离散位错动力学中一排位错偶极子的均匀化
Homogenisation of a Row of Dislocation Dipoles from Discrete Dislocation Dynamics
摘要：
传统的离散-连续方法在描述晶体材料中广泛观察到的位错多极构型的集体行为方面存在局限性。原因是位错偶极子，这在确定晶体的机械性能中起着重要的作用，往往得到涂抹时，传统的均匀化方法。为了解决这样的困难，集体行为的一排位错偶极子研究使用匹配渐近技术。通过引入位错对密度势和位错对宽度两个场变量，实现了从离散到连续的转变。发现位错对宽度的变化比位错对密度的变化快得多。这种层次的演化时间尺度使我们能够描述的位错动力学在粗晶粒的水平上的缓慢变化的变量（对密度）耦合的平衡方程的快速变化的变量（对宽度）的演化方程。这里采用的时间尺度分离方法铺平了道路，适当地将偶极状（零净伯格斯矢量，但非零）位错结构，称为统计存储位错（SSD）到晶体塑性的宏观模型在三维空间。此外，这里发现的不同平衡模式之间的自然过渡也可能有助于理解循环载荷引起的疲劳金属中持续滑移带（PSB）的出现。
英文摘要：
Conventional discrete-to-continuum approaches have seen their limitation in describing the collective behaviour of the multi-polar configurations of dislocations, which are widely observed in crystalline materials. The reason is that dislocation dipoles, which play an important role in determining the mechanical properties of crystals, often get smeared out when traditional homogenisation methods are applied. To address such difficulties, the collective behaviour of a row of dislocation dipoles is studied by using matched asymptotic techniques. The discrete-to-continuum transition is facilitated by introducing two field variables respectively describing the dislocation pair density potential and the dislocation pair width. It is found that the dislocation pair width evolves much faster than the pair density. Such hierarchy in evolution time scales enables us to describe the dislocation dynamics at the coarse-grained level by an evolution equation for the slowly varying variable (the pair density) coupled with an equilibrium equation for the fast varying variable (the pair width). The time-scale separation method adopted here paves a way for properly incorporating dipole-like (zero net Burgers vector but non-vanishing) dislocation structures, known as the statistically stored dislocations (SSDs) into macroscopic models of crystal plasticity in three dimensions. Moreover, the natural transition between different equilibrium patterns found here may also shed light on understanding the emergence of the persistent slip bands (PSBs) in fatigue metals induced by cyclic loads.
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