Transient behavior of diffusion-induced creep and creep rupture
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types of s t e a d y - s t a t e d i f f u s i o n - c o n t r o l l e d d e f o r m a t i o n p r o c e s s e s have been analyzed in the l i t e r a ture: a) diffusional c r e e p in a p o l y c r y s t a l , 1 b) grain boundary sliding by diffusional accommodation,Z and c) growth of voids in a grain boundary. 3'4 The fundamental b a s i s of these calculations is that m a t t e r is t r a n s p o r t e d f r o m one i n t e r f a c e location to another provided there e x i s t s a gradient in the n o r m a l t r a c tion between the two locations. Matter t r a n s p o r t o c c u r s v i a l a t t i c e and boundary diffusion. In the s t e a d y s t a t e , the r a t e of t r a n s p o r t of m a t t e r d e t e r m i n e s the r a t e of c r e e p , sliding o r void growth. F u r t h e r , the g e o m e t r y of the grain boundaries d e t e r m i n e s the r e l ative amounts of m a t e r i a l to be added or r e m o v e d f r o m different p a r t s of the boundary in o r d e r to achieve compatible deformation and uniform s t r a i n , l'z The s o lution to the diffusion equation p r o v i d e s the form of the n o r m a l t r a c t i o n s at the boundaries which will d r i v e the flux which leads to compatible deformation. The magnitz~de of the n o r m a l t r a c t i o n s is d e t e r m i n e d by e n forcing mechanical e q u i l i b r i u m ; this l e a d s to p r o p o r tionality between the applied s t r e s s and the r a t e of the p r o c e s s , the p r o p o r t i o n a l i t y constant being a function of the diffusion coefficients. Therefore, in the steady
state, the shape of the normal tractions is determined by the interface geometry and the diffusion eqz~ations, and their magnitude by the applied s t r e s s . We call these the "diffusional boundary t r a c t i o n s . " At the instant when s t r e s s is applied to the p o l y c r y s t a l , it r e a c t s as a homogeneous l i n e a r e l a s t i c solid. As time p r o g r e s s e s , the s h e a r s t r e s s e s at the boundaries a r e r e l a x e d by sliding which l e a d s to i n homogeneous deformation in the p o l y c r y s t a t ; since boundaries a r e usually nonplanar only a finite amount of sliding can be accommodated by the e l a s t i c d e f o r mation of the g r a i n s . 2 This is Stage I of the t r a n s i e n t . At the end of Stage I " e l a s t i c boundary t r a c t i o n s " a r e e s t a b l i s h e d , z If diffusion is now allowed, then f u r t h e r t i m e - d e p e n d e n t deformation o c c u r s . The n o r m a l boundary t r a c t i o n s eventually change f r o m the e l a s t i c configuration to the s t e a d y state diffusional c o n f i g u r a tion. This is Stage 1I of the t r a n s i e n t . The Stage I t r a n s i e n t has been the subject of a r e RISHI RAJ is Assistant Professor, Department of Mechanical Engineering, University of Colorado, B~mlder, Colo. 80302. Manuscript submitted May 16, 1974. METALLURGICAL TRANSACTIONS A
cent a n a l y t i c a l and e x p e r i m e n t a l investiga
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