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A PHASE INTERFACE DYNAMIC MODEL OF
INTERNAL FRICTION IN THE PROCESS OF
PHASE TRANSFORMATION
Zhang Jinxiu, Li Xiejun
To cite this version:
JOURNAL DE PHYSIQUE
C o l l o q u e C10, s u p p l B m e n t a u n012, Tome 46, d e c e m b r e 1 9 8 5 p a g e C10-617
A PHASE I N T E R F A C E D Y N A M I C M O D E L OF I N T E R N A L FRICTION I N T H E PROCESS OF PHASE T R A N S F O R M A T I O N
ZHANG JINXIU AND L I XIEJUN
D e p a r t m e n t
of
P h y s i c s , Zhongshan U n i v e r s i t y , Guangzhou, C h i n aABSTRACT-The moving i n t e r f a c e i n t h e p r o c e s s o f p h a s e t r a n s f o r - m t i o n ( P T ) c a u s e s a v i s c o e l a s t i c i n t e r n a l f r i c t i o n ( I F ) a n d a modulus d e f e c t , i f some c o u p l i n g b e t w e e n moving i n t e r f a c e a n d s t r e s s e x i s t s . S t a r t i n g w i t h t h e I F a n d PT t h o r i e s , a n e x p r e - s s i o n r e l a t i n g I F a n d modulus d e f e c t bM/M d u r i n g t h e p r o c e s s o f PT w i t h p h a s e i n t e r f a c e dynamic f u n c t i o n ( t h e g e n e r a l r e l a t i o n - s h i p b e t w e e n a v e r a g e v e l o c i t y o f i n t e r f a c e a n d t h e e f f e c t i v e PT d r i v i n g f o r c e b G ' ) v = ~ ( A G ' )
,
t e m p e r a t u r e v a r y i n g r a t e T , a n g u l a r f r e q u e n c y o f I F measurement ul , s h e a r modulus M a n d t h e r a t e o f PT dF/dT w e r e o b t a i n e d a s a n d ( A M / M ) /Q; =2&./n ( 3 ) w h e r e n i s c o u p l i n g c o e f f i c i e n t a n d&.
i s PT s t r a i n . By u t i l i z j n g e q u . ( 1 ) a n d t h e e x p e r i m e n t a l d a t e o f Q: ( a s a f u i n c t i o n of T/ul), a n e x p l i c i t f u n c t i o n r e l a t i o n s h i p o f
v=*( AG r
) c a n be o b t a i n e d .I-INTRODUCTION. -The i n , t e r n a l f r i c t i o n p e a k Q: i n t h e p r o c e s s o f marten-
s i t i c t r a n s f o r m t i o n ( M T ) a t low f r e q u e n c y was c h a r a c t e r i z e d b y 1, t h e p e a k h e i g h t o f I F i n c r e a s e s w i t h a n i n c r e a s i n g o f T/w; 2 , t h e Q" i s i n d e p e n d e n t on t h e s t r a i n a m p l i t u d e o f I F measurement ( a t
t h e
o r d e r , o f 1 0 - 5 ) ; 3 , t h e - f a i r l y h i g h v a l u e o f I F i s o b s e r v e d o n l y f o r T#O; i f T c h a n g e s Erom T=T, t o T=O s u d d e n l y (means T = c o n s t . ), t h e
Q-' d r o p s a l m o s t a t o n c e t o a b a c k g r o u n d v a l u e . Y. J.Wang e t a l / l / , V . S . P o t n i k o v e t 9 1 / 2 / , J.F.Delorme e t a 1 / 3 / , 0 . M e c i e r e t a 1 / 4 / a n d W.R.Xia e t a l / 5 / h a d r e p o r t e d t h i s t y p e o f I F i n t h e p r o c e s s o f v a r i o u s k i n d s o f f i r s t - o r d e r t r a n s f o r m t i o n s u c h a s r e v e r s i b l e MT / 1 , 3 , 4 / , i r r e v e r s i b l e p r o c e s s o f c r y s t a l l i z a t i o n o f m e t a l l i c g l a s s / 5 / a n d a l l o t r o p i c t r a n s - f o r m a t i o n s / 2 / .(30-618 JOURNAL DE
PHYSIQUE
S e r e v a l .models o r t h e o r i e s a s s o c i a t e d w i t h d i s l o c a t i o n i n c o h e r e n t i n t e r f a c e / 6 / , i n e l a s t i c s t r a i n / 2 , 3 / , p h a s e i n t e r f a c e ( 1 ) a n d s o f t mode/$/ had been p r o p o s e d t o e x p l a i n t h i s t y p e of I F .
I t was w e l l known t h a t t h e f i r s t - o r d e r t r a n s f o r m t i o n p r o c e e d t o w a r d c o m p l e t i o n by t h e " g r o w t h " o f t h e c r i t i c a l , i z e d n u c l e i o r t h e motion o f t h e p h a s e i n t e r f a c e , s o t h e p r o c e s s o f t r a n s f o r m t i o n s h o u l d a s s o c i a t e c l o s e l y w i t h t h e moving p h a s e i n t e r f a c e . A p h a s e i n t e r f a c e dynamic mode a s s o c i a t e d w i t h t h i s i d e a l i s p r o p o s e d i n p r e s e n t p a p e r a n d t h e p o s s i b l e a p p l i c a t i o n s a r e d i s c u s s e d .
11-MODE AND RESULTS OF CALCULATION. - C o n s i d e r t h e motion of a p h a s e i n t e r f a c e i n t h e D r o c e s s of f i r s t - o r d e r t r a n s f o r m a t i o n . t h e d r i v i n c r
-
f o r c e e x e r t e d on t h e moving i n t e r f a c e i n t h e p r o c e s s of t r a n s f o r m t . i o n was p r o v i d e d by t h e change i n Gibbs f r e e e n e r g y AG between p r o d u c t a n d p a r e n t p h a s e s , t h e e f f e c t i v e d r i v i n g f o r c e A G ' i s t h e d i f f e r e n c e between t r a n s f o r m t i o n d r i v i n g f o r c e A G a n d a c r i t i c a l r e s i s t a n c e f o r c e ~ G R , A G V = A G - ~ G R . The a v e r a g e v e l o c i t y o f moving i n e t r f a c e V i s a f u n c t i o n o f A G ' , w r i t t e na s
v = $ ( A G - A G ~ ) . I f t h e t o t a l a r e a of p h a s e i n t e r f a c e i s A, t h e n t h e t r a n s f o r m a t i o n r a t e i s where F i s t h e volume f r a c t i o n of p r o d u c t p h a s e . I f a n a l t e r n a t i n g str-t'=
t;sinu)t ( & i s a n g u l a r f r e q u e n c y ) d u r i n g t h e I F measurements e x e r t s on t h e specimen which i s i n t h e p r o c e s s o f p h a s e t r a n s f o r m t i o n , s o t h e t o t a l e f f e c t i v e d r i v i n g f o r c e i s A G 1 + n t ' ( n i s a c o u p l i n g c o e f f i c i e n t ) a n d we havewhere V, i s t h e a v e r a g e u n i d i r e c t i o n a l v e l o c i t y o f i n t e r f a c e d r i v e n b y d G 1 . The v i b r a t i o n e r n e r g y p e r u n i t volume d i s s i p a t e d A W i n a p e r i o d o f v i b r a t i o n by t h e moving i n t e r f a c e a n d t h e I F Q-' a r e
where M i s r e l a t i v e modulus. For t h e a t h e r m l a n d i s o t h e r m a l t r a n s f o r - m t i o n , w e have
Q; = ( n ' / 2 ) ( d l n g ( b G a ) / d d G a ) ( ~ F / ~ T ) M T / w ( a t h e r m l ) ( 5 )
Using t h e same p r o c e d u r e o f c a l c u l a t i o n , a e x p r e s s i o n o f modulus d e f e c t
a M / M a s s o c i a t e d w i t h t h e moving i n t e r f a c e c a n o b t a i n a s
A M / M = n ~ , ( d l n + ( b G ' ) / d A ~ l ) ( d ~ / d ~ ) M + / d ( a t h e r m l ) ( 7 ) a n d
A l l t h e p a r a m e t e r s i n t h e r i g h t s i d e o f e q u . 9 ) c a n be d e t e r m e d b y e x p e r i m e n t s , s o t h e e x p l i c i t e x p r e s s i o n o f V=
d
(AG-hGR) c a n be d e r i v e d b y p r o p e r p r o c e d u r e w i t h t h e e x p e r i m e n t a l d a t a o f I F ( a s a f u n c t i o n o f ?/o) a n d t h e e l e c t r o n i c r e s i s t a n c e b R ( f o r d e t e r m i n e o f dF/dT) a n d t h e c r i t i c a l r e s i s t a n c e o f moving i n t e r f a c e A G R c a n b e d t e r m e d .111-COMPARISION WITH EXPERIMENTS.-
A. A t h e r m l t r a n s f o r m t i o n By u l t i l i z i n g t h e e x p e r i m e n t a l d a t e o f Q-' , AM/M,dR(all a r e a s a f u n c t i o n o f $ / w ) a n d e q u . ( 9 ) . a n e x p r e s s i o n o f i n t e r f a c e dynamic had b e e n d e r i v e d f o r t h e t h e r m a l - e l a t i s i t y MT ( f r o m M p h a s e t o p a r e n t ) i n Ni-49.7 a t % T i a l l o y a s / 7 / where AGR i s 1 0 . 0 + 0 . 5 c a l / m o l .
I n t h e c r y s t a l l i z a t i o n p r o c e s s o f m e t a l l i c g l a s s Fe40 Ni40 Pto Blo
,
t h e i n t e r f a c e dynamic e x p r e s s i o n i s t h e s a m a s e q u . ( l o ) , b u t w i t h bGR-20 c a l / m o l / 8 / . F o r t h e r e v e r s i b l e i n c o m m e n s u r a t e(1)
/ c o m r w n s u r e a t e ( C ) t r a n s i t i o n b e f o r e a n d a f t e r s h a p e memory " t r a i n n i n g " i n N i - T i a l l o y , t h eb
G p c h a n g e s f r o m 4 . 8 c a l / m o l t o 1 . 5 c a l / m o l / 9 / . B. S t r e s s - i n d u c e d I / C t r a n s i t i o n A f t e r a b o u t 2 5 s t r a i n c y c l e s " t r a i n n i n g " , a c o m p l e t e l y r e v e r s i b l e s t r e e - i n d u c e d I / C t r a n s i t i o n c a n b e o b t a i n e d i n s u p e r - e l a s t i s i t y N i - 4 9 a t % T i s p e c i m e n . By u l t i l i z i n g t h e e x p e r i m e n t a l d a t a o f Q-1,
A R( a s
a f u n c t i o n o f & / J ) a n d s u b s t i t u t e T/d w i t h t / u l, w e have
where AGR i s a b o u t 1 c a l / m o l . C. S o f t mode a n d modulus d e f e c tI t was shown f r o m e q u . ( 5 ) a n d ( 7 ) t h a t a modulus minimum a s s o c i a t e d w i t h i n t e r f a c e m o b i l i t y w i l l be c o r r e s p o n d e d t o a I F p e a k i n t h e f i r s t - o r d e r t r a n s f o r m t i o n . The v a l u e o f e q u . ( 8 ) i s i n d e p e n d e n t on
?
i f t h e modulus minimum i s c a u s e d c o m p l e t e l y b y t h e i n t e r f a c e m o Q i l i t y . . The v a l u e o f (LSM/M)/Q" w i l l i n c r e a s e w i t h a n i n c r e a s i n g o f T / d ( o r L/d)
i f t h e s o f t mode e f f e c t e x i s t s .I n t h e c r y s t a l l i z a t i o n p r o c e s s o f m e t a l l i c g l a s s Fe40 NiqoPlo Blo
, a
s h a r p minimum o f modulus i s c o r r e s p o n d e d t o t h e I F p e a k , b u t t h e v a l u e o f (AM/M) /Q-I i s c o n s t a n t when T/w i n c r e a s e s ( 8 ) . T h i s means n o s o f t mode o c c u r e d i n t h e c r y s t a l l i z a t i o n p r o c e s s .F o r t h e MT a n d I / C t r a n s i t i o n j n Ni-Ti a l l o y , t h e v a l u e o f ( A M / M ) / ~ ' d e c r e a s e s w i t h a n i n c r e a s i n g o f T / ~ J o r