The grain size dependence of the yield, flow and fracture stress of commercial purity silver
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AND
R. W. ARMSTRONG
Heavily c o l d - r o l l e d s h e e t m a t e r i a l of 99.9 pct purity Ag has been r e c r y s t a l l i z e d at v a r y i n g t e m p e r a t u r e s to give a v e r a g e g r a i n d i a m e t e r s , l, in the range b e t w e e n 1 and 60 p. F o r this m a t e r i a l , the yield s t r e s s , flow s t r e s s at s e v e r a l s t r a i n v a l u e s , and f r a c t u r e s t r e s s follow the H a l l Petch relation: aE = (ro e + k e l - t / 2
where oe i s the flow s t r e s s at a p a r t i c u l a r v a l u e of s t r a i n , e, and 0% and ke a r e the e x p e r i m e n tal c o n s t a n t s a p p r o p r i a t e to a p a r t i c u l a r s t r a i n value. The range in g r a i n size obtained for this m a t e r i a l was s u f f i c i e n t l y l a r g e to d e t e r m i n e that s i l v e r can be a p p r e c i a b l y s t r e n g t h e n e d by g r a i n size r e f i n e m e n t and that s e v e r a l o t h e r r e l a t i o n s p r e v i o u s l y suggested to r e l a t e the s t r e s s and g r a i n size could be discounted. The f i n e s t g r a i n s i z e s were m e a s u r e d f r o m r e p l i c a s of etched s p e c i m e n s as viewed with the e l e c t r o n m i c r o s c o p e . It is proposed that this type of g r a i n size s t r e n g t h e n i n g m a y be r e s p o n s i b l e for the exceptional s t r e n g t h which o c c u r s in c e r t a i n f i l m s of s i l v e r f a b r i c a t e d by v a p o r deposition t e c h n i q u e s .
T H E c o n v e n t i o n a l s t r e s s - s t r a i n b e h a v i o r of p o l y c r y s t a l s g e n e r a l l y shows that t h e i r s t r e n g t h i n c r e a s e s as t h e i r g r a i n size is refined. ~-3 This is d e m o n s t r a t e d m o s t often by e x p r e s s i n g t h e s e data in t e r m s of the Hall-Petch relation ae = ao e + ke1-1/2
[1]
w h e r e oc is the flow s t r e s s at some s t r a i n value, E, the a v e r a g e g r a i n d i a m e t e r is denoted by l, and aoe and ke a r e the e x p e r i m e n t a l c o n s t a n t s d e t e r m i n e d for the c o r r e s p o n d i n g s t r a i n value. It has been pointed out that u n l e s s the data a r e obtained o v e r a wide range of g r a i n s i z e s , o t h e r r e l a t i o n s , such a s an 1-1/3 dependence o r an l -~ dependence, could e q u a l l y well d e s c r i b e the r e s u i t s . %s These d e p e n d e n c e s give a slightly g r e a t e r o r l e s s e r dependence of s t r e s s on g r a i n size, r e s p e c t i v e l y , than a p p l i e s for the l - l / z r e l a t i o n f l The yield s t r e n g t h of s e v e r a l s t e e l s has been i n v e s t i gated o v e r a wide range of g r a i n s i z e s and the data a r e b e s t d e s c r i b e d by Eq. [1]. 7 E x p e r i m e n t s on A r m c o i r o n over a p p r o x i m a t e l y the s a m e r a n g e in g r a i n size showed a definite c u r v a t u r e on an l - l I e s c a l e and a dependence c l o s e r to 1-1/3 was obtained, a It has been proposed that the h a r d n e s s
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