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INTERNAL FRICTION PEAKS CONNECTED WITH GRAIN BOUNDARY SLIDING IN Al
E. Bonetti, A. Cavallini, E. Evangelista, P. Gondi
To cite this version:
E. Bonetti, A. Cavallini, E. Evangelista, P. Gondi. INTERNAL FRICTION PEAKS CONNECTED
WITH GRAIN BOUNDARY SLIDING IN Al. Journal de Physique Colloques, 1983, 44 (C9), pp.C9-
759-C9-764. �10.1051/jphyscol:19839115�. �jpa-00223350�
Colloque C9, supplt5ment a u n012, Tome 44, d k e m b r e 1983 page C9-759
I N T E R N A L F R I C T I O N P E A K S CONNECTED W I T H G R A I N BOUNDARY S L I D I N G I N A 1 E. Bonetti, A. Cavallini, E. Evangelista and P. ~ondi'
I s t i t u t o d i F i s i c a d e l l 'Universita', Unita' G.N.S.M. d e l C.N.R., V i a I m e r i o , 46, 40126 Bologna, I t a l y
+ ~ s t i t u t o d i F i s i c a d e l l ' U n i v e r s i t d d i Bologna, Unita' G . N.S.M. d e l C. N.R. and I s t i t u t o d i MetalZurgia d e l Z r U n i v e r s i t d , V i a m d o s s i a n a , 18, 00184 Roma, I t a l y
Resume
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C o n d i t i o n s d ' e q u i l i b r e e n t r e e m i s s i o n e t absorption,dans l e s j o i n t s , de d i s l o c a t i o n s Zi l L i n t 6 r i e u r des grains,sans g l i s s e m e n t aux j o i n t s , e m i s s i o n ou a b s o r p t i o n u n i l a t e r a l de d i s l o c a t i o n s montant 1 l 1 i n t 6 r i e u r des g r a i n s avec g l i s s e m e n t a p p a r e n t aux j o i n t s , e t g l i s s e m e n t i n t r i n s e q u e du 1 l ' a c t i o n p r e v a - l e n t e de d i s l o c a t i o n s aans l e s j o i n t s , o n te t e
r a p p o r t % aux p i c s de f r o t t e m e n t i n t e r i e u r p r e s e n t e s 1 t e m p e r a t u r e s moyennes e t h a u t e s p a r A1 p o l y c r y s t a l l i n . A b s t r a c t - C o n d i t i o n s o f dynamic e q u i l i b r i u m between g r a i n boundary s i n k and e m i s s i o n o f l a t t i c e d i s l o c a t i o n s w i t h o u t g.b. s l i d i n g , u n i l a t e r a l s i n k o r e m i s s i o n of c l i i n b i n g l a t t i c e d i s l o c a t i o n s w i t h e x t r i n s i c o r a p p a r e n t g.b. s l i - d i n g , and i n t r i n s i c g.b. s l i d i n g due i n p r e v a l e n c e t o g . b . d i s l o c a t i o n s have been c o r r e l a t e d w i t h t h e medium and h i g h t e m p e r a t u r e Q' peaks p r e s e n t e d by p o l y c r y - s t a l l i n e A l .I n t r o d u c t i o n
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I n p r e v i o u s papers / I - 4 / i t has been shown t h a t t h e 9 - l p e a k f i r s t observed by KG /5/ i n p o l y c r y s t a l l i n e A1 ( f o r a r e v i e w o f c o r r e s p o n d i n g peaks i n o t h e r m e t a l s see e.g./6/) f i n a s correspondence w i t h peaks w i c h can be observea i n A1 s i n g l e c r y s t a l s o r i n m a c r o c r y s t a l l i n e specimens a f t e r s l i g t h d e f o r m a t i o n .:doreover even non deformed s i n g l e c r y s t a l s w h i c h do n o t show e v i d e n c e o f such peakpre- s e n t / 7 / modulus decreases comparable t o t h o s e observed a f t e r s l i g t h a e f o r m a t i o n , so t h a t t h e l a c k o f peak o b s e r v a t i o n i n t h e s a i d s i n g l e c r y s t a l s has been r e f e r r e d t o peaks c o r r e s p o n d i n g t o a b r o a d range o f r e l a x a t i o n t i m e s w i t h a consequent spread l e a d i n g t o a background s i m i l a r b e h a v i o u r .
F o l l o w i n g t h e s a i d o b s e r v a t i o n s , i n t e r p r e t a t i o n s have been d i s c u s s e d /4,8/ a c c o r d i n g t o w h i c h t h e peak ( r e s o l v e d i n two components/3,9/) i s e x p l a i n e d i n terms o f a i f - f u s i v e m o t i o n o f d i s l o c a t i o n s i n s t e a d o f s i m p l e g.b. s l i d i n g , as g e n e r a l l y assumed by t h e v a r i o u s a u t h o r s /6/.
However, g.b. s l i d i n g i s a e v i d e n t phenomenon i n t h e h i g h t e m p e r a t u r e d e f o r m a t i o n and r e l a t i n g c o n t r i b u t i o n s t o i n t e r n a l f r i c t i o n have t o be expected ( s e e a l s o 10).
T h i s paper d e a l s w i t h o b s e r v a t i o n s aimed a t a n a l y s i n g t h i s c o n t r i b u t i o n , which we t h i n k t o have f o u n d as r e f e r a b l e t o a second peak a t h i g h e r temperature, seen d u r i n g t h e p r e s e n t measurements and a l r e a d y observed by W i l l i a m s e t a l . /11/.
On t h e o t h e r hand, a t t h e l o w e r temperatures t h e p o s s i b i l i t y i s d i s c u s s e d t h a t c l i m b phenomena i n t h e g r a i n i n t e r i o r , as h y p o t h i z e d f o r s i n g l e c r y s t a l damping, can g i v e r i s e i n p o l y c r y s t a l s t o e x t r i n s i c , a p p a r e n t , g . b . s l i d i n g . On d e a l i n g w i t h g.b. s l i d i n g o n l y some r e f e r e n c e s i n e v i d e n c e f o r d i s c u s s i o n purposes w i l l be r e c a l l e d e x p l i c i t e l y ; many o t h e r r e f e r e n c e s e x i s t f o r v a r i o u s s p e c i f i c p o i n t s w h i c h would have r e q u i r e d a t o o ample b i b l i o g r a p h y ; so f o r t h e s e same g e n e r a l r e v i e w s a r e o n l y r e c a l l e d /12-16/.
Experimental
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The o b s e r v a t i o n s were c a r r i e d o u t on s h e e t s o f A1 99.99% p u r e 5x1oam Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19839115C9-760 JOURNAL DE PHYSIQUE
t h i c k as obtained a f t e r primary and secondary r e c r y s t a l l i z a t i o n and as deformed a f t e r secondary r e c r y s t a l l i z a t i o n .
I n t e r n a l f r i c t i o n
( 4 - I )
and dynamic modulus (F1 ) measurements were made by t o r s i o n a l and f l e x u r a l v i b r a t i o n s i n t h e frequency range from 5 t o 100 Hz, from ambient tempe- d r a t u r e up t o 850K and under Pa vacuum. V i b r a t i o n amp1 i t u d e s were< lo-'.
For amplitude e f f e c t s r e f e r e n c e i s made t o 191 and 171.
SEN observations were c a r r i e d o u t on specimens f i r s t p o l i s h e d and then deformed a t constant l o a d up t o t h e onset of s t a t i o n a r y creep, a t d i f f e r e n t temperatures ana de- formation r a t e s . To f o l l o w g r a i n boundary s l i d i n g a g r a t i n g o f l i n e s was marked on t h e s u r f a c e p o l i s h e d before deformation.
Results
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Figures l a ) - b ) - c ) show t h e behaviour o f i n t e r n a l f r i c t i o n c o e f f i c i e n t and of dynamic modulus as a f u n c t i o n o f temperature as measured on t h e specimens of r e - c r y s t a l l i z e d A1 b e f o r e and a f t e r deformation. I n a l l cases a peak i s n o t i c e d hence- f o r t h l a b e l l e d HT, a t-
800K, beside those a t-
600K and a t-
670K l a b e l l e dK1
and K2.Fig. 1
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I n t e r n a l f r i c t i o n c o e f f i c i e n t Q-land dynamic modulus (Md) vs temperature f o r r e c r y s t a l l i z e d A1 sheets w i t h g r a i n s i z e s d = 3xIO-'+m (a), d = 7x10-'+m ( b ) , d = 3 ~ 1 0 - ~ m ( c ) and d = 3 ~ 1 0 - ~ m and deformed 5% ( d ) .From t h e peak temperature displacements as a f u n c t i o n o f frequency t h e f o l l o w i n g a c t i v a t i o n energies H and pre-exponentials T, have been determined
Peak '(1 K2 HT
I n general t h e peak widths a r e l a r g e r than t h e Debye ones.
Peak HT may be considered as corresponding t o t h a t observed by Williams-Leak 1111 approximately under equal c o n d i t i o n s and c a l l e d HT, too, even i f a higher a c t i v a t i o n energy r e s u l t s (289 KJ/mol) from t h e measurements of these authors w i t h A1 speci- mens which had bamboo s t r u c t u r e s .
SEM observations r e s u l t s are i 11 u s t r a t e d by Figs. Pa)-b)-c) which show g r a i n bound-
peaks i n q u e s t i o n a t deformation 5% and a t a deformation r a t e
i
o flo-'
sec-l.F i g u r e 3 gives average s l i p l i n e d e n s i t y vs temperature as measured i n
SEM
f o r t h e above deformation and deformation r a t e ; t h e r e g i o n o f e v i d e n t g.b. s l i d i n g i s i n d i - cated i n t h e same f i g u r e by cross hatching.Fig. 2a)-b)-c)
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SEM images o f g r a i n boundaries and adjacent grains a f t e r deformation a t 500K (a), 775K ( b ) , 855K ( c ) . Deformation r a t e sec-l.Fig. 3
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S l i p l i n e d e n s i t y vs temperature a f t e r 5% deformation w i t h deformation r a t e s e c - l .The f i r s t s l i p 1 in e d e n s i t y decrease occurs from temperature TI ; from t h e metal l o - g r a p h i c p o i n t o f view t h i s decrease i s c h a r a c t e r i z e d by t h e appearance o f dissynmetries a t t h e g r a i n boundaries, c o n s i s t i n g i n t h e f a c t t h a t more s l i p l i n e s a r e i n general e v i d e n t ononeofthetwo g r a i n s meeting a t t h e g.b.; one o f t h e g r a i n s o f t e n showed no e v i d e n t s l i p l i n e s . A t l o w e r temperatures i n s t e a d s l i p l i n e s p r e s e n t i n general e q u i v a l e n t d e n s i t i e s on b o t h sides o f t h e g r a i n boundaries. Further, i t i s n o t i c e d t h a t t h e f i r s t decrease from temperature 71 corresponds t o t h e appearance o f g r a i n boundary s l i d i n g . The second decrease occurs from T2; t h i s decrease i s accom- panied i n many g r a i n s by t h e complete disappearance o f e v i d e n t s l i p l i n e s ; i n o t h e r g r a i n s t h e l i n e s observed appear i n general connected w i t h p l a s t i c i t y i n correspon- dence o f t r i p l e p o i n t s .
Both c r i t i c a l temperatures
TI
and T2 depend on t h e deformation r a t ei ,
assumingp r o p o r t i o n a l t o e-H/RT; t h e f i r s t decrease, r e l a t e d t o
TI,
corresponds t o an apparent a c t i v a t i o n energy HI-
100 KJ/mol; f o r t h e h i g h e r temperature drop t h e T2 dependence on deformation r a t e r e s u l t e d smaller, l y i n g w i t h i n t h e e r r o r s ; i t may be o n l y argued f o r an a c t i v a t i o n energy Hz2
250 KJ/mol.C9-762 JOURNAL DE PHYSIQUE
Discussion
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The d i s c u s s i o n i s e s s e n t i a l l y based on t h e c o r r e l a t i o n between Q-I peaks and r e s u l t s o f SEN observations on g r a i n boundary s l i d i n g and s l i p l i n e c h a r a c t e r i s t i c s . I n p a r t i c u l a r i t i s n o t i c e d t h a t t h e temperatures o f t h e K and HT peaks f a l l i n t h e range w h e r e t h e drops o f s l i p l i n e d e n s i t y occurs. So peaks K and HT w i l l be r e l a t e d t o t h e same processes t o which t h e two c r i t i c a l temperatu- res are r e l a t e d , i .e. e x t r i n s i c and i n t r i n s i c g r a i n boundary s l i d i n g . D e t a i l e d con- s i d e r a t i o n s on t h e two mechanisms o f s l i d i n g a r e discussed i n another paper. Here we r e c a l l t h a t we consider e x t r i n s i c g.b. s l i d i n g t h e one due t o t h e s i n k o f l a t t i c e d i s l o c a t i o n s i n t h e g r a i n boundary itse1f;we consider i n t r i n s i c t h e s l i d i n g due t o simple g r a i n boundary d i s l o c a t i o n motion.The processes l e a d i n g t o e x t r i n s i c g.b. s l i d i n g are i l l u s t r a t e d i n Figs. 4a)-b). The e f f e c t s o f s i n k o f one edge d i s l o c a t i o n , say -I-, may be d i s t i n g u i s h e d i n t h e compo- nents o f t h e l a t t i c e Burgers v e c t o r p a r a l l e l and orthogonal t o t h e g.b. plane. The second component c o n t r i b u t e s t o t h e g r a i n boundary angle, i n analogy w i t h small angle t i l t boundaries. The f i r s t component m i g h t be seen as a g.b. d i s l o c a t i o n w i t h Burgers v e c t o r b t = b cos a; however, b/ do n o t correspond t o any extended s l i d i n g on t h e g . b . plane, up t o t h e d i s l o c a t i o n f r o n t , By i n c r e a s i n g r a t e o f s i n k o f head dislocations,-l-,back stresses w i l l grow governing t h e c l i m b by l a t t i c e d i f f u s i o n o f d i s l o c a t i o n l i k e -2-,
----,
i n t h e dynamic p i l e - u p ; i f d i s l o c a t i o n -2-, etc., climbs on a neighbour plane, s i n k i n the g.b. can then occur a f t e r overcoming o f some minor backstresses.Figs. 4a)-b)-c)
-
Reference models f o r t h e d i s c u s s i o n o f e x t r i n s i c (a,b) and i n t r i n - s i c (c), g r a i n boundary s l i d i n g .Repeating these c l i m b and s i n k processes f o r successive d i s l o c a t i o n s g i v e s r i s e t o a g.b.zone o f l e n g t h L i n which a marker l i n e would show a step, passing from o n e g r a i n t o t h e o t h e r , which can be seen as apparent o r e x t r i n s i c g.b. s l i d i n g .
When d i s l o c a t i a n s sink, t h e i r spreading / 1 7 / i n t h e g.b. can be thought t o occur w i t h some c h a r a c t e r i s t i c r e l a x a t i o n t i m e -rg.-,. w i t h a c t i v a t i o n energy corresponding t o t h a t o f g.b. s e l f - d i f f u s i o n .
I f t h e temperature i s t o o low t o a l l o w t h i s r e l a x a t i o n , stresses w i l l be t r a n s m i t t e d through t h e g r a i n boundary w i t h emission o f d i s l o c a t i o n s from t h e g r a i n boundary, and consequent occurrence o f s l i p l i n e s on b o t h sides o f t h e g r a i n boundary and no e v i d e n t g r a i n boundary s l i d i n g . T h i s i s t h e s i t u a t i o n o c c u r r i n g a t T
<
TI; a t T>
T it h e mechanism o f e x t r i n s i c , apparent g.b. s l i d i n g discussed so f a r i s c o n s i s t e n t w i t h t h e appearance o f numerous s l i p l i n e s on one o f t h e g r a i n s meeting a t t h e g.b. I t i s n o t j c e d t h a t t h e apparent a c t i v a t i o n energy deduced from t h e s h i f t of T I as a function o f E i s c o n s i s t e n t w i t h t h e g.b. s e l f - d i f f u s i o n energy. The a c t i v a t i o n energy o f peak
For e x t r i n s i c , a p p a r e n t s l i d i n g t h e s i n k o f many d i s l o c a t i o n s i s preceeded by c l i m b so t h a t cumulative r e l a x a t i o n times r e s u l t
= T + T
'extr g.b. c l
The average time o f c l i m b may be expressed by r \ / ( ~ b2 o/kT)
-
X/vC = .rCl0
where
A
i s t h e average h e i g h t o f climb, vc t h e c l i m b v e l o c i t y , DS l a t t i c e s e l f - d i f - f u s i o n c o e f f i c i e n t a e f f e c t i v e stress.P u t t i n g
r\
= I O - ~ ~ ,a
= 10' N/m2, Do = 10-$ m2/sec t h e r e r e s u l t s .rCl = 5 x 1 t h e pre-exponential f a c t o r o f peak K2 i sloq1=.
Climb phenomena p l a y fundamental r o l e a l s o i n t h e h i g h temperature deformation o f s i n g l e c r y s t a l s : so i t can be understood t h e correspondence w i t h t h e Q-I peaks oc- c u r r i n g w i t h coarse grained samples and s i n g l e c r y s t a l s a f t e r s l i g h t deformation.
The drop i n d e n s i t y o f s l i p l i n e s which occurs above Tp i n d i c a t e s t h a t these p r o - cesses o f e x t r i n s i c , a p p a r e n t s l i d i n g cease above T2, being s u b s t i t u t e d by one n o t r e q u i r i n g l a t t i c e d i s l o c a t i o n s and hence c a l l e d o f i n t r i n s i c s l i d i n g .
The basic processes assumed f o r i n t r i n s i c s l i d i n g a r e e x e m p l i f i e d by t h e c o n d i t i o n s sketched i n Fig. 4c), r e f e r r i n g t o an hexagonal metal as Zn, w i t h g r a i n boundary plane i n c l i n e d r e s p e c t t o t h e basal g l i d e so as t o correspond t o a pyramidal plane.
I n t h i s case gab. s l i d i n g may occur by t h e t h e motion o f pyramidal d i s l o c a t i o n s end- i n g on g.b. Pyramidal g l i d e i n v o l v e s atom rearrangement r e q u i r i n g h i g h a c t i v a t i o n energy which may be c o n s i s t e n t w i t h peak HT. So i t seems worth c o n s i d e r i n g t h e pos- s i b i l i t y t h a t t h e peak HT corresponds t o t h e motion o f d i s l o c a t i o n s ending i n t h e g r a i n boundary and l y i n g i n h i g h i n d i c e s c r y s t a l l o g r a p h i c planes. A s i m i l a r i n t e r - p r e t a t i o n was used t o e x p l a i n t h e c h a r a c t e r i s t i c s o f h i g h T g r a i n boundary s l i d i n g i n Zn / I S / . I n t h i s case i n t e r n a l f r i c t i o n may be r e l a t e d t o t h e damping o f v i b r a t i n g g.b. d i s l o c a t i o n s . I f t h e d i s l o c a t i o n s v i b r a t e i n a h i g h l y d i s s i p a t i v e medium t h e v i b r a t i n g s t r i n g equation may be s i m p l i f i e d /20/ by dropping t h e term i n a 2 y / a t 2 and t h e r e l a x s t i o n t i m e r e s u l t s
T = B L ~ / T ~ C
where C i s t h e l i n e tension, B t h e damping c o e f f i c i e n t . P u t t i n g t h e p i n n i n g l e n g t h L = IO-'m and C = Gb2 t h e r e l a x a t i o n time o f peak HT would correspond t o B = 10-'I
N / s e c . This value appears t o o low, however l a r g e r B ' s a r e obtained i f L decreases and/or C increases occur w i t h temperature, both e v e n t u a l i t i e s which cannot be e x c l u - ded and which would c o n t r i b u t e a l s o t o t h e apparent a c t i v a t i o n energy.
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