The deformation of polycrystalline zirconium
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[1]
where (IF i s the a p p l i e d s t r e s s (ieff is the t h e r m a l o r effective s t r e s s c o m p o n e n t (iI is the a t h e r m a l o r i n t e r n a l s t r e s s c o m p o n e n t The r e s u l t s a r e c o n s i d e r e d in t e r m s of the t h e r m a l l y a c t i v a t e d r a t e equation: = A exp -
I AH -- ~V'*(ieff-I RT
J
[21
B is a c o n s t a n t P m is 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
m* is the v e l o c i t y s t r e s s exponent
EXPERIMENTAL
DETAILS
Crystal bar zirconium of the composition given in Table I was cold rolled from 89 in. diam rod to 0.04 in. t h i c k s t r i p and m a c h i n e d into f l a t t e n s i l e s p e c i m e n s . The s p e c i m e n s w e r e a n n e a l e d u n d e r a v a c u u m to give two g r a i n s i z e s of 10 and 47 ~. T e n s i l e t e s t s w e r e c a r r i e d out on an I n s t r o n at a b a s e s t r a i n r a t e of 0.025 min -z and s t r a i n r a t e i n c r e a s e s of a f a c t o r of 10 w e r e m a d e . T h e v e l o c i t y s t r e s s exponent, m*; and the c o m p o n e n t s , t h e r m a l and a t h e r m a l of the flow s t r e s s at i n c r e a s i n g p l a s t i c s t r a i n s w e r e d e t e r m i n e d by the s t r e s s r e l a x a t i o n technique and a n a l y z e d by the m e t h o d due to L i . 5 In t h i s m e t h o d a plot of the log ( r e l a x a t i o n r a t e , d ( i / d t ) a g a i n s t log ( t i m e , t) i s l i n e a r and the v a l u e of m* is given by the s l o p e of the l i n e a r r e g i o n v i a the equation m* -
slope [4] slope + 1 The a t h e r m a l c o m p o n e n t at any p l a s t i c s t r a i n w a s found by u s i n g the r e l a t i o n
where (ii
-
(iI
_
ftl+a~
z -m~-I
is the p l a s t i c s t r a i n r a t e A is a c o n s t a n t
where
AH is the a c t i v a t i o n e n e r g y V* i s the " e f f e c t i v e " a c t i v a t i o n v o l u m e i . e . A*b w h e r e A* is the a c t i v a t i o n a r e a , b i s the Burger's vector.
(iz and (ie a r e the flow s t r e s s e s a f t e r t i m e s t, and t2 in a s t r e s s r e l a x a t i o n c u r v e a is the d e v i a t i o n f r o m l i n e a r i t y in the l o g ( r e l a x a t i o n r a t e ) - l o g ( t i m e ) plot
R is B o l t z m a n n ' s c o n s t a n t Table I. Analysis of Crystal Bar Zirconium
T is the a b s o l u t e t e m p e r a t u r e . In a d d i t i o n the d i s l o c a t i o n d y n a m i c s e x p r e s s i o n f o r the s t r a i n r a t e is a l s o a p p l i e d to the r e s u l t s : c = Bbpm
((ieff) m *
where S. N. TIWARI, D. J. LLOYD, and K. TANGRI are Graduate Student, Research Associate, and Professor, respectively, Metallurgical Sciences Laboratory, University of Manitoba, Winnipeg, Canada.
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Impurity
Concentration in PPM
O N C H AI Nb Fe Hf Other
140 45
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