A Screw Dipole in Inhomogeneity Interaction with an Elliptical Inhomogeneity Containing a Confocal Crack

Abstract

The paper is aimed to investigate a theoretical model that a screw dipole inside an elastic elliptical inhomogeneity that containing a confocal line crack under longitudinal shear. The analytic solutions of stress fields of matrix and inhomogeneity, the image force and image torque acting on the center of screw, and the stress intensity factor of line crack tip are obtained by using the complex method of elasticity. Then through the numerical analysis, the effects of the relative shear modulus, the dip angle of screw dipole, the shape of inhomogeneity on image force, image torque and stress intensity factor are discussed in detailed. The result show that both the image force and image torque periodically changes as the dip angle and when the inclusion is hard, the moment of image torque is greatly affected by the material constant and the cracks in the inclusions can enhance the repulsion of the hard matrix to dislocation and weaken the attraction of the soft matrix to dislocations.