A novel yet simple method is proposed to derive an analytical solution to the interaction problem of a screw dislocation inside an elastic inhomogeneity of arbitrary shape partially penetrated by a semi-infinite crack. The two analytic functions characterizing the elastic fields of stresses and displacement in the two-phase composite are readily obtained. Furthermore, we derive explicit expressions for the mode III stress intensity factor at the crack tip and the image force acting on the screw dislocation. Several specific examples are presented to demonstrate the obtained solution. An analytical solution to the case in which the screw dislocation is located in the cracked matrix is similarly derived.

提出了一种新颖而又简单的方法来得出对螺位错的相互作用问题的解析解，该问题是由半无限裂纹部分穿透的任意形状的弹性非均质性内部的。容易获得表征两相复合材料中应力和位移弹性场的两个解析函数。此外，我们导出了裂纹尖端处的III型应力强度因子和作用于螺钉位错的像力的显式表达式。给出了几个具体的例子来说明获得的解决方案。类似地得出对于螺钉位错位于裂纹基体中的情况的解析解。