Plane strain compression of copper, Cu 6wt Pct Al, and Ag 4wt pct Sn crystals
- PDF / 825,954 Bytes
- 8 Pages / 612 x 792 pts (letter) Page_size
- 64 Downloads / 200 Views
d W = ~ ~'i d~'i
[1]
t=l
G e n e r a l l y no m o r e than five s y s t e m s a r e n e e d e d b e c a u s e an a r b i t r a r y shape change i s c o m p l e t e l y defined by five independent s t r a i n c o m p o n e n t s ( a s s u m i n g cons t a n t volume). T a y l o r s i m p l i f i e d the t a s k of finding the B. C. WONSIEWICZ and G. Y. CHIN are Members o f the Technical Staff, Bell Telephone Laboratories, Murray Hill, N.J. Manuscript submitted February 9, 1970. METALLURGICAL TRANSACTIONS
m i n u m u m w o r k by a s s u m i n g the CRSS to be the s a m e for a l l s l i p s y s t e m s . T h i s a s s u m p t i o n i m p l i e s that a l l s y s t e m s h a r d e n e q u a l l y w h e t h e r they have o p e r a t e d o r not. In that c a s e Eq. [1] b e c o m e s 12
d W = "r~ IdYll = rdy
[2]
i=1
w h e r e r s t a n d s f o r the s i n g l e CRSS for a l l s y s t e m s , and d~ i s u n d e r s t o o d to be the sum of the s h e a r s on a l l twelve s y s t e m s . Thus, the c o m b i n a t i o n of s l i p s y s t e m s which m i n i m i z e s the t o t a l s h e a r d~, w i l l a l s o m i n i m i z e the work. The l a b o r i o u s c a l c u l a t i o n s of s e l e c t i n g the m i n i m u m have been e l i m i n a t e d by Chin and M a m m e l 6 u s i n g a l i n e a r p r o g r a m m i n g technique. Bishop and Hill 7 r e f o r m u l a t e d the m o d e l in d i f f e r e n t terms using a maximum external work principle, which h a s r e c e n t l y been shown s to be e n t i r e l y e q u i v a lent to that of T a y l o r . One of the m a t e r i a l p a r a m e t e r s that could c h a l l e n g e the v a l i d i t y of the T a y l o r a s s u m p t i o n of e q u a l h a r d e n ing i s the s t a c k i n g f a u l t e n e r g y (SFE). Both c r o s s - s l i p and i n t e r s e c t i n g s l i p p r o c e s s e s a r e m a d e m o r e difficult by the e x t e n d e d d i s l o c a t i o n s a s the S F E i s l o w e r e d . 9 I n i t i a l s t u d i e s t e s t i n g the T a y l o r t h e o r y w e r e conducted by H o s f o r d on a l u m i n u m 1~ and by Chin, Nesbitt, and W i l l i a m s on p e r m a U o y , 12 both high s t a c k i n g fault e n e r g y m a t e r i a l s . S a t i s f a c t o r y a g r e e m e n t with t h e o r y w a s obtained. M o r e r e c e n t l y , M a y e r and Backofen is e x t e n d e d the study to l o w e r SFE m a t e r i a l s c o p p e r and Cu-7wt p c t A1 a s w e l l a s i r o n , a high S F E m e t a l . C r y s t a l r o d s w e r e d r a w n t h r o u g h c o n i c a l d i e s to s i m u l a t e a x i s y m m e t r i c e x t e n s i o n . The m e a s u r e d o r i e n t a t i o n d e p e n d e n c e of the d r a w i n g s t r e s s was in keeping with the T a y l o r t h e o r y in the c a s e of i r o n , but c o n s i d e r a b l y l e s s so in c o p p e r and C u - 7 p c t A1. The a u t h o r s s u g g e s t e d that d i s l o c a t i o n b a r r i e r s such a s L o m e r - C o t t r e l l l o c k s and s e s s i l e j o g s , a s w e
Data Loading...
