Computer simulation of thermally activated dislocation motion: Part III. In fcc solid solutions
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I.
INTRODUCTION
MOST of the
theories of strengthening of fcc solid solutions were developed to account for the increase in strength at absolute zero temperature. There have been some theories which have been developed to predict the temperature dependence of the yield stress of fcc solid solutions. As in the case of theories that have developed to account for the 0 K strengthening, those that have been developed to predict the temperature dependency of the yield stress can be divided into two groups: (1) thermally activated generation of dislocations; and (2) thermally activated "jumping" of the interaction with solute atoms. There are at least two theories that are in the first category: one by Suzuki m and the second by Butt and Feltham.12j The most significant point raised by Suzuki is that his generation mechanism can readily explain the burst of slip line formation 13j observed in some fcc solid solutions. Kocks 141has developed a variation of Suzuki's theory in which chemical locking of the moving dislocation occurs when the dislocation is stopped at some obstacle. In the second category, there have been several analytical theories. Fleischer ISm suggested that the solid solution could be treated as the interaction of individual solute atoms and the dislocation line, neglecting effects due to the overlap of interaction fields due to solute atoms. Kocks I41 has examined the treatment of Fleischer [5,6l and has considered the prospect of thermal activation. From an extension of Fleischer's treatment to concentrated solid solution, Kocks has pointed out the predicted activation energy would be at least a factor of 5 too small. Recently, Nabarro [71 has extended the Labusch theory I81 to predict the temperature dependence of the yield stress. While there are numerous steps in this develop-
R.J. ARSENAULT, Professor and Director, and S. LI, Research Associate, are with the Metallurgical Materials Laboratory, University of Maryland, College Park, MD 20742-2111. Manuscript submitted January 20, 1988. METALLURGICAL TRANSACTIONS A
ment, which are obscure and arbitrary, reasonable relationships were obtained between yield stress and temperature. In the case of the temperature dependence of the activation volume (v*), the comparison can only be made at a constant stress and was predicted by Nabarro to be v*o~Z 1/3. The experimental data available to compare with this prediction are very limited. The data of Basinski et a / . , [9] which also predicts that v * o t T 1/3, c a n be used, and, again, the data of Basinski e t al. are in reasonable agreement with the dependence of the activation volume in the stress (z) and concentration (c) at constant temperature of T 2/3 a n d C 4/9 predicted by Nabarro. The concept of stress equivalence was first put forward by Basinski et al. [9] A simple definition of the stress equivalency is as follows. If we consider two alloys containing different concentrations, cl and c2, with different solutes in the same solvent, such that the yield stresses at absolute zero temperature are
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