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

机译：脱位介导可塑性应变率的双指数应力依赖性

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摘要

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.
机译：脱位介导的塑性中应变率的应力和温度依赖性通常与脱油过程有关。这是一个逃生井的过程，因此这种依赖性是Arrhenius型，作为逃生的渐近近似的功能，井问题或激活能量通常被接受为线性函数压力sigma。描述高应变率，Langer，Bouchbinder和Lookman（Acta Mater，2010,58,3718-3732）的应力 - 应变曲线成功地使用了双指数函数或具有两个参数，并且参数与流量应力相关联。与通常的指数依赖性的主要区别是无论高强度如何高度的应变率的上限都存在。对于大的应力，力量消失，问题出现了双指数应力依赖性是否与避免井问题一致。在本文中，我们对这个问题提供了积极的答案。关键点是应变速率的有界性是由位错速度的有界引起的：位错速度不能超过剪切波速。因此，速度力关系是非线性的。将这种非线性关系掺入避免 - 井问题导致应变率 - 应力依赖性，其具有双指数曲线的形式。

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