KINK PAIR FORMATION MECHANISM (KPF) STUDIED IN ALUMINIUM BY CYCLE BIAS STRESS EXPERIMENTS

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KINK PAIR FORMATION MECHANISM (KPF) STUDIED IN ALUMINIUM BY CYCLE BIAS

STRESS EXPERIMENTS

M. Bujard, G. Gremaud, J. Baur, W. Benoit

To cite this version:

M. Bujard, G. Gremaud, J. Baur, W. Benoit. KINK PAIR FORMATION MECHANISM (KPF)

STUDIED IN ALUMINIUM BY CYCLE BIAS STRESS EXPERIMENTS. Journal de Physique Col-

loques, 1985, 46 (C10), pp.C10-325-C10-328. �10.1051/jphyscol:19851072�. �jpa-00225457�

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JOURNAL DE PHYSIQUE

Colloque C10, supplbment au n012, Tome 46, dbcembre 1985 page

C10-325

KINK PAIR FORMATION MECHANISM (KPF) STUDIED IN ALUMINIUM B Y C Y C L L C BIAS STRESS EXPERIMENTS

M . BUJARD, G . GREMAUD, J . BAUR AND W . BENOIT

Institut de G6nie Atomique, Institut Fed6ral Suisse de

Technologic,

PHB-Ecublens,

CH-1015

Lausanne, Switzerland

Resume : La t e c h n i q u e d e c o u p l a g e e n t r e une c o n t r a i n t e u l t r a s o n o r e e t u n e c o n t r a i n t e b a s s e f r k q u e n c e a k t 6 a p p l i q u b e 5 l ' b t u d e d e l a r e l a x a t i o n d e B o r d o n i d a n s l ' a l u m i n i u m . L e s s i g n a t u r e s m e s u r g e s s o n t p a r f a i t e m e n t e x p l i q u e e s p a r l e m o d s l e d e l a f o r m a t i o n d e p a i r e s d e d e c r o c h e m e n t s dCvelopp6 p a r Esnouf e t S t a d e l m a n n

[ I ,

21.

A b s t r a c t : The c o u p l i n g t e c h n i q u e between u l t r a s o u n d s a n d a low-frequency a p p l i e d b i a s stress i s u s e d f o r t h e s t u d y o f t h e B o r d o n i r e l a x a t i o n i n aluminium. The m e a s u r e d s i g n a t u r e s a r e p e r f e c t l y e x p l a i n e d by t h e k i n k p a i r f o r m a t i o n model d e v e l o p p e d by E s n o u f a n d S t a d e l m a n n [ I , 21.

I . INTRODUCTION

The most r e a l i s t i c model f o r t h e i n t e r p r e t a t i o n o f t h e B o r d o n i p e a k i n FCC m e t a l s i s b a s e d o n t h e r m a l l y a c t i v a t e d k i n k p a i r f o r m a t i o n on t h e d i s l o c a t i o n s (KPF mechanism) [ 3 ] . T h i s mechanism i s i l l u s t r a t e d i n f i g . 1 f o r t h e c a s e o f a d i s l o c a t i o n f i r m l y p i n n e d a t two p o i n t s s i t u a t e d i n t h e same P e i e r l s v a l l e y ( I ) . Due t o t h e combined a c t i o n o f a stress a p p l i e d o n t h e d i s l o c a t i o n a n d t h e r m a l f l u c t u a t i o n s , a b u l g e a p p e a r s o n t h e d i s l o c a t i o n ( 2 ) . I f t h e c r i t i c a l c o n f i g u r a t i o n o f t h e s a d d l e p o i n t i s r e a c h e d , t h e two k i n k s b u i l d i n g t h e b u l g e w i l l s p r e a d o u t from e a c h o t h e r , a l l o w i n g t h e d i s l o c a t i o n t o p a s s from a P e i e r l s v a l l e y t o t h e n e x t o n e ( 3 ) .

But t h e i n t e r p r e t a t i o n o f t h e B o r d o n i r e l a x a t i o n by t h e KPF mechanism is n o t d e f i n i t i v e l y e s t a b l i s h e d , b e c a u s e a l l t h e r m a l l y a c t i v a t e d mechanisms g i v e r i s e t o i n t e r n a l f r i c t i o n p e a k s ( I F ) o f s i m i l a r s h a p e . To c h e c k t h i s i n t e r p r e t a t i o n , we h a v e p l a n n e d t o s t u d y t h e B o r d o n i r e l a x a t i o n by u s i n g a c o u p l i n g t e c h n i q u e between a h i g h f r e q u e n c y s t r e s s o f low a m p l i t u d e ( u l t r a s o u n d o f 8.5 MHz) a n d a s l o w l y v a r y i n g b i a s s t r e s s o f h i g h a m p l i t u d e ( c o m p r e s s i v e s t r e s s , a m p l i t u d e t y p i c a l l y " 1 MPa and f

=

0.02 Hz). The r e a d e r is r e f e r r e d t o t h e p a p e r by G. Gremaud ( t h i s c o n f e r e n c e [ 4 ] ) f o r a d e s c r i p t i o n o f t h i s t e c h n i q u e and o f t h e k i n d o f r e s u l t s o b t a i n e d , which a r e c a l l e d " s i g n a t u r e s " .

F i g . 1 : KPF mechanism i l l u s t r a t i o n .

1 ) I n i t i a l c o n f i g u r a t i o n o f t h e d i s l o c a t i o n .

2 ) C r i t i c a l c o n f i g u r a t i o n c o r r e s p o n d i n g t o t h e s a d d l e p o i n t . 3 ) F i n a l c o n f i g u r a t i o n .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19851072

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11. CALCULATION OF THE SIGNATURE OF THE KPF MECHANISM

To o b t a i n , f o r a g i v e n temperature T, t h e t h e o r e t i c a l s i g n a t u r e a(a) o f t h e KPF mechanism, we need two models. The f i r s t one d e s c r i b e s t h e u l t r a s o n i c a t t e n u a t i o n due t o t h e d i s l o c a t i o n s on which k i n k s have formed: a

=

a {N, a,

t } ,

where N i s t h e number o f k i n k s , a t h e s t r e s s a c t i n g on t h e d i s l o c a t i o n and t t h e time. The second model d e s c r i b e s t h e i n s t a n t a n e o u s number o f k i n k s p r e s e n t on t h e d i s l o c a t i o n s : N

=

N [ a ( t ) , t,

TI.

Concerning a

=

a {N, a, t } , f i g u r e 2 shows a d i s l o c a t i o n f i r m l y p i n n e d a t two p o i n t s and s u b j e c t e d t o a s t r e s s a. Some k i n k s a r e present. They were c r e a t e d t h r o u g h t h e KPF mechanism d e p i c t e d i n f i g . 1. The shaded areas r e p r e s e n t t h e a r e a swept by t h e k i n k s under t h e a c t i o n o f t h e u l t r a s o n i c s t r e s s uu

.

I f t h e e l a s t i c i n t e r a c t i o n between k i n k s i s neglected, t h e c o n f i g u r a t i o n y(x,a? adopted by t h e d i s l o c a t i o n depends o n l y on t h e l i n e t e n s i o n o f t h e d i s l o c a t i o n and may be computed 151. Since aus

<<

u, t h e area swept by t h e d i s l o c a t i o n , i.e. m a i n l y t h e a r e a swept by t h e k i n k s , may be deduced from a l i m i t e d expansion o f y(x,a) i n a [6]. F o r t h e p r e s e n t t a s k , t h e unique r e s u l t o f i n t e r e s t i s t h a t t h e u l t r a s o n i c a t t e n u a t i o n a i n p r o p o r t i o n a l t o t h e number o f k i n k s N.

Concerning N

=

N [ a ( t ) , t, T], t h e r e s e a r c h o f t h e i n s t a n t a n e o u s number o f k i n k s c r e a t e d on a d i s l o c a t i o n by an harmonic s t r e s s a ( t ) a t a g i v e n temperature T i s i n f a c t t h e roblem o f t h e B o r d o n i ' r e l a x a t i o n observed by I F . Thus, many models e x i s t f o r t h i s

bl.

AS t h e p r e s e n t a m p l i t u d e o f t h e a p p l i e d s t r e s s a i s r e l a t i v e l y l a r g e (- G, where G i s t h e shear modulus), we need a model v a l i d f o r such a h i g h amplitude. Only t h e one developed by Esnouf and Stadelmann [5, 6 1 may be a p p l i e d . I n t h i s model, t h e energy f o r t h e c r e a t i o n o f a k i n k p a i r i s computed f o r each i n s t a n t a n e o u s c o n f i g u r a t i o n o f t h e d i s l o c a t i o n . Only t h e l i n e t e n s i o n o f t h e d i s l o c a t i o n i s t a k e n i n t o acount; t h e e l a s t i c i n t e r a c t i o n between k i n k s i s neglected. Once t h e s a d d l e p o i n t i s reached, t h e two k i n k s m i g r a t e w i t h o u t delay t o t h e e x t r e m i t i e s o f t h e d i s l o c a t i o n , For t h e case where no i n t e r n a l s t r e s s e s a r e present, f i g . 3a shows t h e e v o l u t i o n o f t h e number o f k i n k s N as a f u n c t i o n o f t h e a p p l i e d s t r e s s a f o r temperatures T i

<

^Tg

<

^{T j}

<

TI,, as deduced by Esnouf and Stadelmann. A t t h e low temperature TI, t h e t h e r m a l a c t i v a t i o n i s weak, so t h e KPF mechanism cannot act, and t h e r e i s no e v o l u t i o n o f N. A t t h e h i g h temperature TI+, t h e t h e r m a l a c t i v a t i o n i s s o l a r g e t h a t N corresponds always t o t h e number o f k i n k s a t mechanical e q u i l i b r i u m . A t t h e i n t e r m e d i a t e temperatures Tg and T 3 , k i n k s may be created, b u t t h e e q u i l i b r i u m i s never reached; t h e curves N(Q) have a l a r g e h y s t e r e s i s .

The t h e o r e t i c a l e v o l u t i o n (due t o t h e KPF mechanism) o f t h e I F a t v a r i o u s temperatures i s r e a d i l y o b t a i n e d from t h e curves ~ ( o ) ( f i g . 3a). Indeed, i t i s easy from these curves t o deduce t h e curves ~,,(a) ( f i g . 3b) d e p i c t i n g t h e a n e l a s t i c deformation can versus t h e s t r e s s o, t h e enclosed area o f which i s p r o p o r t i o n a l t o t h e mechanical energy l o s s i n t h e ,sample. Thus, p l o t t i n g t h e s e areas computed f o r each temperature versus t h e temperature, we o b t a i n t h e graph o f t h e f i g . 3c.

T h i s graph shows a peak, which i s t h o u g h t by Esnouf and Stadelmann t o correspond t o t h e B o r d o n i peak.

Fig. 2 : I l l u s t r a t i o n o f a d i s l o c a t i o n s u b j e c t e d t o a s t r e s s a and h a v i n g some k i n k s c r e a t e d t h r o u g h t h e KPF mechanism. The shaded areas r e p r e s e n t t h e areas swept o u t by t h e k i n k s due t o t h e u l t r a s o n i c s t r e s s .

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Fig. 3 : T h e o r e t i c a k d e s c r i p t i o n o f t h e I F behavior ( c ) and o f t h e s i g n a t u r e s ( d ) i n presence of t h e k i n k p a i r f o r m a t i o n mechanism (see t e x t ) .

The t h e o r e t i c a l shape o f t h e s i g n a t u r e o f t h e KPF mechanism i s a l s o r e a d i l y deduced from t h e graph N(a) ( f i g . 3a). Owing t o t h e l i n e a r r e l a t i o n e s t a b l i s h e d between a and N, we may r e p l a c e N by a on t h e o r d i n a t e o f t h e graph o f f i g . 3a, a c h i e v i n g so t h e graph a ( o ) ( f i g . 3d), which i s t h e t h e o r e t i c a l s i g n a t u r e o f t h e KPF mechanism.

I t i s i n t e r e s t i n g t o n o t e t h a t t h e enclosed area o f t h e s i g n a t u r e s p l o t t e d versus t h e temperature should have a maximum a t a temperature near t h a t o f t h e B o r d o n i peak ( f i g . 3e).

111. MEASUREMENT OF THE SIGNATURE OF THE BORDONI RELAXATION

The s i g n a t u r e s measured i n a sample o f 6N aluminium i n t h e temperature range o f t h e B o r d o n i r e l a x a t i o n a r e shown i n f i g . 4a. The frequency o f t h e harmonic s t r e s s i s 0.02 Hz, t h a t o f t h e u l t r a s o n i c wave i s 8.5 MHz. F i g . 4b shows t h e e v o l u t i o n o f t h e enclosed a r e a o f t h e s i g n a t u r e versus t h e temperature o f measurement. As expected from t h e t h e o r y o f Esnouf and Stadelmann, a peak appears a t a temperature near t h a t o f t h e B o r d o n i peak which would be

-

⁸⁰^K a t a frequency o f 0.02 Hz. C l e a r l y , t h e shapes o f these s i g n a t u r e s a r e almost t h e same as those o f t h e t h e o r e t i c a l s i g n a t u r e s o f t h e KPF mechanism. Only t h e a m p l i t u d e o f t h e s i g n a t u r e measured a t h i g h temperature (217 K ) i s lower t h a n t h a t expected, b u t t h i s can be e x p l a i n e d by t h e unceasing c r e a t i o n o f p o i n t d e f e c t s due t o t h e h i g h a m p l i t u d e o f t h e a p p l i e d s t r e s s .

I V . DISCUSSION

Our e x p e r i m e n t a l r e s u l t s i n A1 a r e w e l l e x p l a i n e d by t h e model o f t h e KPF mechanism developed by Esnouf and Stadelmann [I 21. T h i s p r o v i d e s a s t r o n g c o n f i r m a t i o n o f t h a t model and o f t h e i d e a o f Seeger (71 t o a t t r i b u t e t h e B o r d o n i peak t o t h e KPF mechanism. I t i s w o r t h w h i l e t o n o t e t h a t t h e u l t r a s o n i c a t t e n u a t i o n model based upon t h e e l a s t i c i n t e r a c t i o n a c t i n g between k i n k s [8, 9, ID] does n o t p r e d i c t t h e

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Fig. 4 :

a) Measured s i g n a t u r e s i n A1 a t d i f f e r e n t temperature. The frequency o f t h e a p p l i e d s t r e s s i n 0.02 Hz, t h e u l t r a - s o n i c frequency i s 8.5 MHz.

b ) E v o l u t i o n versus t h e tempera- t u r e o f measurement o f t h e enclosed areas o f t h e signa- t u r e s . A t t h e fequency o f 0.02 Hz, t h e B o r d o n i peak would appear a t about 80 K.

I t T

(to

+

100 200

observed shape o f t h e s i g n a t u r e s . T h i s i s i m p o r t a n t because, u n t i l now, a l l u l t r a - s o n i c a t t e n u a t i o n measurements were analysed w i t h such a model when t h e presence o f k i n k s i n t h e sample was t a k e n i n t o account.

ACKNOWLEDGMENTS

The a u t h o r s w i s h t o thank P r o f . M.S. Wechsler f o r c r i t i c a l r e a d i n g o f t h e manus- c r i p t .

REFERENCES

[I]

C. Esnouf, T h e s i s INSA-Lyon (1978) & C. Esnouf, G. F a n t o z z i , ICIFUAS 6 ( U n i v e r s i t y o f Tokyo Press, Tokyo 1977, ed. R.R. H a s i g u t i and N. Mikoshiba), p. 557.

[ 2 ] P. Stadelmann, T h e s i s EPF-Lausanne (1978) & P. Stadelmann, W. B e n o i t , Helv.

Phys. Acta,

2

(1979) 637.

[ 3 ] G. F a n t o z z i , C. Esnouf, W. B e n o i t , I.G. R i t e h i e , Progress i n M a t e r i a l s Science,

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(1982) 311.

4 G. Gremaud, M. B u j a r d , t h i s conference.

5 U.F. Kocks, A.S. Argon, M.F. Ashby, Progress i n M a t e r i a l s Science,

19,

Thermo-

1 1

- - dynamics and K i n e t i c s o f S l i p (Pergamon Press, Oxford, 1975).

6.

:7 .8: 9

[ l o :

M. Bujard, T h e s i s EPF-Lausanne (19851, t o be pubished.

A. Seeger, P h i l . Mag.,

1

(1956) 651.

T. Suzuki, C. Elbaum,

J.

Appl. Phys.

2,

no 5 (1964) 1539.

G. A l e f e l d ,

J.

Appl. Phys. 36, no 9 (1965) 2642.

M. Bujard, G. Gremaud, E C I F ~ S 4,

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(1984) C9-673.