Criterion of mechanical instabilities for dislocation structures
Criterion of mechanical instabilities for dislocation structures
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DOI：
10.1016/j.msea.2011.12.027
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发表时间：
2012-02
期刊：
影响因子：
6.4
通讯作者：
Yabin Yan;T. Kondo;T. Shimada;T. Sumigawa;T. Kitamura
中科院分区：
文献类型：
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作者：
Yabin Yan;T. Kondo;T. Shimada;T. Sumigawa;T. Kitamura
位错结构的机械不稳定性在确定晶体金属的塑性行为和疲劳等方面发挥着核心作用，为了了解位错结构的机械不稳定性的本质，有必要研究位错结构崩溃的临界条件。本文提出了任意位错结构机械不稳定性的判据。根据该准则，机械不稳定性可以用Hessian矩阵的最小特征值的正性来描述，该矩阵由系统势能相对位错坐标的二阶微分组成。另外，塌陷模式可以同时由最小特征值的特征向量确定。我们将所提出的准则应用于外部载荷下的矿脉和位错壁，无论结构和尺寸如何差异，它都成功地描述了失稳的发生和相应的塌陷模式。该标准的成功为解决更复杂位错结构的机械不稳定性问题铺平了道路。
To understand the nature of mechanical instabilities of dislocation structures, which plays a central role, for example, in determining the plastic behavior and fatigue in crystalline metals, it is essential to investigate a critical condition in which a dislocation structure collapses. A criterion for the mechanical instability of arbitrary dislocation structures is proposed in this paper. According to the criterion, the mechanical instability can be described by the positiveness of the minimum eigenvalue of the Hessian matrix, which is composed by the second-order differential of potential energy of the system with respect to the dislocation coordinates. In addition, the collapse mode can be simultaneously determined by the eigenvector of the minimum eigenvalue. We applied the proposed criterion to the veins and dislocation walls under external loading, and it successfully describes the onset of instabilities and the corresponding collapse modes, regardless of the difference in structures and sizes. This success in the criterion paves the way to address the mechanical instability issues on more complex dislocation structures.