THE THERMAL EFFECT IN PSEUDOELASTIC ALLOYS

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THE THERMAL EFFECT IN PSEUDOELASTIC ALLOYS

L. Brown

To cite this version:

L. Brown. THE THERMAL EFFECT IN PSEUDOELASTIC ALLOYS. Journal de Physique Collo-

ques, 1982, 43 (C4), pp.C4-629-C4-632. �10.1051/jphyscol:19824100�. �jpa-00221955�

CoZZoque C4, suppZ6ment au n o

12,

Tome 43, ddcembre

1982

page

C4-629

THE THERMAL EFFECT I N PSEUDOELASTIC ALLOYS

L.C. Brown

Department o f MetaZZurgicaZ Engineering, University o f B r i t i s h CoZwnbia, Vancouver,

B. C., V6T ZW5,

Canada

(Revised t e x t a c c e p t e d 2 September 1982)

A b s t r a c t . - Temperature p u l s e s of up t o 15°C have been o b s e r v e d i n s i n g l e c r y s t a l s o f p s e u d o e l a s t i c a l l o y s and a r e a s s o c i a t e d w i t h t h e f o r m a t i o n of s t r e s s - i n d u c e d m a r t e n s i t e . D e t a i l e d s h a p e s of t h e , t e m p e r a t u r f : p y l s e s a r e p r e s y n t e d f o r t h r e e t y p e s of t r a n s f o r m a t i o n : 61-61 CuAlNi, 62-82 CuZnSn and 6 -y CuAlNi.

1 1

I n t r o d u c t i o n . - S i g n i f i c a n t t e m p e r a t u r e changes o c c u r i n p s e u d o e l a s t i c a l l o y s a t h i g h s t r a i n r a t e s due t o t h e f o r m a t i o n o f s t r e s s - i n d u c e d m a r t e n s i t e (S.I.M.). The e f f e c t i s caused by t h e e n t r o p y change of t h e t r a n s f o r m a t i o n . Under a d i a b a t i c c o n d i t i o n s w i t h n o h e a t l o s s t o t h e environment, t h e e n t r o p y change (AS(T1)) can b e c a l c u l a t e d from t h e t e m p e r a t u r e r i s e of t h e specimen (AT) a t t h e specimen s t a r t i n g t e m p e r a t u r e TI, u s i n g t h e formula ( 1 )

where

Cfi

i s t h e s p e c i f i c h e a t o f t h e a l l o y . There i s a c o r r e s p o n d i n g t e m p e r a t u r e drop a s s o c i a t e d w i t h t h e r e v e r s e t r a n s f o r m a t i o n .

Very h i g h s t r a i n r a t e s a r e n e c e s s a r y t o o b t a i n a d i a b a t i c c o n d i t i o n s , and g e n e r a l l y h e a t l o s s t o t h e environ~llent c a u s e s AT t o b e reduced. I n t h e o r i g i n a l p a p e r s ( 1 , 2 ) t h e peak t e m p e r a t u r e s were found a t v a r i o u s s t r a i n r a t e s . These were p l o t t e d a s a f u n c t i o n o f s t r a i n r a t e and e x t r a p o l a t e d t o i n f i n i t e s t r a i n r a t e s t o g i v e t h e a d i a b a t i c t e m p e r a t u r e change, AT. No d e t a i l e d examination of t h e s h a p e o f t h e t e m p e r a t u r e p u l s e was made.

I n t h e p r e s e n t p a p e r , r e s u l t s a r e , p r e s e n t e d f o r t h e t h e r m a l e f f e c t i n t h r e e t r a n s f o r m a t i o n s :

el-@i

i n CuAlNi, B2-62 i n CuZnSn and Rl-yi i n CuAlNi u s i n g a c a t h o d e r a y o s c i l l o s c o p e t o measure t h e s h a p e o f t h e t e m p e r a t u r e p u l s e . A s w i l l b e s e e n , t h e t h r e e sets of r e s u l t s a r e v e r y d i f f e r e n t due t o t h e d i f f e r e n t ways i n which t h e m a r t e n s i t e grows.

R e s u l t s .

-

p1-f3; CuAlNi

The m a r t e n s i t i c t r a n s f o r m a t i o n i n t h i s system i s q u i t e s i m p l e w i t h t h e f3l m a r t e n s i t e n u c l e a t i n g a t one p o i n t and growing i n t o t h e 61 m a t r i x a t c o n s t a n t v e l o c i t y . The m a r t e n s i t e - m a t r i x i n t e r f a c e i s s h a r p and h e a t i s g e n e r a t e d a t a c o n s t a n t r a t e a t t h e m a r t e n s i t e - m a t r i x i n t e r f a c e . A t y p i c a l r e s u l t f o r t h e t h e r m a l e f f e c t i s shown i n F i g . 1. The m a r t e n s i t e n u c l e a t e d c l o s e t o T.C. 1 and had t o move a s i g n i f i c a n t d i s t a n c e b e f o r e p a s s i n g T. C. 2 . The t e m p e r a t u r e r o s e q u i c k l y u n t i l t h e m a r t e n s i t e p a s s e d t h e p o i n t of o b s e r v a t i o n and t h e n r o s e more slowly. The temp- e r a t u r e s t a r t e d t o drop once t h e m a r t e n s i t e had s t o p p e d growing. I f h e a t c o n d u c t i o n i n t h e specimen were n e g l i g i b l e , t h e n t h e specimen t e m p e r a t u r e would remain c o n s t a n t u n t i l i t changed d i s c o n t i n u o u s l y by an amount AT when t h e m a r t e n s i t e i n t e r f a c e p a s s e d i t . It would t h e n remain c o n s t a n t a t t h i s new t e m p e r a t u r e . I n p r a c t i c e , a s

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19824100

C4-630 JOURNAL DE PHYSIQUE

shown i n Fig. 1, t h e t e m p e r a t u r e changes a r e more g r a d u a l due t o t h e r m a l conduc- t i v i t y i n t h e specimen.

F i g . 1. Thermal e f f e c t a t 21°C i n B 1 1 CuAlNi a t a s t r a i n r a t e of 1.25 min-I and a s t r a i n of 8%.

A d e t a i l e d t h e o r y h a s been developed f o r t h e t h e r m a l e f f e c t i n t h i s i d e a l c a s e ( 3 ) . It assumes t h a t t h e r e a r e two h e a t s o u r c e s moving a t c o n s t a n t r a t e away from t h e n u c l e a t i o n p o i n t of t h e m a r t e n s i t e and t h a t h e a t c o n d u c t i o n o c c u r s i n one dimension a l o n g t h e specimen. T h i s t h e o r y e n a b l e s c a l c u l a t e d c u r v e s of t h e t h e r m a l e f f e c t t o b e o b t a i n e d . I n Fig. 2 , f o r example, t h e c a l c u l a t e d c u r v e s correspond t o t h e e x p e r i m e n t a l c o n d i t i o n s of F i g . 1 and o b v i o u s l y a r e i n good agreement w i t h i t .

F i g . 2 . C a l c u l a t e d t e m p e r a t u r e v a r i a t i o n f o r t h e c o n d i t i o n s -5 2 of F i g . 1 assuming a t h e r m a l c o n d u c t i v i t y of 1 . 6 3 x 1 0 m

1s.

Fig. 2 shows t h a t t h e r e i s a s i g n i f i c a n t d e v i a t i o n from a d i a b a t i c c o n d i t i o n s . Indeed t h e d e t a i l e d t h e o r y shows t h a t a s t r a i n r a t e of a t l e a s t 40 min-I i s nec- e s s a r y t o a c h i e v e a d i a b a t i c c o n d i t i o n s w i t h i n an e r r o r of 2 % , a c o n d i t i o n which i s h a r d t o a t t a i n e x p e r i m e n t a l l y .

I n t h i s system s m a l l m a r t e n s i t e p l a t e s form uniformly a l o n g t h e e n t i r e g a g e l e n g t h o f t h e specimen. W-th i n c r e a s i n g s t r a i n more and more p l a t e s form u n t i l f i n a l l y t h e y j o i n up and a s i n g l e c r y s t a l o f m a r t e n s i t e r e s u l t s . Thus t h e specimen h e a t s up i n a uniform f a s h i o n w i t h i t s t e m p e r a t u r e i n c r e a s i n g l i n e a r l y w i t h t i m e and a l l thermocouples on t h e g a g e l e n g t h showing i d e n t i c a l t e m p e r a t u r e v a r i a t i o n s (2).

Fig.

TIME IN SECONDS

t

-

1

Thermal e f f e c t a t 2 I 0 C i n (32 CuZnSn a t a s t r a i n r a t e o f 1 4 min

.

^The

numbers of t h e p l o t s c o r r e s p o n d t o t h e nominal p e r c e n t s t r a i n s given t h e specimen. The p r o c e d u r e f o r d e t e r m i n i n g t h e t r u e a d i a b a t i c temp- e r a t u r e change i s a l s o shown.

specimen i s c o m p l e t e l y t r a n s f o r m e d t o m a r t e n s i t e ( a t 6.2% s t r a i n ) . Subsequently t h e specimen s t a r t s t o c o o l down due t o h e a t l o s s from t h e ends. T h i s h e a t l o s s h a s o c c u r r e d d u r i n g t h e e n t i r e p e r i o d of t h e t e s t and c a u s e s t h e peak t e m p e r a t u r e t o b e l e s s t h a n t h a t c o r r e s p o n d i n g t o a d i a b a t i c c o n d i t i o n s . It i s n o t p o s s i b l e t o p r e d i c t t h i s h e a t l o s s from fundamental p a r a m e t e r s s u c h a s t h e r m a l c o n d u c t i v i t y due t o t h e v a r y i n g geometry o f t h e specimen e n d s and t h e machine g r i p s . It can be c a l c u l a t e d , however, from t h e measured t e m p e r a t u r e l o s s a t t h e end of t h e t r a n s f o r m a t i o n .

The gage l e n g t h o f t h e specimen can b e c o n s i d e r e d t o b e a h e a t s o u r c e w i t h t h e t e m p e r a t u r e v a r y i n g a s b t w i t h b i n OK s-l. The i n s t a n t a n e o u s h e a t f l u x i n t o t h e specimen e n d s a t t h e end of t h e t r a n s f o r m a t i o n a t t i m e t , i s g i v e n by ( 4 )

where K, K and A a r e r e s p e c t i v e l y t h e e f f e c t i v e t h e r m a l d i f f u s i v i t y and c o n d u c t i v - i t y and a r e a o f t h e ends p l u s g r i p s and B i s a c o n s t a n t . T h i s g i v e s r i s e t o a temp- e r a t u r e d r o p of ( d T / d t ) t l . The t o t a l h e a t l o s s t o t h e environment up t o t i m e tl i s g i v e n by

q

= 213 B t 312

1 (3)

T h i s g i v e s a t e m p e r a t u r e drop T in t h e specimen due t o h e a t l o s s . Thus from ( 2 )

and ( 3 ) ^R

I n o r d e r t o c o r r e c t f o r t h i s e f f e c t , t h e p l o t of t e m p e r a t u r e change i n t h e specimen a f t e r t h e t e s t i s complete i s e x t r a p o l a t e d back t o a t i m e t1/3 and t h i s g i v e s t h e a d i a b a t i c t e m p e r a t u r e g a i n i n t h e specimen ( F i g . 3 ) . Note t h a t t h i s g i v e s a s i g n i - f i c a n t c o r r e c t i o n of 0.8OC even a t t h e h i g h s t r a i n r a t e o f 1 4 s e c - l .

C4-632 JOURNAL DE PHYSIQUE

M a r t e n s i t e f o r m a t i o n i n y l CuAlNi I i s complex. I n i t i a l l y a f a i r l y h i g h s t r e s s i s r e q u i r e d t o n u c l e a t e t h e m a r t e n s i t e . It t h e n grows v e r y q u i c k l y u n t i l t h e s t r e s s h a s d e c r e a s e d s u f f i c i e n t l y f o r t h e r e a c t i o n t o s t o p ( F i g . 4 ) . On c o n t i n u e d s t r a i n - i n g e i t h e r t h e same p l a t e s t a r t s t o grow a g a i n o r a new p l a t e n u c l e a t e s and t h e p r o c e s s i s r e p e a t e d . The t h e r m a l e f f e c t i s c o r r e s p o n d i n g l y complex. I f t h e i n i t i a l m a r t e n s i t e n u c l e a t i o n o c c u r s c l o s e t o o n e of t h e thermocouples (T.C. 1 f o r example), i t shows a r a p i d r i s e i n t e m p e r a t u r e , much f a s t e r t h a n would b e e x p e c t e d on t h e b a s i s of t h e s t r a i n r a t e . Other thermocouples (T.C. 2 f o r example) w i l l have p e r i - o d s of t e m p e r a t u r e i n c r e a s e when t h e m a r t e n s i t e i s growing and o t h e r p e r i o d s when t h e t e m p e r a t u r e changes s l o w l y when t h e m s r t e n s i t e i s n o t growing and no h e a t i s b e i n g g e n e r a t e d . I n g e n e r a l , a peak t e m p e r a t u r e w i l l be o b s e r v e d when a m a r t e n s i t e i n t e r f a c e p a s s e s a thermocouple.

It i s h a r d t o d e v e l o p a t h e o r y f o r t h e t h e r m a l e f f e c t i n t h i s system. It c o u l d p r o b a b l y b e a n a l y s e d i n t e r m s of t h e movement of t h e p h a s e i n t e r f a c e a t h i g h v e l o c i t y f o r s h o r t t i m e s . However independent measurements of t h i s v e l o c i t y would b e n e c e s s a r y and would r e q u i r e t a k i n g s u c c e s s i v e p i c t u r e s of t h e moving i n t e r f a c e . I n any c a s e , a major problem i s l a c k of r e p r o d u c i b i l i t y . A s e r i e s of t e s t s c a r r i e d o u t u n d e r t h e same c o n d i t i o n s of t e m p e r a t u r e and s t r a i n r a t e g i v e markedly d i f f e r - e n t s t r e s s - s t r a i n and t e m p e r a t u r e - t i m e c u r v e s .

0 2 4 6 8

TIME IN SECONDS I b l

0 1 2 3 4 5

PERCENT STRAV 10

I

F i g . 4. ( a ) S t r e s s - s t r a i n c u r v e and ( b ) t h e r m a l e f f e c t f o r 61-yl i n CuAlNi a t -10.2'C and a s t r a i n r a t e of 2 . 5 min-l. T e s t c a r r i e d o u t i n e t h y l a l c o h o l .

D i s c u s s i o n . - O b s e r v a t i o n s o f t h e t h e r m a l e f f e c t have been p r e s e n t e d f o r t h r e e d i f f e r e n t t y p e s of m a r t e n s i t e . Presumably o t h e r t y p e s of m a r t e n s i t e would show s i m i l a r t y p e s of growth t o o n e of t h e s e t h r e e . I n two c a s e s , t h e a d i a b a t i c temp- e r a t u r e i n c r e a s e s , AT, can b e found e i t h e r from t h e t h e o r i e s developed o r by p l o t t i n g peak t e m p e r a t u r e - v e r s u s - s t r a i n r a t e and e x t r a p o l a t i n g t o i n f i n i t e r a t e s . S u b s t i t u t i n g i n E q t n . ( l ) t h e n e n a b l e s t h e e n t r o p y change f o r t h e t r a n s f o r m a t i o n t o be determined.

Acknowledgements.- The a u t h o r w i s h e s t o t h a n k M r . Geordon Marchak f o r c a r r y i n g o u t many o f t h e e x p e r i m e n t s r e p o r t e d h e r e . F i n a n c i a l a s s i s t a n c e from t h e N a t u r a l S c i e n c e s and E n g i n e e r i n g Research Council of Canada i s g r a t e f u l l y acknowledged.

References.

-

(1) Rodriguez C. and Brown L.C., Met. Trans. j& (1980) 147.

( 2 ) Brown L.C., Met. Trans.

a

(1981) 353.

(3) Brown L.C., S c r i p t a Met.

16

(1982) 1001.

(4) Carslaw H.S. and J a e g e r J . C . , Conduction o f Heat i n S o l i d s , Clarendon P r e s s , Oxford (1959) 61.