EXPERIMENTAL AND THEORETICAL ASPECT OF THE HIGH TEMPERATURE DAMPING OF PURE METALS

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EXPERIMENTAL AND THEORETICAL ASPECT OF

THE HIGH TEMPERATURE DAMPING OF PURE

METALS

J. Woirgard, A. Riviere, J. de Fouquet

To cite this version:

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JOURNAL DE PHYSIQUE

CoZZoque C5, suppZ6ment au n O I O , Tome 42, octobre 1981 page C5-407

EXPERIMENTAL AND THEORETICAL ASPECT

O F

T H E HIGH TEMPERATURE DAMPING OF

PURE METALS

J. W o i r g a r d , A. R i v i e r e and J . De F o u q u e t

Laboratoire de Me'canique e t de Physique des Mate'riaure, E.R.A. CNRS n o 123, 86034 P o i t i e r s , France

A b s t r a c t .

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I t i s shown t h a t h i g h t e m p e r a t u r e damping s p e c t r a i n p u r e m e t a l s c a n be a n a l y s e d i n t r u e r e l a x a t i o n p e a k s , l o c a - t e d between 0 . 4 and 0.7 T m l and l a r g e non l i n e a r e f f e c t s g i - v i n g i n t e r n a l f r i c t i o n maxima i n t h e same t e m p e r a t u r e r a n g e .

A number o f e x p e r i m e n t s r e l a t i n g w i t h s i n g l e c r y s t a l s i n d i - c a t e t h a t damping o r i g i n a t e s m a i n l y from l a t t i c e d i s l o c a t i o n m o t i o n s and n o t , a s p r e v i o u s l y assumed, from g r a i n boundary s l i d i n g .

I t i s a l s o shown t h a t a n e l a s t i c i t y seems t o be due t o l o n g r a n g e i n t e r a c t i o n s between d i s l o c a t i o n s o r between d i s l o c a - t i o n s and b o u n d a r i e s o r sub-boundaries r a t h e r t h a n t o t h e i n - f l u e n c e o f t h e l i n e t e n s i o n o f t h e bowing o u t segments

.

I . I n t r o d u c t i o n . - High t e m p e r a t u r e i n t e r n a l f r i c t i o n s p e c t r a a r e

made, on most of s t u d i e d m a t e r i a l s , o f one o r s e v e r a l p e a k s s i t u a t e d between 0 . 4 and 0.7 T m ( T m b e i n g t h e m e l t i n g t e m p e r a t u r e ) and of a background which r e g u l a r l y i n c r e a s e s w i t h t e m p e r a t u r e . We s h a l l l i -

m i t o u r s e l v e s i n t h i s p a p e r , b e c a u s e o f , a l a c k of room, t o t h e s t u d y of t h e p e a k s which h a s been c a r r i e d on i n a more i n t e n s i v e way t h a n t h a t o f t h e background.

Numerous works, g a t h e r e d i n v a r i o u s p r e v i o u s r e v i e w p a p e r s (1, 2 , 3 ,

4 ) have p e r m i t t e d t o c l e a r l y p o i n t o u t t h e s e p e a k s i n most p u r e me- t a l s and some a l l o y s , and v a r i o u s i n t e r p r e t a t i o n s have been sugges- t e d f o r them.

Hovever, i t seems t h a t t h e e a r l y a c c e p t a n c e of h y p o t h e s e s which a r e n o t enough based on e x p e r i m e n t s , h a s c o n s i d e r a b l y d e l a y e d a r e a l comprehension o f p r o c e s s e s i n v o l v e d .

i ) I t h a s l o n g been a d m i t t e d t h a t t h e o b s e r v e d s p e c t r a were i n - s e n s i t i v e t o t h e s t r a i n a m p l i t u d e . H o w e v e r r e c e n t o b s e r v a t i o n s ( 5 , 2 , 6 , 7 ) have h e l p e d t o s e t t o e v i d e n c e l a r g e non l i n e a r e f f e c t s t h a t might produce deep p e r t u r b a t i o n s i n t h e s p e c t r a .

i i ) S i n c e

Ksfs

works ( 8 , 9 ) t h e p e a k s have been c o n s i d e r e d t o b e

c h a r a c t e r i s t i c of p o l y c r y s t a l l i n e s t a t e , whereas t h e r e t o o , r e c e n t t e s t s have showed t h a t n o t a b l e e f f e c t s were p e r s i s t e n t on s i n g l e c r y s t a l s , which l e a d s , a s i n c l a s s i c a l c r e e p , t o bestow a prominent

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C5-408 JOURNAL DE PHYSIQUE p a r t t o l a t t i c e d i s l o c a t i o n s and t o b r i n g t o l i g h t t h e importance of t h e h i s t o r y o f t h e s a m p l e s , v i z o f m i c r o s t r u c t u r a l s t a t e . The s i t u a t i o n a p p e a r s a s c o m p l i c a t e d a s f a r a s t h e i n f l u e n c e on a l l o y i n g e l e m e n t s a r e c o n c e r n e d . I n p a r t i c u l a r , i t h a s been pro- v e d ( 6 ) t h a t some p e a k s a t t r i b u t e d t o t h e i n f l u e n c e o f i m p u r i t i e s c o u l d be developped on h i g h p u r i t y m a t e r i a l s by s u i t a b l e thermomecha- n i c a l t r e a t m e n t s . Before t a k i n g up t h e s t u d y o f t h e i n f l u e n c e o f a l l o y i n g e l e - ments, i t seems t h e r e f o r e n e c e s s a r y t o a c q u i r e a s u f f i c i e n t knowled- ge of t h e r e f e r e n c e s t a t e s p r o v i d e d by s i n g l e c r y s t a l s , t h e n by poly- c r y s t a l s o f pure m e t a l s . I n t h i s p a p e r , we s h a l l t h u s l i m i t o u r s e l v e s t o p u r e m e t a l s , and p a r t i c u l a r l y i n s i s t on e x p e r i m e n t a l c o n d i t i o n s ; f o r t h e p o s s e s - s i o n o f r e l i a b l e d a t a a p p e a r s t o u s a s an e s s e n t i a l p r e l i m i n a r y f o r any a t t e m p t o f i n t e r p r e t a t i o n . 11. E x p e r i m e n t a l R e s u l t s . - Amongst t h e e x p e r i m e n t a l p a r a m e t e r s l i a - b l e t o i n f l u e n c e t h e damping s p e c t r a , must be n o t e d :

.

The afore-mentioned a p p l i e d s t r e s s ;

.

The measurement t e m p e r a t u r e ;

.

The v i b r a t i o n f r e q u e n c y ;

.

The number o f a p p l i e d c y c l e s : ( 1 0 )

.

The h e a t i n g ( o r c o o 1 i n g ) r a t e f o r c o n v e n t i o n a l t e s t s a t v a r i a - b l e t e m p e r a t u r e , o r t h e time o f maintenance a t t h e measure t e m p e r a t u - r e f o r i s o t h e r m a l t e s t s .

T h i s l a t t e r p o i n t i s b e s i d e i l l u s t r a t e d i n P i c t u r e 1 where one c a n compare t h e s p e c t r a o b t a i n e d i n v a r i o u s c o n d i t i o n s on a p o l y c r y s - t a l o f 3 N p u r i t y aluminium. When t h e spectrum i s d e s c r i b e d by d i s c r e - t e t e m p e r a t u r e i n c r e a s e s a f t e r a maintenance o f 4 h o u r s t o each mea- s u r e t e m p e r a t u r e , one d i s c o v e r s a v e r y low damping and no i n f l u e n c e o f s t r a i n a m p l i t u d e ( c u r v e a ) . On t h e c o n t r a r y , when on t h e same specimen, t h e measure i s performed w i t h a 60 C/h h e a t i n g r a t e , one o b s e r v e s a n o t a b l e damping from a s t r o n g l y n o n - l i n e a r o r i g i n . These t r a n s i e n t s seem a l l t h e more i m p o r t a n t s i n c e t h e p u r i t y of t h e mate- r i a l i s h i g h ( l l ) , and t h e y c a n l e a d , i n some c a s e s , t o t h e appearan- c e of "pseudo p e a k s " l i a b l e t o c o n c e a l t h e r e a l r e l a x a t i o n p e a k s

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g r a i n s i z e and t h e r e l a x a t i o n t i m e ( 1 2 , 13, 1 4 , 1 5 ) . But one c a n a s - c e r t a i n on e x t r a p o l a t e d c u r v e s a t z e r o s t r a i n t h a t t h e a n n e a l i n g pro- d u c e s i n f a c t a l a r g e d i m i n u t i o n o f t h e i n t e n s i t y o f t h e p e a k , which c a n be c o n c e a l e d by t h e a p p e a r a n c e o f a s t r o n g a m p l i t u d e e f f e c t .

The same phenomenon c a n a l s o be o b s e r v e d on p i c t u r e s 3 and 4 o b t a i n e d on a c o l d worked p o l y c r y s t a l o f t h e same m a t e r i a l a f t e r an- n e a l i n g a 720 and 900 K . P i c t u r e 3 seems t o c o r r o b o r a t e K e ' s o b s e r v a - t i o n s a b o u t t h e t h e a b s e n c e of a s t r a i n a m p l i t u d e e f f e c t . On t h e con- t r a r y , p i c t u r e 4 shows a s t r a i n a m p l i t u d e e f f e c t s i m i l a r t o t h a t on p i c t u r e 2 , such an e f f e c t b e i n g s t i l l v i s i b l e t o s t r a i n a m p l i t u d e s a s low a s I O - ~ . T h i s i n f l u e n c e o f t h e a m p l i t u d e h a s , f o r example, a l s o b e e n s t u d i e d a t h i g h e r s t r e s s e s by Smith ( 1 6 ) on aluminium ( P i c - t u r e 5 ) a n d magnesium. I n t h i s p i c t u r e , one c a n n o t i c e t h a t t h e tempe- r a t u r e o f t h e maximum d o e s n o t seem t o depend, f o r t h e s e l a r g e s t r a i n a m p l i t u d e s , upon t h e s t r e s s l e v e l . However, a t l o w e r s t r e s s e s a l i g h t s h i f t toward t h e h i g h t e m p e r a t u r e s i s g e n e r a l l y o b s e r v e d . Such non l i n e a r e f f e c t s l e a d t o a s c r i b e a n o t a b l e p a r t o f t h e d e f o r m a t i o n t o t h e d i s l o c a t i o n m o t i o n s , and t h u s t o f o r e s e e t h e p r e - s e n c e o f s u c h e f f e c t s on s i n g l e c r y s t a l s , which h a s e f f e c t i v e l y been c o r r o b o r a t e d by numerous o b s e r v a t i o n s on s e v e r a l m e t a l s : A 1 ( 1 7 , 1 8 ) ; N i ( 1 9 , 2 0 ) ; Ag ( 2 0 , 2 1 ) ; Cu ( 1 7 , 22) ; Z r ( 7 ) ; and Zn ( 2 3 ) .

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JOURNAL DE PHYSIQUE

sitiy. However, it has been shown (26) that these parameters are not sufficient enough to characterize the mechanical behavior, which means they do not constitute good state variables. It would be desirable, for example, to have access to gradients of the dislocation density, or to the proportion of grains or subgrains out of equilibrium, namely to the heterogeneities of the internal stress field.

It has been observed that high temperature peaks are wider than the Debye peaks characteristics of a single relaxation time, and in some cases, these peaks can be separated into overlapping elementary peaks. It is even sometimes possible, thanks to suita- ble thermomechanical treatments tending to partially eliminate some of the constituent parts, to put directly to light the maxima corresponding to these elementary peaks (27). The most striking example is probably that of aluminium, in which KG'S peak (12) can be analyzed in 3 distinct peaks (20). Picture 10, connected with a polycrystal, thus shows the initial presence of 2 maxima, and then the total disappearance of the peaks.

Thus on most of the studied materials, whether polycrystals or single crystals, one can perceive the presence of 3 or 4 peaks spread between 0.4 and 0.7 Tm, and whose activation energies seem to vary between 0.5 Hv for the lowest temperature peaks and Hv for the others (Hv = self diffusion energy). However, it is advisable to note that these energies are known with a rather large uncer- tainty, for they must imperatively be obtained on extrapolated curves at zero amplitude because of non linear effects.

The elementary peaks thus obtained are however 2 or 3 times wider than the Debye peaks and to attempt to give a proper expla- nation of this broadening, one has sometimes called forth the existence of a lognormal distribution of the relaxation time (28).

Yet, such a distribution can only result from the activation e-

nergy,for applied to the frequency factor it would give extreme values of some structural parameters (grain sizes, loop lengths, or spacing between pinning points) with no physical meaning. However such an energy distribution does not seem observed in the case of Aluminium (Picture 11) for which the energies of the elementary pics are the same (20), because the width of the peak does not appear sensitive to temperature.

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pear, the lowest temperature peaks being the first to vanish. In some cases, and especially on low stacking fault energy metals, annealings at temperatures as high as 0.9 T are necessary to

m

make completely disappear the highest temperature peaks. As far as the lowest temperature peaks are concerned, one can notice that their disappearance coEncides on the single crystals where phenomenon is not hidden by recrystallisation, with a brutal diminution of the width of the Laue spots (see picture 12), connected to a decrease of lattice distortion.

This observation, as well as the fact that the disappearance of the peaks is faster on high stacking fault energy metals (Al-Ni) points out the importance of climb mechanisms.

In a parallel direction with this decrease of the peaks, we have seen one could observe the appearance of non linear effects, but

it ;.S difficult to know wheter these amplitude effects are due to the non linearity of mechanisms giving the relaxation peaks, or whether distinct mechanisms are involved. This latter assumption seems to be the most likely hypothesis, for one can ascertain in some cases the appearance at high stress levels of maxima distinct from those corresponding to the peaks.

Picture 13 likewise shows that these strain amplitude effects do not seem sensitive to the thermal activation.

Before tackling the interpretation of the results, we shall fi- nally point out that the anelastic strain seems extremely sensitive to the modes of predeformation and sollicitation (See picture 14). This already old (29) and lately corroborated (23) observation on Zn single crystals, seems to indicate the importance of the influence of the intensity of the Schmidt factor in both predeformation and

I.F. measurements.

111. Interpretation of the results. - Various models have been put forward to account for the existence of high temperature peaks based for a great number of them on the hypotheses of a relaxation from in- tergranular origin and calling forth either a grain boundary sliding (30) or a grain boundary-migration (14), or more lately movements of grain boundary dislocations (31, 32, 33, 34, 35, 36).

KG

besides has lately suggested a model calling out continuous dislocation densities (37), which can be applied to all sorts of boundaries (with small or large misorientations). Yet, most of these models have the disadvantage to call forth parameters difficult to be measured :

grain boundary dislocation densities (32), mean spacing between pinning points (34, 35)

...

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C5-412 JOURNAL CE PHYSIQUE

suggestions calling forth the lattice dislocation motions are more probable interpretations.

One must therefore consider the thermally actived motion of dislocations submitted to an effective stress o :

in which is the applied stress and o g a back stress which sets up a

against the dislocation movements. If one considers U as the activation energy at zero stress, one gets a strain rate such as :

2 2v0 ~b h

U (U

-

E =

a exp ( - X ) sinh

-

kT

in which p (dislocation density) a. (mean loop length), h (average spacing between 2 activation events) v * % (bhl/2) (activation volume) are structure sensitive terms.

Several mechanisms can be considered to justify such a deformation law.

(i) small activation volume mechanisms :

- pure climb of edge segments implying small activation volu- mes. When the stress B is a restoring force due to the bowing out of the loops, one then gets stress insensitive peaks (38, 39, 40) and activation energy equal to the self diffussion energy.

-

mobile impurities dragging by the dislocations, as in

Friedel's micro-creep model (38). Such a model calling out the unsa- turated Cottrel cloud around the dislocations might be the explana- tion of some distinctive features of the peaks observed at about 0.4

Tm : appearance after annealings at moderate temperature on slightly

cold-worked specimens, corresponding to cloud formation around fres dislocations, then disappearance during annealing at a higher temperature, corresponding to the saturation of the clouds. The appearance of strain amplitude effects may then correspond to the break away of the dislocations from the saturated clouds.

(ii) Large activation volume mechanisms

- nearly screw dislocation gliding pinned by mobile jogs (38,41)

-

supplementary dislocation gliding by triple nodes diffusion (38) or cross-slip (42).

-

triggered mechanisms coresponding to the fast glide of dislocations between the obstacles overcome by climb or cross-slip.

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thermomechanical unpinning (45, 46) and longitudinal or transversal diffusion of mobile impurities (47) have also been sometimes propo- sed. But all these models do not allow us to account for either the motion of damping maxima toward high temperatures, at increasing stresse, or the unsensitivity to the vibration frequency.

One can also suppose that the dislocation loops are long enough for the influence of the line tension to be negligible, and that the restoring force arises essentially from the long range interactions exerted by other dislocations, or by out of equilibrium boundaries or sub-boundaries (48). The measurements of the anelastic strain during creep (49), by the stress drops method, or the torsion measurements during longitudinal creep (50) reveal that during the primary creep this recoverable deformation increases and can reach considera- ble values, which may be attributed to the developpement of heterogeneities ( 4 8 ) , and corroborates the idea that they can be the primary cause of the restoring force. In internal frictior,, anelasticity would therefore proceed from the preexisting heterogeneities.

According to these hypotheses, the potential to which the dislocations are submitted must consequently be shaped as on Picture 15, which corresponds to a non linear restoring force leading to peaks

tending to develop themselves and move toward high temperatures when the stress increases. In this hypothesis, there must exist a criti- cal stress, over which the dislocations can move on large distances and produce a non recoverable deformation and a damping rapidly increasing with the stress and such a behavior is actually observed on Aluminium (Fig. 16).

If close obstacle which can be overcome by thermal activation are also present and create shortest wave length potential (51). superposed to the preceding one, the elementary activation mechanism is then the overcoming of these obstacles by for example climb or cross slip, and the stresse o g can then be separated into a true restoring stress and a friction stress opposed to the motion of dislocations, whatever their direction.

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C5-4 14 JOURNAL DE PHYSIQUE

l i d a t t h e l o w e s t s t r e s s e s u s e d which a r e sometimes o f t h e same o r - d e r t h a t t h o s e u s e d i n i n t e r n a l f r i c t i o n and i t h a s been showed t h a t such laws a l l o w u s t o v e r y e a s i l y a c c o u n t f o r t h e b r o a d e n i n g of t h e p e a k s ( 5 3 ) .

P h y s i c a l l y , s u c h a h y p o t h e s i s means t h a t t h e d e c r e a s e o f t h e s t r a i n r a t e d o e s n o t p r o c e e d o n l y from t h e a c t i o n o f t h e r e s t o r i n g f o r c e any l o n g e r , b u t a l s o from a d e c r e a s e o f t h e f r e q u e n c y o f a c t i - v a t i o n e v e n t s ; s u c h a d e c r e a s e may be produced e i t h e r by a non-homo- geneous d i s t r i b u t i o n o f o b s t a c l e s , o r by a h a r d e n i n g mechanism s i m i - l a r w i t h t h e one s u g g e s t e d by Mott ( 5 4 ) ; i n t h i s l a t t e r h y p o t h e s i s , one i s however i n d u c e d t o imagine t h a t d u r i n g a c y c l e , t h e e f f e c t s o f r e c o v e r y and h a r d e n i n g a r e i n e q u i l i b r i u m , f o r , a s i t c a n be ob- s e r v e d i n p i c t u r e 1 9 , no l a s t i n g m o d i f i c a t i o n seems t o p r o c e e d from t h e a p p l i c a t i o n o f t h e s t r e s s . C o n c l u s i o n .

-

T h e r e f o r e , i t now seems p r o b a b l e t h a t i n t e r n a l f r i c - t i o n p e a k s o b s e r v e d a t a h i g h t e m p e r a t u r e on p u r e m e t a l s o r i g i n a - t e from t h e s t r e s s a c t i v a t e d m o t i o n s o f l a t t i c e d i s l o c a t i o n s . I t a l - s o a p p e a r s t h a t , f o r s u f f i c i e n t l y h i g h s t r e s s e s (E > l ~ ) -

,

t h e s e mo- ~ t i o n s o c c u r on i m p o r t a n t d i s t a n c e s and t h a t t h e o b s e r v e d a n e l a s t i c s t r a i n s c a n n o t be always e x p l a i n e d by t h e "bowing o u t " o f d i s l o c a - t i o n s e g m e n t s . The l o n g r a n g e s t r e s s e s which a r e opposed t o t h e d i s - l o c a t i o n m o t i o n s and which s u p p l y p e a k s , c a n p r o c e e d from l a t t i c e d i s t o r t i o n s w h i c h - a r e v e r y d i f f i c u l t t o be o b s e r v e d d i r e c t l y . For t h e s t u d y o f t h e s e d i s t o r t i o n s , i t seems t h a t t h e i n t e r n a l f r i c t i o n t e s t s d u r i n g c r e e p c a n r e v e a l t h e m s e l v e s a s a v e r y p r o m i s i n g means o f i n v e s t i g a t i o n . I t would a l s o be d e s i r a b l e t h a t s y s t e m a t i c s t u d i e s on p r e d e f o r - med o r i e n t e d s i n g l e c r y s t a l s s h o u l d be u n d e r t a k e n i n o r d e r t o s t u d y t h e i n f l u e n c e on t h e i n t e r n a l f r i c t i o n o f t h e c o n t r o l l e d a c t i v a t i o n o f d i f f e r e n t g l i d e s y s t e m s . A s f o r t h e e l e m e n t a r y mechanisms which a r e r e s p o n s i b l e t o t h e r - mal a c t i v a t i o n , i t would be d e s i r a b l e t o g e n e r a l i z e t h e i s o t h e r m a l t e s t s w i t h v a r i a b l e f r e q u e n c y p e n d u l a , t e s t s which a l o n e c a n a l l o w u s , on t h e one h a n d , t o g e t r i d o f t h e s t r u c t u r a l c h a n g e s d u r i n g t h e t e s t s , and on t h e o t h e r h a n d , t o d i s p o s e o f a f r e q u e n c y i n t e r v a l s u f - f i c i e n t f o r a p r e c i s e d e t e r m i n a t i o n o f t h e a c t i v a t i o n p a r a m e t e r s . Acknowledgments.

-

The a u t h o r s wish t o e x p r e s s t h e i r a p p r e c i a t i o n t o

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R e f e r e n c e s .

-

1 ) G . R o b e r t s a n d G . M . Leak : P r o c .

vth

I n t . C o n f . o n I n t . F r i c t i o n a n d U l t r a s o n i c A t t . , A a c h e n ,

1,

( 1 9 7 5 ) , 3 7 0 .

2 ) C . C . S m i t h and G.M. Leak : I1 Nuovo Cirnento

S,

( 1 9 7 6 ) , 3 8 8 . 3 ) D . MC Lean : Can. Met. Q u a n t

B,

( 1 9 7 4 ) , 1 4 5 .

4 ) J . T . A . R o b e r t s : Met. T r a n s .

1,

( 1 9 7 0 ) , 2487.

5 ) G . R o b e r t s a n d G . M . Leak : P r o c . I n t . C o n f . on I n t . F r i c - t i o n a n d U l t r a s o n i c A t t . , Tokyo ( 1 9 7 7 ) , 1 1 7 .

6 ) A . R i v i & r e , J . P . A r n i r a u l t a n d J . W o i r g a r d : I1 Nuovo C i m e n t o

338

( 1 9 7 6 ) 3 9 8 .

7 ) I . G . R i t c h i e a n d K . W . Sprungmann : Atomic E n e r g y o f Canada Limi- t e d R e p o r t , AECL. 6810 ( 1 9 8 1 ) . 8 ) T.S. K$ : P h y s . Rev.

72

( 1 9 4 7 ) , 4 1 . 9 ) T.S. KG : J . A p p l . P h y s .

3

( 1 9 4 9 ) , 2 7 4 . 1 0 ) I . G . R i t c h i e , A . A t r e n s a n d K.W. Sprungrnann. Atomic E n e r g y o f C a n a d a L i m i t e d R e p o r t , AECL-6442 ( 1 9 8 0 ) . 11) Y . A . B e r t i n , Thgse D.E., P o i t i e r s ( F r a n c e ) 1 0 7 9 . 1 2 ) T . S . K @ : P h y s . R e v .

2

( 1 9 4 7 ) 5 3 3 . 1 3 ) C.D. S t a n , E.C. V i c a r s , A . G o l d b e r g a n d J . E . Dorn : T r a n s . A.I.M.E.

3

( 1 9 5 3 ) , 2 7 5 . 1 4 ) G . M . Leak : P r o c . P h y s . S o c .

78

( 1 9 6 1 ) 1 5 2 0 a n d 1 5 2 9 . 1 5 ) J . T . A . R o b e r t s a n d P . B a r r a n d . J . o f I n s t . M e t a l s ,

96

( 1 9 6 8 ) 1 7 2 . 1 6 ) C.C. S m i t h a n d G . M . Leak : P r o c .

vth

I n t . C o n f . on I n t . F r i c t . a n d U l t r a s o n i c A t t . , A a c h e n ,

2 ,

S p r i n g e r V e r l a g - B e r l i n ( 1 9 7 5 ) , - 3 8 3 . 1 7 ) J . W o i r g a r d , J . P . A m i r a u l t a n d J . d e F o u q u e t : P r o c .

v t h

I n t . C o n f . on I n t . F r i c t . a n d U l t r a s o n i c A t t . A a c h e n ,

1

( 1 9 7 3 ) 392 1 8 ) E . B o n e t t i , E . E v a n g e l i s t a , P. Gondi a n d R . T o g n a t o : I1 Nuovo Cirnento ( 1 9 7 6 ) 4 0 8 . 1 9 ) V.P. Z u b e k h i n a n d V.S. T u r b i n : S o v . P h y s . S o l i d S t a t e ,

15

( 1 9 7 3 ) 8 8 2 . 2 0 ) A . R i v i G r e a n d J . W o i r g a r d , T h a t i s s u e .

2 1 ) V.S. P o s t n i k o v , I . V . Z o l o t h u k h i n , V . V . Abramov and V . A . Ammer F i z . m e t a l m e t a l l o v e d ,

3

( 1 9 7 3 ) 2 1 8 . 2 2 ) M . M . Kasyan : F i z . M e t a l m e t a l l o v e d ,

3

( 1 9 7 3 ) 1 9 3 . 2 3 ) T . Yokoyama a n d T O k a z a k i : S c r i p t a Met.

8

( 1 9 7 4 ) 1 2 0 1 . 2 4 ) V.S. P o s t n i k o v , A.M. B e l i - k o v , A.T. K o c i l o v a n d V . A . Y o u r ' e v F i z . M e t a l . M e t a l l o v e d

32

( 1 9 7 1 ) 658 2 5 ) R . J . G a b o r i a u d , J . W o i r g a r d , M . G e r l a n d and A . R i v i & r e : P h i l . Mag.

43

( 1 9 8 1 ) 3 6 3

(11)

C5-4 16 JOURNAL DE PHYSIQUE

2 7 ) E. B o n e t t i , E. E v a n g e l i s t a t , P . Gondi a n d R . T o g n a t o : P h y s . S t a t . S o l . ( a )

39

( 1 9 7 7 ) 6 6 1

2 8 ) A.S. Nowick a n d B.S. B e r r y : I.B.M. J . R e s a n d D e v e l

5

( 1 9 6 1 ) 297 a n d 3 1 2 . 2 9 ) W . B e t t e r i d g e : J . I n s t . M e t a l s ,

82

( 1 9 5 4 ) 1 4 9 . 3 0 ) T . S . K$ : J . A p p l . P h y s . ,

20

( 1 9 4 9 ) 2 7 4 . 3 1 ) J . T . A . R o b e r t s a n d P. B a r r a n d : T r a n s A.I.M.E. ( 1 9 6 8 ) 2299. 3 2 ) J. W o i r g a r d a n d J . d e F o u q u e t : S c r i p t a M e t . ,

8

( 1 9 7 4 ) 253. 3 3 ) Yu A . F e d o r o v a n d 0.1. S y s a y e v : F i z . Met. M e t a l l o v e d ,

41

( 1 9 7 6 ) 1 1 5 2 . 3 4 ) G . M . A s h m a r i n , A . I . Z h i k h o r e v a n d Y.A. Shvedov : I X C o n f e r e n c i j g M e t a l o z n a u r k a PAN. P o l a n d Krakow ( 1 9 7 7 ) 3 9 1 . 3 5 ) Y . A . Shvedov : S c r i p t a M e t .

13

( 1 9 7 9 ) 8 0 1 . 3 6 ) B.M. D a r i n s k i i a n d Yu A . F e d o r o v : F i z . Met. M e t a l l o v e d ,

30

( 1 9 7 0 ) 1279 3 7 ) Z . Q . Sun a n d T.S. K5 : T h a t i s s u e 3 8 ) J . F r i e d e l , C . B o u l a n g e r a n d C . C r u s s a r d : A c t a Met.

3

( 1 9 5 5 ) 380 3 9 ) B.M. D a r i n s k i i , S.K. T u r k o v a n d Yu A . F e d o r o v : S o v i e t P h y s . S o l . S t a t e

10

( 1 9 6 8 ) 1 4 6 9 4 0 ) J . W o i r g a r d : P h i l . Mag.

33

( 1 9 7 6 ) 6 2 3 4 1 ) C . E s n o u f , M . Gabbay a n d G . F a n t o z z i : J . P h y s . L e t t .

38

( 1 9 7 7 ) L 4 0 1 4 2 ) J . F r i e d e l : J. P h y s . L e t t .

39

( 1 9 7 8 ) L . 6 1 4 3 ) J. W o i r g a r d : J . P h y s . L e t t .

40

( 1 9 7 9 ) L 3 3 9 4 4 ) C. E s n o u f a n d G . F a n t o z z i : T h a t i s s u e 4 5 ) M. Koiwa a n d R . R . H a s i g u t i : A c t a Met.

13

( 1 9 6 5 ) , 1 2 1 9 . 4 6 ) R . Klam, M . S c h u l t z a n d H.E. S c h a e f f e r : A c t a Met.

3

( 1 9 8 0 )

(12)

Fig. 1 : 3N A I polycristal

(a) 4 h at each temperature ( b ) heating rate : 6O0c/h

800 5 0 0 LOO 3 0 0 zool,(/ 100

,

l

,

1

fl l 0 0 200 300 LOO 500 600 W C Fig. 3 : 3N A1 poly- crystal annealed at 720 K

64d ALuain'm Pol cristal

2 0 r -, q an.106

Fig.5- Influence oi the strain amplitude on the Kg's peak of aldnium Fig. 2 : 3N A 1 polycrystal ( a ) annealed at 720 K ( b ) annealed at 800 K 700

t

Aluminium p l y c r y s t a l 600 500 COO 300 200 100 100 200 300 LOO 500

Fig. 4 : The same specimen as in Fig. 3 after annealing at 900 K

Nickel Single Crystal

0.1.10~

,

I

Em

-

(13)

C5-4 18 JOURNAL DE PHYSIQUE I I I 6 0 0 - x P O L Y C R Y S T A L 1 5 8 3 ~ ~ ) - SINGLE CRYSTAL(~~S'C 1 - 100 4 0 0 -

Fig.8- Canprison of the ~ig.7 -Damping spectra peaks obtained in a ply- obtained in a slightly crystal and a single

deformed and annealed 200-

-

_{crystal of}_{5N copper.}

wiskers (after Postnikcn? et col.) loo-

Pig. 9

-

Canprison of the low temperature

peaks obtained in a single crystal and a plycrystal of 5N Ag annealed at high temperature (1200 K). 0-1,,0~ Muminiurn polycrystal l o o t -\ L O O

Fig.10 - Influence of the annealing temperature on the high tfmperature damping spectrum of a predeformed aluminium plycrystal.

I

I I I I I Pig.11-KG peaks obtained at two tan-

0

.'

nc

O.6

'

TIT,> eratues on an alminiun plycrystal.

(14)

Fig.13-Strain amplitude effects, versus

temprature, obtained at two frequencies Fig.14- Influence of the direction of the

in a 5N Ag plycrystal. applied stress on an intermediate temperature peak obtained in a 5N Ag polycrys-

\

tal

.

Fig.15-Potentials to which a moving dislocation can be submitted

-

a)restirubg force due to the line tension

-

b)lonq ranq interaction stress.

/'?

-

l *P 1 MPa Fig.19-Damping measured as a function of the applied stress :

o increasing stresses Fig.17-Influence of the applied Fig.18-Influence of the X decreasing stresses

stress on the high temperature applied stress on the ma- damping (8 =550°C) of an almi- ximum damping values de- nim single crystal. duced £ran figure 17