creep of copper 4-300k

Materials Science and Engineering, A 147 ( 1991 ) 23- 3223Creep of copper: 4-300 KR. P. Reed, N. J. Simon and R. P. WaishNational Institute of Standards and Technology, Boulder, CO 80303 (U.S.A.)(Received January 25, 1990; in revised form April 8, 1991)AbstractCreep 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. IntroductionFor 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/$3.50where 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 isa -kT Vc*O(2)(1)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 contro

lling 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24mined 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.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

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