RECENT PROGRESS IN DISLOCATION STUDIES USING BIAS STRESS EXPERIMENTS

HAL Id: jpa-00225455

https://hal.archives-ouvertes.fr/jpa-00225455

Submitted on 1 Jan 1985

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

RECENT PROGRESS IN DISLOCATION STUDIES USING BIAS STRESS EXPERIMENTS

G. Gremaud, M. Bujard

To cite this version:

G. Gremaud, M. Bujard. RECENT PROGRESS IN DISLOCATION STUDIES USING BIAS STRESS EXPERIMENTS. Journal de Physique Colloques, 1985, 46 (C10), pp.C10-315-C10-320.

�10.1051/jphyscol:19851070�. �jpa-00225455�

JOURNAL DE PHYSIQUE

Colloque C10, supplement au n012, Tome 46, d6cembre 1985 page C10-315

RECENT PROGRESS IN DISLOCATION STUDIES USING BIAS STRESS EXPERIMENTS

G. GREMAUD AND M. BUJARD

Institut de Genie Atomique,Institut Federal Suisse deTechnologie, PHB- cubl lens, CH-1015 Lausanne, Switzerland

Resume

-

De recents progres ont @t@ r @ a l i s @ s dans l ' u t i l i s a t i o n de l a techni- que de mesure par couplage d'une contrainte quasi-statique a avec une mesure de l l a t t @ n u a t i o n a e t de l a vitesse v d'ultrasons. Ces progres sont l i e s ti l ' u t i l i s a t i o n d'une contrainte cyclique basse frequence qui permet de t r a c e r des courbes fermees Aa(a) e t Av/v(a) dont l a forme e t l'@volution sont cara- c t e r i s t i q u e s pour chaque m6canisme pouvant contrdler l e mouvement des dislo- cations.

Abstract

-

Recent progress in bias s t r e s s experiments has been made using a low frequency cyclic bias s t r e s s . In t h i s technique attenuation a and velo- c i t y v of ultrasonic waves a r e measured in a sample subjected t o a low f r e - quency cyclic s t r e s s a . Closed curves Aa(a) and Av/v(a) a r e measured during each cycle of the applied s t r e s s . The shapes of these curves and t h e i r evo- lution are c h a r a c t e r i s t i c f o r each mechanism controlling the dislocation motion.

I . INTRODUCTION

Bias s t r e s s experiments have been recognized by several authors as a powerful method t o study the dislocation dynamics [l t o 71, specially in the case of a dislocation- point defect interaction.

Recent progress i n bias s t r e s s experiments has been made using a low frequency

c y c ~

l i c bias s t r e s s instead of a s t a t i c or a l i n e a r l y increasing one. There are several advantages t o such a cyclic bias s t r e s s . Closed curves Aa(a) and Av/v(a) a r e obtain- ed, which a r e c h a r a c t e r i s t i c f o r each mechanism controlling the dislocation motion.

For t h i s reason, the shape of these curves has been called '';hg_sjgnm;wt-" of the mechanism.

The time and temperature dependence of the signatures can be measured using cyclic bias s t r e s s e s . The time dependence measurements permit t r a n s i t o r y stages and s t a t i o - nary s t a t e s t o be i d e n t i f i e d . This cannot be done by classical bias s t r e s s experi- ments. The temperature dependence of the signatures can be e a s i l y correlated with the low frequency internal f r i c t i o n spectrum.

11. THE BASIC PRINCIPLES OF BIAS STRESS EXPERIMENTS

The principle of the experimental device i s very simple ( f i g . 1 ) . B u t t h e r e are se- veral possible configurations : t e n s i l e and/or compressive applied s t r e s s or s t r a i n , s t r e s s f i e 1 d direction perpendicular o r pa ral l e l t o the ultrasonic wave propagation direction, ultrasonic wave of shear type o r longitudinal type, e t c .

The physical interpretation of bias s t r e s s experiments i s the following. The quasi- s t a t i c applied s t r e s s i s used t o induce a motion of dislocations interacting with some obstacles, as i l l u s t r a t e d by two examples in f i g . 2 : the depinning from a row of point defects by a catastrophic breakaway mechanism ( a ) and the jumping over l i - near obstacles ( P e i e r l s h i l l s ) by a kink pair formation mechanism ( b ) . On the other hand, the ultrasonic f i e l d , which i s of much higher frequency and much lower ampli- tude than the quasi-static applied s t r e s s , cannot a c t i v a t e the preceding mechanisms.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19851070

JOURNAL DE PHYSIQUE

F i g . 1

-

P r i n c i p l e o f a b i a s s t r e s s Fig. 2

-

P r i n c i p l e o f t h e p h y s i c a l i n t e r p r e t a - equi pement device

.

t i o n o f t h e b i a s s t r e s s experiments i n t h e ca- ses o f a breakaway mechanism ( a ) and o f a k i n k p a i r f o r m a t i o n mechanism ( b ) .

F i g . 3

-

Some experimental- l y obtained and t h e o r e t i - c a l l y e x p l a i n e d s i g n a t u r e s f o r d i f f e r e n t d i s l o c a t i o n mechanisms.

( d )

F i g . 4

-

Time e v o l u t i o n o f t h e s i g n a t u r e s towards a "moustache s i g n a t u r e " : t h e t r a n s i t o r y stages ( a , b ) and the s t a t i o n n a r y s t a t e ( c ) o f t h e s i g n a t u r e s .

I t can o n l y induce a s m a l l v i b r a t i o n ( r e p r e s e n t e d b y t h e shaded a r e a i n f i g . 2) o f t h e d i s l o c a t i o n ( f i g . 2.a) o r o f t h e k i n k s ( f i g . 2.b). The s t r o n g a t t e n u a t i o n o f t h e s e v i b r a t i o n s b y t h e phonon f i e l d - l e a d s t o an a t t e n u a t i o n o f t h e u l t r a s o n i c wave, w h i c h de-pends on t h e average l e n g t h R o f t h e d i s l o c a t i o ~ segEents o r on t h e average

number N o f c r e a t e d k i n k p a i r s on t h e d i s l o c a t i o n s . As . 9. o r N depends on t h e q u a s i - s t a t i c a p p l i e d s t r e s s a ( t ) , t h e u l t r a s o n i c wave can be c o n s i d e r e d as a probe t o mea- s u r e t h e d i s l o c a t i o n m o t i o n induced by t h i s a p p l i e d s t r e s s :

T h i s c l e a r l y shows t h a t two models a r e needed t o i n t e r p r e t e c o r r e c t l y t h e r e s u l t s . The f i r s t model i s concerned w i t h t h e c a l c u l a t i o n - o f t h e h i g h - f r e q u e n c y 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 v i b r a t i o n s Aa{R,o,t} o r t h e k i n k v i b r a t i o n s Aa{N ,o,T} 16, 12, 151. The second model i s concerned w i t h t h e c a l c u l a t i o n o f t h e low-frequency d i s l o c a t i o n - o b s t a c l e i n t e r a c t i o n mechanism, which a l l o w s an e s t i m a t e of t h e e x p r e s s i o n s !L[o(t) ,t,T

. .

^.I o r N [ a ( t ) ,t,T

.

. . ] t h a t have t o be i n t r o d u c e d i n t h e expressions f o r Aa.

111. THE CONCEPT OF SIGNATURE

The c y c l i c b i a s s t r e s s experiments, which have been r e c e n t l y developed [7, 8, 131, c o n s i s t i n a p p l y i n g a c y c l i c low frequency s t r e s s and measuring t h e c l o s e d c u r v e Aa(o) on each c y c l e o f t h e a p p l i e d s t r e s s . Such experiments a r e d i r e c t l y connected w i t h low f r e q u e n c y i n t e r n a l f r i c t i o n measurements when t h e a p p l i e d s t r e s s a m p l i t u d e remains i n t h e a n e l a s t i c range o f t h e m a t e r i a l . But, t h e y can a l s o be c o r r e l a t e d w i t h f a t i g u e experiments i f a c y c l i c p l a s t i c d e f o r m a t i o n i s induced i n t h e sample

[131.

From t h e e q u a t i o n g i v i n g t h e u l t r a s o n i c a t t e n u a t i o n Aa as a f u n c t i o n o f a ( t ) , i t i s c l e a r t h a t t h e shape of t h e " s i g n a t u r e " Aa(o) i s c o r r e l a t e d w i t h t h e d i s l o c a t i o n mo- t i o n m e c h a n i s m . ~ c t u ~ l l y , s e v e r a l d i f f e r e n t s i g n a t u r e s have been e x p e r i m e n t a l l y ob- t a i n e d and t h e o r e t i c a l l y r e l a t e d w i t h a s p e c i f i c d i s l o c a t i o n m o t i o n mechanism, as shown i n f i g . 3 : t h e "bow s i g n a t u r e " ( f i g . 3.a) due t o breakaway f r o m a row of i m n o b i l e p o i n t d e f e c t s [9, 131, t h e "moustache s i g n a t u r e " ( f i g . 3.b) due t o depin- n i n g from long-range dragged p o i n t d e f e c t s [91, t h e "Bordoni s i g n a t u r e " ( f i g . 3.d) due t o k i n k p a i r f o r m a t i o n mechanism [ I 6 1 and t h e " f l i p - f l o p s i g n a t u r e " ( f i g . 3.e) due t o d r a g g i n g o f p o i n t d e f e c t s s i t u a t e d between two k i n k s o r between t h e two p a r - t i a l s o f a d i s l o c a t i o n [15].

I V . TIME AND TEMPERATURE DEPENDENCE OF THE SIGNATURES

--

As a f u n c t i o n o f t i m e , t h e e v o l u t i o n o f t h e s i g n a t u r e s can p r e s e n t two c o m p l e t e l y d i f f e r e n t b e h a v i o r s . The f i r s t one i s c h a r a c t e r i z e d b y t h e f a c t t h a t a s t a t i o n n a r y shape o f t h e s i g n a t u r e s i s o b t a i n e d immediately a f t e r h a v i n g a p p l i e d t h e c y c l i c s t r e s s . T h i s i s t h e case, f o r example, f o r t h e s i g n a t u r e s i n f i g . 3a, c , d and e.

The second p o s s i b l e b e h a v i o r i s c h a r a c t e r i z e d by t h e appearance o f a more o r l e s s l o n g t r a n s i t o r y s t a g e , . b e f o r e o b t a i n i n g a s t a t i o n n a r y s i g n a t u r e shape. An example o f such a t i m e e v o l u t i o n i s g i v e n i n f i g . 4, which shows t h e f o r m a t i o n o f t h e "mous- tache s i g n a t u r e " o f f i g . 3.b [91.

I t i s c l e a r t h a t t h e f i r s t b e h a v i o r can be due o n l y t o i n t e r a c t i o n s o f d i s l o c a t i o n s w i t h immobile o b s t a c l e s ( s i g n a t u r e s o f f i g . 3.a and d) o r w i t h v e r y f a s t moving ob- s t a c l e s ( s i g n a t u r e s o f f i g . 3.c and e ) whereas t h e second b e h a v i o r must be due t o i n t e r a c t i o n s w i t h s l o w l y m i g r a t i n g o b s t a c l e s ( s i g n a t u r e o f f i g . 3.b), i n which case a t i m e dependent i n t e r n a l f r i c t i o n c o u l d a l s o be observed.

The measurement o f t h e e v o l u t i o n o f t h e s i g n a t u r e s as a f u n c t i o n o f t h e temperature i s a p o w e r f u l method t o o b t a i n t h e p h y s i c a l i n t e r p r e t a t i o n o f t h e r e l a x a t i o n peaks observed b y i n t e r n a l f r i c t i o n measurements. As t h e c y c l i c b i a s s t r e s s has t h e same e f f e c t on t h e d i s l o c a t i o n s as t h e c y c l i c s t r e s s f i e l d i n i n t e r n a l f r i c t i o n devices, t h e r e s u l t s o f these two techniques can be d i r e c t l y c o r r e l a t e d [141. T h i s has been done c o m p l e t e l y , f r o m b o t h t h e e x p e r i m e n t a l and t h e o r e t i c a l p o i n t s of view, f o r t h e P C peak i n 6NA1

[ l o ,

111 and f o r t h e Bordoni peak i n b e t t e r t h a n 6N A1 115, 161. By t h i s technique, each p o i n t o f an i n t e r n a l f r i c t i o n spectrum corresponds t o a signa-

C10-318 _JOURNAL DE PHYSIQUE

t ^{"-' - '03 6N A l}

^,

^{deform. 7'10}

F i g . 5

-

a) The PC peak i n 6N A1 a t t h r e e d i f f e r e n t measurement amplitudes and ( b ) t h e s i g n a t u r e s observed f o r t h r e e temperatures measured a t E = These e x p e r i - mental r e s u l t s a r e completely e x p l a i n e d by a mechanism o f depinning from dragged e x t r i n s i c p o i n t d e f e c t s [ l o , 111.

F i g . 6

-

( a ) t h e Bordoni peak i n > 6N A l , ( b ) t h e s i g n a t u r e s observed f o r t h r e e d i f - f e r e n t temperatures and ( c ) t h e area o f t h e s i g n a t u r e s as a f u n c t i o n o f T. These e x p e r i m e n t a l r e s u l t s can be e x p l a i n e d b y a mechanism o f 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 [14, 161.

C10-320 JOURNAL DE PHYSIQUE

t u r e , which contains much more i n f o r m a t i o n than the s i n g l e p o i n t , as shown i n f i g . 5 and 6. I n the case of the PC peak, t h e e v o l u t i o n o f t h e signatures and the ampli- tude dependence o f t h e i n t e r n a l f r i c t i o n peak a r e completely and c o h e r e n t l y e x p l a i n - ed by a mechanism of depinning from dragged e x t r i n s i c p o i n t d e f e c t s 110, 111. I n t h e case o f t h e Bordoni peak, i t has n o t been p o s s i b l e t o e x p l a i n the shape and t h e e v o l u t i o n o f t h e signatures i n any o t h e r manner than by a 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 formation mechanism [15, 161.

The area o f the signatures can sometimes be c o r r e l a t e d w i t h t h e i n t e r n a l f r i c t i o n spectrum. This has been proved i n t h e case o f t h e "bow s i g n a t u r e " ( f i g . 4.a) due t o breakaway from a row o f immobile p o i n t d e f e c t s [13], and i n t h e case o f the k i n k p a i r formation mechanism [14, 161 as shown i n f i g . 6.c.

V

.

CONCLUSION

Recent progress i n d i s l o c a t i o n dynamics s t u d i e s has been made using c y c l i c b i a s s t r e s s experiments. I n t h i s paper, we have t r i e d t o show why the closed curve Aa(o) can be c a l l e d t h e " s i g n a t u r e " o f a p a r t i c u l a r d i s l o c a t i o n motion mechanism and how powerful t h i s technique i s i n f i n d i n g the mechanisms c o n t r o l l i n g t h e d i s l o c a t i o n dynamics

.

REFERENCES

E l ] A. Hikata, R. T r u e l l , A. Granato, B. Chick, K. Lucke, J. Appl. Phys.

2

(1956) 396

[2] A. ~ i k a t a , B. Chick, C. Elbaum, R. T r u e l l , Acta Met.

10

(1962) 423 [3] D. Lenz, Edenhofer, K. L i c k e , S c r i p t a Met.

5

(1971) 387

[ 4 ] A. Vincent, J. Perez, P. F. Gobin, J. Phys. Chem. S o l i d s 3 5 (1974) 1253 151 A. Vincent, t h e s i s , INSA Lyon (1978)

[ 6 ] P. Deterre, t h e s i s , CENG Grenoble (1978) ,

[ 7 ] G. Gremaud, t h e s i s , EPF-Lausanne (1981) [81 G. Gremaud, J. de Phys.

42

(1981) C5-1141

[ 9 ] G. Gremaud, W. Benoit, J. de Phys.

42

(1981) C5-369

[ l o ]

^G. Gremaud, J. de Phys.

3

(1983) C9-607

[ I 1 1 G. Gremaud, L i Ping o,

.

Benoit, J. de Phys.

2

(1983) C9-581 [ I 2 1 M. Bujard, G. Gremaud, J. de Phys.

44

(1983) C9-673

[I 31 M. Omry, t h e s i s , INSA Lyon (1984)

[14] G. Gremaud, i n " D i s l o c a t i o n s 1984" publ. by P. VeyssiPre, L. Kubin, J. Cas- t a i n g , Ed. du CNRS, P a r i s (1984) 191

[ I 5 1 M. Bujard, t h e s i s , EPF-Lausanne, t o be published (1985)

[ I 6 1 M. Bujard, G. Gremaud, W. Benoit, t o be published i n these proceedings ACKNOWLEDGEMENTS

The authors wish t o thank P r o f . M. S. Wechsler f o r c r i t i c a l reading o f t h e manus- c r i p t .

This work was p a r t i a l l y supported by t h e Swiss National Science Foundation.