Stress relaxation, internal stress, and work hardening in some Bcc metals and alloys
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The s t r e s s - t i m e r e l a t i o n during s t r e s s r e l a x a t i o n is i n t e r p r e t e d in t e r m s of a power r e l a t i o n between d i s l o c a t i o n v e l o c i t y and the effective s t r e s s . Such i n t e r p r e t a t i o n gives not only the v e l o c i t y - s t r e s s exponent, but also the i n t e r n a l s t r e s s in the w o r k - h a r d e n e d s t a t e . The v e l o c i t y s t r e s s exponents thus obtained a g r e e with those obtained f r o m etch pit d i s l o c a t i o n v e l o c i t y m e a s u r e m e n t s . The v a r i a t i o n of i n t e r n a l s t r e s s with s t r a i n shows that work h a r d e n i n g is l a r g e l y due to the d e v e l o p m e n t of i n t e r n a l s t r e s s e s . The t e m p e r a t u r e d e p e n d e n c e of flow s t r e s s a r i s e s f r o m the i n c r e a s e of effective s t r e s s with d e c r e a s i n g t e m p e r a t u r e , c o n s i s t e n t with a t h e r m a l l y a c t i vated p r o c e s s for d i s l o c a t i o n motion.
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a r e c e n t review, Li ~ s u m m a r i z e d all the i n d i r e c t m e t h o d s a v a i l a b l e for the d e t e r m i n a t i o n of the d i s l o c a tion v e l o c i t y - s t r e s s exponent. One of these is the s t r e s s r e l a x a t i o n method. In this technique the c r o s s head motion is suddenly stopped d u r i n g a t e n s i l e o r c o m p r e s s i o n t e s t . Since the s p e c i m e n continues to d e f o r m , its p l a s t i c s t r a i n r e p l a c e s the e l a s t i c s t r a i n of the t e s t i n g s y s t e m . Hence, the load drops with t i m e at a r a t e which depends on the s t r e s s dependence of p l a s t i c s t r a i n r a t e for the m a t e r i a l . Since the p l a s t i c s t r a i n due to s t r e s s r e l a x a t i o n is s m a l l (< 0.1 pct), the s t r e s s r e l a x a t i o n takes p l a c e at e s s e n t i a l l y a c o n s t a n t structure. Briefly, the p l a s t i c s t r a i n r a t e , ~p, is given by the Orowan equation, 2 ~p = * p b v
[1]
w h e r e q5 is a g e o m e t r i c f a c t o r , p is the d e n s i t y of m o b i l e d i s l o c a t i o n s , b is t h e i r B u r g e r s v e c t o r , and ~ is t h e i r a v e r a g e velocity. D u r i n g s t r e s s r e l a x a t i o n , the e l a s t i c d i s p l a c e m e n t of the t e s t i n g s y s t e m i n c l u d i n g the s p e c i m e n is r e p l a c e d by the p l a s t i c d i s p l a c e m e n t of the s p e c i m e n , and hence, the p l a s t i c and e l a s t i c s t r a i n r a t e s b a s e d on the gage length of the s p e c i m e n a r e r e l a t e d in the following way: ~
=-~e
=
-1
da
E*
at
[2]
w h e r e ~e is the e l a s t i c s t r a i n r a t e , E* is the c o m b i n e d e l a s t i c modulus of the t e s t i n g s y s t e m including the s p e c i m e n , and d g / d t is the r a t e of change of s t r e s s with t i m e . The r e l a t i o n b e t w e e n s t r e s s and a v e r a g e d i s l o cation velocity is taken f r o m the s
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