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The degree to which the flow s t r e s s of a p o l y c r y s t a l is s e n s i t i v e to g r a i n size is d i s c u s s e d in t e r m s of the d i s t r i b u t i o n of slip and d i s l o c a t i o n s t r u c t u r e that develops in the v i c i n i t y of g r a i n b o u n d a r i e s as d e f o r m a t i o n p r o c e e d s . The point of view is taken that the two p r i n c i p a l c l a s s e s of g r a i n b o u n d a r y h a r d e n i n g m o d e l s , n a m e l y , those b a s e d on d i s l o c a t i o n p i l e - u p s and those b a s e d on d i s l o c a t i o n density concepts r e s p e c t i v e l y r e p r e s e n t s p e c i a l c a s e s of a single r a t i o n a l e developed in this p a p e r . G r a i n b o u n d a r y s t r e n g t h e n i n g is i n t i m a t e l y r e l a t e d to s t r a i n h a r d e n ing which is affected by slip mode, i . e . , the n u m b e r of slip s y s t e m s and the a b i l i t y to c r o s s slip. The effects of s u b s t i t u t i o n a l solute e l e m e n t s on g r a i n b o u n d a r y s t r e n g t h e n i n g s is c o n s i d e r e d to be a c o n s e q u e n c e of t h e i r influence on slip m o d e s r a t h e r than on t h e i r i n t e r a c t i o n with d i s l o c a tion s o u r c e s . l W O p r i n c i p a l a n a l y t i c a l m o d e l s have evolved that p r o v i d e s e m i q u a n t i t a t i v e e x p l a n a t i o n s for the e x p e r i m e n t a l l y e s t a b l i s h e d r e l a t i o n s h i p s between g r a i n size and r e s i s t a n c e of a p o l y c r y s t a l to p l a s t i c d e f o r m a t i o n . In one, the " p i l e - u p " m o d e l , the e s s e n t i a l idea is that in a f a v o r a b l y o r i e n t e d g r a i n a slip band is f o r m e d which t e r m i n a t e s at a g r a i n b o u n d a r y . In o r d e r for the s h e a r d i s p l a c e m e n t a s s o c i a t e d with the i m p i n g i n g slip b a n d to be a c c o m m o d a t e d p l a s t i c a l l y in the a d j a c e n t g r a i n , the s t r e s s c o n c e n t r a t i o n at or n e a r the g r a i n b o u n d a r y m u s t be s u f f i c i e n t to nucleate slip along the t r a c e of the s h e a r zone. T h i s condition can be exp r e s s e d m o s t s i m p l y in the f o r m ~ ( 7 - 70) ~ rnTc

where 7 is the applied r e s o l v e d s h e a r s t r e s s , 70 is a b a c k s t r e s s that depends upon d i s l o c a t i o n i n t e r a c t i o n s with the l a t t i c e , solute a t o m s and f o r e s t d i s l o c a t i o n s , and 7c is the c r i t i c a l r e s o l v e d s h e a r s t r e s s n e c e s s a r y to nucleate slip in the a d j a c e n t g r a i n in the neighborhood of the b o u n d a r y . The a v e r a g e Schmid o r i e n t a t i o n fact o r " m " takes into a c c o u n t the d i f f e r e n c e s in the d i r e c tion and plane of the i m p i n g i n g band and the d i r e c t i o n s and planes of the a c c o m m o d a t i o n slip b a n d s . The i m p o r t a n c e of including a t e r m such as m was f i r s t e m p