Strain hardening and recovery in lead during primary creep
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H. ALDEN
T h e h y p o t h e s i s that s t r a i n h a r d e n i n g o c c u r s d u r i n g p r i m a r y c r e e p is c o n f i r m e d f o r l e a d by m e a s u r e m e n t of an i n c r e a s e of 77 K y i e l d s t r e s s with i n c r e a s e of c r e e p t i m e . Howe v e r , in the f r a m e w o r k of the a u t h o r ' s t h e o r y , s o f t e n i n g a l s o o c c u r s by r e a r r a n g e m e n t of the d i s l o c a t i o n s t r u c t u r e into c e l l s , so that the net c o n t r i b u t i o n of h a r d e n i n g to the d e c l i n i n g c r e e p r a t e m a y be m i n o r . The r e c o v e r y r a t e has a l s o b e e n m e a s u r e d and is found to d e c r e a s e s t r o n g l y a s c r e e p t i m e i n c r e a s e s . The d e c r e a s e i s s u f f i c i e n t to account q u a l i t a t i v e l y f o r m o s t of the d e c r e a s e in c r e e p r a t e a c c o r d i n g to the t h e o r y . T h e d e c r e a s e d r e c o v e r y r a t e is not c o n s i s t e n t , h o w e v e r , with the p r e d i c t i o n of the i n t e r n a l s t r e s s t h e o r y .
T
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o b s e r v a t i o n that the c r e e p r a t e in p u r e m e t a l s u s u a l l y d e c l i n e s in the e a r l y s t a g e s of c r e e p , d e s p i t e the c o n s t a n c y of s t r e s s a and t e m p e r a t u r e T, is a v e r y e a r l y o b s e r v a t i o n of the m e c h a n i c a l p r o p e r t i e s of metals.~ T h e d o m i n a n t m o d e r n t h e o r y b y which t h i s effect i s e x p l a i n e d i s the i n t e r n a l s t r e s s t h e o r y . 2'3 S t r a i n h a r d e n i n g o c c u r s to r a i s e the " i n t e r n a l s t r e s s " a~ which in t u r n d e c r e a s e s the effective s t r e s s and d i s l o c a t i o n v e l o c i t y z'3 o r , in e a r l i e r t h e o r i e s , 4"e r a i s e s the a c t i v a t i o n e n e r g y f o r t h e r m a l l y a c t i v a t e d p l a s t i c flow.* *The physmat models in these theories are distinct but have some important common features with the mternaf stress theory.
In the m o r e r e c e n t r e c o v e r y - r e a r r a n g e m e n t t h e o r y , 7"~ s t r a i n h a r d e n i n g a c t s to d e c r e a s e the a r e a o v e r which n e w l y - f o r m e d d i s l o c a t i o n loops can e x p a n d (the " f r e e a r e a " ) . T h e s t r a i n r a t e equation is [la]
4 = (~ + r) A r Oy
a r = exp - ( - ~ - ~r)
[lb]
Tv
in which A v is a " f r e e a r e a f u n c t i o n " which d e c r e a s e s with the f r e e a r e a and r = (ry + rv) is a g e n e r a l i z e d r e c o v e r y p a r a m e t e r which d e s c r i b e s the t h e r m a l l o s s r y and r e a r r a n g e m e n t r v of d i s l o c a t i o n s (to a m o r e c e l l u l a r s t r u c t u r e ) . Ty = a G b p ~12 i s the y i e l d s t r e n g t h and r v a m e a s u r e of i t s l o c a l v a r i a t i o n . Oy = (aT"y/Oe)t, r y = (---aTy/at)r and r v ~ ( o r v / a t ) e , Ref. 7. W h e t h e r o r not h a r d e n i n g o c c u r s d u r i n g p r i m a r y c r e e
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