Homogenization of a Row of Dislocation Dipoles from Discrete Dislocation Dynamics
Homogenization of a Row of Dislocation Dipoles from Discrete Dislocation Dynamics
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DOI：
10.1137/15m1017910
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发表时间：
2015-01
期刊：
影响因子：
--
通讯作者：
S. Chapman;Y. Xiang;Yichao Zhu
中科院分区：
文献类型：
--
作者：
S. Chapman;Y. Xiang;Yichao Zhu
传统的离散到连续方法在描述晶体材料中广泛观察到的多极位错组态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。为了解决这些困难，一排位错偶极子的集体行为进行了研究，通过使用匹配渐近技术。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。研究发现，位错对宽度的演变速度比位错对密度的演变速度快得多。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，由一个演化方程的慢变变量（对密度）耦合的平衡方程的快变变量（对宽度）。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，被称为统计存储的位错，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的出现。
Conventional discrete-to-continuum approaches have seen their limitation in describing the collective behavior of the multipolar 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 homogenization methods are applied. To address such difficulties, the collective behavior 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 slow-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 the way for properly incorporating dipole-like (zero net Burgers vector but nonvanishing) dislocation structures, known as the statistically stored dislocations, 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 in fatigue metals induced by cyclic loads.