A Fatigue-Life Prediction Methodology For

8/4/2019 A Fatigue-Life Prediction Methodology For

1/7

J M E P E G ( 1 9 9 5 ) 4 : 6 1 7 - 6 2 3 9 I n t e r n a t i o n a l

A Fat igue -L ife Pred iction M ethodo logy forNo tched A lum inum -M agnes ium A l loy inG ulf Seaw ater Env i ronm entZ . K h a n , M . Y ouna s , a nd G . Zuh a i r

L o c a l - s t r a in a n d l i n e a r -e l a s ti c f r a c t u r e - m e c h a n i c s ( L E F M ) m e t h o d o l o g i e s h a v e b e e n in v e s t i g a te d f o rp r e d i c t io n o f t h e c o r r o s i o n - f a t i g u e l if e o f n o t c h e d c o m p o n e n t s o f s p e c ia l l y d e v e l o p e d A I - 2 . 5 M g a l l o y s e x -p o s e d t o A r a b i a n G u l f s e a w a t e r e n v i r o n m e n t . C o r r o s i o n - f a t i g u e c r a c k i n i t i a t io n l if e e s t i m a t e s w e r e o b -t a in e d u s i n g s t r a i n -l i f e r e l a t i o n sh i p s ; c o r r o s i o n - f a t i g u e c r a c k p r o p a g a t i o n l i fe e s t i m a t e s w e r e o b t a i n e du s i n g L E F M r e l a t i o n sh i p s . T h e t o t a l c o r r o si o n - f a t ig u e l if e w a s c o n s i d e r e d t o b e th e s u m o f t h e c r a c k i n -i t ia t i o n a nd c r a c k p r o p a g a t i o n l i v e s. E s t im a t e d c o r r o s i o n - f a t i g u e l i v e s w e r e c o m p a r e d w i t h e x p e r i m e n -t a l ly o b t a i n e d c o r r o s i o n - f a t i g u e l if e d a ta u s i n g c e n t e r - n o t c h e d s p e c i m e n s o f t h r e e t y p e s o f A I - 2 . 5 M ga l l o y s ( c o n t a i n in g d i f f e r e n t a m o u n t s o f c h r o m i u m ) e x p o s e d t o A r a b i a n G u l f s e a w a t e r e n v i r o n m e n t . T w on o t c h g e o m e t r i e s , a c i r c u l a r n o t c h ( Kt = 2 . 4 2 ) a n d a n e l l i p t i c a l n o t c h ( K t - - 4 . 2 ) , w e r e i n v e s ti g a t e d . G o o dc o r r o s i o n - f a t ig u e l if e p r e d ic t i o n s c a n b e o b ta i n e d u s i n g l o c a l - st r a i n a n d L E F M m e t h o d o l o g i e s b y d e t e r -m i n i n g t h e r e l e v a n t m a t e r i a l c o n s t a n t s v i a a f e w s i m p l e f a t ig u e t e s t s o n s m o o t h s p e c i m e n s a n d a f e wc r a c k - g r o w t h - r a t e t e s t s i n th e e n v i r o n m e n t a t th e f r e q u e n c y o f i n t e r e st .

K e y w o r d sa lum inum -m agnes ium a l loy , c rack in i t ia t ion , c rackpropaga t ion , fa tigue , l i fe p red ic t ion , seawate r

1 . I n t r o d u c t i o nD U R I N G t h e p a s t d e c a d e , c o n s i d e r a b l e e f f o r t h a s b e e n d i r e c t e da t t he d e v e l o p m e n t a n d a p p l i c a t i o n o f q u a n t i ta t i v e m e t h o d o l o -g i e s t o e s ti m a t e t h e f a t i g u e li f e o f e n g i n e e r i n g c o m p o n e n t s a n ds t r u ct u r e s e x p o s e d t o t h e c o m b i n e d s i m u l t a n e o u s a c t i o n o f c y -c l i c l o a d i n g a n d a c o r r o s i v e e n v i r o n m e n t . M o s t e n g i n e e r i n gs t r u ct u r e s a n d c o m p o n e n t s c o n t a i n n o t c h l i k e g e o m e t r i c f e a t u r e so r o t h e r n o t c h l i k e d i s c o n t i n u i t i e s ; t h e r e f o r e , t h e d e v e l o p m e n t o fq u a n t i t a t i v e p r o c e d u r e s t o e s t i m a t e t h e c o r r o s i o n - f a t i g u e l i f e o fn o t c h e d m e m b e r s h a s b e e n a p r i m a r y g o a l .

F a t i g u e l i v e s o f n o t c h e d m e m b e r s s u b j e c t e d t o c o n s t a n t - a m -p l i t u d e l o a d i n g s a r e a s s e s s e d b y a v a r i e t y o f a n a l y t i c a l m e t h o d sb a s e d o n s t r e s s - li f e , l o c a l - s t r a i n , a n d l i n e a r - e l a s t i c f ra c t u r e -m e c h a n i c s ( L E F M ) c o n c e p t s ( R e f 1 -8 ). S t r e s s - li f e c o m b i n e dw i t h a f a t i g u e - s t r e n g t h r e d u c t i o n f a c t o r a p p r o a c h f a i l s to a c -c o u n t f o r p l a s t i c b e h a v i o r a t t h e n o t c h r e g i o n a n d t o c o n s i d e rt h e p r o p a g a t i o n l i f e r e g i m e , w h i c h m a y b e o f g r e a t s i g n i f i c a n c et o t h e t o t a l f a t i g u e l i f e. T h e r e f o r e , s t r e s s - l i f e a n a l y s i s i s c o n s i d -e r e d t o b e v e r y c o n s e r v a t i v e a n d h e n c e i n a p p r o p r i a t e f o r t o t a lf a t i g u e -l i f e ev a l u a t io n o f n o t c h e d m e m b e r s ( R e f 9 ) .

T h e t o t a l f a t i g u e li f e o f a n o t c h e d m e m b e r e s s e n t i a l l y c o n -s i s t s o f t w o p o r t i o n s : a c r a c k i n i t i a t i o n l i f e p o r t i o n , c o n t r o l l e db y n o t c h p l a s t i c it y , a n d a c r a c k p r o p a g a t i o n l i f e p o r t i o n , c o n -t r o l l e d b y n o m i n a l s t r e s s a n d c r a c k l e n g t h . F a t i g u e c r a c k i n i t i a -t i o n l i f e i s c o n s i d e r e d t o b e t h e n u m b e r o f c y c l e s c o n s u m e d i nt h e n u c l e a t i o n a n d g r o w t h o f a s m a l l c r a c k t o a l e n g t h w h e r e i tb e c o m e s a d o m i n a n t f a t i g u e c r a c k . F a t i g u e c r a c k p r o p a g a t io nl i fe i s c o n s i d er e d t o b e t h e r e m a i n i n g n u m b e r o f c y c l e s r e q u i re dt o g r o w t h e i n i t i a t e d f a t i g u e c r a c k t o f i n a l f r a c t u r e . T o a c c o u n tZ . Kh an , M . Younas , and G . Zu ha i r , Depar tm ent o f Mechan ica l En-g ineer ing , K ing Fahd Univers i ty o f Pe t ro leum and M inera ls , Dhahran ,Saud i Arab ia

f o r b o t h p o r t io n s , l o c a l -s t r a i n a n d L E F M a p p r o a c h e s h a v e b e e ne x t e n s i v e l y e m p l o y e d i n f a t i g u e - l if e an a l y s i s o f n o t c h e d m e m -b e r s . F o r c r a c k i n i t i a t i o n l i f e e s t i m a t e s , l o c a l s t r a i n i s t h e m o s tw i d e l y e m p l o y e d t e c h n i q u e ; L E F M h a s f o u n d w i d e a c c e p t a n c ef o r c r a c k p r o p a g a t i o n l i f e e s t i m a t e s .

T h e p r e d i c t i o n o f f a t i g u e l i fe u n d e r t h e c o n j o i n t c o n d i t i o n so f c y c l i c l o a d i n g a n d a c o r r o si v e e n v i r o n m e n t b e c o m e s q u i t ec o m p l i c a t e d w h e n t h e n u m e r o u s m e c h a n i c a l , m e t a l l u r g i ca l ,a n d e n v i r o n m e n t a l v a r i a b l e s th a t c o n t r i b u t e to t h e c o r r o s i o n -f a t i g u e p r o c e s s ( R e f 1 0 - 1 2 ) a r e t a k e n i n t o c o n s i d e r a t i o n . H o w -e v e r , f r o m a n e n g i n e e r i n g p o i n t o f v i ew , i t i s o f t e n a s s u m e d t h a tt h e a d v e r s e e f f e c t s o f t h e e n v i r o n m e n t c a n b e i n c l u d e d i n f a -t i g u e - l i fe e s t im a t i o n p r o c e d u r e s b y d e t e r m i n i n g t h e m a t e r i a lf a t i g u e p r o p e r t i e s i n t h e e n v i r o n m e n t a n d t h e f r e q u e n c y o f i n -t e r e s t ( R e f 1 3 ).T h e p r e s e n t s t u d y i n v e s t i g a t e s t h e a p p l i c a b i l i t y o f l o c a l -s t r ai n a n d L E F M f a t i g u e -l i f e es t i m a t i o n m e t h o d o l o g i e s t o t h ec o r r o s i o n - f a t ig u e l i f e e s t i m a t i o n o f n o t ch e d m e m b e r s e x p o s e dt o A r a b i a n G u l f s e a w a t e r e n v i r o n m e n t . T h r e e m o d i f i e d A 1 -2 . 5 M g a l l o y s c o n t a i n i n g v a r i o u s a m o u n t s o f c h r o m i u m w e r es e l e c te d . T w o n o t c h e d g e o m e t r i e s - - o n e , a c i r c u l a r n o tc h w i t ha l o w s t r e s s - c o n c e n t r a t i o n f a c t o r ( K = 2 . 4 2 ), a n d t h e o t he r , a ne l l i p t i c a l n o t c h w i t h a h i g h e r f a c t o r ( K = 4 . 2 ) - - w e r e i n v e s t i -g a t e d . F a t i g u e - l if e e s t i m a t e s a r e c o m p a r e d w i t h e x p e r i m e n t a lf a t i g u e -l i f e d a ta o b t a i n e d f r o m c e n t e r - n o t c h e d s p e c i m e n s f a -t i g u e d i n a i r a s w e l l a s i n A r a b i a n G u l f s e a w a t e r e n v i r o n m e n t .

1 .1 In i t i a ti on L i f e C a lcu la t ionsF a t i g u e c r a c k i n i t i a ti o n l i fe a n a l y s i s o f n o t c h e d m e m b e r s r e -

q u i r e s a m e t h o d t o e s t i m a t e t h e l o c a l s t re s s e s a n d s t r a i n s - - - -aa n d e , r e s p e c t i v e l y - - a t t h e n o t c h r o o t . F o r t h e c u r r e n t a n a l y s i s ,t h e l o c a l s t r e s s -s t r a i n r e s p o n s e w a s e s t i m a t e d u s i n g a n o m i -n a l l y e l a s t i c v e r s i o n o f N e u b e r ' s r u l e ( R e f 1 4 ) :

(ASKt)2 = A a A e ( E q 1 )

J o u r n a l o f M a t e r i a l s E n g i n e e r i n g a n d P e r f o r m a n c e V o l u m e 4 ( 5 ) O c t o b e r 1 9 95 -- -- 61 7


2/7

A l l s y m b o l s a r e d e f i n e d i n t h e N o m e n c l a t u r e s e c t i o n a t t h e e n do f t h is p a p e r . E q u a t i o n 1 r e l a t e s t h e s t r e s s a n d s t r ai n r e s p o n s e a tt h e n o t c h t o t h e n o m i n a l s t r e s s a n d s t r a i n . T h e e q u a t i o n o f t h eh y s t e r e s i s c u r v e c a n b e r e p r e s e n t e d b y :

_ _ ( A ~ . 1 / #T = 2 g + ( E q 2 )

C o m b i n i n g E q 1 a n d 2 g i v e s :AG2 (A ~ ] l /n , (K tAS)22---E-+ AG (,2K' J - 2E ( E q 3 )

i n t e n s i t y f a c t o r r a n g e ( A K ) n e e d e d f o r f a t i g u e c r a c k p r o p a g a -t i o n l i f e c a l c u l a t i o n s i s p r o v i d e d b y P a r i s ( R e f 1 6 ):

dad--N= C ( A K ) m ( E q 6 )

w h e r e C a n d m a r e c o n s t a n t s t h a t c h a r a c t e r i z e m a t e r i a l r e s i s -t a n c e t o c r a c k p r o p a g a t i o n a n d c a n b e d e t e r m i n e d b y t h e b e s t f i tt o t h e c r a c k g r o w t h t e s t d a t a . T h e c r a c k g r o w t h l i f e , N p , c a n b ee s t i m a t e d b y i n t e g r a t i n g E q 6 a s :

a fNp = I d aC ( A K ) m

a i

( E q 7 )

T h u s , t h e v a l u e s o f A o c a n b e d e t e r m i n e d b y s o l v i n g E q 3t h r o u g h a n i t e r a t i v e t e c h n i q u e . O n c e t h e l o c a l s tr e s s a n d s t r a i nr e s p o n s e h a s b e e n d e t e r m i n e d , t h e s t r a i n - l i f e e q u a t i o n

AE o f= -E- (2Nf) b + E - (2Nf) c ( E q 4 )

c a n b e s o l v e d f o r t h e n u m b e r o f r e v e r s a l s t o i n i t i a ti o n , 2 Nf . T oa c c o u n t f o r t h e p r e s e n c e o f m e a n s t r e s s , ~0 , t h e s tr a i n - l i f e e q u a -t i o n is e x p r e s s e d a s ( R e f 1 4 ):

F o r t h e c u r r e n t a n a l y s i s , a i i s a s s u m e d e q u a l t o t h e n o t c h d i m e n -s i on p e r p e n d i c u l a r to t h e m a x i m u m n o m i n a l s t re s s . T h i s s i m p l ed e f i n i t i o n o f t h e i n i t i a l c r a c k s i z e e l i m i n a t e s t h e n e e d t o f i n d an o n a r b i t r a r y i n i t i a l c r a c k l e n g t h t h r o u g h s o p h i s t i c a t e d p r o c e -d u r e s . T h e f i n a l c r a c k s i z e , a f, i s c a l c u l a t e d f r o m t h e l i m i t i n gl o a d c a p a b i l i t y o f t he c r a c k e d m e m b e r b a s e d o n t h e y i e l ds t r e n g t h o f th e m a t e r i a l u n d e r i n v e s t i g a t i o n . M o d i f i c a t i o n s o fE q 6 a s p r o p o s e d b y F o r m a n e t a l . ( R e f 1 7 ) a r e u t i l i z e d to i n -c l u d e m e a n s t r e s s e f f e c ts :

d a C A Kmd N ( 1 - R ) K c - A K ( E q 8 )

w h e r e K c i s t h e f r a c t u r e t o u g h n e s s o f t h e m a t e r i a l s .r 7%AE (f f f - f rO) 1Gf - f rO- ~ - = ~ ( 2 N f ) b + ~ f / - - - - ~ - - | (2 Nf) cL ~ i j

( E q 5 )

1 .2 P r o p a g a t i o n L i f e C a l c u l a t i o n sN u m e r o u s f a t i g u e c r a c k p r o p a g a t i o n l a w s b a s e d o n t h e

L E F M c o n c e p t h a v e b e e n p r o p o s e d ( R e f 1 5 ). P e r ha p s t h e m o s tc o m m o n l y u s e d c o r r e l a t i o n b e t w e e n c o n s t a n t - a m p l i t u d e f a -t i g u e c r a c k g r o w t h r a t e s ( d a M N ) a n d t h e c r a c k - t i p c y c l i c s t r e s s -

2 . E x p e r i m e n t a l P r o c e d u r eT h i s i n v e s t i g a t i o n s t u d ie d t h r e e t y p e s o f m o d i f i e d A I - 2 . 5 M g

a l l o y s t h at w e r e d e v e l o p e d f o r a p p l i c a t i o n i n s e a w a t e r d e s a l i n a -t i o n p l a n t s i n S a u d i A r a b i a . T h e s e m o d i f i e d a l l o y s c o n t a i n d i f -f e r en t a m o u n t s o f c h r o m i u m , w h i c h i s a d d e d t o i m p r o v e t h ec o r r o s io n r e s i s t a nc e o f a l u m i n u m - m a g n e s i u m a l l o y s . T h e t h re ea l l o y s ( d e s i g n a t e d t y p e s I , II , a n d I I I ) c o n t a i n 0 . 0 1 , 0 . 1 , a n d 0 . 3w t % C r , r e s p e c t i v e l y ; a l l w e r e i n t h e H 3 4 t e m p e r c o n d i t i o n . T h e

T a b le 1 C h e m i c a l c o m p o s i t i o n s o f t h e m o d i f ie d a l u m i n u m - m a g n e s i u m a l l o ysAlloy Compos it ion , wt %type S i Fe Cu Mn Mg Cr Zn T i AIi 0.06 0.05


3/7

d e t a i l e d c h e m i c a l c o m p o s i t i o n s o f t h e s e a l l o y s a r e g i v e n i n T a -b l e 1 , a n d t h e i r m e c h a n i c a l p r o p e r t i e s a r e l i s t e d i n T a b l e 2 .

S m o o t h a n d c e n t e r - n o tc h e d f a t i g u e t e s t s p e c i m e n s w e r e m a -c h i n e d f r o m 2 m m t h i c k s h e e t s t o c k o f t h e t h r e e a l l o y s , w i t h th el o n g e r d i m e n s i o n s ( l o a d i n g a x i s ) a l i g n e d p a r a l l e l to t h e r o l l i n gd i r e c t i o n . T h e c e n t e r - n o t c h e d s p e c i m e n s ( 1 7 5 b y 3 8 b y 2 m m )w e r e u s e d t o o b t a i n e x p e r i m e n t a l f a t i g u e - l if e d a t a f o r c o m p a r i -s o n w i t h t h e f a t i g u e - l i f e e s t i m a t e s . T w o n o t c h g e o m e t r i e s , a c i r -c u l a r h o l e ( K = 2 . 4 2 ) a n d a n e l l i p t i c a l n o t c h ( K = 4 . 2 ), w e r ei n v e s t i g a t e d . A l l fa t i g u e t e s t s w e r e c o n d u c t e d o n a n I n s t r o n ( In -s t r o n C o r p o r a t i o n , C a n t o n , M A ) 8 5 0 1 s e r v o h y d r a u l i c t e s t s y s -t e m i n b o t h l a b o r a t o ry a i r a n d i n A r a b i a n G u l f s e a w a t e re n v i r o n m e n t . S i n u s o i d a l l o a d c y c l i n g a t a s tr e s s r a t io o f R = 0 . 1a n d a f r e q u e n c y o f 2 0 H z w a s u s e d f o r t h e t e s t s . A n a c r y l i cc h a m b e r m o u n t e d a t th e m i d s e c t i o n o f t h e s p e c i m e n w a s u s e dt o c o n t a i n t h e s a l t w a t e r d u r i n g f a t i g u e t e s t i n g u n d e r c o r r o s i v ec o n d i t io n s . A s m a l l p u m p m a i n t a i n e d w a t e r c i r c u l at i o n i n s id et h e c h a m b e r .

F u l l y r e v e r s e d s t r a i n - c o n t r o l l e d f a t i g u e t e s t i n g u t i l i z i n gs m o o t h s p e c i m e n s p r o v i d e d t h e r e q u i r e d f a ti g u e p r o p e r t i e s fo rt h e f a t i g u e c r a c k i n i t i a t i o n l i f e c a l c u l a t i o n s . T h e m a t e r i a l c o n -s t a n t s f o r fa t i g u e c r a c k p r o p a g a t i o n l i f e e s t i m a t e s w e r e o b -t a i n e d f r o m c r a c k - g r o w t h - r a t e t e s t s u s i n g c e n t e r - n o t c h e ds p e c i m e n s . T h e c r a c k l e n g th , a , w a s m e a s u r e d o p t i c a l l y u si n g aQ u e s t a r ( Q u e s t a r C o r p ., N e w H o P e , P A ) Q M - 1 0 0 TM l o n g - d i s -t a n c e t r a v e l i n g m i c r o s c o p e e q u i p p e d w i t h a d i g i t a l - r e a d o u tc r a c k - m e a s u r e m e n t s y s t e m . T h i s s y s t e m e n a b l e d c r a c k m e a s -u r e m e n t s w i t h a n a c c u r a c y o f 0. 01 l a m .

3 . R e s u l t s a n d D i s c u s s i o n

3 .1 Fatigue and Corrosion-Fat igue StudiesF a t i g u e a n d c o r r o s i g n - f a t i g u e t e s t r e s u l t s i n a i r a n d i n A r a -

b i a n G u l f s e a w a t e r e n v i r o n m e n t f o r a l l o y t y p e s I , I I , a n d I I I a res h o w n i n F i g . 1 t o 4, w h e r e t h e b e s t l o g - l o g f i t li n e s h a v e b e e n

# _

CO=EE

1 0 2

1 0 11 0 3

F i g . 1

1 0 4 1 0 5 1 0 6C y c l e s t o fa i l u r e , N f

Fat igue- l i fe da ta fo r c i rcu la r no tched spec im ens in a i r

1 0 7

# _

CO=E._E

1 0 2

1 0 ~ 1 0 3

F i g . 3

1 0 4 1 0 5 1 0 8 1 0 7C y c l e s t o fa i l u r e , N f

Fat igue- l i fe da ta fo r e l l ip t ica l ly no tched spe c im ens in a i r

COE

1 0 2

1 0 1

y A 1 - 2 . 5 M g A l lo y, C i r c u l a r n o t c t l , ( k = 2 . 4 2 )I R = 0 . 1 f = 2 0 H z

! ,

I : : I i: j: ! i i [ :

1 0 3 1 0 4 1 0 5 1 0 6 1 0 7C y c l e s t o f a i l u r e , N f

Fig . 2 Effec t o f cor ros ive env i ronm ent on fa t igue l i fe o f c i rcu-la r no tched spec im ens

1 0 8

o , _ _

1 0 11 0 3 1 0 4 1 0 5 1 0 6 1 0 7 1 0 8

C y c l e s t o f a i l u r e , N f

Fig . 4 Effec t o f cor ros ive env i ronm ent on fa t igue l i fe o f e l l ip t i -ca l ly no tched spec im en s

J o u r n a l o f M a t e r i a l s E n g i n e e r i n g a n d P e r f o r m a n c e V o l u m e 4 ( 5 ) O c t o b e r 1 9 9 5 -- - 61 9


4/7

d r a w n t h r o u g h t h e d a t a p o i n t s . T h e f a t i g u e t e s t d a t a f o r a l l th r e et y p e s o f a l l o y s ( F i g . 1 ) s u g g e s t t h a t t h e i n c r e a s e i n c h r o m i u m c o n -t e n t h a s n o n o t i c e a b l e e f f e c t o n t h e f a t i g u e s t r e n g t h o f A 1 - 2 . 5 M g a l -l o y t e s t e d i n l a b o r a t o r y a i r . H o w e v e r , c h r o m i u m c o n t e n t h a s as i g n i f i c a n t i n f l u e n c e o n t h e c o r r o s i o n - f a t i g u e s t r e n g t h o f a l l t h r e et y p e s o f a l l o y s i n A r a b i a n G u l f s e a w a t e r e n v i r o n m e n t .

A s s h o w n i n F i g . 2 , t h e s e a w a t e r e n v i r o n m e n t r e d u c e s t h ec o r r o s i o n - f a t i g u e s t r e n g t h a t 1 06 c y c l e s b y a b o u t 3 4 % f o r a l l o yt y p e I, w h i c h c o n t a i n s 0 .0 1 w t % C r . A n i n c r e a s e i n th e c h r o -

1 0 7

1 0 6

O 1 0 5_,oCO

1 0 4

1 0 31 0 3 1 0 4 1 0 5 1 0 6

C y c l e s t o fa i lu r e ( O b s e r v e d )Fig . 5 P red ic ted versus exper im enta l fa t igue l i fe in a i r fo r c i r -cu la r no tched spec im e ns

1 0 7

1 0 7

m i u m c o n t e n t t o 0 .1 w t % C r ( t y p e I I ) r e s u l ts i n a s i g n i f i c a n t i m -p r o v e m e n t i n t h e c o r r o s i o n - f a t i g u e s t r e n g t h o f A 1 - 2 . 5 M g a l l o y .F o r t y p e I I t h e c o r r o s i o n f a t i g u e s t r e n g t h a t 1 0 6 c y c l e s i s l o w -e r e d b y o n l y a b o u t 2 5 % , c o m p a r e d t o a l m o s t 3 5 % f o r t y p e I. A ni n c r e a s e t o 0 .3 w t % C r , h o w e v e r , r e s u l t s i n a s e v e r e d e g r a d a t i o no f c o r r o s i o n - f a t i g u e s t r e n g t h ( F i g . 2 ). T h e c o r r o s i o n - f a t i g u es t r e n g t h ( a t 1 0 6 c y c l e s ) f o r t y p e I I I , c o n t a i n i n g 0 . 3 w t % C r , isr e d u c e d b y a l m o s t 3 8 % i n t h e s e a w a t e r e n v i r o n m e n t , w h i c h i se v e n l o w e r t h a n t h a t o f t y p e I ,

oJo

CO

1 0 7 - - i - - ! , I . . . . . . . . = = = = i ! = ., i, i ; ; ' = = = = ,i = j i , , i

~ ' A 1 - 2 .5 M g a l l o y ! I I I l l l L " I / 1 ~ "i I C i r c u l a r n o t c h ( k = 2 . 4 2 ) i I I I t ; l l ] , ~ ~ /1 0 ~ R = 0 . 1 f = 2 0 H z ' i I ~ F / l Y " , " I ]E n v i ro n m e n t : S e a w a t e r - : ! ~ ! ~ / ~ . . Jr ' i /

' 1 [ I ' i : i " I ,~ ,'~ I t ; ! /i i " i li I I A C r I I 'i l l ~ o ~ i i i i

1 ~ - I~ i I ~ II ! I i I i Ii i ] , " ~ ! i l l! ! i !; I ! : : ' / " 1 1 : : ] (A l l o y y p e I I ~,0,_ Jr r t!

I i I i i i :~ o ~ i l i l I i i l i

1 0 3 1 0 4 1 0 5 1 0 6C y c l e s t o f a i lu r e ( O b s e r v e d )

F i g . '7 P r e d i c t e d v e r s u s e x p e r i m e n t a l f a t ig u e l i f e i n A r a b i a nGulf seaw ate r fo r c i rcu la r no tched type l I spe c im ens1 0 7

I I i 1! !

i

i t [

1 0 7

CO

1 0 8

1 0 5

1 0 4

1 0 31 0 3 1 0 4 1 0 5 1 0 6

C y c l e s t o f a i lu r e ( O b s e r v e d )Fig . 6 P red ic ted versus exper im enta l fa t igue l i fe in Arab ianGulf seawate r fo r c i rcu la r no tched type 1 specim ens

.9oCO

1 0 7

1 0 6 - - ~

10

1 0

1 0 3 / ~ " I I 1 [ 1 1 i I I I H I = , ' l l ' ' ' '1 0 3 1 0 4 1 0 5 1 0 6

C y c l e s t o f a i l u r e ( O b s e r v e d )F i g . 8 P r e d i c t e d v e r s u s e x p e r i m e n t a l f a t ig u e l i f e i n A r a b i a nGul f seawate r fo r c i rcu la r no tched type I11 spec im e ns

1 0 7

6 2 0 m V o l u m e 4 ( 5 ) O c t o b e r 1 99 5 J o u r n al o f M a t e r i a l s E n g i n e e r i n g a n d P e r f o r m a n c e


5/7

T h i s d e g r a d a t i o n i n c o r r o s i o n - f a t i g u e s t r e n g t h u p o n i n -c r e a s i n g t h e c h r o m i u m c o n t e n t t o 0 . 3 w t % i s c o n s i s t e n t w i t h t h er e s u l ts o f a n e a r l i e r s t ud y o n t h e c o r r o s i o n b e h a v i o r o f m o d i f i e dA I - 2 . 5 M g a l l o y s ( R e f 1 8 ) . T h i s s t u d y s h o w s a c o n s i d e r a b l yh i g h e r c o r r o s i o n r a t e ( 1 4 . 9 8 m p y ) f o r t y p e I I I t h a n f o r a l l o y I I( 5 . 1 8 m p y ) . T h i s o b s e r v a t i o n , h o w e v e r , i s i n c o n s i s t e n t w i th t h er e p o r t e d b e n e f i c i a l e f f e c t o f 0 . 3 w t % C r o n t h e c o r r o s i o n r e s i s -t a n c e o f A I - 2 . 5 M g a l l o y s h a v i n g t e m p e r c o n d i t i o n s o t h e r t h anH 3 4 ( R e f 1 9 ) . I t s e e m s r e a s o n a b l e t o a s s u m e t h a t p e r h a p s t h e

-_o"ID

0

1 0 7

1 06

1 0 5

1 04

1 0 310 3 10 4 10 5 10 6

C y c l e s t o f a il u r e ( O b s e r v e d )Fig . 9 P red ic ted versus exper im enta l fa t igue l i fe in a i r fo r e l l ip -t ica l ly no tched type I and 11 spec im e ns

10 7

o

0

1 0 7

1 06 i '

10 3 ~ ! i I , "1 03 10 4 10 5 10 6 10 7

C y c l e s t o f a i lu r e ( O b s e r v e d )Fig . 10 Pred ic ted versus exper im enta l fa t igue l i fe in Arab ianGu lf seawate r fo r e l l ip t ica l ly no tched type I I spec im ens

H 3 4 t e m p e r t r e a t m e n t p r o d u c e s a w e a k e r p r o t e c t i v e o x i d e f i l mi n t h e a l l o y c o n t a i n i n g 0 . 3 w t % C r t h a n i n t h e a l l o y c o n t a i n i n g0 .1 w t % C r . T h i s w e a k e n i n g o f t h e o x i d e f i l m c o u l d h a v e r e -s u l te d f r o m t h e p o s s i b l e f o r m a t i o n o f m u c h c o a r s e r s e c o n d -p h a s e p a r t i c l e s a t a h i g h e r c h r o m i u m c o n c e n t r a t i o n a n d t h ep o s s i b l e s e g r e g a t i o n o f s e c o n d - p h a s e p a r t i c l e s t o t h e g r a i nb o u n d a r i e s .

F i g u r e 2 a ls o s h o w s t h a t f o r c i r c u l a r n o t c h e d s p e c i m e n s t h ec o r r o s i v e e n v i r o n m e n t h a s a m o r e p r o n o u n c e d e f f e ct i n th eh i g h - c y c l e ( i n i t i a t i o n - d o m i n a n t ) r e g i o n t h a n in t h e l o w - c y c l e( p r o p a g a t i o n - d o m i n a n t ) r e g i o n f o r a l l t hr e e t y p e s o f a l l o y s . Int h e c a s e o f e l l i p t i c a l l y n o t c h e d s p e c i m e n s , f a t i g u e i n a i r e n v i -r o n m e n t a g a i n s h o w s n o n o t i c e a b l e i n f l u e n c e o f c h r o m i u mc o n t e n t ( F i g . 3 ). T h e e f f e c t s o f t h e s e a w a t e r e n v i r o n m e n t o n t h ec o r r o s i o n - f a t i g u e s t r e n g t h f o r e l l i p t i c a l l y n o t c h e d t y p e I I a n dI I I s p e c i m e n s a r e p r e s e n t e d i n F i g . 4 . T h e r e d u c t i o n i n c o r r o -s i o n - f a t i g u e s t r e n g t h f o r e l l i p t i c a l l y n o t c h e d s p e c i m e n s i s s i m i -l a r t o t h a t o b s e r v e d f o r t h e c e n t e r - n o t c h e d s p e c i m e n s .H o w e v e r , i n t h e l o n g - l i f e r e g i o n t h e s e v e r i t y o f t h e d e g r a d i n ge f f e c t o f 0 . 3 w t % C r f o r e l l i p t ic a l l y n o t c h e d s p e c i m e n s e e m sn o t i c e a b l y r e d u c e d . C o r r o s i o n - f a t i g u e s t re n g t h ( a t 1 06 c y c l e s )f o r e l l i p t i c a l l y n o t c h e d s p e c i m e n s f o r t y p e I I I ( c o n t a i n i n g 0 . 3w t % C r ) i s r e d u c e d b y o n l y a b o u t 3 0% , c o m p a r e d t o 3 8 % f o rt h e c e n t e r - n o t c h e d s p e c i m e n s . B a s e d o n t h i s o b s e r v a t i o n , i ts e e m s r e a s o n a b l e t o s u g g e s t th a t t h e c o r ro s i v e e n v i r o n m e n t h a sa m o r e p r o n o u n c e d e f f e c t i n s i tu a t i o n s w h e r e a l a r g e r p e r c e n t -a g e o f f a t i g u e l i f e is s p e n t i n c r a c k i n i t i a t i o n , a s e x p e c t e d i n t h ec e n t e r ( b l u n t l y ) n o t c h e d s p e c i m e n s , t h a n i n s i t u a t i o n s w h e r e f a -t i g u e l i f e is c o n t r o l l e d b y c r a c k p r o p a g a t i o n , a s e x p e c t e d i n e l -l i p t i c a l ly ( s h a r p l y ) n o t c h e d s p e c i m e n s .

3 . 2 Corrosion-Fatigue Life PredictionsC o m p a r i s o n s o f e s t i m a t e d f a t i g u e l iv e s a n d e x p e r i m e n t a l l y

o b s e r v e d f a t ig u e l i v e s f o r c i r c u l a r n o tc h e d s p e c i m e n s o f a l l o y

o

0

1 0 7

1 0 6

10 5

1 0 4

1 0 310 3 10 4 1 05 1 06

C y c l e s t o f a il u r e ( O b s e r v e d )Fig . 11 Pred ic ted versus exper im enta l fa t igue l i fe in Arab ianGulf seawate r fo r e l l ip t ica l ly no tched type I I1 spec im ens

10 7

J o u r n a l o f M a t e r i a l s E n g i n e e r i n g a n d P e r f o r m a n c e V o l u m e 4 ( 5 ) O c t o b e r 1 9 9 5- -- 6 21


6/7

(a ) (b )Fig. 12 Scann ing electron fracto graph s showing fatigue striations. (a) Air environment. (b) Arabian Gu lf seawater env ironm ent

NOMENCLATUREaa i , a fbCCda/dNEAKK'Ktn'

c rack l eng th (mm)init ial and final (respectively) crack length( m m )fat igue s t rength exponentfat igue duct i l i ty exponentPar is crack growth coeff ic ientfat igue crack growth rate (mm/cycle)mod ulus of e las tic i ty (MPa)stress-inten sity facto r rang e (MPa~m-m)cycl ic s t rength coe ff ic ient (MPa)theoret ical s t ress-concent rat ion factorcyc l i c s t reng t h expon en t

Nf2NfN t, N i, NpRASAeAOO0OyOf

numb er of cycles to fa i lurenum ber of reversals to fa i lureTotal , ini t ia t ion, and propagat ion ( respec-tively) l ife estimatesstress ra tio (Omin/Omax)nominal s t ress range (MPa)total strain amplitudefat igue duct i l ity coeff ic ien tlocal s tress range (M Pa)mean s t ress (MPa)0.2% offset yield s t rength (MPa)fat igue s t rength co eff ic ient (MPa)

types I, I I , and I I I in both ai r and A rabian Gulf seawater envi -ronment are shown in F ig. 5 to 8. Data points fa l l ing wi thin thefactor-of- two l ine on ei ther s ide o f the 45 ~ diagonal are consid-ered to represent excel lent predict ions . As F ig. 5 indicates , rea-sonably goo d fat igue- l i fe es timates are obtained for the case ofci rcular notched specimens in laboratory ai r envi ronment foral l three types of modif ied A1-2.5Mg al loy. Excel lent corro-s ion-fat igue l i fe es t imates have also been obtained for a l l c i rcu-l ar no t ched spec i mens i n Arab i an Gul f s eawate r env i ronment(Fig. 6 to 8). All the points are o bse rved to lie within the factor-of- two band for a l loy types I and I I . For type I I I , most of thepoints l ie within the band.

S imi lar compar iso ns for e l lipt icai ly notche d specimens areshown in F ig. 9 to 11. Reaso nably go od fat igue- l ife predict ionsare obtained for laboratory ai r envi ronm ent . Al tho ugh m ost ofthe points are observed to be lying outs ide the factor-of- twoband, the predict ions are on the conserv at ive (safe) s ide wi thinthe factor-of- three l ine and can s t il l be considered to be good .Al l the corros ion-fat igue l i fe predict ions for e l l ipt ical lynotched type I I specimens in Arabian Gulf seawater are foundon the conservat ive s ide wi thin a factor-of- fo ur line (F ig. 10) .Excel lent corros ion-fat igu e l i fe predict ions are obtained for e l -

l iptical ly notc hed type I I I specimen s in the seawater en vi ron-ment (Fig. 11).

Detai led f racture surface analysis wi l l be presented in a sub-sequent paper . For the present , the two f ractog raphs in F ig. 12show the fat igue s t r ia t ions in a i r and seawater envi ronments .F igure 12(b) c lear ly demonst rates the corros ive at tack ofseawater in the fa t igue crack gro wth region.

4. Conclusions

The fat igue res is tance of a modif ied A1-2.5Mg al loy con-taining chro mium is reduced in the presence o f Arabian Gulfseawat e r env ironment . I nc r eas i ng t he chromi um con t en t f rom0.01 to 0.1 wt% significantly increases the fatigue strength ofthe al loy. A fur ther increase in the chrom ium content to 0.3 wt%severely degrades fa t igue res is tance.

Fat igue- l i fe predict ion methodology based on local -s t ra inand LEFM concepts provides excel lent corros ion-fat igue l i fees t ima t es fo r no t ched member s o f AI -2 .5M g a l l oys exposed t oArab i an G ul f s eawat er env i ronment .

622-- Volu me 4(5) October 1995 Journal of Materia ls Engineer ing and Performance


7/7

The effect of corrosive envi ronm ent n the corrosion-fatiguelife estimates can be included by determinin g the relevant ma-terial properties in the en viro nmen t at the freque ncy of interest.Acknowledgment

This investigation was con ducted in the A dvanced Materi-als Science Research Laboratory of the Mechanica l Engineer-ing Department at King Fahd University of Petroleum andMinerals (KFUPM), Dhahran, Saudi Arabia. The authors wishto thank K FUPM for supporting this research.References1. J. Morrow and D.F. Socie, in Materials, Experimentation andDe-sign in Fatigue, F. Sherratt and J.B. Sturgeon, Ed., WestburyHouse, Warwick, England, 1981, p 32. T.H. Topper, R.M. Wetzel, and J. Morrow, J. Mater., Vol 4 (No. 1 ,1969, p 2003. N.E. Dowling, in Fracture Mechanics, STP 677, C.W. Smith,Ed., ASTM, 1979, p 2474. D.W. Hoeppner and W.E. Krupp, Eng. Fract. Mech., Vol 6, 1974,p 47-705. R.A. Smith, Fatigue Crack Growth: 30 Years of Progress, Per-gamon Press, 19866. D.F. Socie, N.E. Dowling, and P. Kurath, in 15th Natl. Symp.Fracture Mechanics, STP 833, R.J. Sanford, Ed., ASTM, 1984, p284-299

7. P. Heuler and Z. Schultz, Assessment of Concepts for FatigueCrack Initi ation and Propagation Life Predic tion, Z. Werkstoff-tech., Vol 17, 1986, p 397-4568. A. Bush, Verification of Fatigue Crack Ini tiation Life PredictionResults, Tech. Israel Inst. Technol., TAE No. 400, 19809. N.E. Dowling, "A Review of Fatigue Life Prediction Methods,"TPS 871966, Society of Automotive Engineers, 1987

10. O. Devereux, A.J. McEvily, and R.W. Staehle, Ed., ConferenceProceedings, "Corrosion Fatigue: Chemistry, Mechanics and Mi-crostructure", National Association of Corrosion Engineers,197211. T.S. Sudarshan, T.S. Srivatsan, and D.P. Harvey, Eng. Fract.Mech., Vol 36 (No. 6), 1990, p 827-85212. D.E Socie, J. Morrow, and W. Chen, Eng. Fract. Mech., Vol 11,1979, p 85113. P. Kurath, Z. Khan, and D.F Socie, J. Pressure Vessel Technol.Vol109, Feb 1987, p 131-14114. H. Neuber, J. Appl. Mech. (Trans. ASME), Vol 28, 1961, p 54415. S.S. Manson and G.R. Halford, NASA Technical Memorandum81517, NASA Lewis Research Center, 1980, p 4916. P.C. Paris, The Fracture Mechanics Approach to Fatigue, Proc.lOth Sagamore Conf., Syracuse Universi ty Press, 1963, p 10717. R.G. Forman, V.E. Keary, and R.M. Engal, Basic Eng. (Trans.ASME), Vol 89, Sept 1967, p 45918. Z. Khan, Z. Ahmad, and B.J. Aleem, Werkst. Korros., submitted

for publication19. Z. Ahmad, Corrosion and Corrosion Inhibitionof A1-3Mg Alloysin Sea Water,Arab. J. Sci. Eng., Vol 6 (No. 3), 1981, p 21

Journa l of Materials Engi nee ring and Performance Volume 4(5) Octob er 1995------623

A Fatigue-Life Prediction Methodology For

Documents

Transcript of A Fatigue-Life Prediction Methodology For