A phase field crystal theory of the kinematics of dislocation lines
A phase field crystal theory of the kinematics of dislocation lines
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DOI：
10.1016/j.jmps.2022.104932
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发表时间：
2021-10
影响因子：
5.3
通讯作者：
Vidar Skogvoll;L. Angheluta;Audun Skaugen;M. Salvalaglio;J. Viñals
中科院分区：
文献类型：
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作者：
Vidar Skogvoll;L. Angheluta;Audun Skaugen;M. Salvalaglio;J. Viñals
本文引入位错密度张量，从三维晶体形变的相场描述出发，导出了位错密度张量的运动学演化规律。相场晶体（PFC）模型被用来定义晶格畸变，包括拓扑奇点，和相关的配置应力。我们推导出一个精确的表达的位错线的速度所确定的相场演化，并表明，在PFC的位错运动是由Peach-Koehler力。正如从早期PFC模型研究中所熟知的，对于一般的场配置，配置应力不是无发散的。因此，我们还提出了一种方法（PFCMEq），通过增加一个独立的和可积的变形，使总的应力发散自由的扩散动力学的机械平衡。在PFCMEq模型中，远场应力与连续弹性的预测非常吻合，而位错核周围的近场应力则由相场的光滑性质正则化。我们应用这个框架来研究位错环在其滑移面中的收缩率。
We introduce a dislocation density tensor and derive its kinematic evolution law from a phase field description of crystal deformations in three dimensions. The phase field crystal (PFC) model is used to define the lattice distortion, including topological singularities, and the associated configurational stresses. We derive an exact expression for the velocity of dislocation line determined by the phase field evolution, and show that dislocation motion in the PFC is driven by a Peach–Koehler force. As is well known from earlier PFC model studies, the configurational stress is not divergence free for a general field configuration. Therefore, we also present a method (PFCMEq) to constrain the diffusive dynamics to mechanical equilibrium by adding an independent and integrable distortion so that the total resulting stress is divergence free. In the PFCMEq model, the far-field stress agrees very well with the predictions from continuum elasticity, while the near-field stress around the dislocation core is regularized by the smooth nature of the phase-field. We apply this framework to study the rate of shrinkage of an dislocation loop seeded in its glide plane.