8/10/2019 1986-A study of cumulative fatigue damage in titanium 6Al-4V alloy.pdf

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I n t J F a t ig u e 8 No 1 (1986) pp 23-27

A s t u d y o f c u m u l a t i v e f a t i g u e

d a m a g e in t i t a n i u m 6A I 4V a l l o y

S . J e e la n i , S. G h e b r e m e d h i n a n d M . M u s i a l

E x per im en ta l da t a w e r e ob t a ined us ing t i tan ium 6A I - 4V a l l oy unde r s tr es s r a ti os o f

- 1 , 0 and - o o . A s t udy o f c um u la t iv e f a t i gue dam age us ing M ine r ' s and K r am er's

e q u a t i o n s f o r s tre ss ra t io s o f - 1 a n d 0 f o r l o w - h i g h , l o w - h i g h m i x e d, h i g h - l o w , a n d

h ig h - l ow m ix ed s t res s s equenc es has r ev ea led c los e ag r eem en t be t w een t he theoret ica l

and ex pe r im en t a l v a lues o f f a t i g u e d a m a g e a n d f a t i g u e l i f e . K r a m e r ' s e q u a t i o n p r e d i c t s

l es s c ons e r v a t iv e a nd m or e r ea li s ti c c um u la t i v e f a t igue dam a ge t han d oes t he po pu la r l y

used Miner ' s ru le .

K e y w o r d s : f a t i g u e ; f a t i g u e d a m a g e a c c u m u l a t i o n ; f a t i g u e d a m a g e p r e d i c t i o n ; stress

s e q u e n ce ; T i - 6 A I - 4 V a l lo y

Fa i l u r e o f s t r uc t u r a l c om pon e n t s i n s e r v i c e is i nva r i a b l y due

t o f a t i gue , c r e e p a nd s t r e s s c o r r o s i on . Fa t i gue f a i l u r e i s t he

c o n s e q u e n c e o f re p e a t e d o r f l u c t u a ti n g l o a d s w h i c h m a y v a r y

o v e r a w i d e r a n g e e x e r t e d o n a p a r t o r a s y s t e m . S u c h

f a i lu r e i nva r i a b l y s t a r t s a t t he s u r f a c e i n t he f o r m o f a c r a c k

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

r u p t u r e o c c u r s . W h e n t h e s t r e s s a m p l i t u d e i s c o n s t a n t a n d

t he va r i a t i on i s c yc l i c , t he l if e o f the c om po ne n t c a n be

d e t e r m i n e d u s i n g t h e s t a n d a r d

S I N

(appl ied s t ress

vs

f a t i gue

l if e) d i a g r a m a va i l a b le i n t he l i t e ra t u r e . S uc h a de t e r m i na t i on

i s i mpos s i b l e whe n t he s t r e s s a mp l i t ude i s no t c ons t a n t

eg

b l oc k l oa d i ng ) .

M i n e r a n d P a l m g r e n I w e r e t h e f i rs t t o p r o p o s e t h e

c u m u l a t i v e f a t i g u e d a m a g e r u l e k n o w n a s M i n e r ' s r u l e f o r

t h e p r e d i c t i o n o f f a il u re o f a c o m p o n e n t s u b j e c te d t o s tr e ss e s

o f v a r y i n g a m p l i t u d e o v e r a g i v e n s e t o f c y c l ic b l o c k s . I f

0 1 , 0 -2 , 0 - 3 r e p r e s e n t t he s t r es s a mp l i t ude s a pp l i e d t o a

p a r t a n d n t, n2 , n 3 . . . r e p r e se n t t h e c o r r e s p o n d i n g n u m b e r

o f c yc l e s , M i ne r ' s r u l e ma y be s t a t e d a s :

1 /1 ?/ 2 /'13

- - N 2~ ' 3 N - - + ~ - + v : - + . . . . 1 ( 1)

w h e r e N 1 , N 2 , N 3 . . . a r e t h e n u m b e r o f c y c le s t o f a il u re

o b t a i n e d f r o m t h e

S / N

dia gra m at s t resses 0 1 , 0-2 , 0 3 '

r e s p ec t iv e l y . V a r i o u s o t h e r t h e o r ie s r s h a v e b e e n p r o p o s e d

b u t n o n e o f t h e se c a n a c c u r a t el y p r e d ic t f a t i g u e d a m a g e f o r

m o s t o f th e c o m m o n l y e n c o u n t e r e d l o a d i n g s i tu a ti o n s.

M i n e r ' s t h e o r y , w h i c h i s t h e m o s t c o m m o n l y u s e d , d o e s

n o t t a k e i n t o a c c o u n t t h e p r e v i o u s h i s t o r y o f t h e m a t e ri a l

i n mu l t i l e ve l l oa d i ng .

I t ha s be e n s ugge s t e d t ha t whe n a ma t e r i a l i s f a t i gue d ,

t h e d a m a g e i s c o n f i n e d i n t h e s u r f a c e l a y e r i n t h e f o r m

o f w o r k h a r d e n i n g . 9m 3 A s t h e n u m b e r o f c y c l e s o r t h e s tr e ss

a mp l i t ude i nc r e a s e s , t he r e i s a n i nc r e a s e i n t he s u r f a c e l a ye r

s t r e s s . As t he f a t i gue da ma ge a c c umul a t e s , t he s u r f a c e l a ye r

s t r e s s a t t a i n s a c r i t i c a l va l ue a nd a c r a c k i s f o r me d i nde pe n -

de n t o f the s t re s s a mp l i t ude , l e a d i ng t o f a t i gue f a i lu r e .

K r a m e r 9 h a s s u g g e s t e d t h a t c u m u l a t i v e f a t i g u e d a m a g e c a n

be e xp r e s s e d i n t e r ms o f t he r a t e o f i nc re a s e i n t he s u r f a c e

l a ye r s tr e s s w i t h t h e nu m be r o f c yc l e s . S i nc e t he c r i ti c a l

0 1 4 2 - 1 1 2 3 / 8 6 / 0 1 0 0 2 3 - 0 5 S 3 . 0 0

I n t J Fa t i gue J anua r y 1986

s u r f a c e s t r e s s i s c ons t a n t f o r a g i ve n ma t e r i a l , i t i s on l y

ne c e s s a r y t o de t e r m i ne t he c o n t r i bu t i on t o t he s u r f a c e s t r e ss

d u e t o f a t i g u i n g a t a g i v e n s t r e s s f o r a g i v e n n u m b e r o f

c y c le s a n d t o s u m u p s u c h c o n t r i b u t io n s . T h e r e f o r e ,

a s l D ( 2 )

wh e r e a , a n d o -s * a r e t he s u r f a c e l a ye r s t r e ss a n d c r i ti c a l

s u r f a c e l a ye r s t r e s s , r e s pe c t i ve l y , a nd D i s t he c umul a t i ve

d a m a g e . T h e f a i lu r e w il l o c c u r w h e n D e q u a ls o n e . K r a m e r

f u r t he r e x t e nde d h i s i nve s t i ga t i on 10 a nd p r o pos e d t he f a i l u r e

e q u a t i o n i n t h e f o l l o w i n g f o r m :