The effect of grain size and stress upon grain-boundary sliding
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n a c c o m m o d a t i o n b y the f o r m a t i o n of t r i p l e - e d g e f o l d s , ]r < 1/3; s,6 the a t t a i n m e n t of the l i m i t i n g v a l u e of 1/3 d e p e n d s upon the r e l a t i o n s h i p of the g r a i n s i z e d to the s u b g r a i n s i z e a. In R e g i m e IIa, which o c c u r s b y diffusion c r e e p v i a the g r a i n b o u n d a r i e s , e x p e r i m ent and t h e o r y 7,8 a g r e e m 9 giving . . V = 1/2. In one s e n s e this follows d i r e c t l y f r o m the f a c t that a l l the d e f o r m a t i o n o c c u r s by diffusion and GBS linked a s mutually accommodating mechanisms. However, c a r e has to be t a k e n to define how GBS i s a s s e s s e d f r o m a p p a r e n t g r a i n d i s p l a c e m e n t s , v and o f f s e t s of m a r k e r s g e n e r a t e d by a c c r e t i o n of m a t e r i a l a t " a c c e p t o r " b o u n d a r i e s have to be e x c l u d e d f r o m the m e a s u r e m e n t s . Gifkins and Langdon es p r o p o s e d that t h o s e b o u n d a r i e s which a c t e d a s s o u r c e s of v a c a n c i e s and t h e r e f o r e r e c e i v e d a t o m s should be d e s i g n a t e d " a c c e p t o r " b o u n d a r i e s in c o n t r a d i s t i n c t i o n to " d o n o r " b o u n d a r i e s which l o s t a t o m s . T h e g e o m e t r i c a l s i t u a t i o n for a c c o m m o d a t i o n in R e g i m e IIb is e x a c t l y the s a m e a s in IIa, but in t h i s c a s e the t r a n s f e r of m a t e r i a l i s a c h i e v e d by d i s l o c a t i o n m o v e m e n t i n s t e a d of v a c a n c y - a t o m flow. In both t h e s e r e g i m e s p l a s t i c d e f o r m a t i o n is confined to a n a r r o w zone a l o n g the g r a i n b o u n d a r i e s . A s p r e v i o u s l y d i s c u s s e d 4 t h i s r e g i o n c a n b e c o n v e n i e n t l y c a l l e d the " m a n t l e " of the g r a i n , the r e m a i n i n g c e n t r a l r e g i o n b e i n g d e s i g n a t e d the " c o r e . " It h a s a l r e a d y b e e n shown 4,~ that t h e s e e q u a t i o n s , u s ing s y s t e m a t i c v a l u e s f o r the p a r a m e t e r s involved, m a t c h e x p e r i m e n t a l s t r a i n r a t e s f o r a wide v a r i e t y of m a t e r i a l s , including the p r e s e n t l e a d - t h a l l i u m a l l o y . Since t h e s e e q u a t i o n s contain t e r m s which d e r i v e f r o m the s t r a i n c o n t r i b u t e d by GBS ( r a t e c o n t r o l l e d by a p p r o p r i a t e a c c o m m o d a t i n g m e c h a n i s m s ) , it is a l s o p o s s i b l e to d e r i v e v a l u e s of eg b f r o m the e q u a t i o n s . F r o m ~gb v a l u e s the amount of s l i d i n g s = kl~b- o r k2~ can then be o b t a i n e d and c o m p a r e d with e x p e r i m e n t a l values. F o r R e g i m e s I and II, s i n c e ~ = 1/2, s = ~ w = k~v = e t d / 2 .
[8]
F o r R e g i m e HI, when d > a, eg b = (1/3) (2 f y a / d e) e w but ~w -- ~t/[ 1 + (2 Fya/d2)] so that e l i m i n a t i n g e w and s u b s t i t u t i n g
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