On double-exponential stress dependence of strain rates in dislocation-mediated plasticity

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Abstract
Stress and temperature dependence of strain rates in dislocation-mediated plasticity is usually associated with the depinning process. This is an escape-from-the-well process, thus such dependence is of Arrhenius type, Function arises as an asymptotic approximation in the escape-from-the-well problem as or The activation energy is usually accepted to be a linear function of stress sigma. To describe stress-strain curves at high strain rates, Langer, Bouchbinder and Lookman (Acta Mater., 2010, 58, 3718-3732) successfully employed a double-exponential function or with two parameters, and Parameter was associated with the flow stress. The major difference from the usual exponential dependence is the existence of an upper bound for strain rates no matter how high stresses are. For large stresses, the power vanishes and the question arises as to whether the double-exponential stress dependence is consistent with the escape-from-the-well problem. In this paper, we give a positive answer to this question. The key point is that the boundedness of strain rates is caused by the boundedness of dislocation velocities: dislocation velocities cannot exceed the shear wave speed. Accordingly, the velocity-force relation is nonlinear. Incorporation of such nonlinear relation into the escape-from-the-well problem results in a strain rate-stress dependence which has a form of a double-exponential curve.

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