Statistical aspects of fatigue crack nucleation from particles
- PDF / 198,259 Bytes
- 2 Pages / 594 x 774 pts Page_size
- 63 Downloads / 204 Views
Statistical Aspects of Fatigue Crack Nucleation from Particles W . L M O R R I S AND M . R . J A M E S T h e s t a t i s t i c a l n a t u r e of f a t i g u e c r a c k n u c l e a t i o n a r i s e s f r o m a v a r i a t i o n in the t y p e and s t r u c t u r e of p o t e n t i a l n u c l e a t i o n s i t e s . R e p o r t e d h e r e is an e x p e r i m e n t a l t e s t of a m o d e l , p r o p o s e d by C h a n g e t al, of f a t i g u e c r a c k n u c l e a t i o n at p a r t i c l e s n e a r an alloy surface. Two sequential steps are identified by C h a n g : 1) f r a c t u r e of the p a r t i c l e , and 2) p r o p a g a t i o n i n t o the m a t r i x . T h e c y c l e s , N, at w h i c h c r a c k i n g e x t e n d s i n t o t h e m a t r i x is N ~
C1 D W m ( r e f f -- 70)2
+ D./W ( C2 r e f f --
7-0)2 "
selected from appropriate probability distributions. T h e D and W s i z e d i s t r i b u t i o n s a r e e x p e r i m e n t a l l y m e a s u r e d and the 7ef f d i s t r i b u t i o n i s c a l c u l a t e d a s follows. For a given grain orientation, the shear s t r e s s e s a r e c a l c u l a t e d on a l l (111) s l i p p l a n e s . T h e l a r g e s t c o m p o n e n t of e a c h of t h e s e , l y i n g b o t h in t h e (111) p l a n e and in t h e s u r f a c e , is d e f i n e d to b e 7ef f f o r t h e g r a i n . Shown in F i g . 2 is t h e p r o b a b i l i t y of o c c u r r e n c e of ~'eff f o r 20,000 r a n d o m g r a i n o r i e n t a tions. (Diffraction examination indicates the alloy has essentially a random grain orientation.) For each D, W, 7ef f c o m b i n a t i o n , N i s c a l c u l a t e d f r o m E q . [1]. A g e o m e t r i c a l p r o c e d u r e is u s e d to e s t i m a t e t h e probability that a particle overlays a grain boundary, in w h i c h c a s e N is c a l c u l a t e d f o r b o t h g r a i n s and t h e m i n i m u m N is u s e d . To i s e x p e r i m e n t a l l y found to b e ~ 0.52 ~'max, f r o m t h e s t r e s s a m p l i t u d e a t w h i c h n u c l e a t i o n f r o m p a r t i c l e s c e a s e s ; a n d Cz, C2 and m a r e a d j u s t e d to g i v e t h e b e s t fit to t h e e x p e r i m e n t a l data. T h e e x p e r i m e n t a l l y m e a s u r e d W and D v a l u e s f o r t h r e e i n c r e m e n t s in N a r e s h o w n in F i g . 3. T h e c o n -
STRESS AXIS
[11
T e r m s one and two d e s c r i b e n u c l e a t i o n s t e p s 1 and 2, r e s p e c t i v e l y . C1, C2 and To a r e m a t e r i a l p a r a m e t e r s , W i s the p a r t i c l e width, and D is the m a x i m u m s l i p d i s t a n c e ( s e e F i g . 1). T h e c o e f f i c i e n t m is r e l a t e d to t h e m a n n e r in w h i c h t h e p a r t i c l e f r a c t u r e s ; r a n g i n g f r o m m = 1 if f r a c t u r e o c c u r s s i m u l t a n e o u s l y on a c r o s s s e c t i o n of t h e p a r t i c l e , to m = 3 if i n i t i a l f r a c t u r e is at a l o c a l i z e d z o n e of w e a k n e s s i n s i d e the p a r t i c l e . T o a c
Data Loading...
