Creep of copper: 4–300 K

Materials Science and Engineering, A 147 ( 1991 ) 23- 32

23

Creep of copper: 4-300 K R. P. Reed, N. J. Simon and R. P. Waish National Institute of Standards and Technology, Boulder, CO 80303 (U.S.A.)

(Received January 25, 1990; in revised form April 8, 1991)

Abstract Creep measurements at 300, 76 and 4 K were conducted on C10400 copper. The specimens were held under a constant tensile load to give ratios of applied stress to yield strength in the range 0.8-2.0. The strain was measured using strain gages (sensitivities of 10-6). Creep data were fitted by a non-linear least-squares procedure to a series of expressions that have been widely used to describe primary, transient, and steady-state conditions. No steady-state creep was observed, even at 300 K. Instead, at all temperatures, the time dependence of creep strain is best described as logarithmic. Activation volumes obtained from logarithmic creep analyses, from tensile strain-rate-change and stress relaxation measurements were compared. It was found that the constant ct in the logarithmic creep expression is linearly dependent on the tensile strain-hardening rate at constant stress.

1. Introduction

For many cryogenic technological applications, such as the operation of high-field magnets for long periods of time, knowledge of creep properties is necessary. Copper is used extensively as a stabilizing material in super-conducting magnets and as a conductor in high-field, normal-metal magnets. The study of the time-dependent mechanical behavior of structural materials at low temperatures has proved very challenging. Maintenance of temperature and mechanical stability, as well as accurate recording of stress and strain over long periods of time, stretch the limits of measurement capabilities. The creep of copper has perhaps been studied more than that of any other metal at low temperatures [1-11]. A wide range of interpretations of results is apparent. Both logarithmic (creep strain proportional to log of time) and steady-state (creep strain proportional to time) have been reported for copper at low temperatures. The first creep data on copper were obtained for relatively short durations (less than 8 h) at 77 K [3] and 1.5-4.5 K [4-6]. Only transient creep was observed and related to logarithmic behavior: e = a ln(Tt + 1) 0921-5093/91/$3.50

(1)

where e is the total creep strain, t is the time, and a and 7 are constants with a dependent on temperature and applied stress. Both Friedel [12] and Seeger [13] considered that low temperature creep involved mobile dislocations cutting through forest dislocations. Their derived expression for a is a -

kT Vc*O

(2)

where k is Boltzmann's constant, T(K) is the absolute temperature, Vc* is the activation volume, and 0 is the strain-hardening coefficient. Since a must approach zero as T approaches zero, the high values of a obtained by the Soviet group [4-6] at temperatures less than 4 K led to the suggestion that dislocation tunneling is the controlling creep mechanism at very low temperatures. Anomalously high values of a were not reported in other creep measurements on copper [1-3, 7-11]. More recently, from experiments of longer duration (less than or equal to 200 h), low temperature steady-state creep has been reported [1, 2, 7-10]. Steady-state creep rates gs~ ranging from 10 -ll to 2 × 1 0 -1° s -1 were measured [7-10]. Apparent activation energies Q~pp were deter© Elsevier Sequoia/Printed in The Netherlands

24

mined from data at 77, 88, and 90 K using an expression derived from the Arrhenius equation: Qapp = K[Alngss/A( 1 / T )]o

(3)

where o is the (constant) applied engineering stress. Low values ranging from 0.013 to 0.021 eV for applied stresses of 34-69 MPa in the temperature range 77-87 K led to the suggestion that double-kink nucleation was the controlling dislocation creep mechanism in copper at low temperatures. Much earlier, Landon et al. [11] reported an activation energy an order of magnitude larger, about 0.17 eV at 77 K. Their experiments were also analyzed using eqn. (3) and varying the temperature slightly to compare strain rates. However, their values of applied stress were much larger (about 275 MPa at 200 K). While Yen et al. [2] report that Q,,pp decreaes with increasing stress (from 0.021 eV at 34.5 MPa to 0.013 eV at 69.0 MPa), Landon et al. report that Qapp is independent of applied stress. This paper reports on the creep of copper at temperatures below 0.22T m (295, 76 and 4 K) and at stress levels about 10-3G (25-60 MPa) where T m is the melting temperature (1356 K) and G is the shear modulus. Test durations up to 1600 h were maintained at low temperatures. Excellent strain sensitivity ( 1 0 -6 ) increased the ability to discriminate between logarithmic, steady-state, or other strain-time dependences. In this study, at 4, 76, and 300 K, no creep range was found within which there was a linear relationship between creep strain and time (steadystate conditions); thus, it was inappropriate to calculate an activation energy for the creep process. Instead, activation volumes were estimated, assuming a logarithmic time dependence on creep strain; these activation volumes were compared at each temperature to those estimated from tensile deformation.

2. Experimentalprocedures Oxygen-free, high conductivity copper (Cu-Ag, 99.99 wt.%, UNS 10200) was obtained in 20 mm diameter bar stock. It was used in the annealed condition (650 °C for 1 h) with a hardness RB = 22 and an average grain size of 36 gm. Subsequently, specimens were reannealed (650 °C for 1 h) after undergoing creep deformation of 0.02-0.04 in previous tests; these specimens are called "reannealed" in the text. For this

copper, average yield strengths of 25, 27, and 30 MPa were measured at 295, 76 and 4 K respectively. The dead-weight loading system used a lever arm pivoted above the specimen. A schematic diagram of the low-temperature cryostat and loading assembly is shown in Fig. 1. For low temperature tests a 900 mm deep superinsulated dewar with a narrow neck was used. The dewar capacity was 30 1. The test fixture consisted of a G-10CR outer compression cylinder and an inner titanium pull rod. Radiation shielding was used in the upper neck of the dewar. Liquid helium boil-off without the test fixture was 0.2 I hand with the test fixture was 0.51 h- 1. Metal film, resistance strain gages (73Ni-20Cr alloy) were bonded to the round specimens with a low-temperature epoxy. The lead wires from these 350 f2 strain gages were attached at soldered tabs on the specimen and wound around the upper pull rod, exiting the cryostat through the canvas-phenolic upper block. The strain sensitivity at room temperature was 5 × 1 0 - 7 ; instrumental and temperature drift resulted in strain readout variability over a period of one month of about + 2 × 10- 7 at room temperature and about + 4 x 1 0 -6 at 4 K . To measure the variability during a test, dummy specimens were inserted in the cryostat. Other environmental factors caused measurement inconsistencies. These included vibrations, ambient temperature variability, cryogenic liquid

L e v e r Arm ~ ,

Alignment C o u p l l n g ~ Stainless Steel •~ tj Reaction Plate ~,~ LHe Fill T u b e ~ Canvae-Phenolio/ Insulating Block .

ead Wire Accae

Foam Baffling w / Radiation Shielding ~" G - 1 0 CR Coml:)raslion Cylinder ------"

ull Rod

Super Insulated Helium Dewer---'~ Load S t r a i n Gage, Bpeclmen--: ---f

Spherical Nut

~ 8telnioss Steel End Cap

Fig. 1. Load train and cryostat system used for creep testing at low temperatures.

25 transfer, and the reduction of the cryogenic liquid level with time. Floor vibrations induced by other laboratory equipment led to spurious sudden jumps (around 10 -s) of strain during testing. The vibrations induced specimen strain despite the use of damping pads. Ambient temperature variability led to daily cylic patterns of strain (at the 10-7 level); to eliminate these thermally induced strain cycles subsequent test specimens were maintained at 303 K using resistance heaters attached to brass specimen grips. The transfer of cryogenic fluids into the dewar produced transient specimen loads of the order of 0.5 kgf that were induced by the differential thermal contraction between the pull rod and compression cylinder. These transient loads, measured by strain gages on the pull-rod and compression cylinder, were not adequately compensated by the leverarm. Similarly, the reduction of liquid level with time is thought to have led to load changes in the filament-reinforced composite cylinder from thermal contraction changes transmitted by the continuous filaments. These strain differences, again in the range of 1 0 - 7 , led to small uncompensated load changes on the specimen. The data in this paper may have been influenced by some of these factors; however, the measurements were either discarded or corrected when spurious data were firmly identified as being influenced by any of these factors. 3. Model analysis The creep strain after a period of elapsed time t is the sum of the initial strain upon loading t o and a time-dependent strain. Both the initial and time-dependent strain components are functions of the temperature T and the applied stress, o a. We have chosen to elucidate this functional dependence by first fitting a series of expressions of the creep strain as a function of time (Table 1) to individual data sets obtained at 4, 76, and 295 K for a series of oa values. Then, the dependence of the constant a i in these expressions on ~x~ and T was determined from plots of the constants vs. o., for the three test temperatures. The 11 expressions in Table 1 were obtained from the literature, or are generalizations of expressions for creep strain found in the literature. The creep strain expression is expected to be logarithmic (eqns. (1) and (3)) when T~<0.3Tm. Equations (2) and (4) allow for steady-state creep (ast, g = as) in addition to logarithmic creep, and eqns. (9), (10),

TABLE Creep

1 strain expressions

gtruc = Ct~ + a l In t flruc = ~'tt + a l In t + ast et,.~,~ = % + a t I n ( a , t

+ 1)

err,, ~, = % + a I l n ( a 2 t + 1 ) + a s t %u,. = % + a l[l - e x p ( - a,t)l + as t Elrllc = El I 4- O it I~3 4- a2 t2/3 4- a5 t

g,,,,c = g~, + a t t": + a3l EllUC : ~'(I 4- a I t"4 4-

05 l'u 4- 05I

%L,~. = % + al l n ( a z t + a3) %u~.= % + a lln(a2t ~'tru¢ : El) 4- a l

+ %) + ast

il) (2) (3) (4) (s) (6) (7) (8) (9) (]0)

In t + ast"'

and (11) are further generalizations of these expressions. Equations (5) and (6) are expressions given in the literature for temperatures of the order of 0.4 Tm and higher. In this temperature regime, the primary stage of creep is represented by { a l [ - e x p ( - a2t)] } o r [alt 1/3 +a2 t2/3] and the secondary, or steady-state regime, by the a st term. Equations (7) and (8) are generalizations of these expressions. The equations in Table 1 were fitted to the data sets by a non-linear least-squares computer program. The constants a i from the expressions that best fitted the data sets were then plotted as a function of oa. A linear least-squares fit was made to the data in these plots. 4. Results and discussion The results are summarized in Table 2, which includes the initial applied stress, the ratio of the applied stress to the yield strength, the initial strain on application of the dead weight E0, and the coefficient for the primary creep term a~ from eqn. (2) in Table 1. When the data sets at 300 and 75 K were fitted to the equations in Table 1, eqn. ( 11 ) usually gave the lowest standard deviation (SD). In many cases, the non-linear least-squares procedure did not give a convergent result when the data set was fitted to eqn. ( 11 ); however, the SD of the fit was the lowest found for 12 out of 15 sets at 300 K, and for 6 out of 7 sets at 76 K (eqn. ( 11 ) was not fitted to 3 of the data sets at 76 K reported in Table 2). The test duration ranged from 15 700 to 50 000 min at 300 K and from 12 600 to 96600 min at 76 K. At 4 K, the test duration was gener-

26 TABLE 2 Summary of creep data Temperature (K)

o~ (MPa)

OJay

300

20.20 24.90 27.00 29.96 31.40 34.00 34.10 36.40 37.60 38.00 41.00 42.20 42.40 45.10 45.30

0.81 1.00 1.08 1.20 1.26 1.36 1.36 1.46 1.50 1.52 1.64 1.69 1.70 1.80 1.81

1.704 3.269 0.709 4.726 4.873 3.131 5.575 5.647 7.031 4.083 5.596 8.208 8.031 9.116 9.032

3.192 4.153 1.67 3.44 3.15 3.663 4.254 4.297 4.871 4.371 5.111 5.845 4.232 4.49 5.672

37440 37440 29986 27300 18856 29986 41640 49950 41640 29986 29986 15695 49950 18856 15695

76

24.30 26.10 29.70 33.20 35.20 35.40 37.10 41.30 45.00 49.50

0.90 0.97 1.10 1.23 1.30 1.31 1.37 1.53 1.67 1.83

0.650 1.659 2.609 2.23 1.188 2.731 4.889 4.815 5.258 7.499

2.323 3.233 2.506 3.934 3.763 3.876 4.684 3,865 4.588 4.642

12591 12591 96600 96600 12591 96600 58894 36345 43455 12820

30.00 30.60 32.00 34.40 35.60 37.60 41.50 43.80 44.00 47.20 48.90 60.00

1 . 0 0 2.199 1 . 0 2 0.838 1 . 0 7 3.521 1 . 1 5 2.563 1 . 1 9 3.817 1 . 2 5 2.178 1 . 3 8 5.743 1 . 4 6 4.933 1 . 4 7 5.834 1 . 5 7 3.926 1 . 6 3 8.225 2.00 17.56

eo

a~

(10 -3) (10 -s)

Duration (min)

0.005 1027 0.361 21339 0.139 1027 0.663 21339 0.101 1488 0.423 21339 0.787 18540 0.16 3612 0.17 1027 0.144 1405 1.166 6935 2.285 6935

ally much shorter ( 1 0 0 0 - 2 1 300 min) and eqn. (11) was not found to give the best fit to the data sets. It is thought that eqn. (11) usually provided the best fit for data sets of longer duration because the power of t(a4) was allowed to vary; in eqns. (2), (4)-(8) and (10), the power of t is 1.0. At the longer elapsed times, it is more likely that a different stage of creep has been entered or that the environmental factors discussed above produced small inconsistencies in the data and, therefore, a more general expression for this allows a better fit to the data. (That multiple stages of creep were present is further substantiated by the observation that in all cases, eqn. (2) was a better fit than was eqn. (1), and eqn. (4) was better than eqn. (3).) However, because small

aberrations in a data set could exert a large influence over the values of a 4 and a 5 for eqn. (11) determined in the non-linear least-squares iterations (a~ is also slightly affected), the functional d e p e n d e n c e of the constants e 0 and a~ on T and a a for eqn. (2) are used in our discussions. At 76 K and r o o m temperature, the contribution from the a 5 term in eqn. (2) was small compared with that from the a~ term for the typical test duration. Before 1 0 0 0 0 min, the contribution from the a 5 term is generally negligible. Although the a5 term is normally considered to represent steady-state conditions, we reiterate that steady-state conditions were not found. Instead, the a 5 term should be considered to represent the average of small deviations from logarithmic behavior. T h e s e deviations generally represent experimental inaccuracies, as two standard deviations of the a 5 term (representative of 95 percentile) are usually larger than the actual value. If extrapolated to longer times (about 4 0 0 0 0 min), as terms calculated from data at earlier times would b e c o m e dominant; yet this extrapolation is unrealistic since the a5 term is expected to be time dependent under non-steady state conditions. 4.1. I n s t a n t a n e o u s s t r a i n

On application of load there is an instantaneous specimen strain. T h e square root of the initial strain e0 is a linear function of the applied stress aa; this is illustrated for all temperatures in Fig. 2 and summarized in Table 2. This result is expected, since the stress-strain curves of copper are approximately parabolic and the primary strain on the application of a load corresponds to this relationship. Two sets of r o o m temperature data are combined in Fig. 2(a) representing annealed and reannealed (same time and temperature) specimens. T h e reannealed specimens have larger e0 values, yet have similar hardness and tensile strengths. T h e decreased values of e0 of the reannealed specimens (Fig. 2(a)) must be attributed to differing dislocation substructure or impurity pinning effects. This metallurgical effect is not discussed additionally in this paper, but deserves further study. T h e extrapolated value of aa at (e0) 1/2= 0 may be regarded as the elastic limit tr0 for high strain rates. At r o o m temperature for the annealed specimens it is nearly zero. At 76 and 4K, o0 is nearly equivalent (within data scatter), about 17.5 MPa.

27

TIME, s 8600

300 K

850C 5C

g_ ~:

102

103

104

105

t

I

I

I

4K Oa = 48.9 MPa

840C 40

o

z

~ 30 2O

820C

10

810C

0

0

I

I

I

1

I

I

0.02

0.04

0.06

008

0.10

012

(a)

0.14

(STRAIN) V2 (Go) 1/2

• .....

830C

800C

........

[

10

........

I

..............

........

100 TIME, min

Fig. 3. Dependence of creep strain under a stress of 48.9 MPa at 4 K.

L

1000

vs.

log time for copper

76 K

50

g_ ~. 40

~ 3c 20

I

t

J

I

I

J

0.02

004

006

0.08

0.10

0.12

(b)

0.14

(STRAIN) V2 ( ( o ) t/2 7O

4K 60

5O ~E

4C

b~

we define exhaustive creep as distinguished by an ever decreasing creep rate, where the creep strain is not a linear function of the log of the time.) In our creep tests the test temperature is less than 0.22 Tm. Steady-state creep rates or a normal secondary creep stage are not expected to occur under these tests conditions [14]. Yet, there have been a numer of papers attempting to analyze for activation energies and to measure steadystate creep rates, even at 77 K. These include the recent studies by Yen and coworkers [7-10], and reviews by Tien and Yen [1], and Yen et al. [2] emphasizing thermally activated steady-state creep processes in copper at 77 K. We found distinct creep characteristics of copper at each test temperature. However, in no case was steady-state creep detected. Results are presented and discussed separately for each test temperature.

~ 3c 2e

0 (C)

L 0.02

I 004

t 0.06

I 0.08

I 0.10

I 0.12

0.14

(STRAIN)I/2 (Co) I/2

Fig. 2. Applied stress vs. specimen strain (to 1/2 power) for copper at (a) 300, (b) 76, and (c) 4 K. In (a), annealed specimens (e) and reannealed specimens (o), are shown.

4.2. Creep behavior." general Tests were conducted at three temperatures (4, 76 and 300 K) and at relatively low stress levels approximately(= 10-3 G). When the test temperature is approximately less than 0.3 Tm, logarithmic or exhaustive creep is normally expected. (Here

4.3. Creep behavior." 4 K Initially, the creep strain at 4 K is linearly related to the log of time. However, after a brief time (usually less than 1000 min) the dependence of strain on log of time decreases. This dependence is illustrated in Fig. 3. The logarithmic coefficient a 1 from eqn. (2) (Table 1) is plotted vs. applied stress cra for 4 K in Fig. 4. Compared with higher temperature coefficients, a 1 is quite low. The data of Yen et al. [2] at 4 K correspond very closely to our data where al is of the order of 10 -5. Startsev [6] reports much higher values of al of the order of 10 -2 for copper at temperatures ranging from 1.5 to 4.2 K. The higher values led to the suggestion that dislocation tunneling played a role in low-temperature creep processes [ 10].

28 6 4K

800O

102

103

i

i

TIME, s 104 .....

5

105

106

i.............

i ..................

....................

i

0 a = 49.5 MPa

7000 76 K 4

6O00

• NIST + Yen (1983)

"3

o

v

z

+

0a

= 41.3MPa

oa

= 26.1 MPa

50oo 4000

aooo

2

2000 1

1000 .... I 10

0 10

20

30 40 STRESS (cra), MPa

50

60

70

Fig. 4. Creep coefficient, a~ vs. applied stress from eqn. (2) (Table 1) for copper at 4 K; data of Yen et al. [2] also included.

610£

........

I

10000

76K

• NIST = 41.5 MPa

+ Yen(1983)

6OO£

"3

o z

I 1000

1000000

4K Oa

I ...... 100 TIME, min

Fig. 6. Dependence of creep strain on log time for copper under stresses of 26.1, 41.3, and 49.5 MPa at 76 K.

TIME, s 500000

620£

.....

,,7

590£ ....

....

580£

+

570C 0 560q

4000

8000

12000

16000

20000

TIME, m i n

Fig. 5. Dependence of creep strain on time for copper under a stress of 41.5 MPa at 4 K.

If the creep strain at 4 K is plotted linearly vs. time (Fig. 5), the curves of 4 K measurements are significantly different from those at higher temperatures. A very brief transient period is noticed. The length of this transient period was less than 500 min in all tests. Owing to the diminishing creep rates with time, creep strains at 4 K did not exceed 150 x 1 0 -6 (not including the instantaneous strain e0). 4.4. C r e e p behavior: 7 6 K

Creep strain is linearly proportional to the log of time at 76 K within experimental uncertainties. Evidence for this dependence is shown in Fig. 6. The coefficient a~ for the logarithmic dependence is plotted vs. applied stress in Fig. 7. While the

I 10

I 20

/ 30 410 STRESS (o'a), MPa

I 50

I 60

70

Fig. 7. Creep coefficient, al vs. applied stress from eqn. (2) (Table 1) for copper at 76 K; data of Yen et aL [2] also included.

values of a I at 76 K have much the same dependence on stress as the 4-K coefficients, they are about 3 times larger. When the creep strain at 76 K is plotted linearly vs. time (Fig. 8), a larger transient regime is apparent compared with curves at 4 K (Fig. 5). It appears that there is a linear portion, corresponding to a steady-state creep rate, in each plot of strain vs. time. Yet, as illustrated in Fig. 9, careful data analyses yield ever-decreasing creep rates. In Fig. 9 the data of Yen and coworkers [7-9] obtained over the time interval from 3000 to 12000 rain are plotted and joined by a curve. Our creep-rate data, obtained over the same time interval from our curves, are plotted for these specimens. They conform excellently to the Yen

29

TIME, s 1000000

58°l 57001

2000000

3000000

8800

8700

~., , t - ~ ~ ,,,,

•

106

!

300 K

o a = 42.4 MPa

'

8600

5600: o z

TIME, s

105

£ 5500

.....-

z 8500

5400

8400 76 K o a = 45.0 MPa

5300

520(

8300

10000

20000

30000

40000

50000

TIME. min

Fig. 8. D e p e n d e n c e of creep strain on time for copper under a stress of 45.0 MPa at 76 K.

20 15

i

76 K, Copper Creep Rates ~: NIS]~ 3.6 x 105
I

8200 1000

i

J

i

i

i

L

i

i

i

10000 TIME, min

50000

Fig. 10. D e p e n d e n c e of creep strain on log time for copper under a stress of 42.4 MPa at 300 K.

I

105
• NIST 18 x • Yen, et al. (1983)• 3.6 x 105
o Ld

.~ 10

I

I

I

I

30

40

50

60

70

STRESS (oa), MPa

Fig. 9. Creep rates vs. applied stress for copper at 76 K, effects of time interval on rates are illustrated; data of Yen etal. [2] also included.

data. However, at longer periods of elapsed time, lower values of the creep rate are calculated and included in Fig. 9. Creep rates as low as 1 × 10- II S-I for stress levels above 33 MPa at 76 K have been obtained• Therefore, we conclude that there is no steady-state creep state in copper at 76 K at the stress levels used in this study• At these stress levels, the creep rate is continuing to decrease, as shown by the linear dependence of strain on log time (Fig. 6). This interpretation conflicts with that of Yen and coworkers, who proceeded to calculate an activation energy for the low temperature creep process, based on steady-state conditions at 76 K and several higher temperatures. Landon e t a l . [ 11 ] found steady-state conditions at much higher stress levels; this is conceivable since the creep

10

210

3'0 410 STRESS (o-a) , MPa

50

60

70

Fig. 11. Creep coefficient a t vs. applied stress from eqn. (2) (Table 1 ) for copperat 300 K.

process may change with stress level• An indication of this is the much higher apparent activation energy calculated by Landon e t a l . (0.17 eV at 77 K, compared with the value 0.01-0.02 calculated by Yen). 4.5. Creep behavior." room temperature A typical creep curve for room temperature is shown in Fig. 10. At ambient temperature the curve of creep strain v s . time can be portrayed as logarithmic at times approximately less than 10000 min. A plot of a~ obtained from eqn. (2) (Table 1) analyses v s . applied stress is shown in Fig. 11. The slopes of a 1 v s . o.~ gradually decrease with decreasing temperature, and the absolute values of oa increase with increasing temperature. However, at elapsed times greater than about 104 min, the dependence of strain on time increases,

30

relative to a logarithmic dependence. This, again, provides an opportunity for the assessment of steady-state conditions. In Fig. 12 a typical creep curve at 300 K is shown. At 300 K, the length of the transient region is longer than that at 76 K. Our calculated values of creep rates range from 2.5x 10 -~ s -~ to 6 x 10 -~ s -~ over a stress range from 20 to 45 MPa at 300 K for time intervals from (20-50)x 103 min. Gohn and Fox [15] and Davis [16] conducted room temperature creep tests of copper for longer periods of time (15 x 105 and 6 x 105 min respectively). The strain vs. time curves of Gohn and Fox for room temperature creep tests exhibit decidedly decreasing strain rates with time. No steady-state range is observed. However, if one uses the tangent of the curve at 12 x 105 min for their data, a strain rate of 0.25 x 10-i1 s-1 is calculated for an applied stress of 69 MPa at room temperature. Similar slow creep rates may be obtained from the data of Davis at lower stress. Thus, longer periods of time lead to diminishing creep rates; steady-state conditions are not achieved at room temperature.

4.6. Activation volume The strain measured in our low temperature creep tests can best be approximated for long times as dependent on the log of time. It is of interest to use eqns. (1) and (2) to estimate an apparent activation volume related to the creep deformation process. In earlier tensile tests [17] we measured the stress-strain behavior at low temperatures for the same copper. From strainrate change measurements during those tensile

tests the activation volumes of copper were estimated. In these estimates, the change in flow stress Ao from a change in strain rate g is related to the apparent activation volume V*: Vt* =

kT(Alng / \~-a/,,

(4)

The apparent activation volumes calculated from eqn. (2)(creep, Vc*) and eqn. (4)(tensile, Vt*) were calculated for three applied stress levels (30, 50, and 70 MPa). Activation volumes are calculated in terms of b 3, where b is the Burgers vector. The strain-hardening coefficient 0 from our tensile results at the same stress levels and strain rate (2 × 10 -4 s -~) were used in the calculation of Vt*. The results for the three applied stress levels were averaged and are presented in Fig. 13 to compare Vt* and Vc*. The Vc* values from creep data are approximately linear with temperature. This implies, from eqn. (2), that the logarithmic creep constant a is linearly related to the inverse of the tensile strain-hardening coefficient at constant stress ( a ~ 1/0). The equating of a creep parameter to tensile strain-hardening rate raises the question of the

I

I

I

I

2000

B

1500

TIME, s 1000000

620C

2000000

i

r

1000 610£ .°

600C 500

z 590C

580£ 300 K 36.4 MPa

oa =

0;

5700

100 200 TEMPERATURE, K 560(

, i,,

10000

I

20000 ' TIME,

3o6o0

L,

4oooo

aoooo

min

Fig. 12. Dependence of creep strain on time for copper under a stress of 36.4 MPa at 300 K.

300

Fig. 13. Temperature dependence of the apparent activation volume determined from tensile V~* and creep Vc* measurements for copper, averaged from constant applied stress levels of 30, 50 and 70 MPa.

31 equivalency of the deformation process for the two loading conditions. The l/'* values for creep and tension in Fig. 13 are equivalent in an order of magnitude sense at room temperature, and at low temperatures are within experimental scatter. Yet, the ratio of Vt*/ Vc* steadily increases with increasing temperature. This suggests that V,* includes a (strain-rate dependent) component that is temperature dependent and, of course, not included in Vc* nor reflected in the temperature dependence of 0. This same conclusion must be drawn from analyses of the tensile deformation of copper. At low stress levels, the strain hardening of copper may be described as athermal, independent of temperature [17, 18], while the activation volumes exhibit a strong, non-linear temperature dependence [19, 20]. The magnitude of the apparent activation volume from our creep measurements is about 70b 3 at 4 K and over 500b 3 at 76 K. The doublekink dislocation mechanism suggested by Yen and coworkers [1, 2, 7-9] is predicted to have lower apparent activation volumes of the order of 10b 3. Dislocation-dislocation interactions are expected to have higher activation volumes, of the order of 100b 3. We conclude that the creep of copper is controlled by the same dislocation process that controls strain-hardening in tensile tests, notably dislocation-dislocation interactions. This mechanism appears to be operative from room temperature to 4 K in both creep and tensile tests.

4. 7. Engineering strain and creep conditions The strains one may expect at the three test temperatures may be summarized for various stresses. At room temperature for a stress equivalent to the yield strength (30 MPa), the maximum total creep strain for 20 years' service is approximately 0.02 (including e0 = 0.004) from our data; if the slower creep rates from longer-time data [15, 16] are used, a total creep strain of less than 0.006 (including e0=0.004) is estimated. At stresses a factor of 1.5 av our rates approximately double, thus a maximum extrapolated (20 years') strain would be 0.04; using the slower rate data [15, 16] this strain would be reduced to 0.01. At 76 K the creep rates are similar to room temperature, therefore the total predicted strains would reflect the difference in instantaneous strain (about 0.0035 at 76 K). At 4 K the creep rates are less but the instantaneous strain is equivalent to that observed at 76 K. Total strain for a stress

level equal to the yield strength (30 MPa) for 20 years' service would be predicted to reflect only the instantaneous strain (approximately 0.0035), since the creep rate exhausts relatively quickly at 4K.

5. Summary The creep characteristics of 99.99% pure oxygen-free copper (C10400) were studied at 4, 76 and 300 K at stress levels between 0.7 and 1.5 of the yield strengths. The major conclusions are as follows. (1) At all temperatures the primary stage is best described by the logarithmic dependence of creep strain on time. (2) No steady-state creep was detected at any temperature. (3) At 4 K logarithmic creep was followed by a relatively quick exhaustion of creep. At 76 K logarithmic creep continued for the duration of the tests, within the limits of experimental imprecision. At room temperature creep rates increased from the logarithmic creep of the primary stage, but did not attain steady-state conditions. (4) The constant ct in the logarithmic creep expression, e=aln(ot+ 1), that best describes low temperature creep of copper, is linearly related to the inverse of the tensile strain hardening rate (at constant stress) of copper. (5) The apparent activation volumes measured from creep and tensile tests at 4, 76, and 300 K are almost identical. Thus, both this equivalency and the relationship between the tensile strain-hardening rate and the logarithmic creep constant suggest that the same deformation mechanism is present. This mechanism is suggested to be dislocation-dislocation interactions. (6) Total creep strains (including strain on application of the load) of less than 0.020 are predicted for oa =Oy at room temperature for a service time of 20 years. At 76 K a total creep strain of less than 0.019 is predicted; at 4 K, the total creep strain is less than 0.004 when o~,= t7,..

Acknowledgments This project was supported by the Office of Fusion Energy (DOE). Elizabeth S. Drexler assisted excellently in data analyses.

32

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