RELATION BETWEEN THE DAMPING SPECTRUM AND THE DISLOCATION MOTION IN MARTENSITIC ALLOYS

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RELATION BETWEEN THE DAMPING SPECTRUM

AND THE DISLOCATION MOTION IN

MARTENSITIC ALLOYS

R. Gotthardt, O. Mercier

To cite this version:

RELATION BETWEEN THE DAMPING SPECTRUM AND THE DISLOCATION MOTION I N MARTENSITIC ALLOYS

R. G o t t h a r d t and 0. ~ e r c i e r *

I n s t i t u t de Ge'nie Atomique, Swiss Federal I n s t i t u t e of Technology, EeubZens CH-1015 Lausanne, ~ w i t z e r t a n d

* ~ r o m Boveri Research Center, CH-5401 Baden, SwitzerZand

Abstract. - I n t e r n a l f r i c t i o n spectra measured on m a r t e n s i t i c a l l o y s a l l e x h i b i t a common f e a t u r e : t h e i n t e r n a l f r i c t i o n i s h i g h i n t h e m a r t e n s i t i c phase and low o r very low a t h i g h temperatures, when t h e m a t e r i a l has a B s t r u c t u r e . Transmission e l e c t r o n microscopy observations revealed a h i g h d e n s i t y o f new i n t e r f a c e d i s l o c a t i o n s i n t h e martensite. A q u a l i t a t i v e model i s proposed which explains t h e h i g h damping o f t h e m a r t e n s i t e by the movement o f these d i s l o c a t i o n s .

1. I n t r o d u c t i o n

-

The i n t e r n a l f r i c t i o n spectra measured i n d i f f e r e n t m a r t e n s i t i c a l l o y s , as e.g. N i T i o r CuZnAl

,

a l l reveal a r e l a t i v e l y h i g h i n t e r n a l f r i c t i o n i n t h e m a r t e n s i t i c phase and a low i n t e r n a l f r i c t i o n i n the m a t r i x o r 6 phase (1,2). I n an o p t i c a l micrograph o f t h e surface o f a completely transformed m a t e r i a l , a h i g h number o f elongated p l a t e s can be observed i n s i d e t h e o r i g i n a l g r a i n s (Fig.1).

F i g . 1 : O p t i c a l micrograph o f a CuZnAl a1 l o y showing t h e d i f f e r e n t m a r t e n s i t e p l a t e s and t h e o r i g i n a l B-grai ns

Transmission E l e c t r o n Microscopy (TEN) observations o f these m a r t e n s i t e p l a t e s show a complicated s t r u c t u r e c o n s i s t i n g o f i n t e r f a c e s , d i s l o c a t i o n s and s t a c k i n g f a u l t s i n the case o f CuZnAl and t w i n s i n t h e case o f N i T i . I n f i g u r e 2, a TEM micrograph o f a s t r e s s induced m a r t e n s i t e p l a t e growing i n s i d e the CuZnAl-matrix i s shown. A t i t s t i p a d i s l o c a t i o n i s seen, bowing i n a convex (Fig. 2a) and a concave form (Fig. 2b) under an i n c r e a s i n g o r decreasing a p p l i e d s t r e s s r e s p e c t i v e l y . I n s i d e t h e m a r t e n s i t i c phase many s t a c k i n g f a u l t s and d i s l o c a t i o n s

(P)

a r e seen, as shown i n t h e f i g u r e s 3 and 5. The i n t e r f a c e s , separating m a r t e n s i t i c and m a t r i x phase (Fig. 4) o r m a r t e n s i t e p l a t e s among each other, c o n s i s t o f many d i s l o c a t i o n s ( S ) .

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Fig. 2: a b Fig. 3:

Fig. 2: Electron microscopy micrograph of a m a r t e n s i t i c p l a t e growing i n a matrix phase

B of a CuZnAl a l l o y , induced by an i n c r e a s i n g ( a ) and a decrea- s i n g ( b ) a p p l i e d s t r e s s . Fig

.

3 : Electron microscopy micrograph of t h e m a r t e n s i t i c phase

( M )

of a CuZnAl-alloy;

P : d i s l o c a t i o n s a t t h e s t a c k i n g f a u l t s end.

Fig. 4: I n t e r f a c e between a

6-

and a m a r t e n s i t i c phase of a CuZnAl a l l o y (S : I n t e r f a c e d i s l o c a - t i o n s , f o r more d e t a i l s , s e e t e x t ) .

-Fig. 5: Electron microscopy micrograph of a completely transformed CuZnAl a1 1 oy ( f o r d e t a i l s , s e e t e x t )

The observation of two s o r t s of d i s l o c a t i o n s , P and S , i n t h e micrographs of t h e f i g u r e s 3,4 and 5 can be understood with t h e a i d of f i g u r e s 6 .

t e x t .

thinning process f o r the preparation of

TEM

samples, such martensite plates can be

cut horizontally or v e r t i c a l l y . The figures 6a and 6c show f o r these two cases the

resulting thin samples. For them the dislocations

P

appear in a quite d i f f e r e n t way,

which i s seen i n the figure 5: the case of f i g . 6a i s shown in the l e f t p a r t , and

the one of f i g . 6c i n the r i g h t part. The habitplane with i t s interface-dislocations

S

can be seen i n figure 5 parallel t o

I-K

and with a higher magnification in figure

4.

From the l a t t e r the distance

A

between the i n t e r f a c e dislocations can be determined

0

as about 45

A .

TEM

studies of i n s i t u deformation of a specimen containing martensite plates

revealed t h a t the i n t e r f a c e dislocations are mobile and migrate 'under the influence

of an applied s t r e s s a l l together i n a block; as a consequence the p l a t e width in-

creases. That means t h a t the phase transformation has created a high number of mo-

b i l e dislocations.

2.

Damping model

-

In order t o understand i f the observed dislocations can contri-

bute t o a large degree t o the high damping of the martensite, the damping f o r both

phases i s discussed i n general terms in order t o find which parameters change d r a s t i -

c a l l y from one phase t o the other and can therefore explain the sharps increase in

damping

.

The damping D(R) of a unit element of a dislocation segment

R

js

:

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due t o a viscous f r i c t i o n w i t h t h e l a t t i c e , Bv, o r due t o t h e i n t e r a c t i o n o f segment R w i t h p o i n t defects, which leads t o a given m o b i l i t y M o f a.

For low frequency measurements, an !L2-dependence o f

D

i s the most g e n e r a l l y accepted one, when t h e f r i c t i o n i s due t o non a t t r a c t i v e obstacles o r t o depinning processus (3)(then R i s t h e d i s t a n c e between s t r o n g p i n n i n g p o i n t s ) , thus

The t o t a l damping D i s then :

CO

D = (a)

a

D ( R ) ~ R

i

where p(R) dR i s t h e d i s t r i b u t i o n o f segments

a,

which has t o be d e f i n e d f o r each phase.

3. Damping o f t h e 8-phase

-

With t h e assumption t h a t 8 d i s l o c a t i o n s a r e random and t h a t t h e s t r o n g p i n n i n g p o i n t s a r e t h e i n t e r s e c t i o n s o f d i s l o c a t i o n s (N p e r u n i t volume), t h e average segment l e n g t h LN i s :

The d e n s i t y o f d i s l o c a t i o n

X

i s

where a i s t h e average number o f segments p e r i n t e r s e c t i o n p o i n t (1

<

a

<

3)

_(4).

For a random network, t h e d i s t r i b u t i o n i s from reference (5):

I n r e p l a c i n g ( 4 ) - (6) i n (3), we g e t

I n t h i s case, D i s independant o f

X

and R.

t h e segment l e n g t h i s L, and p(R)dR = - 6(R-L2)dR 3 ( 9 )

L 2

where 6 i s t h e d e l t a f u n c t i o n . By r e p l a c i n g (8) and ( 9 ) i n ( 3 ) , we g e t :

The values L1, Lp and W, as w e l l as n can be measured i n t h e o p t i c a l and e l e c t r o n microscope micrographs.

5. Discussion

-

The d i s l o c a t i o n damping o f t h e two phases i s made o f 2 terms, a p r e f a c t o r m u l t i p l i e d by t h e damping o f a u n i t element o f d i s l o c a t i o n . The l a t t e r (D ₀

₈

and DOM) a r e n o t easy t o compute w i t h o u t a more d e t a i l e d model o f t h e d i s l o c a - t i o n motion and o f t h e d i s l o c a t i o n i n t e r a c t i o n w i t h i t s surrounding. However, i t i s reasonable t o assume t h a t t h e i r v a l u e ( f o r one u n i t element o f d i s l o c a t i o n ) i s about t h e same, since t h e b a s i c o r d e r o f the a l l o y and the number o f p i n n i n g p o i n t s are n o t changed by t h e t r a n s f o r m a t i o n . From t h e change o f t h e e l a s t i c l i m i t however, which decreases by a f a c t o r o f about 2-5 f o r t h e CuZnAl a l l o y s (6)and by a f a c t o r o f about 5-10 f o r t h e FiiTiCu a l l o y s (7), i t can be deduced t h a t t h e d i s l o c a t i o n s a r e probably more m o b i l e i n t h e m a r t e n s i t e than i n t h e 6-phase, and thus

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o r t h e d i s l o c a t i o n m o b i l i t y have some e f f e c t on t h e l e v e l o f t h e damping; b u t we b e l i e v e t h a t t h e i r e f f e c t s a r e l e s s i m p o r t a n t and would r a t h e r e x p l a i n t h e v a r i a - t i o n i n temperature o f t h e damping i n each phase. The c a l c u l a t e d model p r e d i c t s t h a t t h e h i g h e s t m a r t e n s i t e damping w i l l be f o r m a r t e n s i t e w i t h t h e h i g h e s t number o f s t a c k i n g f a u l t s and w i t h an elongated shape such as L22>>L,W.

References

(1) B. Tirbonod, S. Koshimizu, t o be published i n t h e Froc. o f t h e 7 t h ~ ~ ~ ~ ~ ~ ~ (2) 0. Mercier, K.N. Melton, Y. De P r e v i l l e , Acta Met.

3,

1467 (1979)

(3) R.B. Schwarz, Acta Met.

29,

311 (1981)

(4) a = 1 f o r a l i n e a r chain o f d i s l o c a t i o n s and a = 3 f o r a t h r e e dimensional network o f d i s l o c a t i o n s .

(5) J.S. Koehler, Imperfections i n Nearly P e r f e c t C r y s t a l s , ed. by W. Shockley and a l . , p. 197, W. Ley, New York 1952