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b a s i c a i m of m e c h a n i c a l m e t a l l u r g y i s to r e l a t e the b e h a v i o r of p o l y c r y s t a l l i n e a g g r e g a t e s to s i n g l e c r y s t a l d a t a such a s 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 (CRSS). I n v e s t i g a t i o n s of t h i s s o r t a r e v a l u able not only to d e s c r i b e the y i e l d i n g and p l a s t i c flow of i s o t r o p i c and a n i s o t r o p i c ( t e x t u r e d ) p o l y c r y s t a l l i n e a g g r e g a t e s but a l s o to study the d e f o r m a t i o n t e x t u r e s r e s u l t i n g f r o m g r a i n r o t a t i o n s which a c company crystallographic shear. 1 S e v e r a l a p p r o a c h e s which r e l a t e s i n g l e c r y s t a l to p o l y c r y s t a l l i n e b e h a v i o r have b e e n s u g g e s t e d in the p a s t . A m o n g t h e s e i s the i s o s t r e s s o r l o w e r bound t e c h n i q u e f i r s t e m p l o y e d by S a c h s 2 to r e l a t e the CRSS of fcc m e t a l s to the p o l y c r y s t a l l i n e y i e l d s t r e s s . T h e l o w e r bound p o l y c r y s t a l l i n e y i e l d s t r e s s w a s found by a v e r a g i n g the v a l u e s of u n i a x i a l s t r e s s n e c e s s a r y to r e a c h the CRSS ( u s u a l l y on a s i n g l e s y s t e m ) in fcc s i n g l e c r y s t a l s of s e l e c t e d o r i e n t a t i o n s . Such an a p p r o a c h f o l l o w s d i r e c t l y f r o m a k n o w l e d g e of the CRSS, the i d e n t i t y of the s l i p s y s t e m s , and the o r i e n t a t i o n of the s i n g l e c r y s t a l s c h o s e n to r e p r e s e n t the p o l y c r y s t a l l i n e a g g r e g a t e . It should be p o i n t e d out that the nature of e a c h g r a i n i s a s s u m e d to be s u b j e c t e d to only a u n i a x i a l n o r m a l s t r e s s ; h o w e v e r , the magnitude of that s t r e s s r e q u i r e d to i n i t i a t e s l i p w i l l v a r y with o r i e n t a t i o n . Hence s t r e s s continuity i s s a t i s f i e d only in an a v e r a g e s e n s e while no p r o v i s i o n i s m a d e f o r e n s u r i n g s t r a i n continuity. On the o t h e r hand, i s o t r a i n m o d e l s o r u p p e r bound t e c h n i q u e s e n s u r e g r a i n by g r a i n s t r a i n continuity but m a k e no p r o v i s i o n f o r s t r e s s continuity. H o w e v e r , in o r d e r to e n f o r c e an a r b i t r a r y s t r a i n s t a t e on a s e l e c t e d s i n g l e c r y s t a l , it i s n e c e s s a r y to have a p r o c e d u r e f o r s e l e c t i n g a s u f f i c i e n t n u m b e r of i n d e p e n d e n t d e f o r m a t i o n s y s t e m s to a c c o m m o d a t e the given s t r a i n . Two such i s o s t r a i n p r o c e d u r e s a r e the m i n i m u m s h e a r p r o c e d u r e of T a y l o r 3 and the m a x i m u m w o r k p r o c e d u r e of Bishop and Hill. 4'5 The m a x i m u m w o r k a p p r o a c h w i l l be u s e d h e r e . In o r d e r to u s e t h i s a p p r o a c h , it i s n e c e