X-ray diffraction study of subgrain misorientation during high temperature creep of tin single crystals
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I.
INTRODUCTION
THE creep of pure metals has been thought to depend on diffusion controlled dislocation climb above one half of the absolute melting temperature. The argument that diffusion controls creep depends strongly on the good agreement between the self diffusion activation energy and the creep activation energy, ~which is usually included in the following steady state creep rate equation. L2.3
1978-1981) that cross-slip can be a process parallel to climb if most of the edge dislocations are not mutually destroyed but instead accumulate in subgrain boundaries. If that is the case, in the temperature region in which cross-slip might be the rate controlling process essentially no edge dislocation climb occurs, and the subgrain misorientation angle 0 (in radians) must increase with (longitudinal) creep strain e, according to the following equation (see Appendix): 0 =
Here ~ is the shear modulus, II is the atomic volume, o" is the applied stress, ~ is the steady state creep rate, Qc is the creep activation energy, A is a constant, and so is the expenent n, which usually has a value of 5 for pure metals. However, Arrhenius plots (log ~, vs 1 / T ) for metals such as Cu: Mo,s'6 Sn 7'8 show that two different mechanisms act in parallel at temperatures above half of the absolute melting temperature. Friedel9 (and private communication between J. Friedel and J. Weertman, 1978-1981) and later Poirier 1~ suggested that cross-slip may be the rate controlling process in the lower temperature portion of the high temperature region. Sherby and Weertman 1~have argued that cross-slip is essentially a series process with climb. Cross-slip involves the motion of the screw segments out of the primary slip plane, whereas climb involves the motion of edge dislocations out of this plane. If dislocations do not accumulate during steady state creep (because dislocations of opposite sign are continuously annihilated), the slower of these two processes determines the creep rate, which is the situation for two processes in series. On the other hand, Friedel suggested (private communication with J. Weertman S.H. SUH is Senior Research Engineer, Korea Advanced Institute of Science and Technology, Seoul, Korea; J.B. COHEN is Frank C. Engelhart Professor of Materials Science and Engineering, Northwestern University, Evanston, IL 60201; and J. WEERTMAN is Walter E Murphy Professor of Materials Science and Engineering, Professor of Geophysics, Department of Geological Sciences and the Materials Research Center, Northwestern University, Evanston, IL 60201. Manuscript submitted March 19, 1982. METALLURGICALTRANSACTIONS A
Ke
[2]
Here, the constant K is approximately equal to 1. In Eq. [2], it is assumed that dislocations move a distance of the order of the subgrain size and that only dislocations of one sign accumulate in any given subgrain boundary. On the other hand, Sherby and Weertman H as well as Evans and Knowles 12and Spingarn et a113 argued that even when creep activation energy is lower than the self diffusion energy, a diffusio
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