SIAM Journal on Applied Mathematics, Volume 80, Issue 3, Page 1101-1122, January 2020.
The microstructure of polycrystalline materials consists of networks of grain boundaries (GBs) and triple junctions (TJs), along which three GBs meet. The evolution of such microstructures may be driven by surface tension (capillarity), applied stresses, or other means that lead to a jump in chemical potential across the GBs. Here, we develop a two-dimensional model for the concurrent evolution of the GB/TJ network based upon the microscopic mechanism of motion, the motion of line defects (disconnections) in the GB that have both dislocation and step character. The evolution involves thermally activated disconnection formation/annihilation and migration of multiple disconnections modes/types. We propose this crystallography-respecting continuum model for the disconnection mechanism of GB/TJ dynamics derived with a variational approach based on the principle of maximum energy dissipation. The resultant TJ dynamics is reduced to an optimization problem with constraints that account for local microstructure geometry, conservation of Burgers vectors, and thermal-kinetic limitations on disconnection fluxes. We present an analysis of and numerical simulations based upon our model to demonstrate the dependence of the GB and TJ mobilities and the TJ drag effect on the disconnection properties, and we compare the predictions with molecular dynamics and experimental observations.

中文翻译：

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晶界三重结动力学：连续体断开模型

SIAM应用数学杂志，第80卷，第3期，第1101-1122页，2020年1月。
多晶材料的微观结构由晶界（GB）和三重结（TJ）的网络组成，三个GB沿它们相遇。此类微结构的演变可能是由表面张力（毛细作用），施加的应力或其他导致跨GB的化学势跃升的方式驱动的。在这里，我们基于微观的运动机制，即GB中具有位错和阶跃特征的线缺陷（断路）运动，开发了GB / TJ网络并发演化的二维模型。演变涉及热激活的断路形成/ an灭和多种断路模式/类型的迁移。我们提出了一种尊重晶体学的连续模型，用于基于最大能量耗散原理的变分方法导出的GB / TJ动力学断开机制。最终的TJ动力学简化为一个优化问题，其约束条件包括局部微观结构的几何形状，Burgers向量的守恒性以及对断开通量的热动力学限制。我们提出了基于我们的模型的分析和数值模拟，以证明GB和TJ迁移率以及TJ拖曳效应对断开性能的依赖性，并且将预测结果与分子动力学和实验观察进行了比较。最终的TJ动力学简化为一个优化问题，其约束条件包括局部微观结构的几何形状，Burgers向量的守恒性以及对断开通量的热动力学限制。我们提出了基于我们的模型的分析和数值模拟，以证明GB和TJ迁移率以及TJ拖曳效应对断开性能的依赖性，并且将预测结果与分子动力学和实验观察进行了比较。最终的TJ动力学简化为一个优化问题，其约束条件包括局部微观结构的几何形状，Burgers向量的守恒性以及对断开通量的热动力学限制。我们提出了基于我们的模型的分析和数值模拟，以证明GB和TJ迁移率以及TJ拖曳效应对断开性能的依赖性，并且将预测结果与分子动力学和实验观察进行了比较。