Edge dislocation climb over non-deformable circular inclusions
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i s w e l l known that the p r e s e n c e of a f i n e l y d i s p e r s e d , n o n - d e f o r m a b l e * s e c o n d p h a s e in a m e t a l m a *With the term non-deformablewe mean to imply inclusions which cannot deform plastically; elastic deformations of the inclusion are permitted.
t r i x r e s u l t s in s u b s t a n t i a l s t r e n g t h e n i n g . The p r e c i s e mechanisms for this strengthening are still unclear, e s p e c i a l l y at high t e m p e r a t u r e s . One a p p r o a c h to e x p l a i n i n g d i s p e r s i o n s t r e n g t h e n i n g is to c o n s i d e r the p a r t i c l e s a s b a r r i e r s to the glide m o t i o n of d i s l o c a t i o n s . In t h i s d e s c r i p t i o n , indefinite d i s l o c a t i o n m o t i o n c a n o c c u r only if the d i s l o c a t i o n s a r e c a p a b l e of b y p a s s i n g the p a r t i c l e s , e i t h e r b y c r o s s - s l i p o r b y c l i m b . F o r high t e m p e r a t u r e s t e a d y s t a t e c r e e p , the u s u a l a s s u m p t i o n is that d i s l o c a t i o n c l i m b o v e r the p a r t i c l e s is rate limiting. The t h r e e d i m e n s i o n a l p r o b l e m of a d i s l o c a t i o n m o v ingpast anon-deformable particle is admittedly comp l e x and cannot b e t r e a t e d e x a c t l y with p r e s e n t t h e o r e t i c a l m e t h o d s . Even when the d i s l o c a t i o n is confined to i t s s l i p p l a n e , the d i s l o c a t i o n - p a r t i c l e i n t e r a c t i o n can b e t r e a t e d only with e l a b o r a t e m e t h o d s . 1-~ The m a i n r e a s o n for t h i s d i f f i c u l t y i s that the d i s l o c a t i o n d o e s not r e m a i n s t r a i g h t when p r e s s e d a g a i n s t the s e c o n d p h a s e p a r t i c l e . The s i t u a t i o n would b e even m o r e c o m p l i c a t e d if one w e r e to c o n s i d e r m o t i o n of the d i s l o c a tion out of the s l i p p l a n e . A way to a v o i d s o m e of t h e s e d i f f i c u l t i e s i s to l i m i t o u r a t t e n t i o n to the t w o - d i m e n s i o n a l p r o b l e m in which the i n c l u s i o n is i m a g i n e d to b e an i n f i n i t e l y long c y l i n d e r r a t h e r than a s p h e r e . In t h i s c a s e , the d i s l o c a t i o n is a l w a y s p e r f e c t l y s t r a i g h t and p a r a l l e l to the c y l i n d r i c a l i n c l u s i o n . Although t h i s m o d e l i s u n r e a l i s t i c b e c a u s e it d o e s not e x p l i c i t l y t r e a t the c o n f i g u r a t i o n of the d i s l o c a t i o n , it d o e s p e r m i t us to e x a m i n e the w a y in which a d i s l o c a t i o n s e g m e n t might c l i m b when it is v e r y c l o s e to the p a r t i c l e . Use of a t w o - d i m e n s i o n a l m o d e l to d e s c r i b e d i s p e r s i o n s t r e n g t h e n i n g i s not a new concept. It is the m o d e l that A n s e l l and W e e r t m a n 5 e n v i s a g e d in t h e i r o r i g i n a l
J. H. HOLBROOK is a Graduate Student in the Depa
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