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Influence of cold work on the rigidity of copper
Druyvesteyn, M . J . Schannen, O. F . Z . Swaying, E. C. J. 1959
Physica 25 1271-1274
I N F L U E N C E OF COLD WORK ON T H E R I G I D I T Y OF COPPER b y M. J. D R U Y V E S T E Y N ,
O. F. Z. S C H A N N E N a n d E. C. J. S W A V I N G
L a b o r a t o r i u m voor T e c h n i s c h e P h y s i c a v a n de T e c h n i s e h e Hogesehool, Delft, N e d e r l a n d
Synopsis A decrease of the rigidity of Cu and Ag of about 17% after a plastic deformation of about 0.1% at --190°C was observed. The recovery of this effect between --190 ° and +80°C was studied. T h e torsion m o d u l u s of Cu a n d Ag was m e a s u r e d at --190°C with a torsion p e n d u l u m (length a n d d i a m e t e r of the wire 50 a n d 1.5 m m , f r e q u e n c y 50 till 75 cycles/sec, precision 0.1 till 0.4% d e p e n d i n g on the w a y the frequency was m e a s u r e d , m a x i m u m strain a m p l i t u d e of an o u t e r fibre u n d e r 45 ° with the axis of the wire 8.10 - s till 5.10-5). Copper was m e a s u r e d in three, silver in one q u a l i t y *). Before m o u n t i n g the polycrystalline wires were a n n e a l e d at 550°C for 1½ h o u r in v a c u u m . A plastic torsion at --190°C gives a decrease of the torsion m o d u l u s of
°[/o 1,5
_ ~o in%
x
r
I
r
l
1
de forrnoti0n in%
Fig. 1. Change of the r i g i d i t y of normal Cu as a function of the plastic deformation
of a straight line on the surface (measuring amplitude 8.10-s: x and 5.10-s: O) *) N o r m a l Cu (99.9%); Cu from J o h n s o n and M a t t h e y ( s t a t e d p u r i t y 99.999% ); a n d Cu from A m e r i c a n S m e l t i n g and Refining Co. (99.999%). The r a t i o of the r e s i s t a n c e a t 0°C to the r e s i s t a n c e at 4°K is for the three sorts of Cu: 123; 320 and 787. A c c o r d i n g to these results the A m e r i c a n Cu is the purest.
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-
1271
-
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1272
Iv[. j . DRUYVESTEYN, O. F. Z. SCHANNEN AND E. C. J. SWAVING
about 17%. Fig. 1 shows that a deformation of 0.1% (plastic elongation of a straight line on the surface of the wire) gives a strong decrease, which is hardly altered b y further plastic torsion. As a very small deformation gives a large decrease, the reproducibility was not good (about 5%) This was probably due to deformation of the wire during mounting; no annealing was applied after mounting. The influence of the measuring amplitude is indicated in the figure; this influence is almost equal to the experimental error. Practically the same curve is obtained for the different qualities of copper and also for silver.
1S - ~
6o
in%
-200
-1 0
i -100
I -50
I 0
I +50
I0 +B
T in°C
Fig. 2. --AG/Go a t - - 1 9 0 ° C a f t e r a plastic t o r s i o n of 0 . 4 % a n d r e c o v e r y for 6 m i n u t e s a t d i f f e r e n t t e m p e r a t u r e s . T h e m e a n v a l u e for t h e t w o a m p l i t u d e s m e a s u r e d is g i v e n : • for n o r m a l Cu, O for J o h n s o n a n d M a t t h e y Cu a n d & for A m e r i c a n Cu.
Fig. 2 shows recovery curves for three sorts of copper. A first recovery step is seen, giving a decrease of the effect till I0% between --190 ° and --80°C. A second step begins for the Johnson and Matthey copper at --50°C and for the American copper at + 10°C. This step is not yet finished at the highest recovery temperature of 80°C. In the horizontal part sometimes a slight increase is seen (this is a decrease of the modulus). In silver this effect is more pronounced (fig. 3). The activation energy of the two recovery steps of copper could only be measured roughly. For the first step 0.2 4- 0.1 eV and for the second step about 1 eV was found. A decrease of an elastic modulus of more than 10% by a small plastic deformation has - as far as we k n o w - only been observed for Cu and A1 by C r i t t e n d e n and D i e c k a m p 1). A somewhat smaller effect has been observed by many authors 2).
1273
INFLUENCE OF COLD WORK ON THE RIGIDITY OF COPPER
The decrease of the modulus is generally attributed to mobile dislocations formed b y the plastic deformation. When a tension is applied the dislocations move in their glide planes; when the tension is reduced to zero they return to their original position. In Cu and Ag these dislocations remain mobile at --190°C. The change of the torsion modulus G has been calculated approximately b y M o t t and F r i e d e l 8).
AG
l(NZ31o~)
Go
1 +/(NlS/o~)
N is the number of dislocations with length l per unit volume, the ends of the dislocations being fixed; ~ is a function of the distance between the dislocations, it is about unity; / is a numerical factor between 1/6 and 1/15. It depends on the orientation of the Burgers vector of the dislocations with respect to the applied stress, when only gliding of the dislocations occurs.
15 - -~
)n%
\
lo
500
-,~o
-,~o
-$
~ "
+~
÷4
T in °C
Fig. 3. R e c o v e r y curve, for A g ( J o h n s o n a n d M a t t h e y 99.999).
If the applied shear stress lies in the direction of the Burgers vector for all dislocations / will be 1/6. However when all orientations of the Burgers vectors with respect to the stress occur with equal probability / will be 1/15. As in our case the dislocations are produced b y a plastic torsion and the rigidity is measured with a torsion about the same axis the glide planes of the formed dislocations will not deviate much from the plane of maximum shear stress and / will be only slightly smaller than 1/6. If we assume that Nla is in our case about unity, as it is for the case of a network of dislocations, we find a value of AG/Go somewhat smaller than 20%, as is found experimentally. The recovery of the rigidity occurs in two steps in the temperature range where also the recovery of the electric resistivity occurs in two steps 4) Physica 25
1274
I N F L U E N C E OF COLD W O R K ON T H E R I G I D I T Y OF C O P P E R
Both phenomena could be explained by a diffusion of point defects to dislocations. These point defects pin the dislocations, causing a decrease of l. Other processes, a s a rearrangement of the dislocations to a more stable configuration, where they are less mobile, may however also occur. This rearrangement can be promoted by the arrival of point defects. Received 6-10-59 REFERENCES 1) C r i t t e n d e n , E. C. and D i e c k a m p , H., Phys. Rev. 91 (1953) 232; 94 (1954) 1421; N o w i c k , A. S., Symposium Creep and Recovery, Am. Soc. for Metals (1957) 146. 2) S m i t h , A. D. N.; Phil. Mag. 44 (1953) 453; G o r d o n , R. B. and N o w i c k , A. S., Act. Met. 4 (1956) 514; K 6 s t e r , W. e.a.Z. Metallk. 32 (1940) 282; 46 (1955) 84; 47 {1956) 224; H o r d o n , M. J., L e m e n t , B. S., and A v e r b a c h , B. L., Act. Met. 6 (1958) 446. 3) M o t t , N. F., Phil. Mag. 4:3 (1952) 1151; F r i e d e ] , J., Les dislocations (1956); Phil. Mag. 44 (1953) 444; F r i e d e l , J., B o u l a n g e r , C. and C r u s s a r d , C., Act. Met. :~ (1955) 380; G r a n a t o , A., H i k a t a , A. and L i i c k e , K., Act. Met. ql (1958) 470; J. ~pp]. Phys. 27 (1956) 583 and 789. 4) S e e g e r , A., Encycl. of Phys. VII, I, pag. 383; B e r g h o u t, C. W., Thesis Delft (1956); K o r e v a a r B. M., Act. Met. 6 (1958) 572.
Physica 25 1271-1274
I N F L U E N C E OF COLD WORK ON T H E R I G I D I T Y OF COPPER b y M. J. D R U Y V E S T E Y N ,
O. F. Z. S C H A N N E N a n d E. C. J. S W A V I N G
L a b o r a t o r i u m voor T e c h n i s c h e P h y s i c a v a n de T e c h n i s e h e Hogesehool, Delft, N e d e r l a n d
Synopsis A decrease of the rigidity of Cu and Ag of about 17% after a plastic deformation of about 0.1% at --190°C was observed. The recovery of this effect between --190 ° and +80°C was studied. T h e torsion m o d u l u s of Cu a n d Ag was m e a s u r e d at --190°C with a torsion p e n d u l u m (length a n d d i a m e t e r of the wire 50 a n d 1.5 m m , f r e q u e n c y 50 till 75 cycles/sec, precision 0.1 till 0.4% d e p e n d i n g on the w a y the frequency was m e a s u r e d , m a x i m u m strain a m p l i t u d e of an o u t e r fibre u n d e r 45 ° with the axis of the wire 8.10 - s till 5.10-5). Copper was m e a s u r e d in three, silver in one q u a l i t y *). Before m o u n t i n g the polycrystalline wires were a n n e a l e d at 550°C for 1½ h o u r in v a c u u m . A plastic torsion at --190°C gives a decrease of the torsion m o d u l u s of
°[/o 1,5
_ ~o in%
x
r
I
r
l
1
de forrnoti0n in%
Fig. 1. Change of the r i g i d i t y of normal Cu as a function of the plastic deformation
of a straight line on the surface (measuring amplitude 8.10-s: x and 5.10-s: O) *) N o r m a l Cu (99.9%); Cu from J o h n s o n and M a t t h e y ( s t a t e d p u r i t y 99.999% ); a n d Cu from A m e r i c a n S m e l t i n g and Refining Co. (99.999%). The r a t i o of the r e s i s t a n c e a t 0°C to the r e s i s t a n c e at 4°K is for the three sorts of Cu: 123; 320 and 787. A c c o r d i n g to these results the A m e r i c a n Cu is the purest.
-
-
1271
-
-
1272
Iv[. j . DRUYVESTEYN, O. F. Z. SCHANNEN AND E. C. J. SWAVING
about 17%. Fig. 1 shows that a deformation of 0.1% (plastic elongation of a straight line on the surface of the wire) gives a strong decrease, which is hardly altered b y further plastic torsion. As a very small deformation gives a large decrease, the reproducibility was not good (about 5%) This was probably due to deformation of the wire during mounting; no annealing was applied after mounting. The influence of the measuring amplitude is indicated in the figure; this influence is almost equal to the experimental error. Practically the same curve is obtained for the different qualities of copper and also for silver.
1S - ~
6o
in%
-200
-1 0
i -100
I -50
I 0
I +50
I0 +B
T in°C
Fig. 2. --AG/Go a t - - 1 9 0 ° C a f t e r a plastic t o r s i o n of 0 . 4 % a n d r e c o v e r y for 6 m i n u t e s a t d i f f e r e n t t e m p e r a t u r e s . T h e m e a n v a l u e for t h e t w o a m p l i t u d e s m e a s u r e d is g i v e n : • for n o r m a l Cu, O for J o h n s o n a n d M a t t h e y Cu a n d & for A m e r i c a n Cu.
Fig. 2 shows recovery curves for three sorts of copper. A first recovery step is seen, giving a decrease of the effect till I0% between --190 ° and --80°C. A second step begins for the Johnson and Matthey copper at --50°C and for the American copper at + 10°C. This step is not yet finished at the highest recovery temperature of 80°C. In the horizontal part sometimes a slight increase is seen (this is a decrease of the modulus). In silver this effect is more pronounced (fig. 3). The activation energy of the two recovery steps of copper could only be measured roughly. For the first step 0.2 4- 0.1 eV and for the second step about 1 eV was found. A decrease of an elastic modulus of more than 10% by a small plastic deformation has - as far as we k n o w - only been observed for Cu and A1 by C r i t t e n d e n and D i e c k a m p 1). A somewhat smaller effect has been observed by many authors 2).
1273
INFLUENCE OF COLD WORK ON THE RIGIDITY OF COPPER
The decrease of the modulus is generally attributed to mobile dislocations formed b y the plastic deformation. When a tension is applied the dislocations move in their glide planes; when the tension is reduced to zero they return to their original position. In Cu and Ag these dislocations remain mobile at --190°C. The change of the torsion modulus G has been calculated approximately b y M o t t and F r i e d e l 8).
AG
l(NZ31o~)
Go
1 +/(NlS/o~)
N is the number of dislocations with length l per unit volume, the ends of the dislocations being fixed; ~ is a function of the distance between the dislocations, it is about unity; / is a numerical factor between 1/6 and 1/15. It depends on the orientation of the Burgers vector of the dislocations with respect to the applied stress, when only gliding of the dislocations occurs.
15 - -~
)n%
\
lo
500
-,~o
-,~o
-$
~ "
+~
÷4
T in °C
Fig. 3. R e c o v e r y curve, for A g ( J o h n s o n a n d M a t t h e y 99.999).
If the applied shear stress lies in the direction of the Burgers vector for all dislocations / will be 1/6. However when all orientations of the Burgers vectors with respect to the stress occur with equal probability / will be 1/15. As in our case the dislocations are produced b y a plastic torsion and the rigidity is measured with a torsion about the same axis the glide planes of the formed dislocations will not deviate much from the plane of maximum shear stress and / will be only slightly smaller than 1/6. If we assume that Nla is in our case about unity, as it is for the case of a network of dislocations, we find a value of AG/Go somewhat smaller than 20%, as is found experimentally. The recovery of the rigidity occurs in two steps in the temperature range where also the recovery of the electric resistivity occurs in two steps 4) Physica 25
1274
I N F L U E N C E OF COLD W O R K ON T H E R I G I D I T Y OF C O P P E R
Both phenomena could be explained by a diffusion of point defects to dislocations. These point defects pin the dislocations, causing a decrease of l. Other processes, a s a rearrangement of the dislocations to a more stable configuration, where they are less mobile, may however also occur. This rearrangement can be promoted by the arrival of point defects. Received 6-10-59 REFERENCES 1) C r i t t e n d e n , E. C. and D i e c k a m p , H., Phys. Rev. 91 (1953) 232; 94 (1954) 1421; N o w i c k , A. S., Symposium Creep and Recovery, Am. Soc. for Metals (1957) 146. 2) S m i t h , A. D. N.; Phil. Mag. 44 (1953) 453; G o r d o n , R. B. and N o w i c k , A. S., Act. Met. 4 (1956) 514; K 6 s t e r , W. e.a.Z. Metallk. 32 (1940) 282; 46 (1955) 84; 47 {1956) 224; H o r d o n , M. J., L e m e n t , B. S., and A v e r b a c h , B. L., Act. Met. 6 (1958) 446. 3) M o t t , N. F., Phil. Mag. 4:3 (1952) 1151; F r i e d e ] , J., Les dislocations (1956); Phil. Mag. 44 (1953) 444; F r i e d e l , J., B o u l a n g e r , C. and C r u s s a r d , C., Act. Met. :~ (1955) 380; G r a n a t o , A., H i k a t a , A. and L i i c k e , K., Act. Met. ql (1958) 470; J. ~pp]. Phys. 27 (1956) 583 and 789. 4) S e e g e r , A., Encycl. of Phys. VII, I, pag. 383; B e r g h o u t, C. W., Thesis Delft (1956); K o r e v a a r B. M., Act. Met. 6 (1958) 572.