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THERMALLY ACTIVATED DOUBLE KINK
GENERATION STUDIED BY ULTRASONIC
MEASUREMENTS DURING A CYCLIC
DEFORMATION
G. Gremaud, W. Benoit
To cite this version:
JOURNAL DE PHYSIQUE
CoZZoque C5, suppZ6ment au n0lO, Tome 42, octobre 1981 page C5- 163
THERMALLY ACTIVATED DOUBLE KINK GENERATION STUDIED BY ULTRASONIC
MEASUREMENTS DURING A CYCLIC DEFORMATION
G . G r e m a u d a n d W . Benoit
I n s t i t u t de G h i e Atomique, Swiss Federal I n s t i t u t e of TeehnoZogy, Lausanne, a i t z e r Zand
Abstract. - I n a new measurement technique, a t t e n u a t i o n a and propagation time t o f u l t r a s o n i c waves have been measured on an aluminium sample under a low frequency s i n u s o i d a l a p p l i e d s t r e s s (1). During heating, a l o t o f such Aa(o) and A t / t ( o ) curves (%300) ,each measured d u r i n g one c y c l e o f t h e s t r e s s , have been drawn. These closed curves have some t y p i c a l shapes very d i f f e r e n t from one mechanism t o another c o n t r o l l i n g t h e m o b i l i t y o f t h e d i s l o c a t i o n s
(2)
.
Bordoni peak has been r e c e n t l y s t u d i e d i n d e t a i l by Esnouf and Stadel- mann (3) by 1 ow frequency i n t e r n a l f r i c t i o n measurements and by G o t t h a r d t i n e l e c t r o n microscopy (4). These s t u d i e s show t h a t t h e double k i n k genera- t i o n (DKG) model i s t h e b e s t one 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 t h i s peak.
I n t h i s paper a new model i s presented t o c a l c u l a t e t h e shape and the e v o l u t i o n o f t h e Aa(o)and A t / t ( o ) curves d u r i n g t h e t h e r m a l l y a c t i v a t e d ge- n e r a t i o n o f double k i n k induced by t h e low frequency a p p l i e d s t r e s s . The t h e o r e t i c a l Aa(o) and A t / t ( o ) curves obtained i n t h e presence o f t h i s mecha- nism are completely d i f f e r e n t from those due t o an i n t e r a c t i o n between poin: defects and d i s l o c a t i o n s (5). More p r e c i s e l y they show a t y p i c a l "assymetr~
between Aa(o) and A t / t ( o ) curves.
Experimental 1 y t h e Aa(o)and A t / t ( o ) curves observed i n t h e temperature range o f t h e Bordoni r e l a x a t i o n s B, and B, i n aluniinium a r e very s i m i l a r t o those ~ r e d i c t e d by t h e model.
I n t r o d u c t i o n .
-
The low frequency i n t e r n a l f r i c t i o n Bordoni peaks i n FCC metals have been i n t e r p r e t e d by t h e t h e r m a l l y a c t i v a t e d double k i n k generation on t h e d i s l o c a - t i o n s (6). I n t h e temperature range o f t h i s mechanism a b i a s s t r e s s experiment(cou- p l i n g o f a low frequency s t r e s s and a h i g h frequency s t r e s s ) must have two e f f e c t s on the motion o f t h e d i s l o c a t i o n s :a) t h e low frequency s t r e s s (.lHz) a c t i v a t e s more o r l e s s t h e double k i n k ge- n e r a t i o n mechanism depending o f t h e temperature (below o r above t h e low frequency Bordoni peak).
b ) t h e h i g h frequency s t r e s s ( u l t r a s o n i c waves a t 7 MHz) cannot a c t i v a t e such a mechanism i n t h i s temperature range ( l a r g e l y below an h y p o t h e t i c a l h i g h frequency Bordoni peak). I t can o n l y d i s p l a c e t h e e x i s t i n g k i n k s along t h e P e i e r l s v a l l e y s .
C5-164 JOURNAL DE PHYSIQUE
migration //
A u (kinks)
F i g . 1 The t h r e e cases o f p o s s i b l e motions o f a d i s l o c a t i o n under a low frequency a p p l i e d s t r e s s (ha- chured zones) coupled w i t h a h i g h frequency a p p l i e d s t r e s s (black zones).
Above t h e temperature o f t h e hypo- t h e t i c a l Bordoni peak due t o t h e h i g h frequency s t r e s s , t h e beha- v i o u r o f t h e d i s l o c a t i o n motion f o l l o w s t h e s t r i n g model (8) ( f i g . 1 c ) . Between these two t e r p e r a - t u r e s t h e low frequency s t r e s s a c t i v a t e s t h e mechanism of thermal- l y a c t i v a t e d double k i n k generation, when t h e h i g h frequency s t r e s s can o n l y d i s p l a c e s these k i n k s along t h e P e i e r l s v a l l e y s ( f i g . 1 b ) . T h i s model has been developed t o p r e d i c t t h e Aa(a) and t h e A t / t ( a ) curves which c o u l d be observed i n t h i s temperature range.
Results o f t h e model
-
The be- haviour o f t h e a t t e n u a t i o n and t h e-
I-
propagation time d e f e c t o f t h eu l trasounds obtained w i t h t h i s model i s described by t h e f o l l o w i n g r e l a t i o n s :
where A i s t h e d i s l o c a t i o n density,@ t h e angle between t h e d i s l o c a t i o n and t h e Pei- e r l s valleys,R the d i s t a n c e between t h e two p i n n i n g p o i n t s and I! t h e number o f k i n k s on t h e segment of l e n g t h R. I t i s c l e a r t h a t t h e minimum value o f !I i s R sin@/a, where a i s t h e d i s t a n c e between two a d j a c e n t F e i e r l s v a l l e y s . 6 i s a "hardening term" o f second o r d e r ( 6 = 1) due t o t h e low frequency a p p l i e d s t r e s s 0:
6 = 1 + 4..;rR4cos4@ I.i2+ 2 a2
Gf3a2 (Fl+l)
a Fig. 2
-
V a r i a t i o n s o f u l t r a s o n i c attenu-l?, a t i o n and propagation time defect, due
t o an increase o f t h e nuixber N o f k i n k s
I'
\,,A ,
I c o n e t e n s s on d i s l o c a t i o n segments o f l e n g t h Q.\
' 0 I 6; 1'\
II \o\ The
R 5
dependence o f t h e a t t e n u a t i o n looks1 '
.
I -0.
-
.
strange. But il i s p r o p o r t i o n a l t o Q whenI
--
-
I - 0 - _ I-
0 - - - 0 a d i s l o c a t i o n - p o i n t d e f e c t s i n t e r a c t i o n I I ~ o d i f i e s t h e l e n g t h R. I n t h i s case a and . ; ; : ; ; i t ; 0 A t / t f o l l o w s t h e c l a s s i c a l R4 and !Lzlav! r e s p e c t i v e l y l i k e i n t h e c l a s s i c a l k i n k (7) o r s t r i n g (8) models. F i g u r e 2 shows the a and A t / t values as a f u n c t i o n o f\ the number
r!
o f k i n k s on d i s l o c a t i o n s o f \O f i x e d l e n g t h k.'
\.
O. - - o - - - e - - ~ - - D - - - o - - - o . . . Experimental r e s u l t s-
The d i s l o c a t i o n sI
A.t i n a r e a l m a t e r i a l have a s t a t i s t i c a l d i s t r i b u t i o n o f t h e i r l e n g t h !L and o f t h e i r t i l t i n g angle @. I n t h e case o f a pure mechanism o f t h e r m a l l y a c t i v a t e d double k i n k generation, t h e values o f and @ do n o t change under t h e low frequency s t r e s s . I t i s then p o s s i b l e t o represent t h e a t t e n u a t i o n and t h e propagation time d e f e c t o f t h e ultrasounds, c a l c u l a t e d w i t h t h e d i s t r i b u t i o n s over J?, and4,
as a f u n c t i o n o fthe average number o f created k i n k s by segment ( f i g . 3 a ) .
F i g . 4 Observation o f a peak
--
( 7 5 K) on t h e absolute attenua- t i o n i n t h e presence o f t h e
low frequency Bordoni peak
B,
C5- 166 JOURNAL DE PHYSIQUE F i g . 3 Behaviour o f t h e -- ultrasounds i n t h e presence of a mechanism o f t h e r m a l l y a c t i v a t e d double k i n k genera- t i o n . The a p p l i c a t i o n o f a c y c l i c compression s t r e s s d u r i n g an increase o f temperature modi- f i e s the value o f
fi,
which i m p l i e s t h e f o l l o w i n g f a c t s : a) as t h e double k i n k genera- t i o n i s a t h e r m a l l y a c t i v a t e dT m
processus, t h e average number
z,
fl
o f created k i n k s must i n -' I
(b) crease w i t h t h e increase o f
i-
T3 -'!
t h e temperature and under t h ei To
-!
e f f e c t o f the average compres-c-
4s i o n s t r e s s . A maxinua o f t h e absolute a t t e n u a t i o n must then appear as a f u n c t i o n o f t h e temperature. This maxir,ium has
t- been e x p e r i m e n t a l l y observed a t 75 K i n t h e presence o f t h e
Bordoni peak B, i n aluminium
At/t l c ) ( f i g . 4 ) . 5 I b ) a t a given temperature t h e c y c l i c 1 ow frequency compres- s i o n s t r e s s induces a c y c l i c f l u c t u a t i o n o f t h e value
fi,
1
1
1
which i s represented i nI
I
f i g u r e 3 b. From t h e curvesa(:)
and A t / t ( N ) , i t i s then p o s s i b l e t o draw a p p r o x i m a t i v e l y t h e shapes o f t h e h ( a ) and A t / t ( o ) curves which must be observed a t d i f f e r e n t temperatures ( f i g . 3 c ) . This t y p i c a l e v o l u t i o n o f t h e curves has been e x p e r i m e n t a l l y observed on t h e two Bordoni peaks 6, and B, i n a l u - minium. The most c h a r a c t e r i s t i c curves a r e those obtained near the temperatures T, and T,.Fig. 5 H y s t e r e s i s o f t h e a n e l a s t i c de- f o r m a t i o n due t o t h e h y s t e r e s i s o f t h e double k i n k generation mechanism. The temperature o f t h e Bordoni peak i s approxi- m a t i v e l y T,
.
F i g . 6 T y p i c a l Au(a) and A t / t ( a ) curves obtained i n aluminium i n the presence o f a t h e r m a l l y a c t i v a t e d double k i n k genera- t i o n mechanism ( f o = .1
Hz,
fUS = 7 MHz).n e r a t i o n rnechanism c a l c u l a t e d by Esnouf (3) and represented i n f i g . 5. The correspon- d i n g experimental Au(o) and A t / t ( a ) curves observed on t h e Bordoni peak 61 are p l o t - t e d i n f i g u r e s 6 a and 6 b , and they show very s i m i l a r behaviour than t h a t t h e o r e t i - c a l 1 y p r e d i c t e d .
The shape o f t h e curves obtained i n the h i g h temperature range (T,
-
T,) i s a l s o very c h a r a c t e r i s t i c , because i t s assymetry w i t h regard t o t h e s t r e s s a x i s can never be due t o a d i s l o c a t i o n - p o i n t d e f e c t s i n t e r a c t i o n . This t y p i c a l k i n d o f curves hasbeen named "antisymetric curves". An example o f such experimental curves obtained
above t h e Bordoni peak B2 i n aluminium i s p l o t t e d i n f i g u r e 6 c.
C5- 168 JOURNAL DE PHYSIQUE
F i g . 7 Behaviour o f Actmax (see f i g . 3 c ) as a f u n c t i o n o f t h e temperature. For t h e Bordoni peak B, t h e p o i n t s a,b, c and d corres- pond r e s p e c t i v e l y t o t h e tempe- r a t u r e s To, T,, T, and T, o f t h e f i g . 3 c.
peak B, ( f i g u r e 7 ) . The phenomenon which appears a t 225 K i n f i g u r e 7 has been a t t r i b u t e d t o a d i s l o c a t i o n - p o i n t d e f e c t s i n t e r a c t i o n .
Conclusion
-
A new model has been developed t o d e s c r i b e t h e behaviour o f t h e a t t e - n u a t i o n and t h e propagation time o f u l t r a s o n i c waves, i n t h e presence o f a v a r i a b l e number N o f k i n k s on t h e d i s l o c a t i o n segments.During h e a t i n g under a low frequency s i n u s o i d a l a p p l i e d s t r e s s , t h i s model pre- d i c t s c h a r a c t e r i s t i c Aa(a) and A t / t ( o ) curves, l i k e t h e "antisymetric curves", due t o t h e t h e r m a l l y a c t i v a t e d double k i n k generation mechanism.
A l l t h e p r e d i c t e d behaviours have been e x p e r i m e n t a l l y observed i n aluminium on the two Bordoni peaks B, and B,, which tends t o prove one more time t h a t t h e Bordoni peaks i n FCC metals are r e a l l y due t o a mechanism o f t h e r m a l l y a c t i v a t e d double k i n k generation.
References
(1) G. Gremaud;'h new technique o f measurement...", t o be published a t t h i s conference
(2) G. Gremaud; t h e s i s , EPF-Lausanne (1981) (3) C . Esnouf; t h e s i s , INSA-Lyon (1978)
P.
Stadelmann; t h e s i s , EPF-Lausanne (1978)(4) R. G o t t h a r d t , B. Guisolan, Ph. B u f f a t ; Microsc. Spectrosc. Electron,
4,
p (1979)(5) G. Gremaud, W. Benoit; "The 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 and p o i n t de- f e c t s
...",
t o be published a t t h i s conference(6) G. Fantozzi, W. Benoit, C. Esnouf,
3 .
Perez; Ann.Phys.Fr.,4
p. 7 (1979)(7) T. Suzuki, Ch. Elbaum; J. Appl. Phys.,
