Cracks and screw dislocation arrays in anisotropie bimaterial plates
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a r e c e n t a r t i c l e , Chou and Hirth ~ e x a m i n e d the s t r e s s d i s t r i b u t i o n in an i s o t r o p i c b i m a t e r i a l plate u n d e r u n i f o r m e x t e r n a l loadings. It was found that the i n h o m o g e n e i t y due to the d i f f e r e n c e in e l a s t i c c o n s t a n t s i n d u c e s a d d i t i o n a l s t r e s s c o m p o n e n t s n e a r the i n t e r face. The n a t u r e of the induced s t r e s s is such a s to c a u s e i n t e r f a c e f a i l u r e by s h e a r or by debonding in b i m a t e r i a l p l a t e s and c o m p o s i t e m a t e r i a l s . F u r t h e r m o r e , d i s l o c a t i o n p i l e u p s tend to induce f r a c t u r e in b i m a t e r i a l s y s t e m s when the e l a s t i c c o n s t a n t factor K = (Gz - G1)/(G2 + G~) a s s u m e s an o p t i m u m value i n t e r m e d i a t e between 0 and -1 when G~ > G2. G~ and G2 a r e s h e a r moduti of the two p h a s e s . As to p r o b l e m s c o n c e r n i n g the b e h a v i o r of a r r a y s of d i s l o c a t i o n s , Chou 2 f i r s t d i s c u s s e d t h e i r e q u i l i b r i u m d i s t r i b u t i o n in an a n i s o t r o p i c , h o m o g e n e o u s plate. The p l a n e of d i s l o c a t i o n a r r a y i s a s s u m e d to be n o r m a l to the plate s u r f a c e s . L a t e r , Chou and B a r n e t t 3 e x a m i n e d s i n g l e - e n d e d d i s l o c a t i o n p i l e u p s p e r p e n d i c u l a r to the i n t e r f a c e of an infinite b i m a t e r i a l s y s t e m . They a l s o took the m a t e r i a l a n i s o t r o p y into c o n s i d e r a t i o n . In the p r e s e n t note, we f i r s t extend the t r e a t m e n t of Chou and Hirth ~ by f u r t h e r taking into c o n s i d e r a t i o n the effects of c r y s t a l a n i s o t r o p y on s t r e s s d i s t r i b u t i o n in a b i m a t e r i a l plate under u n i f o r m loadings. T h i s s t r e s s d i s t r i b u t i o n coupled with i m a g e s t r e s s configur a t i o n d e t e r m i n e s the e q u i l i b r i u m l o c a t i o n s of s c r e w d i s l o c a t i o n s in such an a n i s o t r o p i c b i m a t e r i a l plate. Then the b e h a v i o r of d o u b l e - e n d e d d i s l o c a t i o n a r r a y s and a n t i p l a n e s h e a r c r a c k s at these l o c a t i o n s a r e e x a m i n e d . The c r a c k opening d i s p l a c e m e n t a s well a s the s t r e s s i n t e n s i f i c a t i o n at the tip of a m i c r o c r a c k are also discussed.
of c o o r d i n a t e axes is at the c e n t e r of i n t e r f a c e and the m e d i a a r e infinite in extent in the x and z d i r e c t i o n s . The e l a s t i c c o n s t a n t s a r e denoted by c~j and c~) for x > 0 and x < 0 r e s p e c t i v e l y . A s s u m i n g each phase p o s s e s s e s two orthogonal s y m m e t r y p l a n e s at z = 0 and x = 0, the e l a s t i c c o n s t a n t s of the two a d j a c e n t p h a s e s then take the form
[c~j]
TSU-WEICHOU is Assistant Professor, Department of Mechanic
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