A coarse-grained phase-field crystal model of plastic motion
A coarse-grained phase-field crystal model of plastic motion
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DOI：
10.1016/j.jmps.2019.103856
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发表时间：
2019-10
影响因子：
5.3
通讯作者：
M. Salvalaglio;L. Angheluta;Zhi-Feng Huang;A. Voigt;K. Elder;J. Viñals
中科院分区：
文献类型：
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作者：
M. Salvalaglio;L. Angheluta;Zhi-Feng Huang;A. Voigt;K. Elder;J. Viñals
在振幅方程近似的相场晶体模型示出提供一个准确的描述的变形场缺陷的晶体结构，以及位错运动。我们详细分析了应力正则化的位错核心的模型，并显示如何可以直接计算的伯格斯矢量密度从拓扑奇性的相场振幅。由这些振幅引起的变形然后用非奇异位移来补充，以加强机械平衡。这允许在该框架中一致地分离塑性时间尺度和弹性时间尺度。介绍了一种有限元方法来求解振幅和弹性方程的组合，并将其应用于三角形晶格对称晶体在两个空间维度上的几个原型构型：i）刃型位错引起的应力场，分析了振幅方程如何使位错核附近的应力正则化，ii）位错偶极子由于内部相互作用的运动，和iii）旋转晶粒的收缩。我们比较我们的结果与经典弹性理论的其他扩展，如应变梯度弹性和方法的基础上平滑的伯格斯矢量密度附近的缺陷核心。
The phase-field crystal model in an amplitude equation approximation is shown to provide an accurate description of the deformation field in defected crystalline structures, as well as of dislocation motion. We analyze in detail stress regularization at a dislocation core given by the model, and show how the Burgers vector density can be directly computed from the topological singularities of the phase-field amplitudes. Distortions arising from these amplitudes are then supplemented with non-singular displacements to enforce mechanical equilibrium. This allows for a consistent separation of plastic and elastic time scales in this framework. A finite element method is introduced to solve the combined amplitude and elasticity equations, which is applied to a few prototypical configurations in two spatial dimensions for a crystal of triangular lattice symmetry: i) the stress field induced by an edge dislocation with an analysis of how the amplitude equation regularizes stresses near the dislocation core, ii) the motion of a dislocation dipole as a result of its internal interaction, and iii) the shrinkage of a rotated grain. We compare our results with those given by other extensions of classical elasticity theory, such as strain-gradient elasticity and methods based on the smoothing of Burgers vector densities near defect cores.