纵向剪切下含共焦刚性核弹性椭圆夹杂中的螺型位错干涉

摘 要 研究了无穷远纵向剪切下无限大基体中含共焦刚性核弹性椭圆夹杂内任意位置螺型位错的干涉问题。运用复变函数保角映射、解析延拓等方法，获得了基体与夹杂区域的应力场的级数形式精确解，并得出了位错像力的解析表达式，导出了纵向剪切下两椭圆界面最大应力及其比值公式。分析结果表明：夹杂内部的刚性核对位错与夹杂的干涉产生明显的扰动效应，排斥硬夹杂内位错，并使之不断趋近弹性夹杂界面。对于软夹杂，夹杂中的位错存在稳定的平衡位置，当位错位于刚性核和平衡位置之间时，位错会趋于弹性夹杂界面；当位错位于平衡位置和弹性夹杂界面之间时，位错会离开界面。结果还显示，夹杂的长轴和短轴之比对位错与夹杂的干涉也有着不可忽视的影响，尤其当位错在刚性核附近时，随着夹杂的长、短轴比值的减小，核对位错的排斥力也明显减弱。本文解答包含了多个以往文献成果。

THE INTERACTION BETWEEN A SCREW DISLOCATION INSIDE THE INHOMOGENEITY AND AN ELASTIC ELLIPTICAL INHOMOGENEITY WHICH CONTAINS A CONFOCALRIGID CORE UNDER LONGITUDINAL SHEAR

Abstract The interaction between a screw dislocation inside the inhomogeneity and an elastic elliptical inhomogeneity which contains a confocal rigid core under longitudinal shear is investigated. By using the technical of conformal mapping and the method of analytic continuation, the stress fields of matrix and inhomogeneity is obtained explicitly in the series form, and the image force acting on the screw dislocation is obtained. The maximum interfacial stresses and the ratio of the two elliptical interfaces under longitudinal shear are calculated. As a result, the analysis and discussion show that the influence of the rigid core on the interaction effects between a screw dislocation and an elliptical inhomogeneity is significant. It can repel the dislocation , and make it reach the interface of the elastic inclusion constantly when the inhomogeneity is stiff. If the inhomogeneity is soft, there is a stable equilibrium position. As the dislocation is in between the rigid core and the stable equilibrium position , the dislocation will shift near the interface of the elastic inclusion. When the dislocation is in between the stable equilibrium position and the interface of the elastic inclusion , the dislocation will leave away from the interface. The result also show that the ratio of the long and short axes of the inhomogeneity has the noticeable influence on the interaction between the screw dislocation and the inhomogeneity. When the dislocation is on the nearby rigid core, the repulsive force of the core to the dislocation decreased significantly with the ratio of the long and short axes of the inhomogeneity decreases.