The role of internal and effective stresses in the plastic flow of iron single crystals
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is now g e n e r a l l y accepted that the p l a s t i c d e f o r m a t i o n of m e t a l s is t h e r m a l l y a c t i v a t e d and that the flow s t r e s s i s composed of a r e l a t i v e l y a t h e r m a l c o m ponent (7i) , and a t h e r m a l c o m p o n e n t (7*). The a t h e r real c o m p o n e n t is dependent on t e m p e r a t u r e only through the s h e a r modulus, w h e r e a s the t h e r m a l c o m ponent is both t e m p e r a t u r e and s t r a i n - r a t e dependent. T h e r e f o r e , the s h e a r s t r e s s (r) at any point along the s h e a r s t r e s s - s h e a r s t r a i n c u r v e can be e x p r e s s e d as: 1
r = r* + ri
[1]
The 7" c o m p o n e n t of s t r e s s ( r e f e r r e d to as an effective s t r e s s ) is a s s u m e d to r e s u l t f r o m s h o r t - r a n g e o b s t a c l e s to d i s l o c a t i o n m o t i o n (e.g., P e i e r l s s t r e s s , i m p u r i t y a t o m s and f o r e s t d i s l o c a t i o n s ) ; t h e r m a l a g i tation a s s i s t s in moving d i s l o c a t i o n s p a s t these o b s t a cles. The r i component of s t r e s s ( r e f e r r e d to as an i n t e r n a l s t r e s s ) is a s s u m e d to r e s u l t f r o m l o n g - r a n g e o b s t a c l e s to d i s l o c a t i o n m o t i o n (e.g., d i s l o c a t i o n t a n g les and c e l l wails); t h e r m a l f l u c t u a t i o n s a r e not s i g n i f i c a n t in helping a d i s l o c a t i o n o v e r c o m e these obstacles. If a s i n g l e t h e r m a l l y a c t i v a t e d m e c h a n i s m c o n t r o l s the m o t i o n of d i s l o c a t i o n s , ~'* can be e x p r e s s e d as: ~-~
I [A
7" = - ~
( l*g '~1 Ho + k T In \PmAbu*/J
[2]
where V* AHo k T l*
= = = = = =
Pm= A = b = v* =
a c t i v a t i o n volume a c t i v a t i o n enthalpy at r * = 0 Boltzmann's constant temperature length of d i s l o c a t i o n s e g m e n t involved in the t h e r m a l activation strain rate mobile dislocation density a r e a in glide plane swept out by a d i s l o c a t i o n p e r s u c c e s s f u l fluctuation B u r g e r s vector of d i s l o c a t i o n f r e q u e n c y of v i b r a t i o n of the d i s l o c a t i o n s e g m e n t of length l*.
W. A. SPITZIG is Senior Scientist, Edgar C. Bain Laboratory, U. S. Steel Corp., Monroeville,Pa. A. S. KEH, formerly with Edgar C. Bain Laboratory, is deceased. Manuscript submitted May 14, 1970. METALLURGICALTRANSACTIONS
Eq. [2] a s s u m e s that the entropy of a c t i v a t i o n is negligibly s m a l l , in a g r e e m e n t with p r e v i o u s r e s u l t s obtained from the i r o n single c r y s t a l s u s e d in this i n vestigation. 4 At a c o n s t a n t s t r a i n r a t e (4) the f a c t o r s l*, A , and v* a r e taken as c o n s t a n t at a given t e m p e r a t u r e , and the m o b i l e d i s l o c a t i o n d e n s i t y (Pro) is believed to d e t e r m i n e 7". ''2'5 T h e r e f o r e , r* is expected to i n c r e a s e , d e c r e a s e or r e m a i n c o n s t a n t with s t r a i n
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