The strain dependence of the flow stress-grain size relation for 70:30 brass

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R. W. ARMSTRONG

The g r a i n s i z e dependence of the s t r e s s - s t r a i n b e h a v i o r of a n n e a l e d 70:30 b r a s s was e v a l uated u s i n g r o o m t e m p e r a t u r e t e n s i l e t e s t s . The r e s u l t i n g data, which c o v e r e d the p l a s t i c s t r a i n r a n g e f r o m 1 • 10 -5 to 4 • 10 -1, w e r e a n a l y z e d in t e r m s of the c o n v e n t i o n a l H a l l P e t c h s t r e s s - g r a i n s i z e equation, (re = (rOe + ke1-1/2, and, a l s o , in t e r m s of the extended H a l l - P e r c h equation p r e v i o u s l y p r o p o s e d for 70:30 b r a s s , tre troy + A e p + [3(Ep/1) ~/2 + k'1-1/2. The l a t t i c e f r i c t i o n s t r e s s , troe, i n c r e a s e d l i n e a r l y with p l a s t i c s t r a i n over n e a r l y the full s t r a i n r a n g e . The l a t t i c e f r i c t i o n s t r e s s for the i n i t i a t i o n of p l a s t i c flow, troy, was e v a l u a t e d u s i n g two a l t e r n a t i v e double e x t r a p o l a t i o n p r o c e d u r e s . Both e x t r a p o l a t i o n t e c h n i q u e s , which involved the m a c r o s t r a i n b e h a v i o r , gave the s a m e (roy value of 3.4 k_g~mm 2, which a g r e e d with the trOe v a l u e d e t e r m i n e d d i r e c t l y in the m i c r o s t r a i n r e g i o n (e -< 10- ). L a r g e g r a i n s i z e s p e c i m e n s , which y i e l d e d h o m o g e n e o u s l y , exhibited a be v a l u e of only 0.2 kg//mm s/2 at a p l a s t i c s t r a i n of 1 • 10-5; however this s m a l l ke i n c r e a s e d r a p i d l y with i n c r e a s i n g m i c r o s t r a i n . F o r the s m a l l g r a i n s i z e s p e c i m e n s , which y i e l d e d via a L u d e r s e x t e n s i o n , ke was e s s e n t i a l l y c o n s t a n t at 0.8 kg//mm 3/2 for a l l m i c r o s t r a i n s ; h o w e v e r , ke did i n c r e a s e in the m a c r o s t r a i n r e g i o n to a m a x i m u m value of 1.6 kg//mm 3/2. When c o n s i d e r a t i o n was given to a g r a i n size dependent i n c r e a s e in d i s l o c a t i o n d e n s i t y , an i n t r i n s i c g r a i n b o u n d a r y r e s i s t a n c e to p l a s t i c flow of a p p r o x i m a t e l y 0.7 kg//mm 3/2 was obtained. =

T h e r e is a g r e a t deal of e x p e r i m e n t a l evidence showing that the flow s t r e s s e s which a r e m e a s u r e d for p o l y c r y s t a l l i n e m e t a l s obey the H a l l - P e r c h equation: 1'2 [1]

Ze = go e + k e l -lIe

In t h i s equation, ae is the flow s t r e s s c o r r e s p o n d i n g to a p a r t i c u l a r s t r a i n , l is the a v e r a g e g r a i n d i a m e t e r , and aoe and ke a r e e x p e r i m e n t a l c o n s t a n t s , s-5 The p r i n c i p a l l i m i t i n g condition on Eq. [1], it a p p e a r s , i s that the t e s t t e m p e r a t u r e m u s t be s u f f i c i e n t l y low that n e i t h e r g r a i n b o u n d a r y s l i d i n g nor m a s s t r a n s p o r t by diffusion c o n t r i b u t e s i g n i f i c a n t l y to the d e f o r m a t i

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