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NASA Technical Memorandum 86812

' t

Prediction of Service Life of Aircraft Structural Components Using the Half Cycle Method William L. KO

I E 7 - 2 3 0 0 5 (NASA-TH-66d 1;) F A E D I C l I C l GI SCEtVICE LIIP13 C € AXECBAP'I S ' I E l j C Z U E A L CCLICLEEIS C S X N G T H E EALF-CPCLE P l E l H C C (BaSA) 2 7 p A v a i l : 611s t C AC31EP A C 7 C S C L 20x Unclas

H1/39 0076752

May 1987

National Aeronautics and Space Administration

https://ntrs.nasa.gov/search.jsp?R=19870013576 2020-04-17T16:28:54+00:00Z

NASA Technical Memorandum 86812

' Prediction of Service Life of Aircraft Structural Components Using the Half-Cycle Method William L. KO Ames Research Center, Dryden Flight Research Facility, Edwards, California

1987 .

National Aeronautics and Space Administration Ames Research Center Dryden Flight Research Facility Edwards, California 93523-5000

SUMMARY

The s e r v i c e l i f e of a i rc raf t S t r u c t u r a l components undergoing random stress c y c l i n g w a s ana lyzed by t h e a p p l i c a t i o n of f r a c t u r e mechanics. The i n i t i a l c r a c k s i z e s a t t h e c r i t i ca l stress p o i n t s f o r the f a t i q u e - c r a c k growth a n a l y s i s were es t ab - l i s h e d through proof load tests. The f a t ique -c rack growth rates f o r random stress c y c l e s were c a l c u l a t e d u s i n g t h e h a l f - c y c l e method. A new e q u a t i o n w a s developed f o r c a l c u l a t i n g t h e number of remaining f l i g h t s f o r t h e s t r u c t u r a l components. The number of remaining f l i g h t s p r e d i c t e d by the new e q u a t i o n is much lower than t h a t p r e d i c t e d by t h e c o n v e n t i o n a l equa t ion .

INTRODUCTION

A i r c r a f t s t r u c t u r a l components commonly c o n t a i n f l a w s , d e f e c t s , or anomal ies of v a r i o u s shapes ; t h e s e e i ther are i n h e r e n t i n t h e basic material or are in t roduced d u r i n g t h e manufac tur ing and assembly p rocesses . A large p e r c e n t a g e of s e r v i c e c r a c k s found i n a i r c r a f t s t r u c t u r e s a r e i n i t i a t e d from c r a c k n u c l e a t i o n sites s u c h as t o o l marks, manufac tur ing defects, and s u r f a c e m i c r o i n c l u s i o n s ( ref . 1 ) . Under t h e combined i n f l u e n c e s of environment and s e r v i c e l o a d i n g , t h e s e f l aws may grow t o reach c a t a s t r o p h i c s i z e s , r e s u l t i n g i n s e r i o u s r e d u c t i o n of s e r v i c e l i f e or com- p l e t e loss of t h e a i r c r a f t . Thus, t o a g r e a t e x t e n t , t h e i n t e g r i t y of t h e a i rc raf t s t r u c t u r e i s dependent upon the s a f e and c o n t r o l l e d growth of c r a c k s as w e l l as the achievement of r e s i d u a l s t r e n g t h i n t h e i r p resence .

The o p e r a t i o n a l l i f e (service l i f e ) of a i rcraf t s t r u c t u r a l components is a f f e c t e d by t h e magnitude and cumula t ive e f f e c t s of e x t e r n a l l o a d s coupled w i t h any d e t r i m e n t a l envi ronmenta l a c t i o n . The p resence of moi s tu re , chemica ls , s u s - pended con taminan t s , and n a t u r a l l y o c c u r r i n g e l emen t s such as r a i n , d u s t , and sea- c o a s t a tmosphere can c a u s e d e t e r i o r a t i o n i n s t r u c t u r a l s t r e n g t h due t o premature c r a c k i n g and a c c e l e r a t i o n of s u b c r i t i c a l c r a c k growth ( r e f s . 2 and 3 ) .

A s a i r c r a f t S t r u c t u r e s beg in to age ( t h a t is, as f l i g h t h o u r s accumula t e ) , e x i s t i n g s u b c r i t i c a l c r a c k s or new cracks can grow i n some h i g h - s t r e s s p o i n t s of t h e s t r u c t u r a l components. The u s u a l approach is to i n s p e c t t h e s t r u c t u r e s peri- o d i c a l l y a t c e r t a i n i n t e r v a l s . However, even af ter i n s p e c t i o n there may be some unde tec t ed c r a c k s i n a s t r u c t u r e . To ensu re t h a t the s t r u c t u r e s t i l l h a s i n t e g r i t y f o r f u t u r e f l i g h t s , proof load tests are u s u a l l y conducted on t h e ground. The pur- pose of proof load tests i s to load a s t r u c t u r e t o c e r t a i n proof load c o n d i t i o n s ( s l i g h t l y lower t h a n t h e d e s i g n l i m i t load c o n d i t i o n s ) t o t es t i t s i n t e g r i t y . I f t h e r e should e x i s t unde tec t ed c r a c k s i n t h e s t r u c t u r a l component t h a t are larger

t h e proof load tests and w i l l be rep laced . Th i s process can r educe t h e chance of c a t a s t r o p h i c a c c i d e n t s d u r i n g f l i g h t . I f a l l s t r u c t u r a l components s u r v i v e t h e

(number of remain ing f l i g h t s ) f o r each c r i t i c a l s t r u c t u r a l component by u s i n g the i n i t i a l crack s i z e e s t a b l i s h e d f o r each s t r u c t u r a l component du.ring t h e proof load tests and then u s i n g t h e stress c y c l e s ( o b t a i n e d through s t r a i n gage measurements 1 f o r each s t ruc tu ra l component d u r i n g the f i r s t f l i g h t a f t e r t h e proof load tests.

. t h a n t h e c r i t i c a l c r a c k s i z e s , t h a t s t r u c t u r a l component w i l l s u r e l y f a i l d u r i n g

proof load t es t s , t h e n f r a c t u r e mechanics can b e a p p l i e d t o estimate f a t i g u e l i f e

T h i s r e p o r t d e s c r i b e s t h e a p p l i c a t i o n of f r a c t u r e mechanics and t h e h a l f - c y c l e method t o c a l c u l a t e t h e number of remain ing f l i g h t s f o r a i r c r a f t s t r u c t u r a l components.

The a u t h o r g r a t e f u l l y acknowledges c o n t r i b u t i o n s by W i l l i a m W. T o t t o n and J u l e s M. F icke o f Synerne t Corp. i n s e t t i n g up computer programs f o r f l i g h t data r e d u c t i o n s and crack growth computa t ions .

SYMBOLS

A

a

at

0 a C

P a C

C

C

E

Fll

Fa

f

i

j

KI

K I C

Kmax

2

c r a c k l o c a t i o n parameter

c r a c k l eng th of edge c r a c k , one-half t h e c r a c k l e n g t h of through- t h i c k n e s s crack, or depth of s u r f a c e crack

c r a c k s ize ( l e n g t h or d e p t h ) a f t e r t h e t t h f l i g h t

l i m i t c rack l e n g t h ( o r d e p t h ) a s s o c i a t e d w i t h t h e o p e r a t i o n a l peak l o a d

i n i t i a l f i c t i t i o u s c r a c k l e n g t h ( o r d e p t h ) e s t a b l i s h e d by t h e proof l o a d t e s t s

material c o n s t a n t i n Walker c r a c k growth r a t e e q u a t i o n

h a l f - l e n g t h of s u r f a c e c r a c k

comple te e l l i p t i c f u n c t i o n of t h e second k i n d

number of remain ing f l i g h t s a f t e r t h e llth f l i g h t

number of remain ing f l i g h t s a f t e r t h e llth f l i g h t p r e d i c t e d from the newly developed e q u a t i o n of remain ing f l i g h t s

o p e r a t i o n a l peak stress f a c t o r ( f < 1 )

i n t e g e r a s s o c i a t e d w i t h h a l f - c y c l e s , o r c r i t i ca l stress p o i n t s

i n t e g e r a s s o c i a t e d w i t h h a l f - c y c l e s

Mode I stress i n t e n s i t y f a c t o r

Mode I c r i t i c a l stress i n t e n s i t y f a c t o r

Mode I stress i n t e n s i t y f a c t o r a s s o c i a t e d w i t h Qmax, WKamax

k

11

MK

m

N

NE

n

Q

R

A K

0

P ual

U i

* ai

Umax

ami n

modulus of e l l i p t i c func t ion

i n t e g e r a s s o c i a t e d wi th f l i g h t s

f l a w m a g n i f i c a t i o n f a c t o r

walker exponent a s s o c i a t e d w i t h Kmax

number of stress c y c l e s available f o r o p e r a t i o n s

number of stress c y c l e s used d u r i n g t h e i t h f l i g h t

Walker exponent associated w i t h stress r a t i o R

s u r f a c e f l a w shape and p l a s t i c i t y f a c t o r

stress r a t i o , Umin/amax

t h i c k n e s s of p i a t e

f r o n t hook v e r t i c a l l oad

l e f t rear hook v e r t i c a l load

r i g h t rear hook v e r t i c a l load

amount of c r a c k growth dur ing t h e I t h f l i g h t

c r a c k growth increment r e s u l t i n g from one c y c l e of cons t an t - ampl i tude stress c y c l i n g under loading magnitude of AK; and Ri

remote u n i a x i a l t e n s i l e stress

u n i a x i a l t e n s i l e stress a s s o c i a t e d w i t h t h e peak o p e r a t i o n a l l oad l e v e l

proof t e n s i l e stress induced by t h e proof loads

t e n s i l e stress a t c r i t i c a l stress p o i n t i

peak v a l u e of U i induced by t h e proof l o a d s

maximum stress of t h e s t r e s s c y c l e

minimum stress of t h e s t r e s s c y c l e

3

0 t e n s i l e s t r e n g t h U

U y i e l d s t r e s s Y

u l t i m a t e shea r s t r e n g t h U T

4 a n g u l a r c o o r d i n a t e f o r s e m i e l l i p t i c a l s u r f a c e crack

THEORY

F r a c t u r e Mechanics

The t o p p a r t of f i g u r e 1 shows t h e most common t y p e s of c r a c k s : through- t h i c k n e s s crack, s u r f a c e c r a c k , and edge c r a c k . According t o f r a c t u r e mechanics, t h e stress i n t e n s i t y f a c t o r KI f o r t h e Mode I de fo rma t ion ( t e n s i o n m o d e ) a s s o c i a t e d w i t h any t y p e of c rack can be expres sed as

where A i s t h e c r a c k l o c a t i o n pa rame te r ( A = 1 f o r t h e th rough- th i ckness c r a c k , A = 1 . 1 2 f o r b o t h the s u r f a c e and t h e edge c r a c k s (see f i g . 1 ) ; MK is t h e f l a w m a g n i f i c a t i o n f a c t o r ( f o r a ve ry s h a l l o w c r a c k MK = 1 ; as t h e d e p t h of t h e c r a c k r e a c h e s t h e back s u r f a c e of t h e p l a t e , MK = 1.6 (see f i g . 1 ) ) ; 0, i s t h e remote

u n i a x i a l t e n s i l e s t r e s s ; a is one-half t h e c r a c k l e n g t h f o r t h e th rough- th i ckness c r a c k , o r the l e n g t h of t h e edge c r a c k , o r t h e d e p t h of t h e s u r f a c e c r a c k (see f i g . 1 ) ; and Q i s the s u r f a c e f l a w shape and p l a s t i c i t y f a c t o r g i v e n by

Q = [ E ( k ) ] 2 - 0.212 (;r ( 2 )

where 0 i s t h e y i e l d stress and E ( k ) t h e complete e l l i p t i c f u n c t i o n of t h e second Y k i n d , d e f i n e d as

where Q i s t h e angu la r c o o r d i n a t e f o r a s e m i e l l i p t i c a l surface c r a c k , d e f i n e d i n f i g u r e 1 , and t h e modulus k of t h e e l l i p t i c f u n c t i o n is d e f i n e d by

k = JT where c i s t h e h a l f - l e n g t h of t h e s u r f a c e c r a c k (see t o p center of f i g . 1 ) . The bottom p a r t of f i g u r e 1 shows t h e p l o t s of a / 2 c as f u n c t i o n s o f Q f o r d i f -

4

( 4 )

f e r e n t v a l u e s of oW/o p l a t e t h i c k n e s s .

and t h e P lo t of Mk as a f u n c t i o n o f a / t , where t i s t h e Y

Proof Load T e s t s

The purpose of proof load tests i s to load t h e e n t i r e a i r c r a f t s t r u c t u r e (or i t s components) t o c e r t a i n proof l o a d levels to t es t s t r u c t u r a l i n t e g r i t y and to e s t a b l i s h i n i t i a l f i c t i t i o u s c r a c k s i z e s a s s o c i a t e d w i t h c r i t i c a l s t r u c t u r a l com- p o n e n t s f o r f a t i g u e l i f e a n a l y s i s . The proof load levels are u s u a l l y s l i g h t l y lower than t h e d e s i g n l i m i t load c o n d i t i o n s associated w i t h d i f f e r e n t maneuvers. I f t h e r e e x i s t s i n a c e r t a i n s t r u c t u r a l component a p r e v i o u s l y unde tec t ed c r a c k t h a t i s l a r g e r t han t h e c r i t i c a l c r a c k s i z e a s s o c i a t e d w i t h t h e proof load, t h a t component w i l l c e r t a i n l y f a i l d u r i n g the proof load tests and w i l l be replaced. Thus, a c a t a s t r o p h i c a c c i d e n t d u r i n g f l i g h t can be avoided. I f t h e e n t i r e s t r u c - t u r e s u r v i v e s t h e proof load tests, then t h e c r i t i c a l stress p o i n t of t h e s t r u c -

t u r a l component h a s been s u b j e c t e d t o a proof t e n s i l e stress u: induced by t h e

proof loads. I f KI, d e n o t e s t h e c r i t i c a l stress i n t e n s i t y factor (or material

f r a c t u r e toughness ) of t h e s t r u c t u r a l component material, t h e maximum c r a c k l e n g t h

a, t h e s t r u c t u r a l component can c a r r y under t h e proof loads w i t h o u t f a i l u r e (or r a p i d c r a c k e x t e n s i o n ) may be c a l c u l a t e d from e q u a t i o n ( 1 ) by s e t t i n g KI = KI,,

P and OW = us. I n r e a l i t y , t h e r e may n o t be any c r a c k s t h a t deve loped d u r i n g proof

tests; however, it i s assumed t h a t a f i c t i t i o u s crack of l e n g t h ac h a s been cre- a t e d a t t h e c r i t i c a l stress p o i n t of the s t r u c t u r a l component d u r i n g t h e proof load tests. During a c t u a l o p e r a t i o n s , the s t r u c t u r a l component w i l l be s u b j e c t e d to much

lower stress l e v e l s t h a n t h e proof stress l e v e l U-.

o p e r a t i o n a l stress l e v e l ( h i g h e s t peak of t h e stress c y c l e s ) , t h e n a c c o r d i n g to

e q u a t i o n ( 1 1, t h e s t r u c t u r a l component can c a r r y a f i c t i t i o u s c r a c k of s i z e a,,

which is much larger t h a n ac. The va lue a, t h u s de t e rmined is c o n s i d e r e d to be

t h e l i m i t c r a c k s i z e toward which the i n i t i a l c r a c k a, i s a l lowed to grow after

repeated o p e r a t i o n s . The c r a c k s i z e d i f f e r e n c e , ac - a,, i s t h e n the c r a c k s i z e i n c r e a s e permitted fo r t h e s t r u c t u r a l component i n r e p e a t e d o p e r a t i o n s . The l e f t - hand p lo t i n f i g u r e 2 shows c r a c k l eng th , a , as a f u n c t i o n of normal ized stress o,/uu, where o

t h e o p e r a t i o n a l stress leve l , t h e l a r g e r t h e l i m i t c r a c k s i z e a v a i l a b l e f o r t h e s t r u c - t u r a l component. The r igh t -hand plot i n f i g u r e 2 shows c r a c k l e n g t h , a , as a f u n c t i o n o f number of c o n s t a n t stress c y c l e s N.

P

P

P If u: is d e f i n e d as t h e peak

0

P 0

P

0 P

i s t h e t e n s i l e s t r e n g t h of t h e material. It i s s e e n t h a t t h e lower U

Remaining F l i g h t s

I f t h e s t r u c t u r a l component i s cyc led under c o n s t a n t stress a m p l i t u d e ( a n ideal- i z e d case f o r t h e purpose of d i s c u s s i o n ) fo r N1 c y c l e s d u r i n g t h e f i r s t f l i g h t w i t h t h e a s s o c i a t e d c r a c k growth of Aal, then t h e number o f remain ing f l i g h t s F1 before

5

t h e l i m i t c r a c k s i z e i s reached may be estimated from t h e f o l l o w i n g c o n v e n t i o n a l e q u a t i o n (see f i g . 2 ) :

Equat ion ( 5 ) i s based on t h e assumpt ion t h a t t h e amount of c r a c k growth per f l i g h t for a l l subsequen t f l i g h t s w i l l be e q u a l t o Aal of t h e f i rs t f l i g h t . I n r e a l i t y , t h e amount of crack growth per f l i g h t w i l l s t e a d i l y i n c r e a s e w i t h t h e number of f l i g h t s accumulated, and t h e a c t u a l number of remain ing f l i g h t s w i l l be less t h a n t h e v a l u e F1 p r e d i c t e d by e q u a t i o n ( 5 ) i f t h e number of r ema in ing f l i g h t s is l a r g e ( t h a t i s , F1 > > 1 ) . As d i s c u s s e d i n t h e f o l l o w i n g s e c t i o n , f o r a r e l a t i v e l y l o w r ange of Fl, e q u a t i o n (5) may g i v e a r easonab ly a c c u r a t e p r e d i c t i o n of t h e number nf remaining flights, The amount of crack growth Aa: in equation (5) may be calcu- la ted from t h e fo l lowing Walker e q u a t i o n (refs. 4 t o 6 ) f o r f a t i g u e - c r a c k growth ra te under cons t an t - ampl i tude stress c y c l i n g s :

where C , m , and n a r e material c o n s t a n t s , and Kmax, AK, and R are r e s p e c t i v e l y maxi- mum stress i n t e n s i t y factor , stress i n t e n s i t y ampl i tude , and stress rat io , g i v e n by

where amax and O m i n a r e r e s p e c t i v e l y t h e maximum and t h e minimum stresses o f t h e c o n s t a n t - a m p l i t u d e stress c y c l e s .

I n r e a l i t y , t h e stress c y c l e s encoun te red d u r i n g o p e r a t i o n s a t t h e c r i t i - c a l stress p o i n t s of t h e s t r u c t u r a l component are n o t cons t an t - ampl i tude stress c y c l e s . To a p p l y e q u a t i o n s (6) t o ( 9 ) t o v a r i a b l e - a m p l i t u d e stress c y c l e s , d i f - f e r e n t methods must be developed . I n this report a h a l f - c y c l e method (refs. 7 to 1 0 ) i s used i n t h e c a l c u l a t i o n of t h e f a t i g u e - c r a c k growth rate for variable- a m p l i t u d e stress cycles.

d

Half-Cycle Theory

The t o p p a r t of f i g u r e 3 shows an example of random stress c y c l e s ( v a r i a b l e - a m p l i t u d e l o a d i n g h i s t o r y ) . The stress h i s t o r y c u r v e i s t h e combina t ion of a series of b o t h i n c r e a s i n g and d e c r e a s i n g load h a l f - c y c l e s of d i f f e r e n t l o a d i n g magnitude ( A K , R), as shown i n t h e l o w e r par t of f i g u r e 4. The h a l f - c y c l e t h e o r y ( o r half-wave t h e o r y ) (refs. 7 t o 1 0 ) s t a t e s t h a t t h e damage (o r c r a c k growth) caused by each h a l f - c y c l e of e i t h e r i n c r e a s i n g or d e c r e a s i n g load i s assumed to e q u a l one-half t h e damage caused by a complete c y c l e of t h e same l o a d i n g magnitude

I

6

c

(AK, R). T h i s means t h a t t h e damage caused by t h e complete c y c l e c o u l d be e q u a l l y d i v i d e d between t h e t w o phases Of i n c r e a s i n g and d e c r e a s i n g loads . s equence t h u s can be r e s o l v e d i n t o h a l f - c y c l e groups o f i n c r e a s i n g and d e c r e a s i n g l o a d s (see lower pa r t of f i g . 3 ) . Each h a l f - c y c l e ( e i t h e r i n c r e a s i n g or d e c r e a s i n g l o a d ) c a n then be c o n s i d e r e d as a ha l f - cyc le of t h e cons t an t - ampl i tude c y c l i n g s under t h e same l o a d i n g magnitude ( A K , R) and can be computed s e p a r a t e l y i n t i m e s equence t o estimate t h e cor responding damage. The h a l f - c y c l e t h e o r y t h u s p e r m i t s a c c u r a t e e v a l u a t i o n of t h e load spectrum from a r eco rded load t i m e h i s t o r y . I f aR

( 2 = 1 , 2, 3 , . . . I i s t h e f i n a l c rack l e n g t h a f te r N R ( R = 1 , 2, 3 , . . I random

stress c y c l i n g s i n t h e Rth f l i g h t , then a c c o r d i n g t o t h e h a l f - c y c l e t h e o r y , aR may be c a l c u l a t e d from

The l o a d i n g

2 N ~ 6 a i

i = l - - a R - l + c -j-= at-1 + dag

w i t h

P and al-1 = ac

2 N ~ & a i AaR = -

i = l = a & - a R-1 2

( 1 1 )

where 6 a i / 2 is t h e c r a c k growth increment induced by t h e i t h h a l f - c y c l e under t h e l o a d i n g magnitude A K i and R i ; 6 a i / 2 i s assumed t o e q u a l t h e c r a c k growth inc remen t induced by a h a l f - c y c l e of t h e cons tan t -ampl i tude stress c y c l e f a t i g u e test under t h e same l o a d i n g magnitude ( A K i , R i ) . Thus, by u s i n g e q u a t i o n s (6) to (91, 6 a i / 2 may be c a l c u l a t e d from

The c r a c k l e n q t h , a , a s s o c i a t e d w i t h AKi (see eq. ( 8 ) ) w i l l be t h e summation o f the i n i t i a l c r a c k l e n g t h and a l l the c rack growth i n c r e m e n t s created by a l l the pre- v i o u s h a l f - c y c l e s :

( i 2 ) a = a c + P i-l - 6aj 2 j =1

( 1 3 )

S i m i l a r t o t h e case of cons tan t -ampl i tude stress c y c l i n g (see eq. ( 5 1 1 , t h e number o f remain ing f l i g h t s FQ ( R = 1 , 2, 3, . . . I a f t e r t h e Rth f l i g h t o f random stress

c y c l i n g may be c a l c u l a t e d from

FR

0 ac - a R-1

0 - "11-1

ag - a R-1

( 1 4 )

7

F i g u r e 4 g r a p h i c a l l y i l l u s t r a t e s how t o e v a l u a t e t h e c r a c k growth inc remen t 6 a i / 2 a s s o c i a t e d w i t h the i t h h a l f - c y c l e of t h e random stress c y c l i n g by u s i n g t h e p l o t s o f A K ~ a s f u n c t i o n s of da/dN f o r d i f f e r e n t v a l u e s of R.

As mentioned p r e v i o u s l y , e q u a t i o n s ( 5 ) and ( 1 4 ) b o t h may g i v e r e l a t i v e l y a c c u r a t e v a l u e s € o r FQ when the number of remain ing f l i g h t s is r e l a t i v e l y low. When p r e d i c t i n g l a r g e Fg, e q u a t i o n s ( 5 ) and ( 1 4 ) must be modi f ied because AaQ increases w i t h t h e f l i g h t s accumulated.

New Equat ion f o r Remaining F l i g h t s

For t h e cast? o f cons tan t -ampl i tude stress c y c l i n g , t h e amount of c r a c k growth AaL ( 2 = 1 , 2, 3, . . .) d u r i n g t h e g t h f l i g h t ( N E c y c l i n g s ) may be o b t a i n e d by

i n t e g r a t i n g e q u a t i o n (6):

where e q u a t i o n ( 7 ) was used.

For s i m p l i c i t y , i f Urnax, R, and N remain t h e same for a l l t h e f l i g h t s , t h e n

t h e f o l l o w i n g c r a c k growth r a t e s can be e s t a b l i s h e d by u s i n g e q u a t i o n ( 1 5 ) , assuming AaR/aQ-l < < 1 :

II I

a, P + Aal + Aa2 >""=1+2(;3+...

P a,

( 1 7 )

a, P + Aal + Aa2 + Aa3 + . . + Aag-,

P a,

.

8

0 P I f t h e a v a i l a b l e crack s i z e , ac - a,, can a l l o w F1 number of remain ing f l i g h t s , t hen

F1 terms

where t h e l e f t -hand s i d e is F1, t h e number of remain ing f l i g h t s p r e d i c t e d by assuming (see eq. ( 1 4 ) for R = 1 ) . Sub- " . . . = AaFl . = Bag - - t h a t Aal = Aa2 = Aa3 = .

s t i t u t i n g e q u a t i o n s ( 1 4 ) and ( 1 6 ) t o (19) i n t o e q u a t i o n (201,

F 1 terms (F1 - I) terms A

[ l + 2 + 3 + . . . + (F1 - 11; (21 1 m ~ a l f

F1 = ( 1 + 1 + 1 + . . . + 1 ) + - - 2 P a,

o r

Equat ion (22) may be r e a r r a n g e d i n t o t h e form

S o l v i n g f o r F l ,

which g i v e s t h e r e l a t i o n s h i p between F1 and F1.

I f t h e p r e d i c t i o n o f t h e number of r ema in ing f l i g h t s i s based on t h e c r a c k

. growth AaR t h a t o c c u r r e d d u r i n g t h e t t h f l i g h t , e q u a t i o n ( 2 4 ) t a k e s the form

Equa t ions ( 2 4 ) and ( 2 5 ) b o t h app ly t o the case of cons t an t - ampl i tude stress c y c l i n g . However, t h e y may be used f o r t h e case of v a r i a b l e - a m p l i t u d e stress c y c l i n g w i t h o u t i n t r o d u c i n q s i g n i f i c a n t error. F igu re 5 shows t h e p lo t of e q u a t i o n ( 2 4 ) ( t h a t i s ,

F1 a s a f u n c t i o n of F1) f o r m = 3.6 ( Incone l 718 a l l o y ) and Aal/ac = 0.01814 f o r P

9

t h e example d e s c r i b e d i n t h e fo l lowing s e c t i o n s . a re compared i n t h e fo l lowing t a b u l a t i o n :

Some t y p i c a l v a l u e s of P1 and F~

F1: 1 10 50 100 1 5 0 2 0 0 500 1000

- F1: 1 9 33 5 3 7 0 84 1 4 7 21 8

The r a t i o F1/F1 i s 0 .53 for F1 = 100 and d e c r e a s e s t o 0 . 2 1 8 for F1 = 1000. e q u a t i o n (5 1 c e r t a i n l y o v e r p r e d i c t s t h e number of remain ing f l i g h t s , and s a f e t y f a c t o r s r a n g i n g from 2 t o 4 must be used depending on t h e r a n g e o f t h e v a l u e of F 1 .

Thus,

EXAMPLE PROBLEM

For t h i s report, t h e example problem chosen f o r t h e f a t i g u e a n a l y s i s u s i n g t h e h a l f - c y c l e method i s t h e s e v e r e f a t i g u e problem of t h e t h r e e hooks of t h e NASA B-52-008 carrier a i r c r a f t py lon used to c a r r y t h e space s h u t t l e so l id r o c k e t booster d r o p tes t v e h i c l e (SRB/DTV) shown i n f i g u r e 6. The 49,000-lb SRB/DTV w a s a t t a c h e d t o t h e pylon w i t h one f r o n t hook and t w o rear hooks (see f i g . 6). The SRB/DTV w a s carried up to h i g h a l t i t u d e and released to tes t t h e per formance of t h e s o l i d r o c k e t booster main parachute . The shapes of t h e f r o n t hook and the t w o rear hooks are shown i n f i g u r e s 7 and 8 , r e s p e c t i v e l y . The f r o n t hook is made of I n c o n e l 7 1 8 a l l o y and t h e t w o rear hooks o f AMAX MP35N a l l o y (AMAX S p e c i a l t y C o r p o r a t i o n ) . Tab le 1 shows m a t e r i a l properties o f t h e t w o a l l o y s . Because o f t h e g r e a t weight of t h e SRB/DTV, t h e t h r e e hooks had s e r i o u s f a t i g u e l i f e problems. F r a c t u r e mechanics and t h e h a l f - c y c l e method can be a p p l i e d t o p r e d i c t t h e s e r v i c e l i f e (number of remain ing f l i g h t s ) of t h e t h r e e hooks t h a t c a r r i e d t h e SRB/DTV. Refe rence 10 p r e s e n t s t h e d e t a i l e d f a t i g u e a n a l y s i s of t h e NASA B-52 a i rc raf t py lon major components.

C r i t i ca l Stress P o i n t s

Be fo re conduc t ing f a t i g u e - c r a c k growth a n a l y s i s , t h e l o c a t i o n s o f t h e c r i t i c a l s t ress p o i n t s f o r t he t h r e e hooks had to be de te rmined . T h i s w a s done by pe r fo rming NASTRAN f i n i t e - e l e m e n t stress a n a l y s i s of t h e t h r e e hooks ( r e f . 1 1 ) . The c r i t i ca l s t ress p o i n t of e a c h hook is located a t t h e i n n e r c i r c u l a r boundary of t h e hook. F i g u r e s 7 and 8 show t h e e x a c t l o c a t i o n s o f t h e c r i t i c a l stress p o i n t s o f t h e t h r e e hooks. Through t h e NASTRAN stress a n a l y s i s , t h e r e l a t i o n s h i p s between t h e stress a t t h e c r i t i c a l stress p o i n t and t h e hook l o a d s were e s t a b l i s h e d as

U1 = 7 . 3 5 2 2 x 10-3 VA f o r f r o n t hook ( 2 6 )

02 = 5 . 8 4 4 2 x 10-3 VBL f o r l e f t rear hook ( 2 7 1

0 3 = 5 . 8 4 4 2 x 10-3 VBR for r i g h t rear hook ( 2 8 )

where 01, a 2 , and a 3 a r e r e s p e c t i v e l y t h e stresses ( i n k i p s , or l o 3 l b , per s q u a r e i n c h ( k s i ) ) a t t h e c r i t i c a l stress p o i n t s of t h e f r o n t hook, l e f t rear hook, and

10

r i g h t rear hook, and V A ~ VBL, and VBR are t h e co r re spond ing hook v e r t i c a l l o a d s i n pounds. During proof load tests and du r ing f l i g h t , VA, V,,, and VBR were measured by means of s t r a i n gages i n s t a l l e d near t h e c r i t i c a l stress p o i n t s o f t h e hooks ( r e f s . 10 and 1 1 ) . Equa t ions ( 2 6 ) t o ( 2 8 ) were used t o g e n e r a t e stress c y c l e s f o r t h e f a t i g u e - c r a c k growth a n a l y s i s us ing t h e s t ra in-gage-measured v a l u e s of VA, and VBR.

VBL,

I n i t i a l and Opera t iona l Crack S i z e s

Dur ing t h e proof load tests, t h e t h r e e hooks were loaded to t h e i r r e s p e c t i v e

peak proof loads t o e s t a b l i s h t h e i n i t i a l c r a c k s i z e a, fo r each c r i t i ca l stress

p o i n t . The peak proof stresses U i (i = 1 , 2, 3 ) a t t h e c r i t i c a l stress p o i n t s

induced by t h e peak proof hook loads may be c a l c u l a t e d from e q u a t i o n s ( 2 6 ) t o ( 2 8 ) . P The proof c r a c k s i z e ac a t the c r i t i c a l p o i n t of each hook e s t a b l i s h e d by t h e proof

l o a d t es t s may be c a l c u l a t e d from e q u a t i o n ( 1 ) by s e t t i n g KI = K I ~ :

- P

* I

where A = 1 . 1 2 f o r t h e s u r f a c e c r a c k , MK = 1 (which was o b t a i n e d from t h e lower r i g h t p l o t of f i g u r e 1 for a / t << 1 because t h e d e p t h o f t h e c r a c k i s ve ry small compared w i t h t h e d e p t h o f t h e hook) , and t h e v a l u e of QI t h e s u r f a c e f low shape and p l a s t i c i t y f a c t o r , w i l l be de termined a s fo l lows .

The s u r f a c e c r a c k i s assumed to be semiel l ipt ical i n shape w i t h an aspect r a t i o of a /2c = 1 / 4 . ( T h i s v a l u e i s based on t h e o b s e r v a t i o n of s u r f a c e c r a c k s of the

f r a c t u r e d old rear hooks. 1 Taking a/2c = 1 /4 and UJuy = u i / a y = 1 (because t h e

growth of p l a s t i c zones around t h e c r i t i ca l stress p o i n t s w a s neglected, t h e v a l u e s

of a; c a l c u l a t e d f o r t h e t h r e e hooks s l i g h t l y exceeded the c o r r e s p o n d i n g y i e l d

*

stresses ay) , t h e c u r v e f o r u,/uy = 1 i n t h e lower l e f t plots of f i g u r e 1 g i v e s Q = 1 .25 .

* If t h e peak v a l u e of t h e stress cycles d u r i n g o p e r a t i o n (or f l i g h t ) i s f u i ,

where f i s t h e o p e r a t i o n a l peak stress factor ( f < 1 1 , t h e n t h e o p e r a t i o n a l l i m i t

crack s i z e ac may be c a l c u l a t e d from 0

.

* P a r t of table 2 shows t h e peak proof hook loads, t h e peak p roof stresses U i , and

t h e proof c r a c k s i z e s ac a t t h e c r i t i c a l stess p o i n t s . Note t h a t f o r a l l t h r e e

hooks, a i exceeded the f a i l u r e stresses uu of t h e hook materials (see table 11, y e t t h e t h r e e hooks d i d n o t f a i l d u r i n g the proof load tests. The r e a s o n i s t h a t equa- t i o n s (25) t o (271 , e s t a b l i s h e d by t h e NASTRAN a n a l y s i s , are f o r a p u r e l y e l a s t i c

P *

1 1

case w i t h o u t c o n s i d e r a t i o n of p l a s t i c de fo rma t ions . I n r e a l i t y t h e p las t ic zone can d e v e l o p around the c r i t i c a l stress p o i n t , and t h e r e f o r e t h e hook can a c t u a l l y c a r r y a g r e a t e r load than t h e b r i t t l e f a i l u r e load. I n t h e p r e s e n t f a t i g u e - c r a c k growth a n a l y s i s , on ly t h e e l a s t i c case i s cons ide red .

Load S p e c t r a

To perform t h e f a t igue -c rack growth a n a l y s i s , t h e l o a d spectra (stress c y c l e s ) f o r t h e t h r e e c r i t i c a l p o i n t s of t h e hooks must be o b t a i n e d f i r s t . Using t h e s t ra in-gage-measured v a l u e s of t h e t h r e e hook loads, VA, VBLI and vBR, d u r i n g t h e f i r s t tes t f l i g h t , t h e t h r e e stresses a i ( i = 1 , 2, 3 ) may be c a l c u l a t e d by u s i n g e q u a t i o n s (26) t o ( 2 8 ) . F i g u r e s 9 t o 11 (ref. 1 0 ) show p o r t i o n s o f t h e l o a d i n g h i s t o r i e s ( l o a d spectra) calculated f o r t h e c r i t i c a l stress p o i n t s of t h e t h r e e hooks d u r i n g a t a k e o f f run . Those load spectra w e r e o b t a i n e d by f i l t e r i n g t h e o r i g i n a l l o a d s p e c t r a down to 5 Hz t o e l i m i n a t e t h e sma l l - ampl i tude high- f r equency stess c y c l e s t h a t are c o n s i d e r e d un impor t an t i n t h e p r e s e n t f a t i g u e l i f e a n a l y s i s . Notice t h a t t h e load spectra f o r a l l t h r e e c r i t i ca l stress p o i n t s e x h i b i t a high d e g r e e of random c y c l i n g .

C a l c u l a t i o n s of Crack Growth

To a p p l y t h e h a l f - c y c l e method, t h e load spectra (see f i g s . 9 t o 1 1 ) were f i r s t r e s o l v e d i n t o a series of h a l f - c y c l e s of i n c r e a s i n g and d e c r e a s i n g l o a d s of d i f f e r - e n t l o a d i n g magnitude ( A K , R) (see f i g . 3). The c r a c k growth i n c r e m e n t s 6 a i / 2 per h a l f - c y c l e were c a l c u l a t e d from e q u a t i o n ( 1 2 ) i n t i m e sequence and summed ( u s i n g eq. ( 1 0 ) ) t o g i v e t h e t o t a l amount of c r a c k growth p e r f l i g h t f o r each c r i t i c a l stress p o i n t . F i n a l l y , e q u a t i o n s ( 1 4 ) and ( 2 5 ) were used t o c a l c u l a t e t h e number of remain ing f l i g h t s a s s o c i a t e d w i t h each c r i t i c a l stress p o i n t . I t must be empha- s i z e d t h a t i n u s i n g t h e h a l f - c y c l e method, e v e r y h a l f - c y c l e o f d i f f e r e n t stress ampl i tude i n t h e load spec t rum i s c a l c u l a t e d , and t h u s t h e h a l f - c y c l e method can g i v e an a c c u r a t e e v a l u a t i o n of t h e f a t i g u e - c r a c k growth as compared w i t h , s a y , t h e exceedence-count method ( f o r which some of t h e stress peaks l y i n g below t h e mean l i n e cou ld be mis sed ) .

R e s u l t s

F i g u r e s 12 t o 1 4 , t a k e n from r e f e r e n c e 10, show t h e f a t i g u e - c r a c k growth c u r v e s c a l c u l a t e d f o r t h e t h r e e c r i t i c a l stress p o i n t s f o r t h e f i r s t t es t f l i g h t ; t h e maneuver t r a n s i t i o n p o i n t s are i n d i c a t e d . Note t ha t f o r t h e t h r e e hooks, t h e f a t i g u e - c r a c k growth r a t e i s g r e a t e s t d u r i n g t h e i n i t i a l s t a g e o f t a x i i n g and t h e t a k e o f f run and becomes v e r y l o w d u r i n g c r u i s i n g because of r e l a t i v e l y l o w - ampl i tude stress c y c l i n g s . Tab le 2 l ists t h e amount of c r a c k growth Aal, opera-

t i o n a l peak stress f a c t o r f , o p e r a t i o n a l c r a c k s i z e a,, and remain ing f l i g h t s F1

and F1 c a l c u l a t e d r e s p e c t i v e l y from e q u a t i o n s ( 1 4 ) and ( 2 4 ) . F i g u r e 1 5 shows t h e

p l o t s of F1 and F1 as f u n c t i o n s of f f o r t h e t h r e e hooks. p r e d i c t i o n of remaining f l i g h t s based on F1 (eq. ( 1 4 ) ) becomes more pronounced as t h e number of remaining f l i g h t s increases. The arrows i n f i g u r e 15 i n d i c a t e t h e

0

Note t h a t t h e over -

12

a c t u a l o p e r a t i o n a l peak load l e v e l s . A t t h e s e load l e v e l s , s a f e t y f a c t o r s must be

i n t h e r ange of 2 t o 2 . 5 if F1 is used i n s t e a d of F1.

CONCLUSION

F r a c t u r e mechanics and t h e ha l f - cyc le method were a p p l i e d to t h e s e r v i c e l i f e a n a l y s i s of a i r c r a f t s t r u c t u r a l components. The i n i t i a l c r a c k s i z e s a t t h e c r i t - i c a l stress p o i n t s of t h e s t r u c t u r a l components were de te rmined by u s i n g proof l o a d tests. The random stress c y c l e f a t igue -c rack growth rates were c a l c u l a t e d u s i n g t h e h a l f - c y c l e method. A new e q u a t i o n was developed f o r c a l c u l a t i n g t h e number of remain ing f l i g h t s f o r t h e s t r u c t u r a l components. The newly developed e q u a t i o n pre- d i c t e d t h e number of remain ing f l i g h t s more a c c u r a t e l y ( a much lower number) t h a n d i d t h e c o n v e n t i o n a l e q u a t i o n (which is based on t h e assumpt ion t h a t t h e amount of c r a c k growth per f l i g h t remains c o n s t a n t ) .

u

.

13

REFERENCES

1 . Donaldson, D.R.; and Anderson, W.F.: Crack P r o p a g a t i o n Behavior o f Some A i r - f rame M a t e r i a l s . Proceedings of t h e Crack P r o p a g a t i o n Symposium, vo l . 2, C r a n f i e l d , Sept . 1961.

2. B i i t l e r , J.P. : The Material S e l e c t i o n and S t r u c t u r a l Development P r o c e s s for A i r c r a f t S t r u c t u r a l I n t e g r i t y Under F a t i g u e C o n d i t i o n s . AFFDL-TR-70-144, Conference Proceedings , A i r Force Conference , M i a m i , F l o r i d a , December 15-18, 1969.

3. A s t l e y , W. ; and S c o t t , J.: Eng inee r ing P r a c t i c e to Avoid S t r e s s Cor ros ion Cracking . (The Environment Encountered i n A i r c r a f t S e r v i c e . ) AGARD Conference Proceedings No . 53.

4. Forman, R.G.; Kearney, V.E.; and Engle , R.M.: Numerical Ana lys i s of Crack P r o p a g a t i o n i n Cycle Loaded S t r u c t u r e s . J. B a s i c Eng inee r ing , Trans . A.S.M.E. D 89, 1967, p. 459.

5. Walker, E.K.: The E f f e c t o f S t r e s s R a t i o During Crack P ropaga t ion and F a t i g u e f o r 2G24-T3 and 7075-T6 Aluminum, E f f e c t s of Environments and Complex Load H i s t o r y on F a t i g u e L i f e . ASTM-STP 462, 1970, p. 1.

6. S c h i j v e , J.: Four L e c t u r e s on F a t i g u e Crack Growth. Eng inee r ing F r a c t u r e Mechanics, vol . 11, Pergamon P r e s s , New York, 1979, pp. 167-221.

7. S t a r k e y , W.L.; and Marco, S.M.: E f f e c t s of Complex St ress -Time Cyc les on t h e F a t i g u e P r o p e r t i e s of Metals. T rans . A.S.M.E., Aug. 1957, pp. 1329-1336.

8. Inca rbone , C.: F a t i g u e Research on S p e c i f i c Design Problems. F a t i g u e o f A i r c r a f t S t r u c t u r e s , P roceed ings of t h e Symposium h e l d i n P a r i s , 16 th-19th May 1961, W. B a r r o i s and E.L. R ip ley , eds . , Pergamon P r e s s , N e w York, 1963, pp. 209-217.

9. Smith, S . H . : Fa t igue Crack Growth Under Axial N a r r o w and Broad Band Random Loading. Acoust ic F a t i g u e i n Aerospace S t r u c t u r e s , Sy racuse U n i v e r s i t y Press, 1965, p. 331.

10. KO, W i l l i a m L.; Carter, Alan L.; T o t t o n , W i l l i a m W.; and F i c k e , Ju l e s M.: A p p l i c a t i o n of F r a c t u r e Mechanics and t h e Hal€-Cycle Method to t h e P r e d i c t i o n of F a t i g u e L i f e o f B-52 A i r c r a f t Pylon Components. NASA TM-88277, 1987.

1 1 . KO, Wil l iam L.; and S c h u s t e r , Lawrence S.: S t r e s s Analyses of B-52 Pylon Hooks. NASA TM-84924, 1985.

14

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a

c

8

A

m N c

d N c

d N c Y 4 m

Y W

W

N

r . m W . r

d N m . ‘4

m

n

n 7

N I 0

X

0 N N

c

P

0;

c c I 0

X

d Q

N

c

?

c c I 0

X

P d

N

c

9

-4 u m Y W

9 A

4 4 m e” 5

m m c

c P c

m m N

0 m N

c

c d

m m N

0 In (v

A

m 0 c

Y

0 m b 0

0 . I . I .

N 3

A

m I- c

Y

!I J z U

0 t3

3

J g

u 0

4

4 5

P j

0 4

3

I- m N Y

J J O w o o c 28 0 0 uc E

0 c F . d d n

Y 0 - o n yc O Q o a Lco a d

3 X

(u b

m b

c b

JJLcx w s r o

15

Through. thickness

crack

0,

t t t t t t t t t

0,

K, = 0, JR‘

Surface crack

’ “91

t t t t o r t t t t

1

= 0.8 = 0.0\ \‘

Edge crack

O W

t t t t t t t t t

I I 1 1 1 1 1 1 1 1

OOD

K, = 1.12 ow

0 alt

Figure I. f a c t o r and f l a w magnif ica t ion f a c t o r .

Three t y p e s of cracks and the p l o t s of s u r f a c e flaw shape

3 0

0 ? g

0

c

17

I Y QD

h

t

I

N N -

X : 0

Q)

!

Q)

i

--

)r

----I----- -.

u) I

1-

--.. -I--- ----- $-

(3

I N

--I- - . - -. I

0

v)

i!

E

5

z v)

U v)

u C

al E

v % 8 %

E

It: 3-

Y

0

u Q

0 u C ‘1

8 “I

# t v)

u v)

!! E 2 E 0 ‘1 u 3 Y 0

Q 0

a 9

E g ‘1 E

1 8

I I I I I I I I I 1 I I I I I I I 1 I I 1 I I I I + I I I I I I I I I I I I I I I I I

I I I I I I I I I I I I I I I I I I I I I I I I

t

I

I I I I

I I I I I I I I I I I I

i I I I I I I I I I I I I I I I I I I I

i I I I I I I I I I I I I I I I I I I I

r- I I I I I I I I I I I I I I I 1 I I I

i I I I I I I I I I I I I I I I I

I I I

I I I I I I 1 I I

l i

-C

Ri

a

c ( A K ~ ) ~ (I - R ~ ) ~ - ~

F i g u r e 4 . u s i n g the half-cycle method.

Graphical evaluat ion of crack increments for random stress cycles

19

100

1 10

Fl

Figure 5 . Number of remaining f l i g h t s p r e d i c t e d from KO e q u a t i o n of remaining f l i g h t s .

Figure 6 . Geometry of s p a c e s h u t t l e s o l i d rocket booster d r o p test vehicle ( S R B / m Y ) a t t a c h e d to B-52 p y l o n ( v i e w l o o k i n g inboard from r i g h t s i d e ) .

or V~~

o1 = 7.3522 1 0 % ~

Figure 7 . Front hook and t h e loca- t i o n of c r i t i c a l stress point ul.

a1 = 7.3522 x 10-3vA

o2 = 5.8442 10-3 vBL 03 5.8442 x v ~ R

Figure 8 . Rear hook ( left or r i g h t ) and t h e loca t ion of c r i t i c a l stress point (02 or u3) .

125

01' ksi

100

1 Sec? 15 I I I I 1 I I I

Time

F i g u r e 9 . Stress cycles f o r critical stress point UJ a t f r o n t hook.

21

02’ 125 ksi

I 1 rec-q

100 I I I I I I I I 1 Tim

Figure 10. Stress cycles for critical stress point 42 a t left rear hook.

1 r e c y la0 I I I I I I I 1 I

Tim

Figure 11 . stress cycles for critical stress point 43 a t right rear hook.

20 10-4 Denote amas of miaslng data

I I I uu mil

Airborne Takeoff run

growth, 10 in

Rbsurnr taxi

:i 2

IOIO 10-4

1008

1006

1004

1002

Crack lo00 length,

I In ma

9% 3 994 v I I 1 I I I I I I I I I

4 a 1 2 1 t 3 2 0 2 4 2 a 3 2 ~ 4 0 4 4 4 3 5 2 [start taxi Time, min

F i g u r e 1 2 . Crack growth curve f o r stress point 1 (UJ), f l i g h t 1 .

2 2

~4 10-5 Dsnoto areas of missing data c

21 IIII a i i I I I I U .I1 I 5 8 -

48-

40-

Crack

in growth. 32 -

I 8 12 18 20 24 28 32 36 40 44 48 52

lime, mln

7404 10-5

7398

7388

7380

Crack 7372 W t h .

in

7364

7356

7348

7340

Crack growth,

In

Figure 13. Crack growth curve for stress point 2 (az), f l i g h t 1 .

7 2 .

6 4 .

Lstop tax1

Rrume taxi

24

7372

7364

7356

7348

7340

7332

7324

731 6

7308

I 1 I I I I 1 I I I 7300 0 1 4 8 1 2 1 8 2 0 2 4 2 8 3 2 3 8 4 0 4 4 4 8 5 2

Lstart taxi Tim, mln

10-5

Crack I.ngth, In

Figure 1 4 . Crack growth c u r v e for stress point 3 (cr3), f l i g h t 1 .

23

104

103

F1. Pl

102

10

S Actual opomtional

peak load lovd (denoted by )

ol: i = 0.5450

os: i = 0.5906 02: f = 0.5946

I I I I I I I .1 2 3 .4 .5 .6 .7 d

f

Figure 1 5 . Number of remaining f l i g h t s as func t ions of operational peak stress f a c t o r .

1. Report No. NASA "M-86812

I5 Supplementary Notes

2. G o v m m t Accession No. 3. Recipient's Catalog No.

!6 Abstract

4. Title and Subtitle P r e d i c t i o n of Se rv ice L i f e of Aircraft S t r u c t u r a l Components Using t h e Half-Cycle Method

7. Authorls) W i l l i a m L. KO

9. Performing Organization N a m and Address NASA Ames Research Center Dryden F l i g h t Research F a c i l i t y P.O. Box 273 Edwards, CA 93523-5000

12. Sponsoring Agency Name and Address ,

Nat iona l Aeronaut ics and Space Adminis t ra t ion Washington, DC 20546

The s e r v i c e l i f e of a i r c r a f t s t r u c t u r a l components under- go ing random stress c y c l i n g was ana lyzed by the a p p l i c a t i o n of f r a c t u r e mechanics. The i n i t i a l c r ack s i z e s a t t h e c r i t i ca l stress p o i n t s f o r the fa t ique-crack growth a n a l y s i s were estab- l i s h e d through proof load t e s t s . The f a t ique -c rack growth rates f o r random stress c y c l e s were c a l c u l a t e d us ing the ha l f - cyc le method. A new equa t ion was developed f o r c a l c u l a t i n g t h e number of remaining f l i g h t s for the s t r u c t u r a l components. me number of remaining f l i g h t s pred ic ted by the new equa t ion is much lover than t h a t p red ic t ed by t h e convent iona l equat ion .

5. R q m t Date nay 1987

6. Performing Organization code

8. Performing Organization Report No. H-1352

10. Work Unit No. RTOP 505-43-31

11. Contract or Grant No.

13. Type of Report and Paiod Covered

Techn ica l Memorandum

14. Sponsoring Awcy Code

I 7 Key Words (Suggested by AuthorW I

FatLgue l i f e F r a c t u r e Mechanics Hal f -cyc le method Random c y c l i n g Se rv ice l i f e p r e d i c t i o n

18. Distribution Statement

Unc la s s i f i ed - Unlimited

S u b j e c t ca t egory 39

20. Sacurity Classif. (of this page) 19. Security Classif (of this report)

Unc la s s i f i ed Unclass i f ied

21. No. of Pages 22. Rice'

25 A02

i

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