平行滑移面上自锁位错结构形成、迁移和解离的连续动力学
Continuum dynamics of the formation, migration and dissociation of self-locked dislocation structures on parallel slip planes
摘要：
在位错的连续模型中，位错的短程弹性相互作用的适当公式对于捕获晶体材料中形成的各种类型的位错图案是至关重要的。在这篇文章中，分布在两个平行的滑移面上的直位错的连续动力学模型，通过放大潜在的离散位错动力学。两个连续速度场量的引入，以促进离散到连续过渡。第一个是位错系综的局部迁移速度，它与短程位错相关性完全无关。二是位错对的退耦速度受一个阈值应力控制，该阈值应力被认为是单滑移系的有效流动应力。与普遍采用的Taylor关系相比，该公式具有两个更符合离散位错动力学的特点：i）流动应力只随位错密度的面内分量的增加而增加，因此该公式允许滑移面内位错间距最小; ii）当所有位错变为几何上必需的位错时，流动应力平滑地过渡到零。一个制度下，位错密度的不均匀性增长的确定，并通过与离散位错动力学模拟结果的比较，进一步验证。基于本文的研究结果和我们以前的工作，提出了一个将短程位错相关性纳入位错连续模型的一般策略。
英文摘要：
In continuum models of dislocations, proper formulations of short-range elastic interactions of dislocations are crucial for capturing various types of dislocation patterns formed in crystalline materials. In this article, the continuum dynamics of straight dislocations distributed on two parallel slip planes is modelled through upscaling the underlying discrete dislocation dynamics. Two continuum velocity field quantities are introduced to facilitate the discrete-to-continuum transition. The first one is the local migration velocity of dislocation ensembles which is found fully independent of the short-range dislocation correlations. The second one is the decoupling velocity of dislocation pairs controlled by a threshold stress value, which is proposed to be the effective flow stress for single slip systems. Compared to the almost ubiquitously adopted Taylor relationship, the derived flow stress formula exhibits two features that are more consistent with the underlying discrete dislocation dynamics: i) the flow stress increases with the in-plane component of the dislocation density only up to a certain value, hence the derived formula admits a minimum inter-dislocation distance within slip planes; ii) the flow stress smoothly transits to zero when all dislocations become geometrically necessary dislocations. A regime under which inhomogeneities in dislocation density grow is identified, and is further validated through comparison with discrete dislocation dynamical simulation results. Based on the findings in this article and in our previous works, a general strategy for incorporating short-range dislocation correlations in continuum models of dislocations is proposed.
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