复合材料中夹杂内位错和圆弧形界面裂纹的弹性干涉效应

Interaction between a Screw Dislocation in the Circular Inclusion and Interfacial Cracks in Composite Materials

研究了夹杂中螺型位错和圆形弹性夹杂界面裂纹的相互干涉问题。运用复变函数的解析延拓技术与奇性主部分析方法,获得了该问题的一般解答。作为典型例子,求出了含一条界面裂纹时基体和夹杂区域复势函数的封闭形式解,导出了位错在夹杂中任意位置时界面裂纹尖端应力强度因子和位错力的解析表达式。该解答可作为Green函数研究夹杂中裂纹和界面裂纹的干涉作用,且公式的退化结果与已有文献一致。

The interaction effects between circular interfacial cracks and a screw dislocation located inside inclusion is dealt with. By means of Riemann - Schwarz' s symmetry principle integrated with the analysis singularity of complex variable potentials, the general solution of this problem is presented in this paper. For a special case, the closed form solutions for complex potentials in the matrix and the inclusion regions and the appropriate expression of elastic perturbation stress field at the dislocation are derived explicitly when the interface containing single crack. In addition, the stress intensity factor at the crack end and the image force acting on the dislocation is obtained. The closed form solutions presented in this paper can be used as Green' s functions to solve the problem of interaction between an interfacial crack and an arbitrary shape crack inside the inclusion.