136l.

.

06 ûó (Jó u7 ()~ 06 l U6 ll? (;6 06 O? 06

(19)

TABLE 9

;\1 A X H/i U fV': STRESS = 25.00 KSI SA~PLE SIZE = 6 RAW DATA,LIFE(CYCLES) 0.6395E 06 O.8230E 06 0.905?E 06 0.1057E 07 O.1226E 07 O.l311E 07

."1 E AI\! L I FE ,CYCLES = 0.9936E 06

STn..DEVIATION,CYCLES = 0.2534E 06

COEFF.OF VARIATION = 25.5

LOGARITH~tC ~FAN,CYCLES = O.C;6~3E 06 CORRELATIO~ COEFFICIENT = 0.98 LIFE AT 97.5 PRORAPILITY (CYCLES)= O.1888E 07 LIFE AT 02.5 PRORARIlITY (CYClES)= 0.4933E 06 LIrE AT 50.0 PROBARILITY (CYCLES)= O.9649E 06 Tf-\BLE 10

MAx I~UM STRESS = 52.00 KSI SAMPLE SIZE =10 RAW DATA,LIFE(CYCLES) 0.7610E 04 0.7730E 04 0.8098E 04 0.8240E 04 0.8420E 04 0.8490E 04 0.8610E 04 0.8610E 04 O.9060E 04 O.lllAE 05

CO~PUTFD STATISTICAL PARA~ETERS

MEM, L I FE ,CYCLES = O.8604E Ol~

STn..DEVIATION,CYCLES = 0.]0021: 04

LOGARITHMrC MEAN,CYCLES = 0.A556E 04

CORRELATION COEFFICIENT = 0.8~ LIFE AT 97.5 PROBABILITY (CYCLESj= O.lJ71E 85 LIFE AT 02.5 PROHARILITY (CYCLlS)= O.6R36E 04 LIFE AT 50.0 PRORARIlITY (CYCLES)= O.P.557[ 04

(20)

T AHLE 11 FATIGUE TEST RESIJLTS

MAXIMU~ STRESS = 45.00 KSI

SA~PLE SIZE =10 RAW DÄTA,LIFEICYCLES) 0.1590E 05 0.2220E 05 0.2670E 05 0.2840E 05 0.2990E 05 0.3020E 0:> 0.3030E 05 0.3250E 05 0.3510E 05 0.3540E 05

MEAN LIFE,CYCLES = 0.2866E 05 STD.DEVIATION,CYCLES = 0.5932E U4

LOGARITHMIC MEAN,CYCLES = O.2799E 05 CORRELATION COEFFICIENT = 0.90

LIFE AT 97.5 PRORABILITY

ICYCLES)= 0.4684E 05 LIFE AT 02.5 PRORABILITY

(CYCLES)= O.1674E 05 LIFE AT 50.0 PROBARILITY

ICYCLES)= 0.2799E 05

_._----

-TAHLE 12

~AXIMUM STRESS = 38.00 KSr SAMPLE stZE =10 RAW DATA,LIFEICYCLES) O.5850E 0·5 0.9520E 05 0.9910E 05

o

el 050E 06 0.1130E 06

o

el1 70E 06 O.l240E 06 O.l290E 06 O.1450E 06 0.1510E 06

MEAN LIFE,CYCLES = 0.1136E 06 STD.DEVIATION,CYCLES = 0.2666E U5 COEFF.OF VARIATION = 23.4

LOGARITH~IC ~EANtCYCLES = 0.1103E 06 CORRELATION COEFFICIE~T = 0.92

LIFE AT 97.5 PRORARILITY

(CYCLES)= O.1993E 06 LIFE AT 02.5 PRORABILITY

(CYCLES)= 0.6116F. 05 LIFE AT 50.0 PROBABILITY

(21)

1,

TABLE 13 FATIGUE TEST RESULTS

MAXIMUM STRESS = 25.00 KSI SAMPLE SIZE =10 RAW DATA,LIFE(CYCLES)

_.

O.490QE 06 0.545~E 06 0.549q:JE 06 0.558PE 06 0.638.oE 06 0.6650E 06 0.67ioE 06 0.6900E 06 0.7930E 06 0.8880E 06

MEAN LIFE,CYCLES

₌

0.6487E 06

STD.DEVIATION,CYCLES = 0.1223E 06

LOGARITHMIC MEAN,CYCLES = 0.6388E 06 CORRELATION COEFFICIENT = 0.97 LIFE AT 97.5 PROBABILITY (CYCLES)= 0.9759E 06 LIFE AT 02.5 PROBABILITY (CYCLES)= 0.4183E 06 LIFE AT 50.0 PROBABILITY (CYCLES)= 0.6388E 06 TARLE 14 FATIGUE TEST RESULtS

SA~PLE SIZE = 5 RAW DATA,LIFE(CYCLES) O.7760E 04 O.8060E 04 O.8510E 04 O.8540E 04 O.8760E 04

MEAN LIFE,CYCLES ;; _{0.8326E 04}

STD.DEVIATION,CYCLES = 0.4059E 03

LOGARITHMIC MEAN.CYCLES • 0.8317E 04

CORRELATION COEFFICIENT = 0.95 LIFE AT 97.5 PROBABILITY (CYCLES)~ 0.9412E 04 LIFE AT 02.5 PROBABILITY (CYCLES)= 0.7349E 04 LIFE AT 50.0 PROAABILITY (CYCl.ES)= 0.8316E 04

(22)

:

..

....

TARLE I':>

FATIGUF TEST RESlJLTS

/-'·AXlllU~1 STRESS 40.00 KSI

SAvPLE SIZE = 6

RAW DATA,LIFE(CYCLES) O.5840E US 0.6300E 05 O.6327E

o

s

0.6367E 05 o • 7 1 '+ 2 E OS O.7863E 05

COVPUTED STATISTICAL PARA~lTEkS

"'1[M l L I FE ,CYCLES Cl .6639E.

STn.DEVIATIO~,CYCLES O.7315f::

COEFF.OF VARIATIO:-J = 11.0

lOGARITHMIC ~}EAf\l, CYCL ES O.6607E CORREL/\ T IO.\! COEFFICIENT = 0.94 LIFE AT 97.5 PROBAB I L I TV ICYCLES)= 0.8538E LI FE AT 02.5 PRORAB I LI TV (CYCLES)= 0.5112t:: LlFE AT 50.0 PRORAB I LI T Y (CYCLES)= 0.6606E TARLE 17

~AxI~U~ STRESS = 55.00 KSI SAvPLE SIZE = 6 RA~ OATA,LIFE(CYCLES) o ol276E 05 Ool2,S7E 05 O.1336E

o

s

O.15'+8F 05 O.1548E 05

o

ol f,63F 0'5

O~PUTFD STATISTIC/\L PA~A~rTrRS ~fE I\~\ _LI_F_f,C_Y_CL_ES ₌_... ,1.l't43f STn.nEVIATIO~,CYCLlS ₌ ().1637L COfFF.OF VARIATIC~I 11.5

"

LOGt, I·. 1 TI-''' I C .\'FAN ,CYCL F!:> CJol415E

CCPPrl/\TIC~' CO F F F I C I E 1\1 T = 0.94

LlFf- AT 97.5 P'Wl'1AHILITY

(CYCU.S )= OolHb4E

LIF~ 1\ T Cl?5 P>=<Of-'Af'ILITY

(CyeLlS)= ()ol~92f

LIFE AT 50.e P~OPA8ILITY

(CYCLES) = Col435f:. 0':> 04 0') 05 u5 05 05 04 05 05 )'; 05 T MlLE 16

FATIGLJE TEST RESULTS

~AXIVU~ STRESS = 25.00 .KSI SA~PLl SIZE = 6 RA~ OATA,LIFFICYClFS) O.5648t:: 06 0.6237E 06 O.7773E 06 O.7837l 06 O.786?E 06 O.1004E 07

COWPUTED STATISTICAL PARAMETERS

('.'.EA(\J LIFE,CYCLES = 0.7566E

STD.DEVIATION,CYCLES = O.1534E COEFF.OF VARIATION = 20.2 LOGARITH"'IC 1;lEA~!, _{CYCLE S =} _O_.7438E CORRELATION CClEFFICIENT = 0.95 LIFE AT 97.5 PRORARILl TY (CYCLES)= 0.1215E

L,IFE AT· 02.5 PRORARILl TY

(CYCLES)= O.45,OE LI FE AT 50.0 PR08AR I LI TY

(CYCU:S) = O.7436E

TABLE 18

FATIGU~ TEST RESULTS

~AXIMUM STRESS = 40.00 ~SI

SAMPLE SIZE = 6 RAW DATA,LIFE(CYCLES) 0.6470E 05 0.8l00E OS 0.911?t: 05 O.9742E 05 Ool019E 06 Ool019E 06

!"EAN LIFE,CYCLFS = 0.8967E

STD.nEvIATION,CYCLES = Ool456E

COEFF.OF VARI/\TION = 16.2

LOGARITHrvlC ,"1EAN,CYCLES = 0.8857E

CORRELATION COEFFICIENT = 0.91

LIFE AT 97.5 PRORAB I LI TY (CYCLES)= 0.1338t:. LI FE AT 02.5 PROF3ABILITY (CYCLES)= 0.SH63E LI FE AT 50.0 PRORARILITY (CYCLES)= O.88?5E 06 Ob 06 07 06 06 05 05 05 06 05 05

(23)

~ "

TABLE 19

VjAXI~UM STRESS = 25.00 KSI SAMPLE SIZE = 6 RAW DATA,LIFE(CYCLESl 0.8138E 06 0.8715E 06 0.9343E 06 0.9580E 06 0.1068E 07 0.1129E 07

rvlEAN LIFE,CYCLES = 0.9625E 06

STD.DEVIATION,CYCLES = 0.11S5E 06

LOGARITH~IC MEAN,CYCLES = G.9565E 06

CORRELATION COEFFICIENT = 0.99 LIFE AT 97.5 PROBABILITY (CYCLESl= 0.13ü3E 07 LIFE AT 02.5 PROBABILITY (CYCLESl= 0.7020E 06 LIFE AT 50.0 PROBABILITY (CYCLESl= 0.9563E 06 TABLE 20

FATIGUt TEST RESULTS

SA~PLE SIZE =10 RAW DATA,LIFE(CYCLESl 0.1797E 05 Oel800E 05 Oel903E 05 0.1958E 05 0.1958E 05 0.1994E 05 Oel994E 05 O.2212E 05 0.2227E 05 0.2561E 05

MEAN LI FE ,CYCLES = 0.2ü40E 05

STD.DEVIATION,CYCLES = O.2331E 04

LOGARITHMIC ~EAN,CYCLES

=

0.2029E 05

CORRELATION COEFFICIENT

=

0.94 LIFE AT 97.5 PRORARILITY (CYCLESl= 0.2584E 05 LIFE AT 02.5 PRORA8ILITY (CYCLESl= O.l593E 05 LIFE AT 50.0 PROBABILITY (CYCLESl= 0.2029E 05

(24)

TABLE 21

~AXI~UM STRESS

=

45.00 KSI

SAMPLE SIZE =10 RAW DATA,LIFE(CYCLES) 0.8764E 05 0.8945E 05 0.8988E 05 0.9379E 05 0.9412E 05 0.9870E 05 0.1006E 06 0.1009E 06 0.1040E 06 0.1114E 06

MEAN L I FE ,CYCLES = 0.9706E

STD.DEVIATION,CYCLES = 0.7479E COEFF.OF VARIATION = 7.7 LOGAR I TH,"'î I C MEAN,CYCLES = 0.9680E CORRELATION _{COEFFICIEI'\T =} 0.97

LIFE AT 97.5 PROBAB I LI TY

(CYCLES)= 0.1154E LIFE .A, T 02.5 PRORAH I Lr T Y

(CYCLESI= 0.S117E LIFE AT 50.0 PROAARIl.ITY (CYCLESI= J.9680E 05 04 05 06 u5 05

(25)

TABLE 22

SAMPLE SIZE =10 RAvJ DATA.LIFE(CYCLES) 41 0.1866E 06 0.1871E 06 0.1914E 06 0.2048E 06 0.2131E 06 0.2136E 06 0.2152E 06 0.2183E 06 0.2256E 06 0.2306E 06

MEAN LI FE .CYCLES = 0.2086E 06

STD.DEVIATJON.CYCLES = 0.1568E 05

LOGARITH~IC l'I,EAN,CYCLES = 0.2081E 06 CORRELATION COEFFICIENT = 0.96 LIFE AT 97.5 PROBARILITY (CYCLES)= 0.2476E 06 LIFE AT 02.5 PROBAR I LI TY (CYCLES)= O.1749E 06 LIFE AT 50.0 PROBAB I LI T Y (CYCLES)= 0.2081E 06

(26)

T ABLE 23

SAMPLE SIZE =10 RAW DATA,LIFE(CYCLESl 0.4520E 06 0.5268E 06 0.5572E 06 0.6710E 06 0.6746E 06 0.7280E 06 0.7520E 06 0.7671E 06 0.8658E 06 0.1162E 07

r.-1EAN LIFE,CYCLES = 0.7157E STD.DEVIATION,CYCLES = a.2000E COEFF.OF VARIATION = 27.9 LOGAR ITHM IC MEAN,CYCLES = 0.6925E CORRELATION COEFFICIENT = 0.97 LIFE AT 97.5 PROBAB I LI TY (CYCLESl= O.1284E LIFE AT 02.5 PROBAB I LI TY (CY(LESl= O.3737E LIFE AT 50 .. 0 PROAABILI TY (CYCLES)= O.6926E 06 06 06 07 06 06 "

(27)

TABLE 24

DESCRIPTION OF TYPE OF SPECIMEN AND FAILURE MODE

Table Specimen Order Numbers of Order Numbers of

No. Description Specimens that Specimens that

Failed Cohesively Failed in the in the Adhesive ~M t 1

\t-I

-

~

).\t\x)"' ; N ~

1 i=0.125 in. I~-:' ~'"'D 1 to 5 t(

.1

1

2 _" ':>.1_'0 " S"'t. ?)-3 " II _" \0 ~i 4 i=0.25 in. Z'cs- 1 to 6 q.S> 5

"

2,.( " I1b."!:> 6 "

lP

" ~f1 7 i=0.375 in.

"3r

1 to 6 lo,~ 8 " 31 " I \ ~.1-9 " 2)- 1,2,4,5,6

1C'}-

3 10 i=0.5 ln

.

--

_~'L 1 to 10 fY. ,( 11 " t(J- " ?J'J.o 12 _" yf 1,2,3,4,7,8

t

tl>.? 5,6,9,10 13 " '2ç 6~1 1 to 10 14 i=0.625 in. S-L. 1 to 5 tf.~ 15 _" ~v 1 to 6

(6.

t 16 _" zç ~'11( 1 to 6 17 i=0.75 in _Fr- 1 to 4 ft( ~

.,-

5,6 18 " "t ()

PD

.

,

1 to 6 19 " Zj'

r

5 } 1 to 6 20 2024-T3 clad

6!J

_to.~ plain metal

fI,J)

"

"6')-21 t.(Y~ " J ~-22

_bql

_.

₎

23 "

1.g

*Denote s metal failure. The rest are all cohesive failures in the adhesi ve.

TABLE 25 STATIC TEST RESULTS; i = 0.125"; n = 5 Order No. (m) 1 2 3 4 5 Load at Failure (LBS) 1070 1190 1200 1260 1270 TABLE 26 Statie Test Results; i = 0.25"; n = 5 m P(Lbs) 1 2210 2 2280 3 2340 4 2390 5 2470

(28)

Statie Test ResuIts; 1 = 0.375"; n = 5 m P(Lbs) 1 3700 2 3750 3 3800 4 3850 5 3850 TABLE 28

Statie Test Results; 1 = 0 . 5 " ; n = 9 1 2 3 4 5 6 7 8 9 P(Lbs) 4150 4200 4200 4200 4300 4300 4300 4300 4320

(Note: in the following tables the symbol * indiegtes a metal failure. The rest are all eohesive failures in the adhesive)

Statie Test ResuIts;

1=0.625";n=5 P(Lbs) 4200 4250 4280 4300' 4400'

Statie Test ResuIts; Plain Metal Specimens

(2024-T3); n = 5 P(Lbs) 4506 4512 4518 4544 4582

Statie Test qesults

1 = 0 . 7 5 " ; n = 5 1 2 3 4 5 p( Lbs) 4250' 4250' 4250' 4300' 4300' TABLE 32

STATISTICAL PARAMETERS FOR THE STATIC RESULTS; 1=0.125"

True Me an Load True Standard Deviation Coeffieient of Variation(a/~)

Logarithmie Mean Load Correlation Coeffieient Load at 91.5% Probabili ty Load at 02.5% Probability Load at 50.0% Probability

TABLE 33 STATISTICAL PARAMETERS FOR THE STATIC RESULTS; 1=0.25"

lb. 2338 a lb. 99.8 cv J 4.3

.-

lbs 2336 r 1.0 p( 97.5), lbs 2612 p( 02.5) , lbs 2090 p( 50. 0), lbs 2336 TABLE 35 STATISTICAL PARAMETERS FOR

THE STATIe RESULTS; 1=0.5"

lbs 4252 a lbs 63.6 !;.V J 1.5 lbs 4252 r 0.91 p(97. 5), lbs 4393 p( 02.5) , lbs 4116 p( 50.0) , lbs 4252 IJ. Ibs. a. Ibs !;.V,J IJ ,Ibs r p(97.5) ,lbs P(02.5) ,lbs P(50.0) ,lbs 1198 79.8 6.7 1196 0.93 1411 1013 1196 TABLE 34 STATISTICAL PARAMETERS FOR THE STAT IC RESULTS; 1=0.375"

lbs 3790 a lbs 65.2 !;.V J 1.7

"

lb. 3790 r 0.96 p( 97.5), lbs 3957 p (02.5) , lbs 3629 p( 50.0) , lbs 3789 TABLE 36 STATISTICAL PARAMETERS FOR THE STATIC RESULTS; 1=0.625"

lbs 4286 a lbs 74.0 !;.V J 1.7 " lbs 4285 r 0.97 p(97. 5) , lbs 4477 p( 02.5) , lb. 4102 p( 50.0) , lbs 4285

(29)

•

TABLE 37 TABLE 38

STATISTICAL PARAMETERS FOR STATISTICAL PARAMETERS FOR

THE STATIC RESULTS; 1=0.75" THE STATIC RESULTS; P1ain Meta1

II 1bs 4270 II 1bs 4532 cr 1bs 27.4 cr 1bs 31. 3 cv , % 0.6 II 1bs 4270 CV , % 0.7 II 1bs 4532 r 0.85 r 0.93 p(97.5), 1bs 4331 P(02.5), 1bs 4209 p(50.0), 1bs 4270 p(97.5), 1bs 4609 P(02.5), 1bs 4457 p( 50.0) , 1bs 4532 TABLE 39 N(cyc1es) 1/4 10 5 4x105 10 6 Kt 1. 06 1.15 1. Ol 1.0 TABLE 40

PROBABILITY OF FAILURE IN PERCENTAGE (p)

\n

~

5 6 7 8 9 10 11 12 13 14 15 1 20.0 16.7 14.3 12.5 11.1 10.0 09.1 08.3 07.7 07.1 06.7 06.3 2 40.0 33.3 28.6 25.0 22.2 20.0 18.2 16.7 15.4 14.3 13.3 12.5 3 60.0 50.0 42.9 37.5 33.3 30.0 27.3 25.0 23.1 21. 4 20.0 18.8 4 80.0 66.7 57.1 50.0 44.4 40.0 36.4 33.3 30.8 28.6 26.7 25.0 5 83.3 71.4 62.5 55.6 50.0 45.5 41. 7 38.5 35.7 33.3 31. 3 6 85.7 75.0 66.7 60.0 54.6 50.0 46.2 42.9 40.0 37.5 7 87.5 77.8 70.0 63.6 58.3 53.9 50.0 46.7 43.8 8 88.9 80.0 72.7 66.7 61. 5 57.1 53.3 50.0 9 90.0 81. 8 75.0 69.2 64.3 60.0 56.3 10 90.9 83.3 76.9 71.4 66.7 62.5 11 91. 7 84.6 78.6 73.3 68.8 12 92.3 85.7 80.0 75.0 13 92.9 86.7 81-.3 14 93.3 87.5 15 93.8

(30)

TABLE 41

PROBABILITY OF FAILURE IN UNITS THAT LINEARIZE A NORMAL DISTRIBUTION (Xi)

n 4 ₅ 6 7 8 9 10 11 12 13 14 15 m 1 04.87 04.40 04.00 03.60 03.40 03.06 02.91 02.65 02.55 02.30 02.25 02.00 2 07.25 06.55 06.00 05.50 05.25 04.85 04.62 04.30 04.20 03.95 03.85 03.55 3 09.32 08.25 07.55 06.90 06.60 06.09 05.84 05.50 05.35 05.00 04.95 04.60 4 11.70 10.00 09.00 08.25 07.70 07.21 06.85 06.50 06.30 05.90 05.80 05.50

5

12.20 10.55 09.60 08.90 08.25 07.81 07.35 07.12 06.70 06.60 06.25 6 12.55 11.0 10.0 09.29 08.72 08.25 07.90 07.45 07.31 06.90 7 12.90 11. 35 10.41 09.68 09.15 08.70 08.25 07.95 07.55 8 13.20 11. 65 10.69 10.00 09.48 09.05 08.65 08.25 9 13.44 11. 91 11.00 10.30 09.80 09.29 08.95 10 13.62 12.20 11. 25 10.60 10.00 09.60 11 13.85 12.40 11. 50 10.80 10.25 12 14.05 12.55 11.65 11.00 13 14.2 12.75 11. 90 14 14.35 12.95 15 14.5

Note: m

=

order number; n

=

sample size

Xi

=

explained in the notation

~

-~

(31)

>- I-H -.J H

m

«

m

0 0:::: 0.. >- I-H ....J H CD

«

CD 0 0:::: 0.. 93-0 9)-0 70-0 so-o 3)-0 10-0 " 2024-T3 CLAO I-l- f.-L-21+ _o,1" ~O'OM. : I BONDEDWITH

T

FM-123-2 I"

i

Fig. 1. Double strap Joint specimen.

5YI8l.. w,x-STRESS + 15-50 )( 1.3-50 ~ 11-00 02-0·~L-__ ~ __ ~ ____ ~ ____ ~ __ --+ 3-0 4-0 5-0 G-O 7-0 8-0

LOG CYCLE5

93-0 3)-0 70-0 50-0 30-0 iO-O

Fig. 2. Goodness of fit of a log-normal distributlon te

the 1 = O.125-1nch specimens. 5YI8l.. w,x-STRESS + 25-50 )( 21-00 ~ 18-00 02-0'+--L~+-L-__ ~ __ ~~ __ ~ ____ -+ 3-0 4-0 5-0 G-O 7-0 8-0

LOG CYCLE5

Fig. 3. Goodness of fit ot a log-normal distribution te

5Mfl..E SIZE

CCR-CIEFF-5 0-91

5 0-85

5 0-94

5Mfl..E SIZE

CCR-CIEFF-6 0-89

6 0-94

(32)

>- I-H ~ H

m

<C

m

0 0:::: 0.... >- I-H ~ H

m

<C

m

0 0:::: 0.... >- I-H ~ H [TI <C m 0 0:::: 0.... 93-0 5'n6l... MI\X -STRESS + 38-00 )( 31-00 90-0 ~ 25-00 70-0 50-0 30-0 iQ-O 02-0 3-0 4-0 5-0 G-O 7-0 8-0 LOG CYCLE5

Fig. 4. Goodness of fit ot a 1og-normal distribution te

th. 1 = O.375-1neh specimens.

93-0

I

SYIHl... + MI\X 52-00 -STRESS

)( 45-00 90-0 ) _~ _~ ₃₈_-₀₀ " . 25-00 70-0 50-0 30-0 iO-O ~ ~ 02-0+_ __ ~L-J~J~ __ L-~ __ ~ __ _ + 3-0 4-0 5-0 G-O 7-0 8-0 93-0 90-0 70-0 50-0 30-0 iQ-O LOG CYCLE5

Fig. 5. Coodness of fit of a log-normal distributien te the t = O.5-inch specimens.

52-00 40-00 25-00 02-0+-__ -Y __ ~-+ __ ~~ ____ + _ - - _ + 3-0 4-0 5-0 G-O 7-0 8-0 LOG CYCLE5 6. fit 5A\.R..E SIZE 6 6 6 Si\I.f'L.E SIZE W W W W 5 6 6 ca< -c.:EFF -0-90 0-69 0-98 C!.R-CCEFF-0-00 0-90 0-92 O-S? 0-95 0-94 0-95

(33)

..

93-0 SY\.ED.. >- + l- X H ..J 9)-0 H CD < CD 70-0 0 0::: 0.. so-o 3)-0 iQ-O 02- 01 I , " 3-0 4-0 5-0 6-0 7-0 8-0 LOG CYCLE5

WJ( -STRESS SMF\..E SIZE 55-00 6 40-00 6 25-00 6 aR -a:EF'F -

$

O

Oj

i

Ij

t

SY\.ED.. WJ(-STRESS 0-94

~

gooo + 60-00 0-91 X 45-00 0-99 35-00 26-00 CD < CD 70-0 0 0::: 0.. so-o 3)-0 -iQ-O 02-C 3-0 4-0 5-0 6-0 7-0 8'0 LOG CYtLE5

Fig. 7. GoodneS8 ot rit of a log-normal dlstributlon to the 1 = O.75-inch specilllens.

FiS. 8. Goodness ot rit ot a lOB-normal distributloD te the plain 2024-T3 cl.d specimens.

98 98

\ PLAIN METAL SPECIMENS (2024-T3CLAOI ~\ 1-0'62:1"

\ R -0·1 ~I - - LEAST SQUARES FIT \ R-O·I

95 t- \ \ \ I 95 {LOGN(P-84'l1t)-p.,+tr, I

90 • \ 1 · 90 '-" I

8:1

t

0'liliiii' 26·0kli \ 0in0Il-35-QkIi \ , 0in0Il-4:1·0kli <Tmall • 8:1 I

~

80 \ ,-0-94 \ SMF\..E SIZE 1D 1D 1D 1D \ I --- LOGN(P-16'l1t)-u-cr. I , -M8 • ,.0·97

i

t'

-

0·98 aSO-Okll 80 \ ~ l-70 \

i

~

\

70 la t i

~:

\

j

t

:=

I ._... ..."'....

ltO' __

:l2.okli Go 40

1 \

-

40 ,-0'96 ,-0'94 ,'0-96

~:

\ l

I

I:

CV.,.,

\

cv·,,~

l

CV,"

11:1 LEAST SQUARES FIT \ \ \\ 1:1

10 {LOGN(P-84"l1oI-p.+cr. ~

i

~ 10 aR -a:EF'F -D-94 oog, 0-$ 0-'37 : [ "

coeNIP".%I"~,~" ,~

.I

1 "

I~:

__________

_

d8 6 4 2 106 8 6 4 2 105 8 6 4 2 10· tiF8 6 4 2 1058 6 4 2 1048 6 4 2 ~ CYCLES(N) CYCLES(NI

(34)

a-98 9:1 90 8:1 80 70 60 ~!IQ i: -40 §30 jij

I~

10 5 o ... ...

'"

... ~ ~~, "~ • I-0' 12:1-CTmoa -11·0 k1i R-O'I r -0·94 CV-93·6

LEAST SQUARES FIT

{ LOG N(P-84%) -JA-,+"i

LOG N(P-16%)-"'i"i

•

1078 6 4 2 1068 6 4

CYCLES (N) 2 1058 6 4

Fig. 11. COlII.pariaon ot the approximate and rigorous lysee when CV is large.

40 38 36 34 32 30 28 26 :: 24 ~ 22 ti 20 18 16 IC! 1-0'2:1" R-C>I 0 - - 0 MEDIAN A--- 4 9!5% CONFIDENCE LlMITS

t ·

A ...

\

... I ... ... i ... ...

~ ~

... 'A

-"""

1111 1111111 ItHl 111 104 (J5 _10' CYCLES(NI

FIg. 13. S-R curve tor t .0.25 inch

107 2 104 18 17 16 1-0'12:1" R-O'I 1:1 'ii 14 M A

~.

0 - 0 MEDIAN

" ' . " '-... A--A 9:1 .. ., CONFIDENCE LlMITS

\,

~

'

'''''''''''A

'

1113 ~ 12 11 10 10 55 !IQ 45 40 'ii ~

..

35 a bE 30 25 20 103

\

~

...

.

\

.

---A

l (Je ₁₀7 CYCLES (N)

Fig. 12. 5-N curve tor I. = 0.125 inch.

1=0'375"

R=O'I

<>---4 MEDIAN

A---4 95% CONFIDENCE LlMITS

A A ... O~ ... ,

""

·""

'

~>~

_'

_.

_,

"

A

...

... " "A "A 11111 I 11111111 10" 105 106 CYCLES(NI

Fig. lt.. S-lf curve tor t - 0.375 inch.

111

107

(35)

..

60 ~~ 50 45 -40 ~ oe 3~

I

30 25

t

20 103 60 55 50 45 1-0'5-R-O·I A. " _ . MEDIAN \~ 6--4 95'1(, CONFIDENCE " " LlMITS

A,~

"

'"

"'~

.~\\

\

\ 't. • '. 11111111 I I I 11111 11111111 104 105 106 CYCLES(NI

Fig. 15. S-N curve tor .t ,. 0.5 inch

_ . MEDIAN A.A \ \ 1-0-75" ' \ \ R-O·I

,

",..,1

107 )40 \ \ ' \ A - - - 4 95'1(,CONFIDENCE LlMITS

\\

6<\,~\

\

:'\

"''-~

oe 35

I

30 25 20 I 1111111 I " l i l ! ! I I I II"I! 1111111 _"!!,,I ~ d ~ ~ d ~ CYCLES (NI

Fi g. 17. s-n curve tor 1 : I 0.75 inch

60 ~~ 50 45

=

40 •

...

~p~ ~ ₃₀ 25 20 -103 70 65 60 55 50 45 -_• 40

...

';35 ₀ ~30 25 20 !Ol _ . MEDIAN A , . 6_._6 95% CONFIDENCE UMITS '>:.~ ~~~ 1-0'625" "IJ:'}.,. R -0·1 104

,

.

'

~ \.

,

.\ _\

'"

_'\.

,"\

" -' ... '-á 10' CYCLES(NI 106 107

Fig. 16. S-N curve for.t 0.625 inch.

PLAlNMETAL (2024-T3 CLADI R-O·I \ ~ 6-._." 95'1(, CONFIDENCE UMITS

A~\\

_

MEDIAN

\:~ \~ '\\ .~

\~

\. \

\~~

_\\

\ _A

",

_A J)4 KJ' _JJ' CYCLES (NI J)T

Fig. 16. S-N curve tor plain 2024-T3 clad specimens.

iJl tOl

(36)

70

65

60

55

50

45

40

35 -

'ji ~

30

JC 0

S

25

20

15

10 ---...

... ... ... 11

- - - -

- -

1-0,25

---...

-...

... ...

...

'o~O

_ _ _ _ O

1=0'125

11

---0_

10°

10

2

10

3

10

5 CYCLES(N)

10

6

APPROXIMATE BOUNDARY ABOVE WHICH NO GLUE FAILURES CAN OCCUR

APPROXIMATE BOUNDARY BELOW WHICH NO METAL FAILURES CAN OCCUR

_.

__

.--_._.-

THE REG ION BETWEEN THESE TWO L1NES IS A REGION OF MIXED FAILURES

.

Fig. 19. Comparison of the S-N 'curves for joints of various

lengths of overlap with the plain metal specimens.

(37)

....

..

...

-Kt

2·0

r·o

o

100 _lOl

₁₀₂

₁₀₃

_lOT

CYCLES (N)

(38)

~

lJrIAS TECHNICAL NOTE NO. 160

Institute for Aerospace Studies, University of T oronto

Statie and Fatigue Strength of FM-123-2 Adhesive in Double Strap Joints of Various Lengths of Overlap

Niranjan, V., Hamel, D.'R., Yang, C.

1. Bonded Joints 2. Lap Joints 3. I. Niranjan, V.,Hamel,D.R.,Yang, C.

4 pages 20 figures

Fatigue Testing

Ir. lJrIAS Teehnieal Note No. 160

Statie and fatigue test results on 160 dOl.ible-strap joints of 2024-T3 elad aluminum bonded with FM-123-2, a modified nitrile epoxy adhesive manufactured by the Bloomiligdale Department of the Ameriean Cyanamid Company are reported. The results

are statistically analyzed. S-N curves are presented. with 95 per cent confidence

limits. A computer program for the statistical analysis of fatigue results is appended.

~

Available copies of this report are limited. Return this card to UTIAS, if you require a copy.

Statie and Fatigue Strength of FM-123-2 Adhesive in Double Strap Joints of

Various Lengths of Overlap

Niranjan, V., Hamel, D. R., Yang, C. 4 pages 20 figures

1. Bonded Joints 2. Lap Joints 3. Fatigl.ie Testing

I. Niranjan, V.,Hamel,D.R.,Yang~ C. 11. tJrIAS Technical Note No. 160

Statie and fatigue test results on 160 double-strap joints of 2024-T3 clad aluminnm.

bonded w1th FM-123-2, a modified nltrile epoxy adhesive manufactured by the

Bloomingdale Department of the American Cyane.mid Company are reported. The results

are statistically analyzed. S-N curves are presented. with 95 per cent confidence

limits. A computer program for the statistieal analysis of fatigue results is

appended.

~

Available copies of ~his report: are limited. Return this card ~o UTIAS, if you require a copy.

Statie and Fatigue Strength of FM-123-2 Adhesive in Double Strap Joints of Various Lengths of Overlap

Niranjan, V., Hamel, D.'R., Yang, C.

1. Bonded Joints 2. Lap Joints 3.

r. Niranjan, V.,Hamel,D.R.,Yang, C.

4 pages 20 figures

Fatigue Testing

Ir. lJrIAS Technical Nate No. 160

Statie and fatigue test results on 160 double-strap joints of 2024-T3 elad aluminum bonded with FM-123-2, a modified nitrile epoxy adhesive manufactured by tbe Bloomirigdale Department of the American Cyanamid Company are reported. The results

are statist1cally analyzed. S-N curves are presented w1th 95 per cent confidence

limits. A computer program for the statistical analysis of fatigue resUlts is

appended.

~

Available copies of th is report are limited. Return this card to UTIAS, if you require a copy.

Statie and Fatigue Strength of FM-123-2 Adhesive in Double Strap Joints of

Vsu-ious Lengths of Overlap

N1ranjan, V., Hamel, D. R., Yang, C. 4 pages 20 figures 1. Bonded Joints 2. Lap Joints 3. Fatigue Testing

r. Niranjan, V.,Hamel,D.R.,Yang, C. Ir. lJrIAS Teehnieal Note No. 160

Statie and fatigue test results on 160 doub1e-strap joints of 2024-T3 elad aluminum

bonded with FM-123-2, aO modif'ied nitrile epoxy adhesive manufactured by tbe

Bloomingdale Department of tbe American cyan8.m1d Company are reported. The resul.ts

are statistically analyzed. S-N curves are presented with 95 per cent conf1dence

limits. A computer program for the statistical analysis of fatigue results is appended.