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NONLINEAR INTERNAL FRICTION AND THE
FORMATION OF MARTENSITE
Manfred Wuttig, Chi-Yuan Lei, In-Cheol Hwang
To cite this version:
JOURNAL DE PHYSIQUE
Colloque C10, suppl&ment au n 0 1 2 , Tome 46, dgcembre 1985 page C10-621
NONLINEAR INTERNAL FRICTION AND THE FORMATION OF MBRTENSITE MANFRED WUTTIG, CHI-YUAN LEI AND IN-CHEOL HWANG
Metallurgy Department, University of Missouri-Rolla, Rolla,
M O 65401, U.S.A.
A b s t r a c t
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The n o n l i n e a r i n t e r n a l f r i c t i o n was measured i n an In-TI (24.0 a t % m a Cu-A&-Ni ( 1 4 w t % A%, 3 w t % N i ) s i n g l e c r y s t a l . I t was f o u n d t h a tb o t h t h e l i n e a r and n o n l i n e a r damping v a r y s t r o n g l y as t h e 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 t e m p e r a t u r e i s approached. The d a t a a r e i n t e r p r e t e d i n terms o f p r e t r a n s f o r r n a t i o n f l u c t u a t i o n s which f o r t h e In-TI a l l o y a r e c h a r a c t e r i z e d by an a c t i v a t i o n energy o f .63 eV.
I
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INTRODUCTIONThe mechanism o f t h e 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 can be s t u d i e d by a n a l y z i n g t h e t r a n s f o r m a t i o n p r o d u c t s
111
o r by i n v e s t i g a t i n g p r e m o n i t o r y e f f e c t s 121. I n t h i s paper, measurements o f t h e w e l l known s t r o n g p r e r n a r t e n s i t i c i n t e r n a l f r i c t i o n a r e d e s c r i b e d which, c o n t r a r y t o p r e v i o u s i n v e s t i g a t i o n s , have been extended i n t o t h e n o n l i n e a r regime. The main r e s u l t o f t h e s e s t u d i e s i s t h a t t h e i n t e r n a l f r i c t i o n does n o t n e c e s s a r i l y i n c r e a s e a l l t h e way down t o t h e m a r t e n s i t e s t a r t temperature. The r e s u l t s a r e i n t e r p r e t e d i n terms o f t h e model w h i c h d e s c r i b e s t h e h i g h e r symmetry h i g h temperature a u s t e n i t i c phase as t h e t i m e average o f v a r i a n t s o f t h e l o w t e m p e r a t u r e l o w e r symmetry m a r t e n s i t i c phase 131.I 1
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EXPERIMENTAL DETAILSI n d i u m - T h a l l i u m and Copper-Aluminum-Nickel s i n g l e c r y s t a l s were grown i n vacuums u s i n g t h e C z o c h r a l s k i t e c h n i q u e . S i n g l e c r y s t a l reeds were c u t f r o m t h e b o u l e s such t h a t t h e l o n g dimension o f t h e r e e d was p a r a l l e l t o a
[ l o o ]
d i r e c t i o n and t h e r e e d v i b r a t e d i n a [110] d i r e c t i o n . The v a r i a t i o n o f t h e r e e d dimensions and t h e Co-Sm dermanent magnets a l l o w e d f r e q u e n c y a d j u s t m e n t s i n t h e range between 9 Hz and 200 Hz. The a c t u a l apparatus was t h e same as d e s c r i b e d b e f o r e 1 4 1 e x c e p t t h a t i t has now been automated by i n t e r f a c i n g a l l components t o a PDP-11/23. The i n t e r n a l f r i c t i o n was determined by a c a r e f u l numerical a n a l y s i s o f t h e resonance curves. T h i s a n a l y s i s c o n s i s t e d of an i t e r a t i v e m i n i m i z a t i o n o f t h e v a r i a n c e o f t h e d a t a when f i t t e d t o t h e a n a l y t i c a l resonance c u r v e 151.I 1 1
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THE DATA AND THEIR INTERPRETATIONA l l p e r t i n e n t d a t a a r e p r e s e n t e d i n F i g u r e s 1 t h r o u g h 4.
F i g u r e 1 demonstrates t h e n o n l i n e a r c h a r a c t e r o f t h e resonance curves o f a Cu-14wt%Aa-
C10-622 JOURNAL
DE
PHYSIQUE3wt%Ni a l l o y (A =-16°C). I t can be seen t h a t t h e character o f these resonances changes systematically. A m u l t i v a r i a t e l e a s t square a n a l y s i s /5/ i n terms o f t h e phenomenological theory o f n o n l i n e a r i n t e r n a l f r i c t i o n /6/ shows t h a t both t h e l i n e a r and n o n l i n e a r damping as w e l l as t h e s t r a i n dependence o f t h e r e l a x e d e l a s t i c constant increase as t h e 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 s approached.
Figures 2 through 4 show the r e s u l t s o f measurements erformed a t small (0.0.
am l i t u d e s o b t a ~ n e d f o r an In-24at%Ta a l l o y . I t i s cBear t h a t t h e i n t e r n a l f r i c t i o n , Q-!, i s frequency as w e l l as temperature dependent. The a c t i v a t i o n energy o f t h e process g i v i n g r i s e t o t h e energy l o s s i s .63 eV/atom. The n o n l i n e a r resonance curves measured a t a l y o s t t h e same maximum amplitude i n t h e unrelaxed (below Q-I and r e l a x e d (above Q- ) regions demonstrate t h a t the process which gives risemaX t o t h e i n t e r n a l fricti!flxal so causes t h e nonl i n e a r i t i e s . A d d i t i o n a l data taken under r e l a x e d c o n d i t i o n s demonstrate t h a t t h e n o n l i n e a r i t i e s increase as t h e 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 s approached. I t i s thus concluded t h a t t h e maximum o f t h e i n t e r n a l f r i c t i o n has t o do w i t h a process which i s i n t i m a t e l y r e l a t e d t o t h e transformation. For an i n t e r p r e t a t i o n f o r the observed maximum o f the i n t e r n a l f r i c t i o n , consider Fig. 5 taken from reference 3. This f i g u r e i n d i c a t e s schematically how t h e h i g h temperature f c c phase above Ms can be considered a time average o f two i n c i p i e n t v a r i a n t s o f t h e low temperature f c t phase. I t i s envisioned t h a t t h e d i s t r i b u t i o n o f these i n c i p i e n t v a r i a n t s domains i s changed under s t r e s s . The motion of t h e domain w a l l s would thus g i v e r i s e t o t h e i n t e r n a l f r i c t i o n . According t o t h i s i n t e r - p r e t a t i o n t h e 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 would represent t h e condensation of t h e more symmetrical h i g h temperature phase i n t o t h e l e s s symmetrical low temperature phase. ACKNOWLEDGEMENT
The authors would l i k e t o thank Dr. Tetsuro Suzuki f o r most h e l p f u l discussions. They a l s o appreciate t h e f i n a n c i a l support o f t h e National Science Foundation.
Resonahce
Curves
o f C u - 1 ~ A I - 3 f i iAlloy
IR1
;\
:-
11
*CF i g . 2
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The l i n e a r i n t e r n a l f r i c t i o n o f an In-24at%Tn, a l l o y ( M s = - 1 0 " ~ ) measured o f v a r i o u s f r e q u e n c i e s i n t h e a u s t e n i t i c temperature range.JOURNAL DE
PHYSIQUE^
Fig. 4
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Schematic p r e s e n t a t i o n o f t h e n o n l i n e a r resonance curves o f an I n - 2 4 a t % T ~ a l l o y measured i n t h e u n r e l a x e d and r e l a x e d r e g i o n w i t h i n t h e a u s t e n i t i c t e m p e r a t u r e range.U
Fcf'
F ~ CFCT'
(In-TI)
Orth'
FCCotth?
(CIAIN;)
Potential.
Enerqr 6~'Furrt;on
of
StrainF i g . 5
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Double w e l l p o t e n t i a l showing t h e t i m e averaged f c c s t r u c t u r e o f T>MS and t h e condensed f c t s t r u c t u r e a t T<Ms.REFERENCES
111
Olsen, G.B. and Cohen, M., J. de Physique43
(1982) C4-75./2/ Shape Memory E f f e c t s i n A l l o y s , ed. by J. Perkins, Plenum Press, NY (1975). /3/ Suzuki, T e t s u r o , t o appear i n Proceedings o f t h i s conference.
/4/ W u t t i g , Manfred and Suzuki
,
T e t s u r o , S c r i p t a Met.,14
(1980) 229./5/ Hwang, In-Cheol, PhD t h e s i s , U n i v e r s i t y o f M i s s o u r i - R o l l a (1985). /6/ Aning, A., Suzuki, T. and W u t t i g , M., J. A p l . Phys.
