简单立方晶体中混合位错分析方法

 表征晶体中位错的Peierls-Nabarro(PN)模型的控制方程十分复杂，求解往往直接给出解答，而没有给出求解过程，这为PN模型的应用带来了困难。针对Peierls-Nabarro模型的这一局限性，提出一种新的方法分析简单立方晶体中混合位错的成核过程。该方法将位错密度场表示成第一类Chebyshev多项式的形式，而滑移面上的剪应力表示成三角级数的形式，得到了新的控制方程，最后运用Newton-Raphson法对新的控制方程进行求解。计算结果表明，本文提出的方法对于分析简单立方晶体中混合位错的成核过程具有简单、精确的特点。

An Analytical Method for Mixed Dislocation in a Simple Cubic Crystal

The governing equation of Peierls-Nabarro (PN) model is very complex, and its solution is given often without any solving process, which restricts the application of the PN model. A new method is proposed to describe the propagation of a mixed dislocation in a simple cubic crystal. First, the shear stress field and the dislocation density field on the slip plane are expressed as the trigonometric series and the first Chebyshev polynomial series, respectively, and then a set of governing equations are obtained; finally, the Newton-Raphson method is used to solve the governing equations. The results show that the method proposed in this paper is simple and effective for analyzing the propagation of mixed dislocations in a simple cubic crystal.