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INTERNAL FRICTION ASSOCIATED WITHPRECIPITATION AND RECRYSTALLIZATION

R. Schaller, W. Benoit

To cite this version:R. Schaller, W. Benoit. INTERNAL FRICTION ASSOCIATED WITH PRECIPITATIONAND RECRYSTALLIZATION. Journal de Physique Colloques, 1983, 44 (C9), pp.C9-17-C9-27.�10.1051/jphyscol:1983902�. �jpa-00223324�

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INTERNAL FRICTION ASSOCIATED WITH PRECIPITATION AND RECRYSTALLIZATION

R. Schaller and W. Benoit

Institut de Genie Atomique, Swiss Federal Institute of Technology, PHB-Ecublens, CH-101S Lausanne, Switzerland

Résumé - L'étude de la précipitation dans les alliages à base d'Al et de Cu par mesures de frottement intérieur montre que les stades de précipitation peuvent être détectés par l'apparition ou la disparation de pics de relaxation qui sont dus soit à la solution solide (pics de Zener) soit aux précipités. Pendant longtemps, il a été admis que tous les pics dus aux précipités avaient la même origine, c'est-à-dire étaient dus à des relaxations anélastiques aux interfaces précipités-matrice (théorie de Schoeck) . En fait le problème est plus complexe. Les caractéristiques des pics de précipités peuvent être différentes d'un alliage à l'autre. -Des résultats ont été obtenus qui rendent compte de relaxations à l'intérieur des précipités ou encore de mécanismesd'interactions dislocations-précipités. L'évolution du réseau de dislocations au cours de la recristallisation modifie profondément les valeurs du frottement intérieur. En particulier, on observe que la recristallisation apparaît après un accroissement du frottement intérieur. Ce résultat apporte un nouveau critère de recristallisation : la recristallisation est conditionnée par un accroissement de la mobilité des dislocations. De ce point de vue, le frottement intérieur devient une des meilleures méthodes pour étudier les interactions précipitation-recristallisation.

Abstract - The study of precipitation in Al and Cu based alloys by internal friction measurements shows that the precipitation stages can be revealed by the appearance or disappearance of relaxation peaks due either to the solid solutions (Zener peaks) or to the precipitates. For a long time, it has been thought that all the peaks due to the precipitates have the same origin/ i.e. are due to anelastic relaxations at the boundaries of the precipitates (Schoeck's theory). It is shown that the problem is more complex. The characteristics of these "precipitates peaks" can be different depending on the alloy. Some results, which give an account for relaxations inside the precipitates and also for mechanisms of interactions between dislocations and precipitates, have been obtained. The evolution of -the dislocations network during recrystallization modifies strongly the values of the internal friction background. In particular, the results show that recrystallization occurs after an increase of the internal friction. This leads to a new criterion for recrystallization .: recrystallization is conditioned by the increase of the dislocations mobility. From this point of view, internal friction seems to be one of the better method for studying the interactions between precipitation and recrystallization.

INTRODUCTION - Precipitation and recrystallization are the two main solid-state transformations of aluminium and copper based alloys, which condition the- quality of the semi-finished product. Internal friction measurements, which are particularly sensitive to the evolution of microstructure of the materials [l], have been advantageous in the determination of the precipitation stages of various alloys, or in the study of the evolution of the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983902

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C9-18 J O U R N A L D E PHYSIQUE

d i s l o c a t i o n network during r e c r y s t a l l i z a t i o n . Yet, it has t o be noted t h a t , during these l a s t t en years , i n t e r n a l f r i c t i o n has not been used extensively i n the study of p r e c i p i t a t i o n and r e c r y s t a l l i z a t i o n . Indeed workers, who a r e concerned with d i f fu- s ion a s s i s t e d phase transformations, p re fe r more d i r e c t o r e a s i e r methodsas forexam- p l e transmission e lec t ron microscopy, hardness, e l e c t r i c a l r e s i s t i v i t y o r thermoelec- t r i c power. In comparison with these more c l a s s i c a l techniques, the disadvantage andsimultaneous- l y t h e advantage of i n t e r n a l f r i c t i o n is t h a t the characteristic spec t ra of a l loys can be a f fec ted by a l l kinds of evolut ions of the microstructure. Therefore t h e in- t e r p r e t a t i o n of the a n e l a s t i c phenomena is sometimes d i f f i c u l t . The i n t e r p r e t a t i o n o f the i n t e r n a l f r i c t i o n spectrum and of i ts modifications during t h e t ransformationre- qu i res general ly comparisons with the r e s u l t s obtained by the other techniques. I n t h i s context , t h e research of t h e a n e l a s t i c mechanisms can bring precious informa- t i o n s on the microscopic mechanisms which a r e involved i n t h e transformation i t s e l f .

Usually the i n t e r n a l f r i c t i o n spectrum of the aluminium a l loys is composedofrela- xa t ion peaks, which a r e due e i t h e r t o t h e s o l i d so lu t ions (Zener peaks) o r t o the p r e c i p i t a t e s , and of a background which can sometimes be considered a s t h e low tempe- r a t u r e p a r t of a high temperature peak due t o d i s loca t ions [21. The re laxa t ion peaks inform on t h e d iverse phases which appear i n the a l loy during ageing. The evolut ions of t h e background and simultaneously of t h e e l a s t i c modulus can express the changes i n t h e mechanical p roper t i es . From t h i s point of view, i n t e r n a l f r i c t i o n is very wel l s u i t e d t o t h e study of t h e transformations i n which a r e involved some problems r e l a t e d t o t h e d i s loca t ions mo- b i l i t y : p r e c i p i t a t i o n hardening, annealing ou t of t h e defec t s a f t e r deformation, r e c r y s t a l l i z a t i o n .

11. PRECIPITATION : Experimental r e s u l t s

a ) Aluminium a l loys : ---------------- Among the aluminium a l loys , t h e most s tudied system has c e r t a i n l y been A1-Cu, espe- c i a l l y with a concentrat ion of 4wt% Cu 13 t o 71. The precipitation of t h e 8 phase follows t h e sequence :

0. + GP + 8 " + 8 ' + 8 A l s s s

The GP zones a r e t h i n c l u s t e r s r i c h i n Cu, p a r a l l e l t o t h e (100) planes of themat r ix and coherent. The 8" p r e c i p i t a t e s a r e p l a t e l e t s of t e t ragona l s t r u c t d r e andcoherent. The 8 ' d i f f e r s from t h e 8" p r e c i p i t a t e s by t h e l o s s of coherency on t h e l a t e r a l faces, where i n t e r f a c e d i s loca t ions appear i n order t o r e l e a s e t h e m i s f i t . F ina l ly , 8 i s t h e s t a b l e configurat ion of t h e A12Cu te t ragona l equilibrium phase. 8 i s incoherent . Hanauer e t a 1 [51 have s tudied t h i s p r e c i p i t a t i o n sequence through the evolut ion of the i n t e r n a l f r i c t i o n spectrum ( f i g . 1). A f i r s t re laxa t ion peak P1 i s associated with t h e s o l i d so lu t ion . After t h e reversion of t h e GP zones, t h i s peak i s s t a b l e . I t appears a t 185OC f o r a frequency of QlHz. I t is a Zener peak [81 , because its height i s proport ional t o the square of t h e Cu concentrat ion i n so lu t ion . PI peak i s s t i l l presen t i n t h e a l l o y a f t e r t h e appearance of t h e GP zones. I t s h e i y h t is even too g r e a t , i f t h e a n e l a s t i c r e l a x a t i o n i s only due t o the Cu atoms which re- main i n t h e s o l i d so lu t ion . I n t h i s case, Hanauer e t a l think t h a t t h i s Zener peak must a l s o be due t o some s t r e s s induced ordering i n the GP zones. P1 peak disappears and the i n t e r n a l f r i c t i o n background goes down, when t h e 8 ' ' p r e c i p i t a t e s appear-The 8 ' p r e c i p i t a t e s give r i s e t o a s t rong increase of t h e background above 2 0 0 ~ ~ and t o the appearance of a second re laxa t ion peak P2 . The height of t h i s peak i s proportio- na l t o t h e volume f r a c t i o n of Cu which has p rec ip i ta ted . The re laxa t ion i s then a t - t r i b u t e d t o the movement of t h e in te r face d i s loca t ions a t t h e boundaries of the 8 ' p r e c i p i t a t e s .

P2 peak vanishes during t h e p r e c i p i t a t i o n of 8. I n t e r n a l f r i c t i o n increases then monotonously with t h e temperature.

0 - [s s] , - [ ~ d a - [o"] . - [a'] A - [el

In case of Al-4wt%Cu, t h e p r e c i p i t a t i o n s tages a r e very well marked by the evolu- t i o n s of t h e i n t e r n a l f r i c t i o n spectrum. In o ther systems, t h e obtained r e s u l t s a r e not s o c lea r . For example, the A1-Mg binary a l loysexhi - b i t a re laxa t ion peak a f t e r ageing [9,10, 111 Belson e t a 1 1111 show t h a t t h i s peak is not due t o the p r e c i p i t a t i o n of t h e f3 phase (A13Mg2). Ef fec t ive ly , t h e peak i s a l s o observed a f t e r quenching bu t a t lower temperature. The s h i f t intemperature of t h e peak is a t t r i b u t e d t o t h e presence of vacancies which a r e i n excess i n the quenched specimen. On the o ther hand, the peak height depends l i n e a r l y on the product of t h e square of the concentra- t ions C& . c $ ~ . From these considerat ions, Belson e t a 1 a t t r i b u t e the o r i g i n of t h e peak t o a Zener type re laxa t ion whichcan be described by t h e more general modelof Leclaire and Lomer 1121. Zener type re la - xat ions a f fec ted by t h e presence of the quenched-in vacancies have a l s o been de- t ec ted i n o ther aluminium a l l o y s which contain s i l i c o n atoms. In A1-Si s i n g l e c r y s t a l s , Entwist le e t a1 [131 have observed a broad peak a f t e r

Fig. 1 : Charac te r i s t i c evolut ion of the treatments which a r e suscep t ib le t o form

i n t e r n a l f r i c t i o n during p r e c i p i t a t i o n i n f i n e p r e c i p i t a t e s of S i around t h e vacan-

Al-4wt%Cu ( a f t e r C. Hanauer, e t a1 [ 51 ) . cies. The peak is then interpreted as due t o t h e re laxa t ion of t h e "Si-vacancy" e- l a s t i c dipoles .

In Ai-Cu-Si-Mg, a peak is growing during ageing near room temperature. E l l i o t t and Entwist le 1141 a t t r i b u t e the o r i g i n of t h i s peak t o a s t r e s s induced ordering mechanism i n t h e zones which a r e formed by s o l u t e atoms and vacancies. The p e a k i s a Zener peak because its height v a r i e s l i n e a r l y with t h e square of t h e Mg concentration. A peak is a l s o observed a f t e r ageing i n an Al-Mg-Si i n d u s t r i a l a l l o y [151. This peak seems t o be due t o re laxa t ions i n t h e f3(Mg2Si) p r e c i p i t a t e s . These re laxa t ions a r e favoured by t h e presence of vacancies i n t h e p r e c i p i t a t e s . Prec ip i ta t ion can a l s o modify the i n t e r n a l f r i c t i o n without giving r i s e t o r e l a x a t i o n peaks. In Al-Zn a l l o y s , t h e i n t e r n a 1 , f r i c t i o n background increases during prec ip i ta - t ion. Nowick 1161 has a t t r i b u t e d t h i s increase t o the p r e c i p i t a t i o n of t h e 6 p h a s e a t the g ra in boundaries. By means of microcreep experiments, he has shown t h a t t h e ane- l a s t i c s t r a i n does not reach an equilibrium value. He explained then t h i s behaviour by t h e idea of coupled re laxa t ions . Through t h e evolut ions of t h e i n t e r n a l f r i c t i o n background, Mer l inanda l 1171 determined four p r e c i p i t a t i o n s t a g e s associated with the diverse p r e c i p i t a t e s (GP, R , a' and 6) i n Al-25 and 30wt%Zn.

The study of p r e c i p i t a t i o n by i n t e r n a l f r i c t i o n has a l s o been performed i n some copper based a l loys . Peaks have been observed owing e i t h e r t o t h e s o l i d s o l u t i o n a s i n t h e case of Cu-Zn (discovery of t h e well known Zener peak [ 1 8 l ) , o r t o t h e p r e c i p i t a t e s .

I n a CU-3wt%Co a l l o y , Mondino and Schoeck [19] have obtained a re laxa t ion p e l k a f - t e r ageings which lead t o t h e coherency l o s s of t h e p r e c i p i t a t e s . The o r i g i n of the peak has then been a t t r i b u t e d t o t h e re laxa t ion , a s s i s t e d by t h e d i f f u s i o n of the Co atoms, of t h e i n t e r f a c e d i s loca t ions . In the same way, Mondino and co-workers [20,21] give an account f o r a peakassociated with the semi-coherent x p r e c i p i t a t e s i n Cu-17wt%Si.

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On the contrary, t h e Cu-Fe a l loys exh ib l t a peak associated with coherent p rec ip i ta - t e s . This peak has been s tudied by P e l l e t i e r 122,231. I t disappears when t h e precipi- t a t e s become incoherent. P e l l e t i e r i n t e r p r e t e s then t h e peak as due t o a complex re- l axa t ion of Zener type i n the p r e c i p i t a t e s of Fe. A mechanism of s t r e s s induced ordering has a l s o been observed i n the "ferromagnetic" p r e c i p i t a t e s of t h e Cu-Ni system [24,25,26].

Conclusions : The d iverse examples presented here show t h a t each a l l o y exhib i t s an i n t e r n a l f r i c t i o n spectrum more o r l e s s complex, which is modified by prec ip i ta t ion .

The i n t e r p r e t a t i o n of the a n e l a s t i c re laxa t ions is mainlybasedontwomechanisms : the reor ien ta t ion under the applied s t r e s s of e l a s t i c dipoles (Zener re laxa t ion) and t h e movement of t h e precipi tates-matr ix in te r faces . I t seems a l s o t h a t the r e a l mechanisms can be more complex than those which a r e described by t h e e x i s t i n g models. Ef fec t ive ly , i n many cases, these models do not o f f e r a s u f f i c i e n t descr ip t ion o f t h e i n t e r n a l f r i c t i o n behaviour. The involved mechanisms may be d i f f e r e n t depending on the system which e x h i b i t s the peak.

111. PEAKS DUE TO PRECIPITATES : Theoret ical considerat ions

" P r e c i p i t a t e s peaks" a r e re laxa t ion peaks which appear associated with the presence i n the a l l o y of p r e c i p i t a t e s . Usually, t h e height of these peaks is proport ional t o the volume f r a c t i o n of t h e pre- c i p i t a t e s , i . e . t o the concentration of the a l l o y , when p r e c i p i t a t i o n is complete. Hence they d i f f e r from the Zener peaks, t h e height of which var ies l i n e a r l y with t h e square of t h e concentration. The ac t iva t ion enercrv of these weaks i s alwavs l i a h t l v lower than the d i f f u s i o n ener- av of t h e s o l u t e atoms. Hence the re laxa t ion is cont ro l led bv t h e movement of s o l u t e atoms which a r e i n n a r t i c u l a r wosition. f o r examwle. near t h e d i s loca t ions . The value of the l i m i t frequency 1012-1015~z gives a l s o an account f o r atoms movements.

Taking i n t o account t h e r e s u l t s obtained i n diverse a l l o y s , Schoeck has e l a b o r a t e d i n 1969 a theory of the a n e l a s t i c i t y due t o the p r e c i p i t a t e s [ 2 7 ] . I n h i s research, Schoeck considers the p r e c i p i t a t e s a s inclusions i n t h e matrix. He determines then t h e in te rac t ions between t h e p r e c i p i t a t e s and the applies s t r e s s t a - king i n t o account t h e t h e o r e t i c a l works of Eshelby [28,29]. The i n t e r a c t i o n energy gives t h e maximum value of the i n t e r n a l f r i c t i o n due t o t h e p r e c i p i t a t e s . The conclusions of t h e Schoeck's theory a r e t h a t only t h e incoherent o r semi-coherent p r e c i p i t a t e s can give r i s e t o an i n t e r n a l f r i c t i o n peak. This peak would be causedby a n e l a s t i c re laxa t ions which take place a t t h e i n t e r f a c e s between matrix and precipi- t a t e s . I n t h e case of semi-coherentprecipitates,the a n e l a s t i c s t r a i n is due t o t h e in- t e r face d i s loca t ions . Coherent p r e c i p i t a t e s cannot give r i s e t o an i n t e r n a l f r i c t i o n peak. They cont r ibu te t o the background which increases monotonously with the tempe- ra tu re . An equilibrium value f o r t h e relaxation i s never reached because the movement of t h e i n t e r f a c e s depends on t h e d i f fus ion k i n e t i c s which increase with tempe- ra tu re .

Remarks : I f the Schoeck's theory i s v e r i f i e d i n the case of the a l l o y s a s Cu-Co [19& where t h e peak appears only a f t e r t h e coherency l o s s of the p r e c i p i t a t e s , it cannot be appl ied t o t h e system Cu-Fe, where t h e peak appears with t h e coherent p rec ip i ta - t e s and disappears during the coherency loss . This theory is then too much r e s t r i c t i v e with re ipec t t o t h e condit ions of the appearance of a " p r e c i p i t a t e s peak".

A t f i r s t , Kohen shows t h a t t h e a n e l a s t i c s t r a i n is always d i f f e r e n t from zero when the p r e c i p i t a t e s present an anisotropy i n t h e mobility of t h e i r d i f f e r e n t in te r faces . This is, i n p a r t i c u l a r , the case of the semi-coherent p r e c i p i t a t e s . Incoherent pre- c i p i t a t e s can give r i s e t o an a n e l a s t i c re laxa t ion only when t h e i r i n t e r f a c e s have

a g l i s s i b l e s t r u c t u r e . The model considers p l a t e shaped p r e c i p i t a t e s . A t a constant temperature, t h e preci- p i t a t e can be character ized by th ree thermodynamical var iab les : t h e shear s t r e s s , the so lu te concentration a t t h e i n t e r f a c e and t h e p r e c i p i t a t e diameter. The appl ied s t r e s s induces across t h e i n t e r f a c e a d i f fe rence i n t h e thermodynamical p o t e n t i a l . The p r e c i p i t a t e growths then o r dissolves i n order t o reach a new equilibrium s t a t e . The movements of t h e i n t e r f a c e s a re con t ro l led by the d i f f u s i o n of t h e so lu te atoms.

When the i n t e r f a c e mobility is grea t , t h e i n t e r n a l f r i c t i o n exhib i t s a peak, whose half-width is only 13% g r e a t e r than t h e one of a Debve peak. I f t h e i n t e r f a c e mobil i ty goes down, the ac t iva t ion energy is modified. The peak s h i f t s then towards the high temperatures, broadens out and vanishes i n t h e background. In conclusion, i n t e r n a l f r i c t i o n associated with the p r e c i p i t a t e s depends on t h e na- t u r e of t h e i r in te r faces . The a n e l a s t i c phenomena a r e only important when t h e i n t e r - face has a g l i s s i b l e s t r u c t u r e . F ina l ly , it has t o be remarked t h a t the above mentioned theor ies a r e not concerned with t h e p o s s i b i l i t y of a n e l a s t i c re laxa t ions ins ide t h e p r e c i p i t a t e s . They a r e only based on problems r e l a t e d t o the i n t e r f a c e s created by p r e c i p i t a t i o n . The A1-Ag system : ---------------- The A1-Ag a l l o y s have been s tudied by many authors [31 t o 383. After ageing , a s t a - b l e re laxa t ion peak appears associated with the presence of t h e y ' (Ag2Al-hcp) pre- c i p i t a t e s (peak P 3 o n . f i g . 2 ) .

This peak was considered a s t h e i l l u s t r a - t i o n of the Schoeck's theory 1271. I t w a s

F(Hz) 4 then a t t r i b u t e d t o t h e re laxa t ion of the A Q-' . lo3 A I - A ~ 30%:

p a r t i a l d i s loca t ions whichsurround t h e I :After quenching 2:After lomi" 520K -.a5 y T p r e c i p i t a t e s .

But t h i s i n t e r p r e t a t i o n h a s b e e n questio-

10- ned by Mer l inanda l 1351 and Scha l le r [36l. Ef fec t ive ly , i f t h e peak is due t o i n t e r -

-.'' faces re laxa t ions , i t s height must decrea- 5 - se during t h e coalescence of the precipi-

t a t e s , because, i n t h i s case, t h e a r e a o f the i n t e r f a c e s is reduced, while t h e to-

o T(K): .75 t a l volume of t h e p r e c i p i t a t e s remains

3&J 350 400 450 500 constant . Now t h e peak height is not affected by the coalescence of the y' pre- c i p i t a t e s . The peak height i s constant

Fig. 2 : Evolution of the i n t e r n a l f r i c t i o n spectrum of an Al-30wt%Ag during prec ip i ta -

during a l l overageing. The Schoeck's model [33] of t h e anelas-

t i o n [ 3 6 1 . t i c re laxa t ions a t t h e boundaries of the y' p r e c i p i t a t e s has been completely re-

fu ted by t h e r e s u l t obtained by Schal ler [37] i n a pure y phase a l loy . I t is shown t h a t the re laxa t ion peak i s maximum i n height i n a monophased specimen ( f i g . 3 ) . The peak must then be due t o some reor ien ta t ion under t h e appl ied s t r e s s of e l a s t i c dipoles i n the Y' p r e c i p i t a t e s [38].

Discussion : This l a s t r e s u l t shows t h a t the a n e l a s t i c re laxa t ions associated with the p r e c i p i t a t e s do not a l l have t h e same or ig in . I f we consider the p r e c i p i t a t e s peak i n aluminium a l l o y s , the temptation is g r e a t t o search f o r an universal theory. Ef fec t ive ly , a l l these peaks appear i n the samerange of temperature f o r measurements a t low frequency ( % ~ H z ) , because t h e i r ac t iva t ion e- nergy, which is bound with the d i f fus ion energy of t h e so lu te atoms, is not very d i f - f e r e n t i n one or the o ther system.

Though some c h a r a c t e r i s t i c s of the peaks can be d i f f e r e n t depending on t h e a l loy . For example, it is possible t o compare A1-Ag with A1-Cu. The peak due t o t h e y ' precipi- t a t e s i n A1-Ag presents a small broadening f a c t o r (6=1.12) and t h e l i m i t r e laxa t ion

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time (To = 4'10-15s) is low 1363. This tends

Fig- 3 : The precipitates peak of the A1-Ag alloys is maximum in a pure y phase alloy, i.e. in an A1-85wt%Ag.

to show that the peak is due to atomic movements. On the contrary, the peak associated withthe 8 ' precipitates in the A1-Cu alloys has a greater broadening factor (B=3) and the li- mit relaxation time is higher (To = l ~ - ~ ~ ~ ~ . ~ S

131- These characteristics are nearer of those of the peaks associated with the movements of dislocations. Moreover, the 8 ' precipitates peak vanishes during the coherency loss. In this case, it seems that the interface relaxation models are correct. In conclusion, precipitates peaks cannot be explained by a unique theory. The anelastic relaxations can take place as well at the interfaces as inside the precipitates. This last possibility is of a great interest. Effectively, internal friction is then the technique very well suited to the study of the internal properties of a second phase particles which are dispersed in a matrix.

The particles are excitated by the stress applied through the interfaces. They can give then a response as an anelastic strain which is proportional to the volume frac- tion of the second phase.

IV. RECRYSTALLIZATION

Free energy of a metal increases with the density of defects (mainly dislocations) produced by plastic deformation. The return towards a more stable thermodynamical state is achieved by the annealing out of the defects during the formation of new grains, which present a crystallographic orientation different from the one of the matrix. This transformation is called recrystallization and is usually preceded by a recovery stage (annihilation of some point defects and of dislocations of opposite sign, rearrangement of the dislocations network) [39]. In this case too, internal friction seems to be very well suited to the study of the evolution of the microstructure. In pure metals, recrystallization exhibits first an increase of the internal friction followed by a subsequent decrease at the end of the transformation. This behaviour has been observed in diverse metals as Cr [40], Cd 1411, Fe 1431, Au [44,45], Ag [42 and 46 to 481, Co and Ni [49,50], and interpreted thanks to the well-known Granato- Liicke theory for dislocations damping [51]. As a typical example, one can consider the results obtained in pure silver by Isord [52]. The internal friction, measured at room temperature and reported as a function of the temperature of the annealings of deformed specimen, presents three stages in its evolution (fig. 4) : a light decrease associated with the recoverystage,a strong increase up to a maximum due to the primary recrystallization and finally a decrease during a post.recrystallization stage, which is interpreted as due tothere-arrangement of the dislocations in the recrystallized phase. Thestronglncrease of the internal friction is attributed by Isor6 et a1 [53] to a high degree of mobility ofthe dislocations in the freshly recrystallized domains behind the migrating grain boundary. Thanks to the Granato-Lucke model, Isord determines than the evolutions during recrystallization of the density "i\" and the loops length "R" of the dislocations. Rather than measuring the evolutions of the internal friction background, J. Petit et a1 1543 have studied the recrystallization in Zr and Ti through the recovery stages of a peak due to the dislocations.

Three stages have also been observed. But,in 0.'. lo3 -AEIE VJ the present case, the peak height increases

0 i . . Jo o Y) m w m zro m k m

Fig. 4 : Internal friction (

defect of elastic modulus 99,995 %, measured at 20°C as a function of the temperature (TR) of isochronal (lh) annealings. Three stages of evolution appear. (after Iso- r& et a1 [52]).

before recrystallization and decreases when recrystallization takes place. The increase in internal friction is then attributed toan increase in the loops length "I." by the migration of the pinning defects along the dislocations. The decrease of the internal friction during recrystallization has also been observed by Yamane in Ti [55,561 and in steel 157,583. In alloys, it is easy to understand that internal friction goes down during recrystallization. Effectively, in this case, the loops length "R" of the dislocations aredetermined by the pinners solute atoms, and "P does not depend strongly on the dislocations density "I\". Internal friction which is proportional to "A" is then greater in the deformed samples than in the recrystallized ones. The decrease of the internal friction value gives then an account for the decrease of the dislocations densityduringrecrystallization.

All the above mentioned examples give an evidence for the sensitivity of internal friction to the evolution of the dislocations network during recrystallization. As internal friction is affected by the interactions of the dislocations with other defects, it can be interesting to use it for the study of the interactions precipitation-recrystallization in alloys.

V. RECRYSTALLIZATION IN A1-Mn ALLOYS

The problem of the interactions between precipitation and recrystallization in the A1-Mn alloys has received considerable attention in the last few years C59 to 621. In all these works, techniques such as electrical resistivity, hardness, optical and electron microscopy have been used. These techniques allow one to observe the microstructure at each stage of its evolution. But they are not well suited to the study of the dynamlcal interactions between the dislocations and the second phase particles. Therefore, Diallo [63,64,65] has studied the recrystallization in A1-Mn alloys by means of internal friction measurements, and obtained the following results. Theheavalydeformed Al-0.5 to 2wt% Mn alloys present, during isochronal annealings, two main stages in the evolution of the internal friction spectrum (fig. 5)

4 0 -

o after 10' at 473 K Evolution of the lnternal friction v .. .. .. 5 7 3 ~ -1.10 spectrum of a commercial A1-1%Mn x .. .. ,, 650K alloy during isochronal annealings

- 1,05 [63

2 0 -

1 0 - - 0.95

T(K) 0.90 250 350 450 550 650

- Isochmnal treatments J 1.15 Fl9- 5 :

C9-24 JOURNAL DE PHYSIQUE

Fig. 7 : Dependance of the peak height and the background on the thermomechanical treatments. Re- mark the effect of deformation.

The first stage is characterized by an increase in internal friction, observed after annealing at a temperature of 573K. This increase in internal friction has been attributed to the increase in length of the dislocation loops, when the pinning Mn a- toms are clustering to form new precipitates. This stage is then due toprecipitation, an interpretation confirmed by the measurement of the residual electrical resistivity and of the thermoelectric power (fig. 6).

The second stage appears after ageing at

tion peak :

Q-' = !AT 1+!A2~2

- 1L -

-1.6

where Ci is a proportionality constant, I\ the dislocation density,

and k the dislocations loops length. The high temperature internal friction background has been attributed to an interaction mechanism of the dislocations with theMnso- lute atoms. For this case, the model leads to an expression of the type :

As a consequence the peak and the high temperature internal friction backqround are both sensitive to the evolution of the dislocation microstructure. The product gives then a measure of the total driving force for recrystallization In effect, the self driving force due to the dislocation elastic energy is propor-

! S(pvIYIK1 At - lw t% Mn-05wt% Fe A0 - P

Isochronal (IOmn) annealtngs :-07/eF0s ;;

*\ 4

o - ' D TRIK]

tional to A, while the dragging force due to the Mn solute atoms, which pin the dis-

A %65OK. It is associated with astrongdecrea- se in internal friction, due to the reduc- tion of the dislocation density during recrystallization. This has been confirmed by microscopic ob-

-I.oo servations. After the decrease of the internal friction, a relaxation peak appears at V20K (fig.5)

-ma In fact, this peak appears already at the first stage of the evolution of the deformed alloy, but is only detectable when the

0.60 internal friction is relatively weak (fig.8).

300 500 700

locations, is proportional to the inverse of the length k. Consequently the higher

The existence of this peak seems to be con-

the peak or thehightemperature internal friction background, the lower the recrys-

nected with the presence of metastable pre-

Fig. 6 : Evolution of the electrical cipitates of GI (Al12Mn,bcc) type [ G O ] . Yet,

resistivity and the thermoelectric its characteristics are not those of the

power during precipitation in classical peaks due to precipitates. More

Al-lwt%Mn [ 6 5 ] . precisely its height is not proportional to the concentration of the alloy, but depends on the dislocation density (fig. 7) : the peak is absent in the undeformed specimen. In conclusion, the relaxation peak in the A1-Mn system is associated with the simulta- neous presence of dislocations and precipitates.

A ' l o A\ - iwl l . Mn

Diallo has then elaborated a theoretical model, based on a microscopic mechanism of interactions between dislocations and precipitates, the formalism of which is similar to

20 the Schiller's model [ 6 6 ] . It leads to the following expression for the internal fric-

40

I 'Aged 2Lhrs at 573K 2:60% deformed 3:Aged 30mn at 573K+60'1. deformed 4. " 2Lhrs ', " a. "

-

tallization temperature (fig. 8 ) .

In the A1-Mn alloys, precipitation favours recrystallization, because it decreases the

' ' ~ " ' ~ a o dragging forces due to the solute atoms which pin the dislocations. In this case, internal friction increases during precipitation. On the contrary, in A1-Ag alloys, recrystallization is impeded by precipitation which

-70 gives rise to an increase of the dragging forces due to the pinning of thedislocations by the precipitates 1361. In this case, ac- cording to Diallo's interpretation, the high temperature internal friction background de-

300 500 700 creases during precipitation.

Discussion : All the results found in theli- Fig. 8 : Internal friction spectrum terature show that internal friction is affec- of two Al-lwt%Mn specimen. A great ted by recristallization through the evolu- relaxation peak leads to a low re- tions of the dislocations microstructure. In crystallization temperature. addition, the results obtained by Diallo [651

show that the advantage of using internal friction is the possibility to study the dy-

namical aspects of the re-arrangement of the dislocations. This is not possible with classical techniques. The internal friction results obtained in A1-Mn show that recrystallization is conditioned by the liberation of the dislocations which have to be re-arranged. Effec- tively, if the dislocations cannot move, the formation of the subgrains boundaries, which are at the origin of the nucleation of the new grains [39], is impossible and consequently recrystallization cannot start as it was the case in A1-Ag [361. From this point of view, dislocations play the most prominent part in the nucleation of the primary recrystallization. Internal friction, which measures the product h i [651, is then sensitive to the driving force for nucleation. Before recrystallization, the dislocations density can be considered as constant. Thus, the variations of the internal friction give an account for the evolution of the dragging forces which act on the dislocations. Therefore internal friction must increase before recrystallizationstarts.1nthis di- rection, Diallo's results are confirmed by the results obtained by Petit et al in Zr and Ti [541. On the contrary, Isore [52,53] attributes the increase of internal friction to the apparition of domains which are already recrystallized. But,in this case, the mode of nucleation of the new grains is different. Effectively, the deformation of the samples measured by Isori. is small (%lo%), and in this case the nucleation can be achieved by the migration of a grain boundary which was pre-e- xistent to the plastic deformation [391. Effectively, Isor6 [ 5 3 ] has observed the nucleation of new grains on the "old" grain boundaries. This mechanism does not requi- re the formation of subgrains during the recovery stage. It would be interesting to study more in details the different modes of nucleation of the new grains by the method developed by Diallo et al [63 to 651.

CONCLUSIONS

Internal friction is sensitively affected by precipitation and recrystallization.The results found in the literature show that the origins of the anelastic phenomena can be different depending on the material. For example, the peaks associated with the precipitates can be due either to interfaces mechanisms as in A1-Cu alloys [S] or to relaxations which take place in the pre-

cipitates as in A1-Ag alloys [371. Internal friction is then a powerful method for studying the problems related to the coherency of the interfaces as in the Cu-Co system 1191 or the internal properties of second phase particles dispersed in the matrix. This last aspect has already been used withsuccessby Millet [671 in the study ofthe damping capacity of grey cast iron : here the damping is due to internal frictionme-

C9-26 JOURNAL DE PHYSIQUE

chanisms in the graphite precipitates. Now, if the precipitation stages can be revealed by the evolution of the internal friction spectrum, the method is not well suited to the study of the first stages of the rapid decomposition of the quenched solid solutions. In this case it is nearly impossible to measure the internal friction under equilibrium conditions. In recrystallization, internal friction would have to be used for the study of the dynamical interactions between the dislocations and other defects. Effectively, the results obtained in this field show clearly the prominent part which is played by the dislocatio:~~ in the nucleation of the new grains. Internal friction seems then to be sensitive to the driving force acting on the dislocations which have to be re-arranged. It would be of a great interest to search further for the microscopic mechanisms whish can give an accoupt for the thermodynamical models of recrystallization. Such a research requires naturally thecomparisons of the results obtained by different techniques. In this field, and more generally in diffusion assisted phase transformations, internal friction is advantageous in the problems, where the dislocations mobility is involved.

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a n d SCHALLER R. , T h e s l s , E P F - L a u s a n n e ( 1 9 8 0 )

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internal friction associated with precipitation and ... · introduction - precipitation and...

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