NASA-CR-242 · Some considerations in the fatigue design of launch and spacecraft structures

APPENDIX A CUMULATIVE FATIGUE DAMAGE ANALYSIS FOR LABORATORY SPECTRUM LOAD TESTS n

T h e cumulative fatigue damage concept, En, originally f o r m u l a t e d suggested

that damage accumulated a t a l i n e a r rate. Since i t s conception, t h i s has b e e n proven f a l s e many t i m e s . It is now known that physical d a m a g e to s t r u c t u r e by fatigue action p r o g r e s s e s a t a n exponential r a t e similar t o the r a t e of Also the effects of p r i o r h i s t o r y , s u c h as the effects of fatigue c r a c k growth.

intermittent high tensile o r c o m p r e s s i v e loads, have b e e n shown t o g r e a t l y a l t e r nominal fatigue l i v e s , B a s e d on these observations, modifications have b e e n made to the fatigue d a m a g e rule which a r e quite general. T h e method to be p r e s e n t e d has b e e n u s e d in the fatigue analysis of s p e c t r u m loaded s t r u c t u r e i n the l a b o r a t o r y and h a s been quite successful.

The Mean Damage Rate Method (Reference 4 ) A s i m p l e mathematical e x p r e s s i o n h a s been found whereby the value of x n / N c a n b e computed f o r s p e c t r u m loadings when c e r t a i n conditions a r e m e t .

T h e s e conditions a r e as follows: 1. The nonlinear damage c u r v e s a r e known as functions of the c y c l e ratio and the p r i o r history.

The loading h i s t o r y is a periodic function of time. Within a p e r i o d 2.

o r block, the load levels a s s u m e a c e r t a i n p a t t e r n which is r e p e a t e d i n each subsequent block.

The n u m b e r of cycles p e r block is small c o m p a r e d to the t o t a l life. 3.

Under these assumptions, the cumulative cycle r a t i o is given by T h e derivation of this e x p r e s s i o n is given i n R e f e r e n c e 4. T h e meanings of the symbols are m o s t e a s i l y understood through r e f e r e n c e to the d a m a g e I M-22498

s!! FOR SPECTRUM LOADINGS BASED ON

N HENRY'S EQUATION MODIFIED*

b l Figure A2 Example computation by m e a n damage r a t e method. --Given a s p e c t r u m con- s i s t i n g of cycle blocks defined by the following table. The m a x i m u m s t r e s s , the endurance limit, the n u m b e r of cycles p e r block, the life, and the c r i t i c a l c r a c k length f o r each s t r e s s l e v e l a r e a s s u m e d to be known.

The calculation is c a r r i e d out using H e n r y ' s constant a s K = E/(S-E).

HENRY'S EQUATION MODIFIED H e n r y ( R e f e r e n c e 27) has given the equation / N D = (5) l + K ( l - n / N ) as t h e equation of the d a m a g e c u r v e , where K = E/(S-E), S = m a x i m u m s t r e s s , and E = a n e n d u r a n c e l i m i t s t r e s s .

.

T h e integration indicated i n Equation 1 can b e p e r f o r m e d graphically, n u m e r - o r , when the d a m a g e c u r v e s a r e given by integrable m a t h e m a t i c a l ex- ically, p r e s s i o n s , directly. In R e f e r e n c e 4, this integration h a s b e e n p e r f o r m e d d i r e c t l y f o r curves corresponding to a modification of H e n r y ' s f o r m u l a f o r d a m a g e propagation.

I

T h e f o r m u l a corresponding to Henry'e damage w a s used to calculate the value of z n / N f o r vanishing block s i z e for the s a m e n u m e r i c a l values used i n the T h e digital computer calculation, p r e s e n t e d in F i g u r e 66 of R e f e r e n c e 4.

f o r m u l a gives x n / N = 0. 730, which a g r e e s with the digital computation as AncO.

F o r continuous s p e c t r a , the summation of Equation 2 m u s t be replaced by a n integration a s follows:

x' ( X ) = 1 r (a) X ' (a) do

( 3 ) -00 where a is an environmental p a r a m e t e r , and r (a) is a probability density I distribution having the p r o p e r t i e s

r (a) 5 1 and

(4) -00 T h e limiting value of x n / N f o r s p e c t r u m loadings, according to H e n r y ' s f o r m u l a , can b e obtained by substituting Equation (6) into the m e a n d a m a g e r a t e formula (Equation 1).

T h i s manipulation is p e r f o r m e d i n Appendix A of R e f e r e n c e 4.

T h e r e s u l t is s u m m a r i z e d i n F i g u r e A2, which gives n / N as a function of the p a r a m e t e r s involved. An example of the u s e of this f i g u r e follows.

If o t h e r formulas f o r damage propagation should t u r n out to b e m o r e suitable than Henry's, they c a n b e substituted into Equation 1 t o give new e x p r e s s i o n s f o r x n / N . T h e r e f o r e , the m e a n d a m a g e r a t e f o r m u l a is quite g e n e r a l .

~ ~ - T a b l e A1 I C r i t i c a l Max. S t r e s s End A u = Cycles r = C r a c k L.

N xc S t r e s s -mzE- Level L i m i t 6 n E A U

s 6 n E K ' m

(cycles)

-6 xC T

110,000 11 7,800 160 9,000 14. 1 0.01 780 0.4826 0.388 110,000 132,100 40 4,200 4.98 0,2588 0.345 0.00954 110,000 146,400 8 2, 800 3.02 0.00286 0.0775 0.308 110,000 165,900 2,200 1 0.0122 0 . 2 6 3 1.970 0.00045 135,000 138,200 32 8, 500 42. 2 0.1022 0 . 4 4 3 0.00377 152,500 135,000 5,000 0.0434 7. 71 0.00160 0. 397 166,800 135,000 3,500 4.25 0.0233 0 . 3 5 5 0.00086 1.0000 0.03688 .L - a .

If a l t e r e d by p r e l o a d effects, the d i s c r e t e value of N m a y b e obt'ained f r o m ad-hoc t e s t s as shown in F i g u r e A3.

S t r e s s r r k k r k rx

-

L e v e l

l+k X l t k l t k

1 0.0320 0.451 0.01 241 16.41 36.4 0.215 0.0433 0.01493 14.41 3.10 0.0582 0.01925 0.00594 0.570 9.80 0.00410 0.001080 0.0606 0.00810 7.49 0.001956 0.0827 0.000866 7. 90 95.5 6 0.00497 0.0384 0.001 975 0. 746 19.42 7 0.00444 0.01890 0.001 578 0.226 11.98 0.0388 (ao)

= 0.0388 x 29.0 - 0. 8722 = 0. 365

bl b2 = 0.0388/0.263 t 0.8723 = 1.020

oo.cb = 0. 890 ( f r o m F i g u r e A2)

T h e following modification of Henry's f o r m u l a is proposed f o r s o m e applications: D / N C = 1 t K ( l - " / N ) w h e r e Dc is the c r i t i c a l damage, which is the damage a t which the p a r t frac- With Equation t u r e s completely. In Equation 5, the c r i t i c a l d a m a g e is unity.

T h e 6, the damage c u r v e s tend to have the c h a r a c t e r shown i n F i g u r e A l .

c u r v e s for high s t r e s s tend to have less c u r v a t u r e and a lower value of c r i t i c a l d a m a g e ( c r i t i c a l c r a c k length) than the c u r v e s f o r low stress.

F i g u r e A3 shows the fatigue r e s u l t s of p r i o r loaded l a b o r a t o r y s p e c i m e n s b y both tension and c o m p r e s s i o n p r e s t r a i n s . If the preload is tension and exceeds the m a x i m u m cycling load i n the fatigue t e s t , a n i,mprovement in life is observed.

If the p r i o r preload is c o m p r e s s i o n , a (See reduction i n o v e r a l l life o c c u r s .

footnote in T a b l e A l . ) IRD951A

EFFECT OF PRIOR PRELOAD

(REFERENCE 21) CYCLES TO FAILURE Fieure A3 F i g u r e B1 shows fatigue-crack growth c h a r a c t e r i s t i c s as a function of environ- m e n t a l t e m p e r a t u r e . In this d i a g r a m , the s t r e s s r a n g e and s t r e s s l e v e l p r o - ducing c r a c k i n g a r e the s a m e f o r all t e s t t e m p e r a t u r e s noted.

S e v e r a l distinctive c h a r a c t e r i s t i c s a r e evident in this figure.

The d i a g r a m shows that the fatigue l i f e i n c r e a s e s a s the t e m p e r a t u r e d e c r e a s e s . It a l s o il- l u s t r a t e s a reduction in the c r i t i c a l flaw size o r c r a c k length that c a n be t o l e r a t e d as the t e m p e r a t u r e of a m e t a l d e c r e a s e s .

It a l s o indicates that as the t e m p e r a t u r e d e c r e a s e s the c r a c k nucleation period o r t i m e to produce a n o b s e r v a b l e c r a c k i n c r e a s e s . Conversely, as t e m p e r a t u r e d e c r e a s e s , the period of o b s e r v a b l e fatigue c r a c k growth d e c r e a s e s .

F i g u r e B2 shows e x p e r i m e n t a l r e s u l t s of a study of c r a c k growth under steady- s t a t e loading conditions and at elevated t e m p e r a t u r e s . In t h e s e t e s t s , fatigue T h e panels w e r e then cracks w e r e grown i n 6-in. -wide aluminum panels.

held under constant loads and t e m p e r a t u r e s . Within a few h o u r s , c r e e p c r a c k i n g h a d advanced to a c r i t i c a l stage. Although the t e m p e r a t u r e l e v e l u s e d i n the e x p e r i m e n t s w a s higher than the useful t e m p e r a t u r e of the m a t e r i a l , i t should b e r e a l i z e d that the s a m e phenomenon could o c c u r a r o u n d 2 0 0 ° F ( s o l a r radiation) a n d probably in fewer than 10, 000 h o u r s (long-operational spacecraft).

F i g u r e s B 3 and B4 show fatigue t e s t r e s u l t s as dependent on t e s t t e m p e r a t u r e .

In t h e s e i l l u s t r a t i o n s the total n u m b e r of cycles-to-rupture as a function of the various t e s t s t r e s s levels are shown. T h e total life includes the combined c r a c k nucleation p e r i o d and the fatigue-crack propagation period.

T h e r a t e of f a t i g u e - c r a c k propagation as affected by r a t e of cyclic loading and test-load f r e q u e n c y is a n additional p a r a m e t e r to b e considered. In elevated- t e m p e r a t u r e fatigue testing, i t is known that the n u m b e r of cycles to f r a c t u r e d e c r e a s e s , and the c r a c k - g r o w t h r a t e i n c r e a s e s as the s p e e d o r f r e q u e n c y of cyclic loads is d e c r e a s e d ( F i g u r e BS). The damaging, t h e r m a l l y activated m e c h a n i s m of c r e e p o r c r e e p cracking, acting conjointly with fatigue, is r e - sponsible f o r this behavior. In general, this is t r u e b e c a u s e , i n the a c c u m u l a - tion of s t r e s s c y c l e s , s l o w e r r a t e s of load cycling r e s u l t in e x p o s u r e of the metal to t e m p e r a t u r e f o r longer periods of t i m e than i n high-speed t e s t s .

-

APPENDIX B ENVIRONMENTAL E F F E C T S ON T H E FATIGUE STRENGTH OF STRUCTURE Phenomena such as fatigue, c r e e p , s t r e s s c o r r o s i o n , e m b r i t t l e m e n t , and a r e all delayed f r a c t u r e ( s t a t i c fatigue), acting alone o r in combination, damaging t o s t r u c t u r a l m a t e r i a l s . The damaging effect of each of t h e s e environments on s t r u c t u r e i s not single-valued but will v a r y a s often a s the This m a k e s calculations f o r the prediction conditions of s e r v i c e a r e a l t e r e d .

of environmental effects e x t r e m e l y difficult. Meaningful evaluations of the effects on s t r u c t u r e c a n be m a d e by c a r e f u l simulation of the environment during t e s t s . However, s u c h simulation often is a difficult and costly a p p r o a c h t o the solution of the problem, F o r t h i s r e a s o n , a c c e l e r a t e d t e s t methods a r e constantly being sought. Historically, i t c a n be shown that no a c c e l e r a t e d t e s t technique yet devised will a c c u r a t e l y predict the "time" r e q u i r e d to C o n c e r n f o r the r e a c h c r i t i c a l cracking o r c r i t i c a l d a m a g e in s t r u c t u r e .

Since damaging effect of fatigue in s t r u c t u r e was r e p o r t e d as e a r l y as 1829.

that time, a g r e a t amount of r e s e a r c h and p r o g r e s s h a s b e e n m a d e . It is n e e d l e s s to i t e m i z e the s u c c e s s e s and f a i l u r e s in controlling this phenomenon s i n c e they a r e well known. However, many f a i l u r e s i n the predictions f o r b e - havior c a n probably b e attributed to inadequate t e s t evaluation methods, many of which a r e s t i l l i n u s e today. F o r example, the u s e of high s p e e d testing m a c h i n e s to evaluate fatigue r e s i s t a n c e a t elevated t e m p e r a t u r e and i n oxi- dizing a t m o s p h e r e s w i l l yield invalid d a t a f o r p a r t s designed f o r low s t r a i n r a t e s It is not the purpose of this appendix to r e c o m m e n d acceptable analytic o r t e s t evaluation methods, n o r is i t the p u r p o s e t o d i s c u s s t h e i r limitations, T h e p u r p o s e is to i l l u s t r a t e the effects of a v a r i e t y of environments. T h e char- a c t e r i s t i c e f f e c t s of m a n y environments a r e not w e l l known t o the a v e r a g e s t r u c t u r a l d e s i g n e r , but this knowledge is both useful and n e c e s s a r y i f s a f e s t r u c t u r e s a r e to be designed. T h e following d i s c u s s i o n s and i l l u s t r a t i o n s define s o m e of the m o r e pertinent fatigue c h a r a c t e r i s t i c s of metals and m e t a l s t r u c t u r e s

FATIGUE LIFE AS A FUNCTION OF TEST TEMPERATURE

(TYPICAL FOR MOST METALS) fn fn Y K

t i

N, CYCLES TO FRACTURE

Figure 63

IRD-954A

EFFECT OF TEMPERATURE

AXIAL FATIGUE TEST IO0 T I - ~ A I - ~ M o - ~ V , MILL ANNEALED K T = 2.33 R = 0.05

- FREQ. = 700 CPM

\. \

> v 0 0 A M ' 0 0 0 L \ . 900°F- 800°F I I I 1 l l l l I 1 I I I I I I I I I I I I Fieure B4 IRD.987A

GROWTH OF FATIGUE CRACKS AS A

FUNCTION OF TEMPERATURE (SCHEMATIC)

---- C

7 70°F

---- de, 0

-,-iJ /-320'2

-423'F N NUCLEAT.-+ I

4 N prop. L-

STARTER STRESS CYCLES (N) FLAW

Fieure B1

M. 14657A

GROWTH OF CRACK UNDER STEADY

LOAD AND TEMPERATURE

CRACK LENGTH (IN.)

0 2 4 6 8 1 0 2 4 6 8 100 2 4 6 8 1000 TIME ( M I N )

Figure 02

M-22530

C-B FATIGUE DIAGRAM

UNNOTCHED So816 AT 1,35OoF (SIN U SO1DAL SPECIMENS F = 3.600 CYCLES/MIN LOADING WAVE)

--- 0.2% CREEP (STATIC CREEP AT R = 1.0)

MIN, STRESS -FATIGUE FAILURE (STATIC RUPTURE AT R = 1.0) = MAX. STRESS MIN. STRESS - KSI - Figure 66 f o r fatigue r u p t u r e and the dashed c u r v e s a r e constant life l i n e s f o r 0.270 deformation. F i g u r e B6 gives the fatigue f a i l u r e and deformation d a t a f o r S-816 alloy a t 1350°F. T h e alloy is s e e n t o b e deformation c r i t i c a l at 1350°F a t all R r a t i o s h i g h e r than -0. 3, and fatigue c r i t i c a l only a t R r a t i o s l e s s than -0. 3.

I t is c l e a r f r o m F i g u r e B6 that d e s i g n e r s cannot b e guided by fatigue f a i l u r e d a t a a l o n e i n making a judgment about the useful life of a s t r u c t u r e when that is subject to loading a t elevated t e m p e r a t u r e .

s t r u c t u r e F a t i g u e f a i l u r e d a t a and d a t a of deformation o c c u r r i n g under fatigue loading a r e both needed f o r the design of s t r u c t u r e loaded a t elevated t e m p e r a t u r e .

Deformation m e a s u r e - New t e s t i n g techniques are r e q u i r e d to get t h e s e data.

T h i s adds UP m e n t s will have to be m a d e during the c o u r s e of fatigue testing.

t o v e r y expensive testing, and i n the i n t e r e s t of keeping c o s t u n d e r control i t is desirable t o h a v e s o m e m e a n s of extrapolating t e s t data.

IRD-950A

EFFECT OF FREQUENCY AT

ELEVATED TEMPERATURE

Ti-BAI-IMo-IV, MILL ANNEALEO K ~ z 2 . 3 3 .- ~ M A X = 82.4 KSI w ~JMIN = 4.1 KSI a 1 .

I- REF. 21 U .

a Y ______ I 1 1 1 1 , I L I , 0 I Figure B5 However, f r o m cryogenic t e m p e r a t u r e s t o r o o m t e m p e r a t u r e , no damaging, thermally activated m e c h a n i s m s a r e active. It is believed that fatigue lives and crack-growth r a t e s a t cryogenic t e m p e r a t u r e s w i l l b e independent of load frequency f o r m o s t m e t a l s .

At elevated t e m p e r a t u r e both deformation and f r a c t u r e under fatigue o r s t a t i c loading are t i m e dependent, and the limitation on design s t r e s s e s , i m p o s e d by deformation, b e c o m e s significant. A consistent s e t of d a t a which c a n be u s e d to show these effects is difficult to find. R e f e r e n c e 28 contains fatigue and deformation data f o r s e v e r a l alloys t e s t e d a t high t e m p e r a t u r e .

The d e f o r - mation data do not e n c o m p a s s small deformations.

However, the data p r e - sented for s-8 16 alloy a r e sufficiently c o m p r e h e n s i v e t o p e r m i t extrapolation t o d e t e r m i n e approximately the s t r e s s e s corresponding to 0 . 2 7 0 deformation.

T h e d a t a for fatigue f a i l u r e and the extrapolated d a t a f o r d e f o r m a t i o n w e r e used to construct the c u r v e presented i n F i g u r e B6. T h e f i g u r e is called a creep-boundary fatigue d i a g r a m . T h e solid c u r v e s a r e constant life l i n e s I w h e r e A H = is the activation energy f o r c r e e p o r f o r r u p t u r e R = is the g a s constant t = is the t i m e T = is the t e m p e r a t u r e i n absolute units.

T h i s m a s t e r d i a g r a m p e r m i t s one to relate the t i m e t o f a i l u r e , f o r example, a t one s t r e s s , t e m p e r a t u r e , and R ratio to another t e m p e r a t u r e at the s a m e s t r e s s and R r a t i o .

F i g u r e B8 shows typical t e s t r e s u l t s of fatigue c r a c k growth under mixed load r a n g e s and c r a c k i n g t e m p e r a t u r e s T h e s e c u r v e s show significant changes i n a c c e l e r a t i o n and d e c e l e r a t i o n of growth r a t e as the loading conditions a r e a l t e r e d . S o m e s u c c e s s in predicting the behavior and c r a c k length under a T h e techniques c a n b e found i n p r o g r a m m e d s e t of conditions h a s been made.

Techniques f o r predicting c r a c k growth under random R e f e r e n c e s 30 and 31.

loading a r e d i s c u s s e d i n Appendix D.

2.8 M-22517 2.4 7225 0 5 200 2.0 20 c 5 235 NOTE INCREASE I N C FATIGUE-CRACK FROM STEP 2 TO 3, 1.6 YET A DECREASE IN

GROWTH UNDER

CRACK GROWTH RATE

PROGRAMMED

1.2

LOADS

RATE OF GROWTH (NOT LEVEL) = .a LO-HI-LO-LO LOO' - 3 .

_ _ 70 .4

I 4 8 12 16

c n. STRESS CYCLES x 10-3 Figure B8 It a p p e a r s that m a s t e r fatigue d i a g r a m s would be a useful m e a n s f o r the ex- trapolation of d a t a over a wider range of t e m p e r a t u r e than would b e used to obtain the data. If this technique is successful, it would m a k e possible the gathering of d a t a f o r a r a n g e of t e m p e r a t u r e s with a m i n i m u m of testing.

T h e Dorn p a r a m e t e r , R e f e r e n c e 29, h a s been a useful c o r r e l a t i o n m e a n s f o r relating time and t e m p e r a t u r e as a function of s t r e s s f o r s o m e specific s t r a i n deformation or rupture. Thus, a m a s t e r d i a g r a m would c o n s i s t of a f a m i l y of R c u r v e s f o r fatigue r u p t u r e and a second family of R c u r v e s f o r 0.270 deformation covering a t e m p e r a t u r e r a n g e established by the extrapolation p e r m i s s i b l e f r o m the r a n g e of t e m p e r a t u r e s under which t e s t s a r e made.

is a m a s t e r d i a g r a m f o r 0. 270 deformation. T h i s f i g u r e w a s F i g u r e B7 obtained f r o m the d a t a p r e s e n t e d i n F i g u r e B6.

D o r n ' s p a r a m e t e r takes the f o r m AH 8 = t e - m M 22512

MASTER FATIGUE DIAGRAM S-816 ALLOY

REF. 38 e = te- AHIRT

Figure B7

M 22516

DELAYED FRACTURE (STATIC FATIGUE) OF AIS1 4340

STEEL IN WATER ENVIRONMENT. (PH=.5 TO 1.0)

1 IO 1 00 1000 t 1 MINUTES TO RUPTURE Figure B9 M 22513

CRACK GROWTH IN INERT GASES.GAS

PRESSURES NOTED (MM. HG.)

-

-+

v Y u a a u W P l- a LL LL I I- z 0: N , CYCLES OF STRESSING Figure B10 It is becoming increasingly c l e a r that the c r a c k - g r o w t h period i n fatigue c o m - p r i s e s a v e r y large percentage of the total fatigue life.

F o r this r e a s o n , m o r e investigations a r e r e q u i r e d to define the r a t e of c r a c k p r o g r e s s i o n , s i n c e t h e s e observations lead to a b e t t e r insight concerning the p r o g r e s s i n the ac- cumulation of physical damage. I m p r o v e m e n t s to the non-linear d a m a g e con- cepts w i l l r e s u l t f r o m this knowledge, and t h e s e modifications will r e s u l t i n m o r e a c c u r a t e predictions of s t r u c t u r a l behaviour.

T h e complex m e c h a n i s m s of delayed cracking and delayed f r a c t u r e , which o c c u r under steady s t a t e r a t h e r than cyclic loading conditions, a r e additional subjects f o r investigation. T h e concept of a "critical s t r a i n l e v e l ' ' f o r design operation should be pursued, Many of the high-strength s t e e l s f o r c u r r e n t and f u t u r e use are particularly susceptible t o the phenomenon of delayed frac- t u r e in the everyday c o r r o s i v e environment of the a t m o s p h e r e , F i g u r e B9 shows the r e s u l t s of testing one s t e e l alloy in a mildly s e v e r e e n - vironment. It h a s been d e m o n s t r a t e d that the f o r m of the s t r e n g t h equation, shown on the graph, c a n b e u s e d f o r o t h e r environments.

In g e n e r a l , the fatigue life of a m e t a l is longer in a n i n e r t a t m o s p h e r e than in air. When its action is c o m p a r e d to that of i n e r t g a s e s , a i r i s c o n s i d e r e d to b e a c o r r o s i v e environment. A d e c r e a s e i n c o r r o s i v e n e s s of the environ- m e n t r e s u l t s in l e s s attack both on the s u r f a c e of the m e t a l and on the newly f r a c t u r e d s u r f a c e s generated i n the p r o c e s s of fatigue cracking. T h e r e f o r e , the g r e a t e r the reactivity of the environment the m o r e rapid the c r a c k growth and the s h o r t e r the fatigue life. F i g u r e B10 and B11 show the r e l a t i v e effects of various environments on a n aluminum and titanium alloy.

In F i g u r e B12 a r e the d a t a f r o m e x p e r i m e n t s testing the fatigue c h a r a c t e r i s t i c s of l o w carbon s t e e l mechanically s t r a i n e d within the influence of a s t r o n g m a g n e t i c field. T e s t loading of the m e t a l coupons under cyclic conditions was applied i n a uniaxial s p e c i m e n d i r e c t i o n and n o r m a l to the m a g n e t i c f i e l d axis.

P o l e s of a 3000 g a u s s permanent magnet e n c i r c l e d the c r i t i c a l t e s t section of the coupons and provided a high intensity magnetic induction. T h e fatigue life as well as the number of s t r a i n cycles r e q u i r e d t o g e n e r a t e a c r a c k of a given length w a s found to i n c r e a s e f o r the f e r r o m a g n e t i c m 3 t e r i a l t e s t e d while within the field. Conversely, nonmagnetic aluminum alloy exhibited no differences i n fatigue c h a r a c t e r i s t i c s when tested either i n o r out of the influence of t h e m a g n e t i c field. In this example, neither m a g n e t o s t r i c t i o n n o r magneto - elasticity are s u g g e s t e d as r e a s o n s f o r altering m e t a l fatigue c h a r a c t e r i s t i c s .

Instead, m a g n e t i c induction of the s t r a i n cycled coupons w a s o b s e r v e d to m a g - n e t i z e and r e t a i n the m e t a l d e b r i s g e n e r a t e d during the fatigue cracking p r o c e s s . T h e d e b r i s b e c a m e wedged between the mating c r a c k s u r f a c e s and w a s shown by photoelastic techniques to mechanically r e d u c e the s t r e s s i n - tensity a t the growing c r a c k tip. T h e reduction i n s t r e s s r a n g e by this m e c h - a n i s m w a s r e s p o n s i b l e for i n c r e a s e s i n fatigue life and reductions i n c r a c k growth r a t e s e S o m e investigations have been m a d e on the effect of nuclear i r r a d i a t i o n on m e c h a n i c a l fatigue p r o p e r t i e s of m e t a l s Radiation-induced changes a r e usually r e f e r r e d to as radiation d a m a g e since in many c a s e s the effects have b e e n d e t r i m e n t a l i n one f o r m or another. Damaging effects s u c h as loss i n Beneficial effects evidenced by ductility h a v e been noted f o r many m e t a l s .

i n c r e a s e d yield and ultimate yields and ultimate s t r e n g t h s , fatigue strength, and s u r f a c e hardening a l s o have b e e n noted. Rotating b e a m fatigue t e s t s on 7075-T6 a l u m i n u m alloy shown i n F i g u r e B13 indicate a n i m p r o v e m e n t in life due to the effects of a total integrated flux of 2 ~ 1 0 ~ 8 fast n e u t r o n s / c m . , Although the amount of i r r a d i a t i o n received by the s p e c i m e n s i n t h e s e t e s t s is believed sufficient to a l t e r m e c h a n i c a l p r o p e r t i e s , i t is not known if the r e - s u i t s are significant f o r the c h a r a c t e r i s t i c s of m e t a l s during the conjoint Additional studies need to b e u n d e r - action of fatigue s t r a i n i n g and irradiation.

taken f o r the s i m u l t a n e o u s action of i r r a d i a t i o n and m e c h a n i c a l s t r a i n i n g a t low t e m p e r a t u r e s It h a s b e e n e x p e r i m e n t a l l y d e m o n s t r a t e d ( s e e F i g u r e B14) that fatigue c r a c k i n g u n d e r uniaxial d i r e c t s t r e s s i n g of a n aluminum alloy o c c u r s i n h a r d vacuum T h i s is c o n t r a r y to g e n e r a l a l m o s t as r e a d i l y as within a t m o s p h e r i c p r e s s u r e .

belief. E x p e r i m e n t s now indicate t r e n d s toward i n c r e a s e d c r a c k growth r a t e s which m a y eventually r e s u l t in c h a r a c t e r i s t i c s m o r e c r i t i c a l than those f r o m i n - a i r t e s t s . R e s u l t s on aluminum continuously held i n vacuum f o r p e r i o d s M-22514 ALLOY. CRACKING STRESS CONSTANT

CRACK GROWTH

OF TITANIUM

IN OZONE.

N. CYCLES OF STRESSING Figure B11 M-22515 2 4

- CRITICAL dc

( MAX CRACKING STRESS h = 20,000 PSI; R = 0.05

r

1 6 MATL. = 1020 C. STEEL

E

T = 7OOF.

REFERENCE 35 J V a a

FATIGUE OF u

LL

FERROMAGNETIC

I MATE R I A L.

I- s ~ e

B

u MAGNETIC FIELD t i = 3,000 GAUSS I 4 8 1 2 CYCLES OF STRESSING x

Figure B12

7 1 g r e a t e r than a week yielded d r a s t i c reductions i n fatigue p r o p e r t i e s . This strongly indicates the t i m e dependency of the phenomenon.

Results f r o m s h o r t - t i m e t e s t e x p o s u r e s i n vacuum as shown in F i g u r e B15 showed is the u s u a l accepted belief. However, f o r many i m p r o v e d p r o p e r t i e s . This c a s e s a n extensionof the vacuum outgas sing t i m e is m o r e a r e a l i s t i c environment than the s h o r t - t i m e t e s t e x p o s u r e s previously investigated. B e c a u s e of this anomaly, prolonging the vacuum exposure i s suggested a s the only reliable p r o c e d u r e a t p r e s e n t f o r evaluating m e t a l s for s e r v i c e in the s p a c e envi r onment .

T h e possibility of a m e c h a n i s m which can o c c u r during p a r t i a l out-gassing of the n a t u r a l amorphous aluminum oxide film on the m e t a l c a n b e p r o p o s e d to explain o b s e r v e d differences in the s h o r t - t i m e as c o m p a r e d to long-time vacuum e x p o s u r e t e s t s .

T h e combined effect of vacuum and high t e m p e r a t u r e on fatigue life of a m e t a l is shown i n F i g u r e B16. In the low-cycle-to-fracture r a n g e the fatigue life is M.22487

SHORT TIME VACUUM TESTS. (<20 HRS.)

CYCLES OF STRESSING x 10-3

Figure B15

M.22522

EFFECT OF PRIOR IRRADIATION ON UNNOTCHED

7075-T6 ALUMINUM ALLOY (ROTATING BEAM )

I I I n

'"I

I I I 0 1 Figure 813 M-22489

EFFECT OF OUTGASSING TIME

1.3 I I AIR / I

E 1.1

a c1 Y a .9 a w I?

I- .i i SLOl I 8 16 24 32 40 NUMBER OF CYCLES x 10-3 Figure B14 Now, it is generally a g r e e d that the effects of the s p a c e environments on engineering m a t e r i a l s a r e l a r g e l y unexplored and relatively unknown. Since useable mechanical p r o p e r t i e s of a metal in s p a c e a r e dependent upon "time" during the simultaneous action of the range i n environments, w e m a y have to r e l y on l a b o r a t o r y e x p e r i m e n t s conducted i n s p a c e i t s e l f f o r the determination of s o m e allowables.

M-12809A

INFLUENCE OF ATMOSPHERE ON FATIGUE LIFE

REFERENCE 41 % PLASTIC STRAIN CYCLES TO FAILURE F i g u r e B16 g r e a t e r when tested in vacuum. As the s t r e s s l e v e l o r cyclic s t r a i n r a n g e is T h i s reduced, a g r e a t e r n u m b e r of cycles are r e q u i r e d to produce f r a c t u r e .

i n c r e a s e in t i m e to f r a c t u r e r e s u l t s i n longer e x p o s u r e t o vacuum, and i n this region the fatigue life i n vacuum is s h o r t e r than the life i n air.

In s u m m a r y , the p r e l i m i n a r y r e s u l t s of m a n y e x p e r i m e n t s have identified en- vironments that enhance as w e l l as d e g r a d e fatigue s t r e n g t h p r o p e r t i e s . O n e g r e a t difficulty i n m a t e r i a l s evaluation p r o g r a m s h a s b e e n the inability to e f - f ectively simulate the environment. It is believed that the time-dependency of many m a t e r i a l p r o p e r t i e s if not adequately explored will lead to invalid conclusions concerning the s t r e n g t h behavior of m e t a l s . In s o m e c a s e s , the r e s u l t s have been contradictory to generally accepted notions. T h e s e dif- f e r e n c e s may b e attributed to d i f f e r e n c e s i n the imposed conditions of lab0 r a t o r y t e s t s M.22491

BIAXIAL SN CURVES FOR 24ST

EXTRUDED TUBES, ( NACA 1889)

Figure C 1

M-22490

BIAXIAL SN CURVES FOR 14ST-4 TUBING

(NACA T N 1889) Figure C2

APPENDIX C FATIGUE L I F E , FATIGUE CRACKING AND RESIDUAL STRENGTH - - _ _ ~ -- O F FLAWED STRUCTURE UNDER BIAXIAL LOADING

-_

T h e m a j o r i t y of s t r u c t u r e s which a r e designed, f a b r i c a t e d , and operated a r e subject to some d e g r e e of multiaxial o r biaxial s t r e s s i n q while in s e r v i c e .

Yet, m a j o r e m p h a s i s in evaluating the fatigue r e s i s t a n c e of s t r u c t u r e , by Evaluations by t h i s l a b o r a t o r y t e s t , i s placed on uniaxial loading methods.

method will i n many c a s e s r e s u l t in unconservative designs aid p r e n i a t u r e f a i l u r e .

T h e fatigue of m e t a l s under multiaxial straining i s a complex phenomenon.

F a c t o r s which have contributed to t h i s complexity a r e : loss in ductility, anisotropy, and texture hardening of m a t e r i a l s . T h e effect of t h e s e f a c t o r s on biaxial fatigue p r o p e r t i e s h a s not been adequately investigated. T h e r e f o r e , a t the c u r r e n t s t a t e of knowledge, i t should be cautioned that the e m p i r i c a l c h a r a c t e r i s t i c s defined for one m a t e r i a l do not n e c e s s a r i l y apply f o r o t h e r s .

For example, s o m e m a t e r i a l s have g r e a t e r tensile s t r e n g t h s i n the longi- tudinal rolling direction; o t h e r s have higher strength in the t r a n s v e r s e d i - r e c t i o n .

Many of t h e s e same m a t e r i a l s have higher biaxial s t r e n g t h s than uniaxial, yet when these m a t e r i a l s contain flaws, the uniaxial s t r e n g t h c a n be g r e a t e r than the biaxial strength. A l s o , to be c o n s i d e r e d i s the value of the s t r e s s r a t i o of the biaxial principal s t r a i n s . F o r s o m e s t r e s s r a t i o s the m a x i m u m principal s t r a i n may be n o r m a l to the w e a k e s t strength a x i s of the m a t e r i a l . When the s t r e s s r a t i o is a l t e r e d , i t c a n be n o r m a l to the s t r o n g e s t s t r e n g t h axis of the m a t e r i a l .

I t i s the purpose of this section to i l l u s t r a t e s o m e fatigue c h a r a c t e r i s t i c s of m e t a l s that a r e not well known o r understood In a few c a s e s a n a w a r e n e s s of t h e s e m a t e r i a l p r o p e r t i e s existed but w a s neglected in d e s i g n . T h e r e s u l t s w e r e catastrophic. F i g u r e s C 1 and CZ shows biaxial S - N c u r v e s f o r two alumi- In both examples, the biaxial s t r a i n i n g conditions r e s u l t e d in num alloys.

lower fatigue allowables than unidirectional straining.

F i g u r e C 3 i l l u s t r a t e s the t r e n d s i n fatigue c r a c k growth as d function of loading. The t e s t r e s u l t s w e r e obtained on the aluminum alloy 2014-T6 f o r

FLAW GROWTH UNDER UNIAXIAL

AND BIAXIAL LOADING

- r Y BIAXIAL BIAXIAL (CYL.) 2:l ROLLING DIR. WITH

' (PLATE) 2 1 ~ = C M A X = 14.000 LOAD

2.01 1 1 - 1.8

.6 -

.

5 10 15 20 25 30 35 40 45 STRESS-CYCLES (n) x Figure C 3 M-182906

FRACTURE

STRENGTH AS A

FUNCTION OF

FLAW

ORIENTATION

e = ANGLE LOAD DIRECTION TO ROLLING DIRECTION @ = ANGLE FATIGUE CRACK TO ROLLING DIRECTION d = %"-e goo = ANGLE CRACK TO LOAD. (CONST.)

e (DEGREES)

Figure C4 two conditions of biaxiality a s well as under uniaxial loading. The i n c r e a s e d c r a c k growth r a t e s and s h o r t e r fatigue lives under b i a x i a l loading a g r e e with the t r e n d in fatigue l i v e s in F i g u r e C1, ~ U n l e s s otherwise noted, the nominal m a x i m u m p r i n c i p a l s t r e s s f o r a l l s p e c i - 14,000 p s i . The biaxially loaded p l a t e m e n configurations on F i g u r e C 3 w a s (2:l s t r e s s field) a p p e a r s to have a slower c r a c k growth r a t e than the p r e s - s u r i z e d cylinder (2: 1 s t r e s s - f i e l d ) . T h i s is r e a s o n a b l e , s i n c e the m e m b r a n e s t r e s s field i n the simple-supported p l a t e i s v a r i a b l e and d i m i n i s h e s a s the c r a c k extends and a p p r o a c h e s the edge of the plate specimen. The nominal i n the p r e s s u r i z e d cylinder and uniaxially loaded p l a t e on the s t r e s s field o t h e r hand is c o n s t a n t .

F i g u r e C 3 also shows the d i f f e r e n c e s in c r a c k growth r a t e as a function of anisotropy. It c a n be s e e n f r o m the f i g u r e that the s l o w e s t r a t e of c r a c k growth o c c u r s when the c r a c k is propagating n o r m a l to t h e m a t e r i a l rolling I d i r e c t i o n . The r e a d e r a g a i n is cautioned that this r u l e is not m e a n t to b e applicable for a l l m a t e r i a l s . T h e r e a r e unpublished d a t a indicating an opposite r u l e f o r s o m e titanium a l l o y s , 2014-T6 plates. F a t i g u e c r a c k s 1.8-in. long w e r e grown in the 6-in. wide T h e s e p l a t e s w e r e then ruptured at 75O uniaxial loaded p l a t e s of F i g u r e C3.

and -320OF. If t h e f r a c t u r e s t r e n g t h s in t h e longitudinal and t r a n s v e r s e S m a l l undetected a n d / o r a c c i d e n t a l f l a w s c a n p r o m o t e c a t a s t r o p h i c r u p t u r e in p r e s s u r e v e s s e l s a t s t r e s s e s far below d e s i g n l e v e l s . D e s i g n e r s and i n - s p e c t o r s r e q u i r e knowledge concerning the s i z e of s m a l l f l a w s , and t h e i r g r a d u a l extension by fatigue a c t i o n , that m a y lead to instability f r o m loads i n c u r r e d by proof testing o r in s e r v i c e . T h i s information is n e c e s s a r y i n o r d e r to define s a f e l i m i t s f o r the working s t r e s s e s in s t r u c t u r e . One method = length of c r a c k I C W = panel width - R - e m p i r i c a l constant d e t e r m i n e d f r o m P t e s t (figure C -7) T h e f r a c t u r e envelopes f o r other widths of panels can be calculated f r o m this equation by substituting a p p r o p r i a t e values of W into the f o r m u l a . The I value of R r e m a i n s constant f o r a given m a t e r i a l in a given t e m p e r and P f a b r i c a t e d condition. The derivation of this equation i s given in R e f e r e n c e 30.

Good a g r e e m e n t between calculated and experimental r e s u l t s a r e shown in F i g u r e C5.

The equation c a n a l s o be modified to p r e d i c t the behavior of flawed s t r u c t u r e u n d e r biaxial loading. I t i s f i r s t n e c e s s a r y to calculate the f r a c t u r e envelope of uniaxially loaded p a n e l s in a width equal to the length of the cylinder in is then calculated from: question. The f r a c t u r e s t r e n g t h of the cylinder 9 Kuhn ( R e f e r e n c e 32) The l o w e r c u r v e in F i g u r e C5 has been calculated f r o m this equation and shows good a g r e e m e n t with t e s t d a t a on 5 in. - d i a m e t e r c y l i n d e r s 20 in. long.

Another e x a m p l e of the usefulness of this equation in design is shown in F i g u r e C6. In this example, c r a c k e d t e s t panels 1 2 in. in width and of the s a m e s t r u c t u r a l configuration w e r e ruptured in uniaxial tension. F r o m t h e s e data, \ of obtaining this information in the l a b o r a t o r y is by rupturing s t r u c t u r a l panels i n various widths and s i z e s and containing fatigue c r a c k s .

F i g u r e C 5 shows the f r a c t u r e strength o r r e s i d u a l s t r e n g t h of s o m e uniaxially loaded panels of aluminum alloy 2014-T6 in a v a r i e t y of widths and c r a c k Data f o r any one panel s i z e can be r e p r e s e n t e d by the equation s i z e s .

w h e r e r e s idu a 1 s t r e n g t h ( c r a c k e d ) u It. ten s i le s t r e n g t h (unc r acked) M- 18286A

PREDICTION OF FRACTURE STRENGTH OF

FLAWED STRUCTURE UNDER BIAXIAL LOADING

Figure C5 M.22496 2 .

m, I!

NOTCH

I

RESISTANCE AS

A FUNCTION OF

Y

9 10

MATER I AL

z

DUCTILITY

N E

(FOR FATIGUE

z ALUMINUM ALLOYS

CRACKED

p s

TITANIUM ALLOYS a STEEL ALLOYS U

STRUCTURE) z SEMI-AUST. STEEL ALLOYS

NICKEL ALLOYS.

REFERENCE 30,31 4 6 8 10 Rp, PLASTIC ZONE NOTCH RESISTANCE FACTOR Figure C 7 M-182aaA

S-IV B HYDROSTATIC BURST

TEST SPECIMEN

= 1.3 FROM FIGURE C 7 ._ FLAW sizE OR CRACK (IN.)

Figure C6

the f r a c t u r e envelope f o r a 660-in. -long cylinder w a s calculated and then modified f o r biaxial loads and radius of c u r v a t u r e effects with Kuhn's c o r r e c t i o n factor ( R e f e r e n c e 32).

Nominal values of (T and R used in the equation w e r e obtained f r o m coupon U P t e s t s of weld m e t a l p r o p e r t i e s b e c a u s e f r a c t u r e initiated at a flaw in the weld seam. The hoop s t r e s s a t b u r s t f o r the 130-in.-radius v e s s e l was 13,000 psi. The predicted f r a c t u r e envelope in F i g u r e C6 at this s t r e s s defines a c r i t i c a l flaw s i z e of 4 in. P o s t - t e s t examination of the f r a c t u r e d tank r e v e a l e d a f l a w ( t e r m e d incomplete fusion) in the weld s e a m o v e r 3 - 1 / 4 in. in length.

Such close a g r e e m e n t between actual and predicted behavior suggests that the analysis method can be u s e d in design. Additional data that would be useful to the designer would be the r a t e of growth of such flaws with p r e s s u r e c y c l e s .

T h e d e c r e a s e i n strength of p r e s s u r e v e s s e l s f r o m cycling i n operation could then b e e x p r e s s e d as shown in F i g u r e G-1 of Appendix C .

M 22518

SINUSOIDAL AND RANDOM SN DATA

ALTERNATING STRESS (KSI) A A M

DATA FROM i

\ I REFERENCE \ I REFERENCE

MEAN SN CURVE MEAN SN CURVE ~~ MIN. MIN. \.

SN CURVE

-I

I

\

I

~ R M S = 11,260 PSI

Q & ( T Y 8 ~ ~ o

ASINUSOIDAL CONST. AMPLITUDE (N VS. ALTERNATING U ) L R A N W M NOISE (N VS. RMS STRESS) O

' '

BlOS 2 6 E l 0 6 '107 N. CYCLES TO FAILURE Figure D1 In this e x e r c i s e , a c l a s s i n t e r v a l of one-third h a s b e e n used f o r the value of AX.

Use Rayleigh probability distribution function for prediction of peak s t r e s s proportionment i n random p r o c e s s -X

z

= xe P ( x) w h e r e ' x = r a t i o of (I peak to o R . M . S T h e n , n u m b e r of c y c l e s under r a n d o m loading, N R , c a n be calculated from, -X _ _

-

1 1 A x - - (2) r a n d o m load c y c l e s = ' xe N ( s ) RR to f a i l u r e

APPENDIX D FATIGUE CHARACTERIS TICS UNDER RANDOM LOADING In t h i s section, working examples a r e given of acceptable methods for p r e - dicting fatigue c h a r a c t e r i s t i c s of s t r u c t u r e subjected t o random loads f r o m l a b o r a t o r y t e s t r e s u l t s under sinusoidal constant amplitude loading. In the f i r s t example, fatigue lives of s a m p l e s under random loading a r e calculated f r o m known fatigue lives under d i s c r e t e loading.

The calculated l i v e s a r e then compared to experimentally d e t e r m i n e d lives under random loading.

Good agreement between predicted and experimental r e s u l t s show the method t o b e satisfactory f o r u s e in design.

In the second example, a s i m i l a r method i s outlined f o r the prediction of fatigue c r a c k growth under random loads.

By t h i s technique i t is believed that additional a c c u r a c y in predicting fatigue life will r e s u l t , T h e b e s t i n - dication a t p r e s e n t f o r the r a t e of nonlinear d a m a g e accumulation i n s t r u c t u r e is f r o m the observed crack-growth c h a r a c t e r i s t i c s . F u t u r e e x p e r i m e n t s should be designed to gather t h i s information. Now, if the t o t a l d a m a g e to f r a c t u r e is integrated over small i n c r e m e n t s of time to grow a c r a c k to a given length, and these i n c r e m e n t s during c r a c k extension a r e successively added along the o b s e r v e d nonlinear path of physical d a m a g e accumulation, then the calculated t i m e t o failure will b e p r e c i s e .

Fatigue Life F i g u r e D1 shows the fatigue t e s t r e s u l t s f o r notched aluminum s p e c i m e n s under both sinusoidal constant amplitude loading and r a n d o m noise.

The d a t a h a s been taken f r o m R e f e r e n c e 26.

Table D1 shows the analysis technique for calculating the proportion of peak s t r e s s e s experienced in a random p r o c e s s . T h e Rayleigh probability d i s t r i - bution function i s used and will a c c u r a t e l y p r e d i c t the number of o c c u r r e n c e s f o r simple one-degree -of f r e e d o m s y s t e m s within relatively n a r r o w bands of load frequency.

0 0 0 4 0 0 0 0 0 0 0 .

4 I n N r - I n 9 0 . w D 9 \ D m 0 N 9 0 . r - 9

0 0 0 0 2 0 0

m nl X II " 0 d d u ?

II O m * 0 . I n N d o 0 0 N d d 0 0 0 0 0 0 0 . . .

d I In

W

m K) 9 N r - 0 L n r - m d 0 r - N A 0 0 0 8 8 8 d V .r( a a , k

cl

P4 0 0 0 0 0 0 0 0

0 0 0 z

a , O N o d r 0 . 0 In 9 a 3 4 r - D r n d ! 4

2 r- m N d o

d r * 3 0 0 0 0 0 0 p : V 6 ( X N

a

0 . 0 T Y d r - i o 0 0 0 0 a , X 0 6 9 0 9 ,-d C O N 'u? G In: 0 9 o m r - d r 8 8 8 8 m d 0 0 rd II D d

n

0 0 0 0 0 0 0 0 0 0 - l m 9.49 N r - N m m m d r N o r - Ln N O r - I n N O r- d l n m N 9 0 m r - 4 1 0 d d d d N N m m m d r * a a , &I X V -4 A N d N d N O a I I I 1 I I 0) d d d N N N m m m d r k i w h e r e N = cycles to f a i l u r e u n d e r s i n u s o i d a l c o n s t . , amplitude a t ( s ) d i s c r e t e v a l u e s of (x) A x 0.33 weighting f a c t o r (choose A x = 1 / 3 c l a s s i n t e r v a l ) T a b l e D1 shows r e s u l t s of the n u m e r i c a l calculations which a r e r e q u i r e d to p r e d i c t the number of c y c l e s to f a i l u r e ( N ) f o r r a n d o m load excitation.

R Two s e t s of calculations a r e m a d e , one b a s e d on the m i n i m u m S - N c u r v e and the o t h e r on the a v e r a g e S-N c u r v e in F i g u r e D1.

T a b l e D2 shows the c o m p a r i s o n between p r e d i c t e d and a c t u a l e x p e r i m e n t a l r e s u l t s .

Fatigue Crack Growth S t r u c t u r a l test a r t i c l e s m a y be t e s t e d to s e v e r a l d i s c r e t e s t r e s s l e v e l s under constant amplitude loading. E a c h s a m p l e i s to be subjected to only one r a n g e Nine d i s c r e t e s t r e s s r a n g e s may be chosen f o r t h e s e of cyclic s t r e s s i n g .

t e s t s , corresponding to nine v a l u e s of (x), w h e r e (x) equals the r a t i o of peak s t r e s s t o r o o t - m e a n - s q u a r e s t r e s s within a cycle. T e s t s t r e s s l e v e l s of (x) f r o m 0 . 6 7 to 3 . 3 3 m a y be selected. During t h e s e t e s t s , the growth of the fatigue c r a c k should be r e c o r d e d a s a function of the n u m b e r of s t r e s s cycles. Typical data a r e illustrated in F i g u r e D2.

E x p e r i m e n t a l r e s u l t s of this kind depict the nonlinear n a t u r e of d a m a g e accumulation m o r e a c c u r a t e l y than the r e s u l t s obtained by the m e a s u r e m e n t of total n u m b e r of c y c l e s to f r a c t u r e .

F r o m t h e s e data, f a t i g u e - c r a c k growth under random loading then m a y b e calculated i n a m a n n e r s i m i l a r to that used f o r fatigue life. The number of I c y c l e s of random loading, nri, r e q u i r e d to g e n e r a t e a c r a c k equivalent i n length to the s a m e length of c r a c k produced u n d e r d i s c r e t e loadings is c a l c u -

I

lated f r o m : M.22523

FATIGUE CRACK GROWTH UNDER DISCRETE

AND RANDOM CYCLIC LOADING

..

N x (STRESS CYCLES)

Figure D2

0 I = 0

w h e r e 0 . 3 3 class interval i n Rayleigh distribution function defining peak s t r e s s e s in d i s c r e t e amplitude loading t e s t s n u m b e r of cycles to successively grow c r a c k f r o m

p = 0 to 8 = pi to 8 = f e t c . , under constant

j amplitude, sinusoidal loading.

Table D2 I Experimental Fatigue P r e dic t e d Life u n d e r Random Fatigue Life Noise ( c y c l e s ) ( c y c l e s ) RMS Reference 26 Table D1 11, 260 psi 2 , 0 2 0 , 0 0 0 2, 630, 000 1 , 3 8 0 , 000 2,490, 000 850, 000 1 , 1 1 0 , 0 0 0 5, 660, 000 7 , 8 9 0 , 0 0 0 3 , 4 1 0 , 0 0 0 2 , 7 3 0 , 0 0 0 = avg. 7 predicted Ratio experimental = 0 . 9 6 to 2. 07 ~~ .

T o check the validity of the above a n a l y s i s , the next objective should be t o conduct a r a n d o m cyclic load t e s t . During the t e s t , m e a s u r e m e n t s a r e to b e taken of the growth of the c r a c k w h e r e v e r it m a y o c c u r in the s a m p l e .

Hypothetical r e s u l t s a r e shown in F i g u r e DZ. It should be noted that this technique m a y r e v e a l t h e nonexistence of a single s t r e s s - p r o d u c i n g d a m a g e a t a r a t e equivalent t o t h a t m e a s u r e d u n d e r random loading. This c o n t r a d i c t s p r e v i o u s l y accepted b e l i e f s . I t i s r e a l i z e d that the a s s u m p t i o n that a n equivalent damaging s t r e s s level did e x i s t has b e e n m a d e i n the p a s t because of the lack of e x p e r i m e n t a l proof.

Additional e x p e r i m e n t s a r e n e c e s s a r y . Encouraging r e s u l t s f r o m such p r o - g r a m s will indicate that a s e r i e s of l e s s costly d i s c r e t e t e s t s c a n be used to p r e d i c t behavior of s t r u c t u r e s subjected to random loads.

. Approach

An a c c e p t a b l e a p p r o a c h f o r the evaluation of safe - s t r u c t u r e by a n a l y s i s and t e s t which h a s been used in the p a s t i s a s follows: D e t e r m i n e the f r a c t u r e envelope of the m a t e r i a l s of c o n s t r u c t i o n .

1.

This c a n be p r e s e n t e d a s a variation in the s t r e n g t h of the m a t e r i a l p o s s e s s i n g v a r i o u s flaw s i z e s . The envelope can b e obtained f r o m uniaxial o r multiaxial load t e s t s , whichever is a p p r o p r i a t e .

2. If the s t r u c t u r e to be evaluated i s e x t r e m e l y l a r g e , and n e c e s s i t a t e s a c o s t l y t e s t p r o g r a m , then s m a l l e r t e s t a r t i c l e s may be used. S e m i - e m p i r i c a l equations a r e available f o r calculating the behavior of l a r g e s t r u c t u r e f r o m the r e s u l t s of s m a l l coupons. F o r m u l a s a r e a l s o available f o r predicting the behavior u n d e r biaxial loads f r o m the F i g u r e s C5 and C6 of Appendix C r e s u l t s of uniaxial load t e s t s .

d e m o n s t r a t e the s u c c e s s of t h e analytical methods and show c l o s e a g r e e m e n t between experimental and analytical r e s u l t s . F i g u r e C 5 shows good a g r e e m e n t between p r e d i c t e d and a c t u a l f r a c t u r e s t r e n g t h s of flawed and s m a l l p r e s s u r e v e s s e l s f r o m the r e s u l t s of s i m p l e uniaxially loaded panels. F i g u r e C6 shows the f r a c t u r e envelope f o r a 260-in. - d i a m e t e r p r e s s u r e v e s s e l which h a s been p r e d i c t e d f r o m the r e s u l t s of 12-in. wide uniaxially r u p t u r e d panels.

T h e next s t e p in evaluating a f r a c t u r e - s a f e design is the d e t e r m i n a - 3 .

tion of the s t r u c t u r a l r e i n f o r c e m e n t s and the a s s o c i a t e d r e d u c t i o n s in s t r e s s l e v e l s a t the r e i n f o r c e m e n t that will a r r e s t the f a i l - s a f e f r a c t u r e . F i g u r e E l shows some a c t u a l e x p e r i e n c e i n v a r i o u s s t r u c t u r e s . The e x i s t e n c e of t h r e e r e g i o n s should be noted.

In the f i r s t r e g i o n , the s t r e s s e s are u n n e c e s s a r i l y low and the c r a c k s and f l a w s a r e nonpropagating. T h i s region r e s u l t s in a n overweight design. The middle region is acceptable, and within this boundary, is controlled c r a c k s m a y develop into r a p i d f r a c t u r e but the f r a c t u r e and a r r e s t e d . The control of the f r a c t u r e is a function of the working s t r e s s and the s t r u c t u r a l r e i n f o r c e m e n t . The upper r e g i o n is not acceptable for d e s i g n , since f r a c t u r e arrest is irr.possiS!c.

An a l t e r n a t e m e a n s of depicting the d a t a of F i g u r e E l is shown in F i g u r e E2. In this g r a p h , the variation i n r e s i d u a l s t r e n g t h with f l a w s i z e is shown as a function of s t r u c t u r a l r e i n f o r c e m e n t . I t should be noted that higher allowable working s t r e s s e s c a n be u s e d with g r e a t e r amounts of r e i n f o r c e m e n t .

4. A final a n a l y s i s f o r the p r o p e r choice of ductile m a t e r i a l s and a t t a c h m e n t s is r e q u i r e d . In addition, a tradeoff study should be as a m a d e by c o m p a r i n g the weights of s t r u c t u r a l l y r e i n f o r c e d panels function of t h e i r design working s t r e s s e s . The r e s u l t s of s u c h a study c a n be depicted as shown i n F i g u r e E3. In the f i g u r e , the o p t i m u m d e s i g n weight i s plotted as a function of s t r u c t u r a l r e i n f o r c e m e n t .

APPENDIX E FRACTURE -SAFE DESIGN O F SPACECRAFT STRUCTURES

- --

(SPACE - CABIN RELIABILITY)

Statement of P r o b l e m Inadvertent damage to s p a c e c r a f t s t r u c t u r e c a n o c c u r during the operation of a vehicle. The damage can c o m e f r o m a v a r i e t y of c a u s e s such as: (1) m e t e o r o i d penetration (point of impact o r d i s p e r s e d through shield), ( 2 ) un- detected flaws and c r a c k s during fabrication, ( 3 ) components flung f r o m runaway ( i n t e r n a l ) m a c h i n e r y , ( 4 ) m i n o r collisions, ( 5 ) fatigue c r a c k s generated f r o m high-frequency loading and high s t r e s s e s during the launch p h a s e of flight, (6) m a t e r i a l degradation i n the space environment (long - t i m e ) , ( 7 ) a c t s of demented p a s s e n g e r s and accidental d a m a g e , (8) damage f r o m the effects of blast loads.

Initial damage i n c u r r e d through any of t h e s e c a u s e s c a n p r o m o t e explosive d e c o m p r e s s i o n and complete loss of a highly s t r e s s e d and p r e s s u r i z e d vehicle. However, the extent of d a m a g e o r f r a c t u r e c a n be partially con- trolled by the p r o p e r choice of working s t r e s s e s in combination with sufficient s t r u c t u r a l r e i n f o r c e m e n t . The importance of vehicle reusability, and r e - t r i e v a l of personnel, equipment, and d a t a n e c e s s i t a t e s the solution to t h i s p r o b l e m through improved d e s i g n .

Cur r e n t E x p e r i e n c e T h e c u r r e n t analysis and testing p r o c e d u r e s used to define the f r a c t u r e s t r e n g t h of flawed s t r u c t u r e a r e adequate f o r design p u r p o s e s . T h e methods now take into account the effect of biaxial loads on s t r u c t u r e . In the p a s t , the s t r e n g t h of s t r u c t u r e often w a s d e t e r m i n e d d i r e c t l y f r o m the r e s u l t s of Now, i t has been d e m o n s t r a t e d that uniaxial load t e s t s which w e r e adequate.

biaxial o r multiaxial loads a r e far m o r e s e v e r e f o r the c a s e of c r a c k e d s t r u c t u r e . The successful designs p r o d u c e d , however, w e r e in a 1 a i r c r a f t s t r u c t u r e . The application of the p r e s e n t design methods to igation, welded spacecraft p r e s s u r e v e s s e l s will r e q u i r e s o m e additional inves although a c a r r y o v e r of p a s t knowledge and experience will be helpful.

M-22499

OPTIMUM WEIGHT VS. STRUCTURAL REINFORCEMENT

FOR FRACTURE-SAFE DESIGN

(PANEL EDGE LOADING CONSTANT) c ‘ 3 -

+ !

cl w E I 0.2 0.3 0.4 0.5 Ar/Lt

Finure E3

I t would a p p e a r , however, that the optimum f r a c t u r e - s a f e design f o r space - c r a f t s t r u c t u r e would be highly s t r e s s e d skins and closely spaced s t r u c t u r a l r e i n f o r c e m e n t s . i n Fatigue life i s a n additional p a r a x e t e r to be checked.

F i g u r e E3, i t should be noted that the optimum design weight s t r u c t u r e f o r a f r a c t u r e - s a f e design does not p o s s e s s the optimum life. If i n c r e a s e d fatigue l i f e is an important consideration f o r a given design, then a h e a v i e r T h e concept of an allowable flaw s i z e , even s t r u c t u r e will be r e q u i r e d .

though a r r e s t e d , m a y be another design consideration. F o r t h i s c a s e , a n a l t e r n a t e off-optimum design weight will have to be chosen.

.

M.22529 rl I CATASTROPHIC I (ALUMINUM, TITANIUM, STEEL CONSTRUCTION)

BOUNDARY

BETWEEN

CATASTROPHIC

1 n P I / l E

AND

FRACTURE-SAFE

UNSTABLE CRACKS

DESIGN

FRACYAR: ... . _.

t - - -

(NONPROPAGATING CRACKS) I I I 0.2 0.4 0.6 0 REA, STRUCTURAL REINFORCEMENT ,AyL.

AREA, SKIN

Figure E l

M 22500

SAFE-FRACTURE AS A FUNCTION OF

REINFORCEMENT AREA

ALUMINUM ALLOY CONSTRUCT".

U

--- --_

a CRACKS 1 , CRACK LENGTH (IN.)

Figure € 2

M.22502 Ar (AREA, STRUCTURAL n REINFORCEMENT)

STRUCTURAL

I

REINFORCEMENTS

PROVIDING

FRACTURE ARREST

Figure E4 (cont) Recommendations for F u t u r e R e s e a r c h .

I t h a s been mentioned previously that the design of s a f e - s t r u c t u r e h a s been m o s t successful in the a i r c r a f t field. The s t r u c t u r a l r e i n f o r c e m e n t s that have provided the mechanisrn f o r f r a c t u r e a r r e s t a r e shown as I t e m A and B in F i g u r e E4. No experience is available for the few s a m p l e s shown a s I t e m C - F ( F i g u r e E4). However, it is believed that each of these configurations will provide s o m e d e g r e e of f r a c t u r e a r r e s t . T h e anioant of c r o s s - s e c t i o n a l area of reinforcement and i t s a s s o c i a t e d reduction in s t r e s s level a t the reinforcement in o r d e r to a r r e s t f r a c t u r e , will have to be e m p i r i c a l l y d e t e r m i n e d .

M.22495

STRUCTURAL REINFORCEMENTS

PROVIDING FRACTURE ARREST

s L T - STRINGER

‘TIG FUSION SPOTWELD

Figure E 4

APPENDIX F VARIABILITY O F FATIGUE CHARACTER ISTICS ' The fatigue p r o p e r t y of a m e t a l o r a s t r u c t u r e i s not a n absolute m e c h a n i c a l It h a s no fixed value and c a n be a l t e r e d d r a s t i c a l l y by s m a l l p r o p e r t y , i changes in one of the many v a r i a b l e s producing the phenomenon. T h i s m a k e s the calculation of an a c c u r a t e prediction f o r the t i m e - o f - o c c u r r e n c e of fatigue e x t r e m e l y difficult and often questionable.

It is g e n e r a l l y recognized that a l a r g e variability o c c u r s in the t e s t r e s u l t s of even the m o s t carefully controlled r e s e a r c h o r s t r u c t u r a l development 1 fatigue r e s e a r c h p r o g r a m s . However, i t is not the intent of this section to I , d i s c u s s the m e c h a n i s m s by which v a r i o u s p a r a m e t e r s quantitatively affect fatigue life variability.

I Rather, the intent i s to shed s o m e knowledge

concerning typical t r e n d s in fatigue-life s c a t t e r .

This knowledge has b e e n d e t e r m i n e d f r o m l a b o r a t o r y o b s e r v a t i o n s and is believed t o be of u s e in 1 ~ guiding the d e s i g n e r .

The c h a r a c t e r i s t i c fatigue behavior of s t r u c t u r e is i l l u s t r a t e d in a qualitative m a n n e r in the following d i a g r a m s .

F i g u r e F1 shows t h e life s c a t t e r in fatigue a s a function of s t r e s s level. A s t h e l e v e l of stress in a s t r u c t u r e d i m i n i s h e s , the v a r i a b i l i t y in the t i m e r e q u i r e d to produce r u p t u r e i n c r e a s e s . The s a m e r u l e a l s o a p p l i e s i f the s t r e s s r a n g e of the cyclic a l t e r n a t i o n in s t r e s s diminishes. F u r t h e r m o r e , fatigue-life v a r i a b i l i t y d e c r e a s e s as t h e s e v e r i t y of the s t r e s s concentrations in a s t r u c t u r e i n c r e a s e s . T h e s e d i f f e r e n c e s a r e depicted in F i g u r e F1, which a l s o shows t h a t s e v e r e l y notched m e m b e r s p o s s e s s l e s s s c a t t e r in life than unnotched m e m b e r s . S i m i l a r c h a r a c t e r i s t i c s are evidenced in the phenomenon of fatigue-crack growth. F i g u r e F 2 depicts t h e growth of c r a c k s with c y c l e s of s t r a i n i n g .

F o r p u r p o s e s of s i m p l i f i c a t i o n , m e t a l fatigue m a y be c o n s i d e r e d as a two- s t a g e p r o c e s s . The f i r s t s t a g e , t e r m e d a damage nucleation p e r i o d , i s d i f - ficult to define in engineering terminology but h a s been o b s e r v e d to be l a r g e l y r e s p o n s i b l e f o r the s c a t t e r in fatigue r e s u l t s . The life v a r i a b i l i t y in the M-22509

LIFE VARIABILITY IN FATIGUE

TEST RESULTS

Fiaure F1 M.22492

SCATTER OF FATIGUE CRACK

GROWTH CHARACTERISTICS

SCAlTER ? 1:2 1 11/2 2 SCAlTER 2 1:lO 300 5 .

Figure F2 second stage, t e r m e d the c r a c k propagation period, i s e a s i l y rnonitored and i s known to be relatively s m a l l . T h e r e f o r e , it c a n be concluded that the s c a t t e r in fatigue t e s t r e s u l t s is a s s o c i a t e d rnzinly with the incubation stage o r f i r s t stage of the fatigue phenomenon. S t r u c t u r e s relatively f r e e of s t r e s s concentrations have longer l i v e s , longer damage nucleation p e r i o d s , s h o r t e r c r a c k propagation p e r i o d s , and correspondingly g r e a t e r variability i n life than s t r u c t u r e s p o s s e s s i n g s e v e r e s t r e s s r a i s e r s . C o n v e r s e l y , s e v e r e l y notched p a r t s p o s s e s s relatively s h o r t damage incubation p e r i o d s , long c r a c k propagation p e r i o d s , and s m a l l s c a t t e r r e c o r d s , as h a s b e e n shown i n the r e s u l t s of r e p l i c a t e t e s t s .

If the e x p e r i m e n t a l d a t a i n F i g u r e F2 f o r s t r u c t u r e p o s s e s s i n g high s t r e s s concentrations w e r e replotted a s the tinie required to grow a c r a c k f r o m i t s f i r s t detectable length, the variahility in life i s f u r t h e r reduced. The d a t a in F i g u r e F 2 have been normalized and replotted in F i g u r e F3. A p r a c t i c a l value f o r thelengthof c r a c k t h a t c a n b e detectedin s e r v i c e is 1 / 8 in. to 1 / 4 i n .

M-22510

SCATTER OF

CRACK GROWTH

t

BEHAVIOR IN 3

I C

TEST PANELS

Y I

BEYOND THE

I

DETECTABLE

1--

CRACK STAGE

t-

I

' 0

I

I I

' 12.3 NRUPTURE Fiaure F3

In the figures, this is identified as I,, which is witnessed at n, cycles. A

normal scatter of 3:l in overall fatigue life may be reduced t o a 10% scatter These i n behavior, if only the crack propagation period is considered.

characteristics suggest that separate probability analyses should be made for each stage of the fatigue damaging process.

IAD.996A

STRENGTH OF STRUCTURE AS A

FUNCTION OF LIFE

I CATASTROPHIC FA1LURE

Figure G 1 functions of the orientation of the p r i n c i p a l straining to the rolling d i r e c t i o n of the m a t e r i a l . These d i f f e r e n c e s should be d e t e r m i n e d f o r m o s t m e t a l s if safe design working s t r e s s e s a r e to be defined.

Some p r e l i m i n a r y r e s u l t s a r e d e s c r i b e d in Appendix C .

Fatigue Life a s a Function of Environment

More investigations a r e needed to e x p l o r e t h e time -dependent c h a r -

a c t e r i s t i c s of fatigue and f r a c t u r e phenomena.

Tests a-re r e c p i r e d ts deterililrie the e f i e c t s of i n e r t g a s e s , ozone, c o r r o s i v e g a s e s , liquid m e t a l s , v a c u u m , i r r a d i a t i o n , and combinations of these a t elevated, high, and cryogenic t e m p e r a t u r e s . Long-time a s well a s s h o r t - t i m e e x p o s u r e p e r i o d s should a l s o be investigated.

F a i l - s a f e and F r a c t u r e - S a f e Design The l e a k - b e f o r e - r u p t u r e design philosophy used in a i r c r a f t m a y be a p p r o p r i a t e f o r s o m e s p a c e c r a f t s t r u c t u r e s but not f o r o t h e r s .

Additional s t u d i e s a r e needed in this field to define those vehicle c a t e g o r i e s which a r e and a r e not applicable.

I t i s r e c o m m e n d e d that future work be d i r e c t e d to analytical and e x p e r i m e n t a l p r o g r a m s defining the s t r u c t u r a l stiffening r e q u i r e - m e n t s and s t r e s s field gradients f o r a r r e s t i n g f r a c t u r e a f t e r its initiation.

T h i s should be done f o r integrally stiffened s t r u c t u r e

APPENDIX G SOME RECOMMENDED AREAS FOR RESEARCH IN FATIGUE AND FRACTURE O F METALS The principal a r e a s in which knowledge of fatigue and f r a c t u r e c h a r a c t e r i s t i c s of m e t a l s and s t r u c t u r e s i s limited a r e listed below. T h e s e a r e a s will have to be r e s e a r c h e d before the m o s t serviceable fatigue- and f r a c t u r e -safe d e - sign c r i t e r i a can b e formulated f o r n e a r -future a i r c r a f t and space -vehicle The s t a t u s of p r o g r a m s now underway to study these a r e a s s t r u c t u r e s .

indicates that the situation will not change appreciably in the coming y e a r .

However, the need for this knowledge is so p r e s s i n g that i t s e e m s a p p r o p r i a t e to periodically review and update the l i s t of m a t e r i a l r e s e a r c h p r o g r a m s that should be undertaken. Without such r e v i e w s , the independent r e s e a r c h e r s have little guidance i n selecting a r e a s w h e r e t h e i r p a r t i c u l a r talents can b e s t be applied. I t is hoped that this approach will r e s u l t i n m o r e useful design d a t a on c u r r e n t m a t e r i a l s and new d a t a on s o m e m e t a l s that o t h e r w i s e would r e m a i n unexploited.

o R a t e of Flaw Growth i n Monocoque P r e s s u r e V e s s e l s and Tubing --- Data on the r a t e of c r a c k growth i n m e t a l s a r e predominantly f o r c a s e s of uniaxial cyclic straining. T h e s e d a t a a r e inappropriate f o r the design of multiaxially loaded s t r u c t u r e . More p r o g r a m s a r e needed to obtain multiaxial information, since m o s t s t r u c t u r e s are subjected to complex straining.

F i g u r e G1 graphically depicts one a p p r o a c h to m e e t t h e s e needs. F o r example, many s t r u c t u r e s a r e subjected to initial proofing p r o g r a m s . T h e number of proof loadings (n,) should be accounted for i n the d e s i g n . In addition, the anticipated operational c y c l e s m u s t be c o n s i d e r e d . T h e i r continued effects ( a t x n o ) can then be used t o e s t a b l i s h safe design working s t r e s s e s . The m a r g i n f o r safety in t h i s c a s e is b a s e d on the p r o p e r selection of a working s t r e s s to m e e t the r e q u i r e d useful life of the s t r u c t u r e .

Fatigue Life and C r a c k Growth in Metals as a Function of Anisotropy L a r g e d i f f e r e n c e s in r e s i d u a l s t r e n g t h and c r a c k - g r o w t h r a t e s have been noted in the few observations m a d e of t h e s e c h a r a c t e r i s t i c s as c 0 Out-of - P h a s e Cyclic Loading Many s t r u c t u r e s a r e subjected to a v a r i e t y of cycric loading p a t t e r n s f r o m v a r i o u s load s o u r c e s . The straining d i r e c t i o n s within the v a r i o u s loading s o u r c e s a r e seldom about the s a m e s t r e s s axes.

The accumulation of d a m a g e during cyclic straining consequently would b e different f o r e a c h loading s o u r c e T h i s accumulation probably h a s an appreciable effect on the r e s u l t a n t fatigue life of a s t r u c t u r e . Although t h e s e a r e r e a l i s t i c conditions f o r cyclically loaded s t r u c t u r e , no investigations yet have been attempted.

Fracture C h a r a c t e r i s t i c s under Hypervelocity Impact Knowledge of the effect of f l a w s g e n e r a t e d by hypervelocity i m p a c t and penetration on b r i t t l e m a t e r i a l s is r e q u i r e d f o r establishing It h a s not been d e m o n s t r a t e d that n o r m a l r e l a t e d design data.

f r a c t u r e - m e c h a n i c s t h e o r i e s will apply to the instantaneous stress s t a t e at a flaw produced in this m a n n e r .

F l a w s g e n e r a t e d by m e t e o r o i d i m p a c t o r penetration c a n b e nucleii f o r fatigue c r a c k growth. This subject a l s o r e q u i r e s investigation.

( F i g u r e E4 - G 2 ) , which f o r v a r i o u s r e a s o n s is a promising candi- d a t e f o r both internally p r e s s u r i z e d s p a c e cabins and externally p r e s s u r i z e d s u b m e r s i b l e s t r u c t u r e s .

0 Safe-Life and C r a c k - F r e e Design Although t h e philosophy of safe -life design h a s not proved too successful in a i r c r a f t , t h e r e m a y be s o m e space -vehicle s t r u c t u r e f o r which i t i s appropriate. Design r e q u i r e m e n t s for i n c r e a s e d safety of s t r u c t u r e s that have no tolerance f o r c r a c k s ( c r a c k - f r e e s t r u c t u r e ) will probably demand minimally s t r e s s e d , g r e a t e r weight components in s o m e a r e a s . P r o g r a m s a r e needed to define t h r e s h - old levels of working s t r e s s where no c r a c k s a r e generated through- out the useful life of the s t r u c t u r e .

Scale Effects and Effect of C u r v a t u r e -____- Most e x p e r i m e n t s have been conducted on relatively s m a l l , flat t e s t panels. No adequate scaling laws exist for the prediction of behavior of l a r g e vehicles f r o m the t e s t r e s u l t s of s m a l l e r sections. S i m i l a r l y , the complex s t r e s s s t a t e s caused when curved panels a r e loaded a r e not adequately accounted for in a n a l y s i s , More investigations a r e r e q u i r e d to establish scaling laws and to predict the behavior of flawed p r e s s u r e v e s s e l s ( c u r v e d p a n e l s ) .

M- 1 8 2 9 4 ~ SLIGHT DECREASE IN f T I c o W CATASTROPHIC a c

PRESSURE

v) W

VESSEL a

=I c V

STRUCTURE

a

E

E REDUCTION CRACK (FLAW) SIZE Figuie G2 19. G . F . Deneff: Fatigue Prediction Study. WADD TR 61-153, May 1961.

An Engineering Evaluation of Methods f o r the P r e d i c t i o n of Fatigue Life 20.

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J. Appl. Mechanics, D e c e m b e r 193'7, p . A160.

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25. R . H. Christensen: Cumulative Damage i n Fatigue of Steel. Douglas R e p o r t STR 9656, D e c e m b e r 1944.

26. A . K . Head and F . H . Hooke: Random Noise Fatigue Testing, I n t e r - I. M. E. and A . s. M . E. , national Conference on Fatigue of Metals.

New York and London, September 1956.

27. D . L. Henry: A Theory of Fatigue Damage Accumulation in S t e e l .

T r a n s . ASME, Vol. 77, August 1955, pp. 913-918.

28. F. H. Vitovec and B. J. Lazan: Fatigue C r e e p , and Rupture P r o p e r t i e s of Heat R e s i s t a n t M a t e r i a l s . WADC TR 56-181, August 1956.

R . L. O r r ; 0. D. Sherby, and J. E. Dorn: C o r r e l a t i o n of Rupture Data 29.

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30.

C r a c k Strength and C r a c k Propagation C h a r a c t e r i s t i c s of High Strength M e t a l s , Douglas A i r c r a f t Co. ASD-TR -61 -207, J a n u a r y 1962.

31. Notch R e s i s t a n c e and F r a c t u r e Toughness C h z r a c t e r i s t i c s of High Strer.3t.h Metals. Douglas A i r c r a f t CO. ASD-TDR -63 -494, S e p t e m b e r 19 63.

32.

P. Kuhn: Notch Effects on Fatigue and Static Strength. P r e s e n t e d a t Symposium on Aeronautical Fatigue, R o m e , A p r i l 1963.

33. G e o r g e C . M a r s h a l l S. F . C . P r e l i m i n a r y Vibration, Acoustic, and Shock Specifications f o r Cornponents on Saturn IB Vehicle. IN-PXrVE - S-63 -1.

34 * G e o r g e C . M a r s h a l l S. F. C . P r e l i m i n a r y Vibration, Acoustic, and Shock Specifications f o r Cotnponents on Saturn V Vehicle. I N - P k V E - S-63-2.

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1 .

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4.

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5.

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7.

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11.

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17.

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C r a c k Propagation and C r a c k -Stopper Techniques f o r Stiffened and Unstiffened F l a t Sheet i n a Supersonic T r a n s p o r t Environment.

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~ 38, G . E. Bockrath: M a s t e r F a t i g u e C u r v e s . ASM W e s t e r n Metals Los Angeles, C a l i f o r n i a , M a r c h 1961.

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I

~ 39. J . C . McClymonds and J. K. Ganoung: Combined Analytical and E x p e r i m e n t a l Approach for De signing and Evaluating S t r u c t u r a l S y s t e m s f o r Vibration Environments. 34th Shock, Vibration, and *4s sociated E n v i r o n m e n t s , F o r t O r d , California, October 1964.

1 40. H. R. Spence and H. N . L u h r s : S t r u c t u r a l F a t i g u e under Combined Random and Swept Sinusoidal Vibration.

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