Van den Beukel_1976_Inhomogeneous plastic deformation in a Au-Cu alloy

This assumption was used by hc cormick 3 as a c r i t

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Unformatted text preview: Hc. Cormick [3] as a c r i t e r i o n f o r the s t a r t o f the P L ' e f f e c t . This a u t h o r assumea the c r i t i c a l c o n c e n t r a t i o n t o equal 1 ( s a t u r a t i o n ) . I t a l s o f o l l o w s from van den B e u k e l ' s [4] m odel o f the o n s e t o f s e r r a t e d y i e l d i n g , g i v i n g c r i t i c a l excess c o n c e n t r a t i o n s much s m a l l e r than 1. In the p r e s e n t paper the c r i t e r i o n o f a c r i t i c a l concentration i s used f o r f i r s t and r e p e a t e d y i e l d i n g as w e l l . In f a c t t h i s assumption was a l s o implicitly made in a r e c e n t p a p e r by van den B r i n k and Mc. Cormick [ 1 ] . V ol. i0, No. 6 INHOMOGENEOUS The i n c r e a s e o f s o l u t e c o n c e n t r a t i o n b y F r i e d e l [5] as c whe re - K: c° DEFORMATION c a t the d i s l o c a t i o n s = Ac = ( K D t a ) 2 / 3 3.... Wm b 2kT IN A u - C u during ALLOY 535 t a was g i v e n (3) (~Co)312 W = solute - dislocation m b i n d i n g energy co = s o l u t e o f the a l l o y T he d i f f u s i o n concentration coefficient D can be w r i t t e n as O = c v O e xp (-Em/kT) O (4) c v a nd Em b e i n g the c o n c e n t r a t i o n and m i g r a t i o n energy o f vacancies , r e s p e c t i v e ] y • The vacancy concentration depends on plastic strain by m cv = C c The c o n d i t i o n (5) for inhomogeneous d e f o r m a t i o n is A c >. ACcr C ombination o f (6) (3), (4), (5) and (6) y i e l d s that inhomogeneous d e f o r m a t i o n occurs if E; . t a . e xp (-Em/kT) m AC wi th or, ( >+ K1 3/2 cr) K1 = K D C o at constant temperature: m E . t a >. K2 with (7) (8) K2 = (ACcr) 3/2. exp (Em/kT) K~ o C" (9) I n the case o f - r e p e a t e . . v.i e. l d i n a . the a g i n g t me t e0ua]s the band p o p a g a t i o n d r • . .. _ t !me t L. I t Is seen t h a t t~ie e x p e r i m e n t a l r e s u l t (29 is in accordance w i t h (8) g f v i n g Ko = ' / 1 0 = 2 sec. The v a l u e m = 1.47 is in good agreement w i t h the r e s u l t o...
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This document was uploaded on 01/23/2014.

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