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Rate-dependent plastic flow in polycrystalline silver at ambient temperature
Vol. 17, p p . 741-744, 1983 Printed in the U.S.A.
Scripta M E T A L L U R G I C A
P e r g a m o n Press
Ltd.
RATE-DEPENDENT PLASTIC FLOW IN POLYCRYSTALLINE SILVER AT AMBIENT TEMPERATURE M, E. K a s s n e r Lawrence Lives'more N a t i o n a l L a b o r a t o r y , L i v e r m o r e , C a l i f . A. K. Mukherjee Dept. of Mechanical Engineering University of California, Davis, Calif.
94550
95616
(Received F e b r u a r y 14, 1983J. (Revised April 8, 1983) I n t r o d u c ti o n T h i s i n v e s t i g a t i o n i s a c o n t i n u a t i o n o f work by Logan, C a s t r o , and Mukherjee (1) i n which t h e m e c h a n i c a l p r o p e r t i e s o f c o l d - w o r k e d ( a b o u t 12 p e r c e n t ) p o l y c r y s t a U i n e s i l v e r a t low t e m p e r a t u r e (77 t o 473 K) were s t u d i e d . Those a u t h o r s i n t e r p r e t e d t h e i r r e s u l t s a s s u p p o r t f o r t h e i n t e r s e c t i o n o f d i s l o c a t i o n s a s t h e c o n t r o l l i n ~ mechanism f o r p l a s t i c f l o w . That c o n c l u s i o n seems t o have b e e n b a s e d l a r g e l y on t h e o b s e r v a t i o n t h a t t h e a c t i v a t i o n a r e a , A, d e c r e a s e s w i t h i n c r e a s i n g s t r a i n , a s would be t h e o r e t i c a l l y e x p e c t e d . However, from s t r a l n - r a t e change t e s t s p e r f o r m e d o v e r a s t r a i n r a n g e o f 20 p e r c e n t a t 77 K, t h o s e i n v e s t i g a t o r s found a d e c r e a s e o f o n l y a f a c t o r o f two i n A. I n our i n v e s t i g a t i o n , t h e p r o p o s i t i o n o f t h e d i s l o c a t l o n - i n t e r s e c t i o n mechanism was a n a l o g o u s l y t e s t e d w i t h a n n e a l e d p o l y c r y s t a l l i n e s i l v e r . If the dislocationi n t e r s e c t i o n mechanism i s a p p r o p r i a t e , a more d e m o n s t r a t i v e d e c r e a s e i n A ( e . g . , o v e r a f a c t o r o f t e n ) would be e x p e c t e d i n t h i s c a s e o v e r t h e same s t r a i n r a n g e o f 20 p e r c e n t . Background
Over low temperatures and for nominal rates of strain, plastic flow in crystals is usually d e t e r m i n e d p r i n c i p a l l y by combined r e s u l t s o f a t h e r m a l and t h e r m a l l y a c t i v a t e d mechanisms. S p e c i f i c a l l y , f o r f c c m e t a l s , t h e most p e r t i n e n t t h e r m a l l y a c t i v a t e d mechanism i s t h e i n t e r s e c t i o n model f o r d i s l o c a t i o n s . I n t h i s model, g l i d e d i s l o c a t i o n s p r o d u c e j o g s upon i n t e r s e c t i n g r e p u l s i v e "forest" dislocations. A r a t e e q u a t i o n t h a t d e s c r i b e s t h i s p r o c e s s was o r i g i n a l l y p r o p o s e d by S e e g e r (2): = M exp -(U 0 - Ab~*)IkT
(I)
where ~ i s t h e s h e a r s t r a i n r a t e , M i s a p r e - e x p o n e n t i a l c o n s t a n t t h a t i n c o r p o r a t e s t h e m o b i l e d i s l o c a t i o n d e n s i t y and t h e a t t e m p t f r e q u e n c y , e t c . U0 i s t h e f r e e e n e r g y o f a c t i v a t i o n a t z e r o s t r e s s , ~* i s t h e t h e r e ~ l l y a c t i v a t e d component o f t h e t o t a l f l o w - s t r e s s ~, A i s t h e a c t i v a t i o n a r e a and i s e q u a l t o d~ where d i s t h e w i d t h o f t h e o b s t a c l e and ~ i s t h e d i s t a n c e between the o b s t a c l e s . Here t h e o b s t a c l e s a r e t h e d i s l o c a t i o n " t r e e s " r i s i n g from t h e f o r e s t f l o u r , w h i c h i s t h e g l i d e p l a n e . Whereas o t h e r more p h e n o m e n o l o g i c a l r a t e e q u a t i o n s can a l s o be u s e d t o d e s c r i b e t h e r a t e phenomenon, Eq. ( 1 ) , which s p e c i f i c a l l y a p p l i e s t o t h e i n t e r s e c t i o n mechanism and e x p l i c i t l y i n c o r p o r a t e s t h e t e r m f o r t h e a c t i v a t i o n a r e a , w i l l be found more u s e f u l in analyzing the current experimental data in fcc silver. The a t h e r a a l back s t r e s s , Tb = T • * i s v e r y l i k e l y a s s o c i a t e d w i t h t h e l o n g - r a n g e s t r e s s f i e l d due t o d i s l o c a t i o n s . From Eq. ( 1 ) , Ab, sometimes r e f e r r e d t o a s an " a p p a r e n t a c t i v a t i o n volume" can be d e s c r i b e d by
/a~__~_i\1 '~' " ~ %, ' " *
lIT,-,
(2)
741 0036-9748/83/060741-04503.00/0
742
PLASTIC
FLOW
IN S I L V E R
Vol.
17,
No.
6
If strain-rate change t e s t s are performed over the course of p l a s t i c s t r a i n i n g , t h e change in flow s t r e s s ( A t ) a c c o m p a n i e d by a c h a n g e i n p l a s t i c s t r a i n - r a t e for a given structure (strain) is e q u a l t o AT*. T h i s i s b e c a u s e i n p r i n c i p l e t h e a t h e r m a l component o f t h e s t r e s s i s n o t e x p e c t e d to change in a constant-structure strain-rate change t e s t . F o r s u c h s t r a i n - r a t e c h a n g e t e s t s t h e c r o s s h e a d s p e e d i s s u d d e n l y i n c r e a s e d f r o m ~1 t o ~2, and t h e i n c r e a s e i n s t r e s s i s m e a s u r e d at constant structure (i.e., strain). Therefore
=
~
[
j
(3)
S i n c e A ~ t and 1 / t ~ ~ ~ x, g q . (3) p r e d i c t s t h a t Ab v a r i e s i n v e r s e l y w i t h t h e f l o w s t r e s s . Logan e t a l . f o u n d a b o u t a f a c t o r o f two d e c r e a s e i n Ab w i t h s t r a i n i n g c o l d - w o r k e d ( a b o u t 12 p e r c e n t ) s i l v e r a b o u t 20 p e r c e n t a t 77 K. A l t h o u g h t h e a s s o c i a t e d f l o w s t r e s s e s were n o t r e p o r t e d by t h e a u t h o r s , e x t r a p o l a t i o n and i n t e r p o l a t i o n o f t h e i r 77 K t e n s i l e d a t a s u g g e s t a c o r r e s p o n d i n g i n c r e a s e i n f l o w s t r e s s by a f a c t o r b e t w e e n 2 and 3. T h i s seems c o n s i s t e n t w i t h t h e dlslocation-intersectionmechanlsm. A more d r a m a t i c d e c r e a s e i n Ab m i g h t be d e m o n s t r a t e d i f strain-rate c h a n g e t e s t s were p e r f o r m e d on a n n e a l e d s i l v e r i n s t e a d o f on c o l d - w o r k e d s i l v e r . For e x a m p l e , F i g . 1 and t h e p r e c e d i n g t h e o r y p r e d i c t t h a t a t c = 0, Ab i s a b o u t a f a c t o r o f 10 h i g h e r t h a n t h e v a l u e f o u n d a f t e r 20 p e r c e n t s t r a i n i n g . I n o u r s t u d y , we u s e c o n s t a n t - s t r u c t u r e strain-rate c h a n g e t e s t s t o d e t e r m i n e Ab f o r a n n e a l e d s i l v e r a s a f u n c t i o n o f s t r a i n from ¢ - 0.006 to ¢ - 0.27. I
I
[
Experimental Procedure
298 K Uniaxial ~rain mrs ~ = 8.3 X 10~S "1 200 -
--
150 -
_
100
--
L ~-~
. ~
D
50
--
.~-oy 0
~ 0
0.10
0.20
0.30
Unmxisl ~rain, e FIG. 1. Stress versus strain behavior of annealed polycrystaUine silver at 298 K.
0.4(1
Our s t u d y u s e d s i l v e r o f t h e same c o m p o s i t i o n a s was u s e d i n ( 1 ) , ( i . e . , 99.99X pure), C y l £ n d r l c a l t e s t s p e c i m e n s were a r m e a l e d i n vacuum a t 600°C f o r one h o u r . The r e s u l t i n g g r a i n s i z e was a b o u t 1 5 0 - ~ a v e r n g e intercept. Mechanical tests using extensometry were p e r f o r m e d on a n I n s t r o n T T C - L . Specimens were i n i t l a l l y deformed a t a n n a x i a l s t r a i n r a t e o f 8 . 3 3 x 10"5s - 1 . Strain-rate change t e s t s were p e r f o r m e d by i n c r e a s i n g t h i s r a t e by f a c t o r s o f lO t o 100. When t h e s e t e s t s were p e r f o r m e d , t h e s u b s e q u e n t y i e l d s t r e s s was d e t e r m i n e d t h r o u g h u s e o f a 10- 4 p l a s t i c strain offset. After a small (<0.01) amount o f p l a s t i c s t r a i n a t t h e h i g h r a t e , d e f o r m a t i o n was r e s u m e d a t t h e i n i t i a l r a t e until the subsequent strain-rate change test. R e s u l t s and D i s c u s s i o n Figure 2 shows the variation of Ab with strain at ambient temperature. Here we see that Ab dramatically decreases with increasing strain f o r s t r a i n s l e s s t h a n 0 . 1 0 . The o r d e r o f m a g n i t u d e d e c r e a s e i n Ab f r o m ¢ = 0 . 0 0 6 t o ¢ = 0 . 2 7 i s c o n s i s t e n t w i t h a f a c t o r o f 10 i n c r e a s e i n f l o w s t r e s s and t h e d i s l o c a t i o n i n t e r s e c t i o n m e c h a n i s m m o d e l . The s t r a i n r e g i m e o v e r w h i c h t h e p r e v i o u s 77 K s t u d y (1) was performed is also shown. We see that the previous finding of only a small change in activation area with strain is understandable in terms of the findings of our study. Figure 2 a l s o shows t h a t t h e o n l y a m b i e n t t e m p e r a t u r e a c t i v a t i o n - a r e a d a t a p o i n t r e p o r t e d by t h e study is in reasonable agreement with the p r e s e n t s t u d y . The r e s u l t s g i v e n i n t h i s figure are supportive of the intersection of dislocations as the controlling mechanism for plastic flow of silver at low temperatures.
Vol.
17, No.
6
PLASTIC FLOW IN S I L V E R
2500 -
745
298 K • This stuoy O Logan, Castro, and Mukherjee (1) 298 K
2000 • e
1500 -
% < 1000 • L
500-
Logan, Castro, and Mukherjee (1) Strain regime
_I
I--
-1
eee
O
•
J
I
I
0.1
0.2
0.3
J 0.4
Uniaxial strain, e FIG. 2.
Variation of the product (Ab) of the activation area and the Burger• v e c t o r with strain.
298 K 300 --
• This study O Logan, Castro, and Mukherjee (1)
% E: i_~ •~ 200 --
a
iqpe
•
•
258: Basinski 131 = 163: Fuith, Widke and S c h ~ k (4)
N =
7
-
N
o .E IO0-
0.1
0.2
0.3
0,4
Uniaxial strain, e FIG. 3.
Variation of the con•rant-structure •train-rate sensitivity exponent (N) with •train.
744
PLASTIC FLOW IN SILVER
An a l t e r n a t i v e , with plastic strain
Vol.
17, No. 6
t h o u g h p e r h a p s l e s s f u n d a m e n t a l , way t o e x p r e s s t h e change i n f l o w s t r e s s rate is the constant structure straln-rate s e n s i t i v i t y e x p o n e n t , N, where
(4) Figure 3 is a plot of the constant-structure strain-rate sensitivity exponent versus strain. The e x p o n e n t N v a r i e s w i t h ¢ i n a manner a n a l o g o u s t o Ab. The f i g u r e a l s o shows t h e o n l y a m b i e n t t e m p e r a t u r e e x p o n e n t r e p o r t e d frem t h e p r e v i o u s s t u d y and shows s i n g l e - c r y s t a l N v a l u e s r e p o r t e d by B a s l n s k i ( 3 ) , and F u i t h , W i e l k e , and Sch~ck ( 4 ) , b o t h from c o n s t a n t - s t r u c t u r e strain-rate change tests. The t o t a l p l a s t i c s t r a i n p r e s e n t b e f o r e t h e s t r a l n - r a t e c h a n g e was n o t r e p o r t e d . N o n e t h e l e s s , t h e r e p o r t e d N v a l u e s from t h e s e s t u d i e s a r e i n r e a s o n a b l e a g r e e m e n t w i t h t h e p r e s e n t work. ¥1Eure 3 a l s o s u g g e s t s t h a t t h e r e may be p o s s i b l e e r r o r ( a t l e a s t a t t h e lower s t r a i n s ) i n determining the "instantaneous" increase in stress associated with an increase in straln-rate. A l t h o n g h t h e s o u r c e ( s ) o f t h i s e r r o r a r e n o t c l e a r , t h e m a g n i t u d e would n o t a l t e r o u r c o n c l u s i o n that the results of the strain-rate change tests support the dlslocatlon-intersectionmechanism. AcknowledEmnts We w l s h t o acknowledge C. L. Raymond and R. C a s t r o f o r t h e i r a s s i s t a n c e i n m e c h a n i c a l testing. Work p e r f o r m e d u n d e r t h e a u s p i c e s o f t h e U. S. D e p a r t m e n t o f Energy by Lawrence L i v e r m o r e N a t i o n a l L a b o r a t o r y u n d e r C o n t r a c t W-7405-Eng-48. References 1. 2. 3. 4.
R . W . Logan, R. G. C a s t r o , A. S e e g e r , D i s l o c a t i o n and 1957. Z. S. Basinski, P h i l . Meg. A. F u i t h , S. Wielke and G.
and A. K. N u k h e r j e e , S c r i p t a M e t a l l . , 17 (1983) 63. M e c h a n i c a l P r o p e r t i e s o f C r y s t a l s , J o h n Wiley and Sons, New York, 4 (1959) 393. Sch6ck, Z. M e t a l l k d e ,
72 (1981) 295.
Scripta M E T A L L U R G I C A
P e r g a m o n Press
Ltd.
RATE-DEPENDENT PLASTIC FLOW IN POLYCRYSTALLINE SILVER AT AMBIENT TEMPERATURE M, E. K a s s n e r Lawrence Lives'more N a t i o n a l L a b o r a t o r y , L i v e r m o r e , C a l i f . A. K. Mukherjee Dept. of Mechanical Engineering University of California, Davis, Calif.
94550
95616
(Received F e b r u a r y 14, 1983J. (Revised April 8, 1983) I n t r o d u c ti o n T h i s i n v e s t i g a t i o n i s a c o n t i n u a t i o n o f work by Logan, C a s t r o , and Mukherjee (1) i n which t h e m e c h a n i c a l p r o p e r t i e s o f c o l d - w o r k e d ( a b o u t 12 p e r c e n t ) p o l y c r y s t a U i n e s i l v e r a t low t e m p e r a t u r e (77 t o 473 K) were s t u d i e d . Those a u t h o r s i n t e r p r e t e d t h e i r r e s u l t s a s s u p p o r t f o r t h e i n t e r s e c t i o n o f d i s l o c a t i o n s a s t h e c o n t r o l l i n ~ mechanism f o r p l a s t i c f l o w . That c o n c l u s i o n seems t o have b e e n b a s e d l a r g e l y on t h e o b s e r v a t i o n t h a t t h e a c t i v a t i o n a r e a , A, d e c r e a s e s w i t h i n c r e a s i n g s t r a i n , a s would be t h e o r e t i c a l l y e x p e c t e d . However, from s t r a l n - r a t e change t e s t s p e r f o r m e d o v e r a s t r a i n r a n g e o f 20 p e r c e n t a t 77 K, t h o s e i n v e s t i g a t o r s found a d e c r e a s e o f o n l y a f a c t o r o f two i n A. I n our i n v e s t i g a t i o n , t h e p r o p o s i t i o n o f t h e d i s l o c a t l o n - i n t e r s e c t i o n mechanism was a n a l o g o u s l y t e s t e d w i t h a n n e a l e d p o l y c r y s t a l l i n e s i l v e r . If the dislocationi n t e r s e c t i o n mechanism i s a p p r o p r i a t e , a more d e m o n s t r a t i v e d e c r e a s e i n A ( e . g . , o v e r a f a c t o r o f t e n ) would be e x p e c t e d i n t h i s c a s e o v e r t h e same s t r a i n r a n g e o f 20 p e r c e n t . Background
Over low temperatures and for nominal rates of strain, plastic flow in crystals is usually d e t e r m i n e d p r i n c i p a l l y by combined r e s u l t s o f a t h e r m a l and t h e r m a l l y a c t i v a t e d mechanisms. S p e c i f i c a l l y , f o r f c c m e t a l s , t h e most p e r t i n e n t t h e r m a l l y a c t i v a t e d mechanism i s t h e i n t e r s e c t i o n model f o r d i s l o c a t i o n s . I n t h i s model, g l i d e d i s l o c a t i o n s p r o d u c e j o g s upon i n t e r s e c t i n g r e p u l s i v e "forest" dislocations. A r a t e e q u a t i o n t h a t d e s c r i b e s t h i s p r o c e s s was o r i g i n a l l y p r o p o s e d by S e e g e r (2): = M exp -(U 0 - Ab~*)IkT
(I)
where ~ i s t h e s h e a r s t r a i n r a t e , M i s a p r e - e x p o n e n t i a l c o n s t a n t t h a t i n c o r p o r a t e s t h e m o b i l e d i s l o c a t i o n d e n s i t y and t h e a t t e m p t f r e q u e n c y , e t c . U0 i s t h e f r e e e n e r g y o f a c t i v a t i o n a t z e r o s t r e s s , ~* i s t h e t h e r e ~ l l y a c t i v a t e d component o f t h e t o t a l f l o w - s t r e s s ~, A i s t h e a c t i v a t i o n a r e a and i s e q u a l t o d~ where d i s t h e w i d t h o f t h e o b s t a c l e and ~ i s t h e d i s t a n c e between the o b s t a c l e s . Here t h e o b s t a c l e s a r e t h e d i s l o c a t i o n " t r e e s " r i s i n g from t h e f o r e s t f l o u r , w h i c h i s t h e g l i d e p l a n e . Whereas o t h e r more p h e n o m e n o l o g i c a l r a t e e q u a t i o n s can a l s o be u s e d t o d e s c r i b e t h e r a t e phenomenon, Eq. ( 1 ) , which s p e c i f i c a l l y a p p l i e s t o t h e i n t e r s e c t i o n mechanism and e x p l i c i t l y i n c o r p o r a t e s t h e t e r m f o r t h e a c t i v a t i o n a r e a , w i l l be found more u s e f u l in analyzing the current experimental data in fcc silver. The a t h e r a a l back s t r e s s , Tb = T • * i s v e r y l i k e l y a s s o c i a t e d w i t h t h e l o n g - r a n g e s t r e s s f i e l d due t o d i s l o c a t i o n s . From Eq. ( 1 ) , Ab, sometimes r e f e r r e d t o a s an " a p p a r e n t a c t i v a t i o n volume" can be d e s c r i b e d by
/a~__~_i\1 '~' " ~ %, ' " *
lIT,-,
(2)
741 0036-9748/83/060741-04503.00/0
742
PLASTIC
FLOW
IN S I L V E R
Vol.
17,
No.
6
If strain-rate change t e s t s are performed over the course of p l a s t i c s t r a i n i n g , t h e change in flow s t r e s s ( A t ) a c c o m p a n i e d by a c h a n g e i n p l a s t i c s t r a i n - r a t e for a given structure (strain) is e q u a l t o AT*. T h i s i s b e c a u s e i n p r i n c i p l e t h e a t h e r m a l component o f t h e s t r e s s i s n o t e x p e c t e d to change in a constant-structure strain-rate change t e s t . F o r s u c h s t r a i n - r a t e c h a n g e t e s t s t h e c r o s s h e a d s p e e d i s s u d d e n l y i n c r e a s e d f r o m ~1 t o ~2, and t h e i n c r e a s e i n s t r e s s i s m e a s u r e d at constant structure (i.e., strain). Therefore
=
~
[
j
(3)
S i n c e A ~ t and 1 / t ~ ~ ~ x, g q . (3) p r e d i c t s t h a t Ab v a r i e s i n v e r s e l y w i t h t h e f l o w s t r e s s . Logan e t a l . f o u n d a b o u t a f a c t o r o f two d e c r e a s e i n Ab w i t h s t r a i n i n g c o l d - w o r k e d ( a b o u t 12 p e r c e n t ) s i l v e r a b o u t 20 p e r c e n t a t 77 K. A l t h o u g h t h e a s s o c i a t e d f l o w s t r e s s e s were n o t r e p o r t e d by t h e a u t h o r s , e x t r a p o l a t i o n and i n t e r p o l a t i o n o f t h e i r 77 K t e n s i l e d a t a s u g g e s t a c o r r e s p o n d i n g i n c r e a s e i n f l o w s t r e s s by a f a c t o r b e t w e e n 2 and 3. T h i s seems c o n s i s t e n t w i t h t h e dlslocation-intersectionmechanlsm. A more d r a m a t i c d e c r e a s e i n Ab m i g h t be d e m o n s t r a t e d i f strain-rate c h a n g e t e s t s were p e r f o r m e d on a n n e a l e d s i l v e r i n s t e a d o f on c o l d - w o r k e d s i l v e r . For e x a m p l e , F i g . 1 and t h e p r e c e d i n g t h e o r y p r e d i c t t h a t a t c = 0, Ab i s a b o u t a f a c t o r o f 10 h i g h e r t h a n t h e v a l u e f o u n d a f t e r 20 p e r c e n t s t r a i n i n g . I n o u r s t u d y , we u s e c o n s t a n t - s t r u c t u r e strain-rate c h a n g e t e s t s t o d e t e r m i n e Ab f o r a n n e a l e d s i l v e r a s a f u n c t i o n o f s t r a i n from ¢ - 0.006 to ¢ - 0.27. I
I
[
Experimental Procedure
298 K Uniaxial ~rain mrs ~ = 8.3 X 10~S "1 200 -
--
150 -
_
100
--
L ~-~
. ~
D
50
--
.~-oy 0
~ 0
0.10
0.20
0.30
Unmxisl ~rain, e FIG. 1. Stress versus strain behavior of annealed polycrystaUine silver at 298 K.
0.4(1
Our s t u d y u s e d s i l v e r o f t h e same c o m p o s i t i o n a s was u s e d i n ( 1 ) , ( i . e . , 99.99X pure), C y l £ n d r l c a l t e s t s p e c i m e n s were a r m e a l e d i n vacuum a t 600°C f o r one h o u r . The r e s u l t i n g g r a i n s i z e was a b o u t 1 5 0 - ~ a v e r n g e intercept. Mechanical tests using extensometry were p e r f o r m e d on a n I n s t r o n T T C - L . Specimens were i n i t l a l l y deformed a t a n n a x i a l s t r a i n r a t e o f 8 . 3 3 x 10"5s - 1 . Strain-rate change t e s t s were p e r f o r m e d by i n c r e a s i n g t h i s r a t e by f a c t o r s o f lO t o 100. When t h e s e t e s t s were p e r f o r m e d , t h e s u b s e q u e n t y i e l d s t r e s s was d e t e r m i n e d t h r o u g h u s e o f a 10- 4 p l a s t i c strain offset. After a small (<0.01) amount o f p l a s t i c s t r a i n a t t h e h i g h r a t e , d e f o r m a t i o n was r e s u m e d a t t h e i n i t i a l r a t e until the subsequent strain-rate change test. R e s u l t s and D i s c u s s i o n Figure 2 shows the variation of Ab with strain at ambient temperature. Here we see that Ab dramatically decreases with increasing strain f o r s t r a i n s l e s s t h a n 0 . 1 0 . The o r d e r o f m a g n i t u d e d e c r e a s e i n Ab f r o m ¢ = 0 . 0 0 6 t o ¢ = 0 . 2 7 i s c o n s i s t e n t w i t h a f a c t o r o f 10 i n c r e a s e i n f l o w s t r e s s and t h e d i s l o c a t i o n i n t e r s e c t i o n m e c h a n i s m m o d e l . The s t r a i n r e g i m e o v e r w h i c h t h e p r e v i o u s 77 K s t u d y (1) was performed is also shown. We see that the previous finding of only a small change in activation area with strain is understandable in terms of the findings of our study. Figure 2 a l s o shows t h a t t h e o n l y a m b i e n t t e m p e r a t u r e a c t i v a t i o n - a r e a d a t a p o i n t r e p o r t e d by t h e study is in reasonable agreement with the p r e s e n t s t u d y . The r e s u l t s g i v e n i n t h i s figure are supportive of the intersection of dislocations as the controlling mechanism for plastic flow of silver at low temperatures.
Vol.
17, No.
6
PLASTIC FLOW IN S I L V E R
2500 -
745
298 K • This stuoy O Logan, Castro, and Mukherjee (1) 298 K
2000 • e
1500 -
% < 1000 • L
500-
Logan, Castro, and Mukherjee (1) Strain regime
_I
I--
-1
eee
O
•
J
I
I
0.1
0.2
0.3
J 0.4
Uniaxial strain, e FIG. 2.
Variation of the product (Ab) of the activation area and the Burger• v e c t o r with strain.
298 K 300 --
• This study O Logan, Castro, and Mukherjee (1)
% E: i_~ •~ 200 --
a
iqpe
•
•
258: Basinski 131 = 163: Fuith, Widke and S c h ~ k (4)
N =
7
-
N
o .E IO0-
0.1
0.2
0.3
0,4
Uniaxial strain, e FIG. 3.
Variation of the con•rant-structure •train-rate sensitivity exponent (N) with •train.
744
PLASTIC FLOW IN SILVER
An a l t e r n a t i v e , with plastic strain
Vol.
17, No. 6
t h o u g h p e r h a p s l e s s f u n d a m e n t a l , way t o e x p r e s s t h e change i n f l o w s t r e s s rate is the constant structure straln-rate s e n s i t i v i t y e x p o n e n t , N, where
(4) Figure 3 is a plot of the constant-structure strain-rate sensitivity exponent versus strain. The e x p o n e n t N v a r i e s w i t h ¢ i n a manner a n a l o g o u s t o Ab. The f i g u r e a l s o shows t h e o n l y a m b i e n t t e m p e r a t u r e e x p o n e n t r e p o r t e d frem t h e p r e v i o u s s t u d y and shows s i n g l e - c r y s t a l N v a l u e s r e p o r t e d by B a s l n s k i ( 3 ) , and F u i t h , W i e l k e , and Sch~ck ( 4 ) , b o t h from c o n s t a n t - s t r u c t u r e strain-rate change tests. The t o t a l p l a s t i c s t r a i n p r e s e n t b e f o r e t h e s t r a l n - r a t e c h a n g e was n o t r e p o r t e d . N o n e t h e l e s s , t h e r e p o r t e d N v a l u e s from t h e s e s t u d i e s a r e i n r e a s o n a b l e a g r e e m e n t w i t h t h e p r e s e n t work. ¥1Eure 3 a l s o s u g g e s t s t h a t t h e r e may be p o s s i b l e e r r o r ( a t l e a s t a t t h e lower s t r a i n s ) i n determining the "instantaneous" increase in stress associated with an increase in straln-rate. A l t h o n g h t h e s o u r c e ( s ) o f t h i s e r r o r a r e n o t c l e a r , t h e m a g n i t u d e would n o t a l t e r o u r c o n c l u s i o n that the results of the strain-rate change tests support the dlslocatlon-intersectionmechanism. AcknowledEmnts We w l s h t o acknowledge C. L. Raymond and R. C a s t r o f o r t h e i r a s s i s t a n c e i n m e c h a n i c a l testing. Work p e r f o r m e d u n d e r t h e a u s p i c e s o f t h e U. S. D e p a r t m e n t o f Energy by Lawrence L i v e r m o r e N a t i o n a l L a b o r a t o r y u n d e r C o n t r a c t W-7405-Eng-48. References 1. 2. 3. 4.
R . W . Logan, R. G. C a s t r o , A. S e e g e r , D i s l o c a t i o n and 1957. Z. S. Basinski, P h i l . Meg. A. F u i t h , S. Wielke and G.
and A. K. N u k h e r j e e , S c r i p t a M e t a l l . , 17 (1983) 63. M e c h a n i c a l P r o p e r t i e s o f C r y s t a l s , J o h n Wiley and Sons, New York, 4 (1959) 393. Sch6ck, Z. M e t a l l k d e ,
72 (1981) 295.