螺型位错与含共焦裂纹弹性椭圆夹杂的干涉效应

研究了基体与夹杂中任意位置螺型位错与含共焦裂纹弹性椭圆夹杂的干涉问题,运用复变函数的分区全纯理论、柯西型积分、应力函数奇性主部分析方法与Rieman边值理论,将问题归结为一个初等复势函数方程的求解.获得了基体与夹杂区域复势函数的级数形式精确解,导出了裂纹尖端应力强度因子解析表达式和作用于位错的像力公式.计算结果表明:夹杂中的裂纹对于位错与夹杂的干涉具有强烈的扰动效应,它增强软夹杂对位错的吸引,减弱硬夹杂对位错的排斥,甚至将排斥转变为吸引.裂纹尖端附近的应力强度因子等值线表明,螺型位错位于裂纹尖端附近特定区域时对于裂纹扩展具有屏蔽效应.

Interaction between a Screw Dislocation and a Confocal Crack in an Elastic Elliptical Inhomogeneity

The interaction between a screw dislocation and a crack in a confocal elastic elliptical inhomogeneity was investigated.By combining the sectionally holomorphic function theory,Cauchy singular integral,singularity analysis of complex functions and Riemann boundary problem,the problem was focused on solving an elementary complex potentials equation.Explicit series solutions were obtained for the two cases when the screw dislocation was located in the inhomogeneity or in the matrix.Stress intensity factor and the image force acting on screw dislocation were calculated.As a result,numerical analysis and discussion showed that the crack had a strong influence on the interaction between a screw dislocation and an elastic elliptical inhomogeneity.It attracted the dislocation evidently.Stress intensity factor isolines around the crack tip showed that screw dislocation could retard the crack initiation when it was located in the certain region.The present solutions contain a number of new and previously known results which can be shown to be special cases.