The Interaction between a Screw Dipole in Matrix and an Elliptical Inhomogeneity Containing a Confocal Crack

Abstract

The interaction between a screw dipole inside the matrix and an elastic elliptical inhomogeneity containing a confocal crack under longitudinal shear is investigated. By using the complex method of elasticity, singularity analysis of stress function and Riemann boundary problem, the complex functions of matrix and inhomogeneity are obtained in the series form. And the singularity stress field of matrix, the image force and image torque acting on the center of screw dipole and the stress intensity factor of crack tip are deduced. Then the influence of the dip angle of screw dipole, the size of inhomogeneity and the misfit of materials on image force, torque of couple and the stress intensity are analyzed. The results show that the image force varies periodically as and there is two critical value of to make image force getting its maximum and minimum; the decreasing of relative shear modulus and the increasing of inhomogeneity may lead to the increasing of image force; the variation of will change the direction of screw dipole on stress intensity factor.