INFLUENCE OF PLASTIC DEFORMATION ON MAGNETOMECHANICAL DAMPING OF Co-Pt ALLOY

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INFLUENCE OF PLASTIC DEFORMATION ON MAGNETOMECHANICAL DAMPING OF Co-Pt

ALLOY

B. Augustyniak

To cite this version:

B. Augustyniak. INFLUENCE OF PLASTIC DEFORMATION ON MAGNETOMECHANICAL DAMPING OF Co-Pt ALLOY. Journal de Physique Colloques, 1983, 44 (C9), pp.C9-455-C9-460.

�10.1051/jphyscol:1983966�. �jpa-00223416�

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INFLUENCE O F PLASTIC DEFORMATION ON MAGNETOMECHANICAL DAMPING OF Co-Pt ALLOY

B. Augustyniak

I n s t i t u t e of Physics, Technical University of Gdalisk, 80-952 GdaGsk, Poland

RQsum6. La variation du frottement intsrieur, en fonction de l'amplitude de la vibration, a St6 mesur6e sur en alliage d e Co-Pt d6form6 plastiquemevt 2 des taux allant jusqu'h 1 , 2 %. L'amortissement magn6tom6canique est discut6 quantitativement en liaison avec le model de Smith et Birchak. La

corr6lation entre la contrainte interne et la densit6 de dislocation est estimEe.

A b s t r a c t . A m p l i t u d e dependent i n t e r n a l f r i c t i o n o f a d i s o r d e r e d Co-Pt a l l o y was measured a s f u n c t i o n o f a t o r s i o n a l p l a s t i c d e f o r m a t i o n up t o 1.2 %. Magnetomechanical damping was q u a n t i t a t i v e l y d i s c u s s e d u s i n g t h e S m i t h and B i r c h a k model.

The c o r r e l a t i o n between i n t e r n a l s t r e s s and d i s l o e a t i o n d e n s i t y w a s e s t i m a t e d .

INTRODUCTION

C o b a l t - p l a t inum a l l o y s n e a r t h e e q u i a t o m i c composit i o n have a d i s o r d e r e d f a c e - c e n t e r e d c u b i c s t r u c t u r e a t h i g h t e m p e r a t u r e b u t below 1098 K t h e y undergo a phase t r a n s f o r m a - t i o n t o f o r m an o r d e r e d t e t r a g o n a l s t r u c t u r e w i t h c/a = 0.88 The degree o f o r d e r s t r o n g l y a f f e c t s v a r i o u s p r o p e r t i e s o f t h i s a l l o y , among o t h e r s i t s magnetic b e h a v i o u r [1,2,31 and a l s o t h e i n t e r n a l f r i c t i o n . The i n t e r n a l f r i c t i o n i n a d i s o r d e r e d a l l o y i s found t o be much h i g h e r t h a n i n an o r d e r e d one [ 4 ] and s t r o n g l y depends on v i b r a t i o n a m p l i t u d e C53. These e f f e c t s a r e due t o magnetomechanical h y s t e r e s i s . I n o r d e r t o complete t h e i n v e s t i g a t i o n o f t h i s phenomenon we r e p o r t t h e e x p e r i m e n t a l d a t a on t h e i n t e r n a l f r i c t i o n f o r samples i n d i s o r d e r e d s t a t e w h i c h were cold-worked. These r e s u l t s a r e compared w i t h t h e o r y of S m i t h and B i r c h a k L 6 ] .

EXPERIMENTAL RESULTS

The specimens were made i n a f o r m o f w i r e s o f 1 mm i n

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983966

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C9-456 JOURNAL DE PHYSIQUE

F i g . 1 . A m p l i t u d e d e p e n d e n c e o f m a g n e t o m e c h a n i c a l damping a f t e r p l a s t i c d e f o r m a t i o n

F i g .2. A m p l i t u d e d e p e n d e n t i n t e r n a l F i g - 3 . Low , a m p l i t u d e

f r i c t i o n a f t e r p l a s t i c damping a s f u n c t i o n

d e f o r m a t i o n o f t h e i n i t i a l

v i b r a t i o n a m p l i t u d e %

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and c a l c u l a t e d ( 2 ). d e f o r m a t i o n .

d i a m e t e r and a l e n g t h o f 50 mm. A c c o r d i n g t o t h e c h e m i c a l a n a l y s i s t h e y c o n t a i n e d 50.4 a t % o f P t . The a l l o y i n t h e d i c o r d e r e d s t a t e was o b t a i n e d by quenching t h e sample from 1273 K i n t o m i n e r a l o i l a t room t e m p e r a t u r e . The r a t e o f quenching was e s t i m a t e d t o be about 600 K/s.

The measurements o f i n t e r n a l f r i c t i o n 0-I were p e r f o r m e d on an i n v e r t e d t o r s i o n pendulum a s a f u n c t i o n o f shear s t r a i n r a n g i n g from 1-10" t o 1.10'~ and w i t h o r w i t h o u t s a t u r a t i n g magnetic f i e l d /H = 1.3.10 5 A/m/. The v i b r a t i o n frequency o f t h e t o r s i o n pendulum was 40 Hz.

P l a s t i c d e f o r m a t i o n by t o r s i o n was p e r f o r m e d i n t h e pendulum f o r t h e f o u r f o l l o w i n g v a l u e s o f Lo= 0.21 0.6; 0 . 8 ~ 1.2

/%/.

F i g . 1 shows t h e r e s u l t s o f t h e magnetic i n t e r n a l f r i c t i o n measurements f o r an undeformed sample / c u r v e 1/ and f o r c o l d - -worked one / c u r v e 2 t o 5/. The d i s t i n c t i n t e r n a l f r i c t i o n maximum appears and i t can be remarked t h a t cold-work s h i f t s t h i s maximum t o h i g h e r v a l u e s o f s t r a i n a m p l i t u d e s . The p l o t t e d i n F i g . l , v a l u e s a r e a f t e r two c o r r e c t i o n s . A t f i r s t t h e c o r r e c t i o n on u n i f o r m shear s t r e s s was made u s i n g s t a n d a r d f o r m u l a Q-' = ';Q

+

0.25r-

a ¹ ² ^;

13-6

.

A f t e r t h a t t h e a m p l i t u d e dependent magnetic damping Q-' was e s t i m a t e d u s i n g t h e r e s u l t s ,

Q

; '

, o f measurements i n s a t u r a t i n g magnetic f i e l d . The ';Q

v a l u e s a r e p l o t t e d I n Fig.2 a s a f u n c t i o n o f t h e shear s t r a i n . The a m p l i t u d e dependence measurements were performed s t a r t i n g

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from t h e h i g h e s t v a l u e o f v i b r a t i o n a m p l i t u d e because t h e e f f e c t o f p r e s t r a i n appears L l j . Fig.3 shows t w o s e t s o f damage curves.

The two s e t s o f 'Q;

/r/

dependences were measured w i t h o u t / s o l i d l i n e / and w i t h s a t u r a t i n g f i e l d /dashed l i n e / . These p l o t s show t h a t h i g h o s c i l l a t i n g a m p l i t u d e i n c r e a s e s l o w a m p l i t u d e i n t e r n a l f r i c t i o n Qs -1

.

On t h e o t h e r hand, magnetic damping i s decreased when

6

i s h i g h e r t h a n 2 t o 5-10", The subsequent r e c o v e r y p r o c e s s

i s g o i n g f o r 5 t o 1 0 hours.

DISCUSSION

Model o f magnetomechanical damping, a s proposed by B i r c h a k and S m i t h , g i v e s a synonymous r e l a t i o n s h i p between i n t e r n a l f r i c t i o n Q-I v a l u e s and m i c r o s c o p i c parameters such a s i n t e r n a l s t r e s s e s Gi and magnetost r i c t i o n

A s .

A m p l i t u d e dependent magnetic damping i s g i v e n by f o l l o w i n g f o r m u l a [6]

r

~ i x ) = A

I

-&':(I+

2~

+zx')

/I/

K x E

^{x Z}

where A = A

F

w i t h x = G / G ~ =

$-/c

^; ^6; i s t h e average e f f e c t i v e i n t e r n a l s t r e s s . Under t o r s i o n a l v i b r a t i o n , f i s r e l a t e d t o G ^by

6 = & G T .

E and G

-

a r e y o u n g O s and shear m o d u l i , r e s p e c t i v e l y ; K i s a shape c o e f f i c i e n t f o r t h e magnetomechanical l o o p /K 4 3/. From t h e maximum p o s i t i o n o f Q-'/x/ f u n c t i o n t h e 6; v a l u e can be c a l c u l a t e d . The maximal v a l u e o f damping i s p r o p o r t i o n a l t o t h e A parameter.

The e x p e r i m e n t a l r e s u l t s were d e s c r i b e d by f u n c t i o n /1/

u s i n g t h e l e a s t square p r o c e d u r e and

d;

and A parameters were e s t i m a t e d

.

Fig.4 shows, f o r example, t h a t c a l c u l a t e d f u n c t i o n /dashed curve/ f i t s w e l l t h e e x p e r i m e n t a l r e s u l t s / s o l i d l i n e , undeformed s t a t e / . The q u a n t i t a t i v e a n a l y s i s g i v e s t h a t f o r i n i t i a l s t a t e

6; = 3 4 t 4 MPa. Knowing t h e m a g n e t o s t r i c t i o n v a l u e A, A,,, =

32.10 -6 L 8 3 , t h e K parameter was e s t i m a t e d : K = 1.5

2

0.5, w i t h agreement w i t h t h e model. From o u r experiment r e s u l t s t h a t t h e v a l u e o f

I

A,,,

. Gi I

p r o d u c t /11-

l o 2

J/m 3

/

i s much l o w e r t h a n

m a g n e t o c r y s t a l l i n e energy /K1 = -6.25

l a 4

3/m3 [91/. T h i s r e l a t i o n p o i n t s a u t t h a t e x t e r n a l s t r e s s e s which a r e n e a r t h e

Gi

v a l u e can n o t i n d u c e t h e r o t a t i o n o f m a g n e t i z a t i o n v e c t o r i n s i d e t h e domain.

So t h e a m p l i t u d e dependence of Q-' r e s u l t s from t h e i r r e v e r s i b l e d i s p l a c e m e n t s o f m a g n e t i c domain w a l l s .

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o f maximum damping h e i g h t and s h i f t s i t t o h i g h e r shear s t r a i n . Our r e s u l t s , a s shown i n Fig.1, a r e g e n e r a l l y i n agreement w i t h

t h i s r e l a t i o n s h i p .

From t h e magnetic damping measurements t h e G i v a l u e s a s f u n c t i o n o f p l a s t i c d e f o r m a t i o n r a t i o / &,/ can be determined.

We want t o f i n d t h e c o r r e l a t i o n between t h i s parameter and d i s l o - c a t i o n d e n s i t y 9 w h i c h can be e s t i m a t e d f r o m

Ogl / f /

dependence.

The a m p l i t u d e dependent damping can be r e l a t e d t o t h e models o f Granato and ~ i i c k e

171,

~ r a n a t o - ~ i j c k e p l o t s a r e shown i n Fig.5.

Theory p r e d i c t s a l i n e a r r e l a t i o n s h i p , b u t t h e o n l y d a t a w h i c h can be adjudged t o even a p p r o x i m a t e t o l i n e a r i t y a r e t h o s e from t h e l o w e r a m p l i t u d e s . Fig.5 shows t h a t c o l d - w o r k s h i f t s o n l y t h e G-L p l o t s w i t h o u t changing t h e slope. I t s u g g e s t s t h a t p l a s t i c d e f o r m a t i o n i n c r e a s e s d i s l o c a t i o n d e n s i t y and t h a t d i s l o c a t i o n l e n g t h i s unchanged. Thus t h e Q G ~ i n t e r n a l f r i c t i o n s h o u l d be p r o p o r t i o n a l t o

c ,

a s measured a t t h e same a m p l i t u d e o f v i b r a - t i o n and f o r d i f f e r e n t E o v a l u e s .

The G i parameter v a l u e s w h i c h were d e t e r m i n e d f r o m t h e mag- n e t o m e c h a n i c a l damping measurements a r e p l o t t e d a s f u n c t i o n o f

L, i n Fig.6 / c u r v e l/. T h i s c u r v e i n d i c a t e s t h a t i n t e r n a l f r i c t i o n i n c r e a s e s r a p i d l y f o r €,a 0.2 0/, and t h a t G, i s p r o p o r - t i o n a l t o f o r h i g h e r p l a s t i c d e f o r m a t i o n . On t h e o t h e r hand we have c a l c u l a t e d t h e v a l u e s o f A parameter w h i c h i s p r o p o r t i o - n a l t o t h e damping maximum h e i g h t /eq.l/. The A

/

E o

/

f u n c t i o n i s r e p r e s e n t e d by c u r v e 2 i n Fig.6. F o r Eo = 0.2 t h i s parameter i s i n c r e a s e d unexpectedly. F o r t h e h i g h e r v a l u e s o f E, t h e magnetomechanical damping decreases monotonously a s shown by c u r v e 2 i n Fig.6. F o r t e s t i n g t h e v a l i d i t y o f adopted model a f t e r c o l d - w o r k , t h e K/ E ,

/

dependence was examined. The p r o d u c t v a l u e s were p l o t t e d v s 6, i n Fig.6 / c u r v e 3/. The assumption was made t h a t E and A parameters d i d n o t change

s t r o n g l y a f t e r t h e cold-work.

From t h e shape o f c u r v e 3 one can deduced t h a t t h e K parameter i n c r e a s e s a t f i r s t about t w i c e l y and r e s t s c o n s t a n t f o r h i g h e r v a l u e s , b e i n g s m a l l e r t h a n 3. That c o n f i r m s t h e B i r c h a k and S m i t h model.

F i n a l l y , t h e l a s t r e l a t i o n s h i p

-.-.?-

between G' and g can be examin d.

The square r o o t v a l u e s o f

Qa

/

f =8.10'5/ a r e p l o t t e d a s c u r v e 4 i n Fig.6. The e v i d e n t l i n e a r dependence appears. The

-'"'-'

comparison between two c u r v e s : 1 m : 3 - A . 6 , and 4 i n Fig.6 l e a d s t o t h e con-

%

4-w c l u s i o n t h a t G; parameter i s w e l l

I I I I 1 c o r r e l a t e d w i t h t h e d i s l o c a t i o n 0.2 0.6

ID

d e n s i t y and f o r h i g h e r v a l u e o f

&,I°/o]

6, ,

t h i s r e l a t i o n i s l i k e

<.-\TS;.

The

Qgl

i s s e n s i t i v e t o t h e d i s l o c a t i o n s w h i c h a r e m o b i l e i n F i g .6. Cold-work dependence t h e f i e l d o f p e r i o d i c s t r e s s .

Magnetomechanical damping

oh'

^{i s}

o f : " s e n s i t i v e t o t h e f i x e d d i s l o c a - 2

-

magnetic damping,

3

-

h y s t e r e s i s l o o p t i o n s w h i c h a r e a b l e t o a n c h o r parameter. 3

-

d i s l o c a - t h e B l o c h w a l l s

L l l ] .

We assume t i o n d e n s i t y .

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C9-460 JOURNAL DE PHYSIQUE

t h a t s m a l l p l a s t i c d e f o r m a t i o n /I1 e t a p o f h a r d e n i n g / c r e a t e s new d i s l o c a t i o n s L 1 2 7

.

I t c o n f i r m s t h e r e s u l t s shown i n Fig.2.

H i g h s t r a i n , d u r i n g 9-1 measurements, i n c r e a s e s a l s o t h e m o b i l e d i s l o c a t i o n d e n s i t y and t h u s r a i s e s t h e damping a t l o w e r s t r a i n /Fig.3/. The p a r t o f new d i s l o c a t i o n s , c a n be p i n n e d by s m a l l

i n c l u s ~ o n s o f o r d e r e d phase / d ³ 1 0 0 A/. I t i n c r e a s e s t h e l o c a l i n t e r n a l s t r e s s e s n e a r by t h e s e i n c l u s i o n s and decreases t h e magnetomechanical damping. The r e m a r k a b l e i n c r e a s e o f ~ ' 1 w h i c h appears f o r E o = 0.2

96

can be e x p l a i n e d a s f o l l o w s . Such d e f o r m a t i o n changes t h e domain s t r u c t u r e o f m a t e r i a l . The magnetic domain w a l l a r e t h e n unpinned f r o m s t a b l e d e f e c t s / v a c a n c i e s a s quenched and second phase p r e c i p i t a t i o n s / .

P h e n o m e n o l o g i c a l l y i t i n c r e a s e s t h e K parameter v a l u e

.

CONCLUSIONS

1. Magnetomechanical i n t e r n a l f r i c t i o n i n d i s o r d e r e d Co-Pt a l l o y can be d e s c r i b e d q u a l i t a t i v e l y by B i r c h a k and S m i t h t h e o r y . 2. M a g n e t i c damping i s i n f l u e n c e d by c o l d - w o r k because o f

i n c r e a s i n g d e n s i t y o f d i s l o c a t i o n s . REFERENCES

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188,

1249/19 50/

.

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216/1963/.

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M e t a l l o v e d . 34, 633/1972/.

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5 CHOMKA IV., AUGUSTYNIAK B., NuOvO Ciment0,

33,

375/1979/

6 SMITH G .W., BIRCHAK J.R., J.Appl.Phys. 40, 5174/1969/, 41, 3315/1970/.

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-

DE BATIST R., I n t e r n a l F r i c t i o n o f S t r u c t u r e D e f e c t s i n C r y s t a l l i n e S o l i d s , N o r t h H o l l a n d p u b l i s h i n g Co. /1970/pp.

347-352.

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2,

567/1966/.

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