Continuum representation of systems of dislocation lines: A general method for deriving closed-form evolution equations
Continuum representation of systems of dislocation lines: A general method for deriving closed-form evolution equations
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DOI：
10.1016/j.jmps.2016.05.009
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发表时间：
2015-09
影响因子：
5.3
通讯作者：
Mehran Monavari;S. Sandfeld;M. Zaiser
中科院分区：
文献类型：
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作者：
Mehran Monavari;S. Sandfeld;M. Zaiser
塑性是由位错系统的演化决定的，一般来说是各向异性的。我们试图忠实地代表这种演变的平均在离散位错微观结构的密度样变量。从T开始。Hochrainer的位错连续理论（CDD）（Hochrainer，2015），我们介绍了一种基于“最大信息熵原理”（MIEP）的方法，用于推导不同阶位错密度测量的闭合形式演化方程。这些方程提供了弯曲和连接的位错线系统的运动学特性的最佳表示，其中包含在给定的一组密度测量中的信息。推导出的方程的性能基准对其他模型提出的文献中，使用离散位错动力学模拟作为参考。作为一个基准问题，我们研究位错移动在一个高度异质性，持久的滑移带状的几何形状。我们证明，离散模拟的优良协议，可以得到在一个非常小的数量的平均位错场包含信息的边缘和螺丝组件的总和多余的（几何上必要的）位错密度。从这些完整的位错取向分布出现的位错移动通过通道壁结构可以忠实地重建。
Plasticity is governed by the evolution of, in general anisotropic, systems of dislocations. We seek to faithfully represent this evolution in terms of density-like variables which average over the discrete dislocation microstructure. Starting from T. Hochrainer's continuum theory of dislocations (CDD) (Hochrainer, 2015), we introduce a methodology based on the ‘Maximum Information Entropy Principle’ (MIEP) for deriving closed-form evolution equations for dislocation density measures of different order. These equations provide an optimum representation of the kinematic properties of systems of curved and connected dislocation lines with the information contained in a given set of density measures. The performance of the derived equations is benchmarked against other models proposed in the literature, using discrete dislocation dynamics simulations as a reference. As a benchmark problem we study dislocations moving in a highly heterogeneous, persistent-slip-band like geometry. We demonstrate that excellent agreement with discrete simulations can be obtained in terms of a very small number of averaged dislocation fields containing information about the edge and screw components of the total and excess (geometrically necessary) dislocation densities. From these the full dislocation orientation distribution which emerges as dislocations move through a channel-wall structure can be faithfully reconstructed.