A technique for studying interaction between a screw dislocation dipole or a concentrated load and a mode III crack crossing an interface

A method of potentially wide application is developed for deriving analytical expressions of the elastic interaction between a screw dislocation dipole or a concentrated force and a crack cutting perpendicularly across the interface of a bimaterial. The cross line composed of the interface and the crack is mapped into a line, and then the complex potentials are educed. The Muskhelishvili method is extended by creating a Plemelj function that matches the singularity of the real crack tips, and eliminates the pseudo tips’ singularity induced by the conformal mapping. The stress field is obtained after solving the Riemann–Hilbert boundary value problem. Based on the stress field expressions, crack tip stress intensity factors, dislocation dipole image forces and image torque are formulated. Numerical curves show that both the translation and rotation must be considered in the static equilibrium of the dipole system. The crack tip stress intensity factor induced by the dipole may rise or drop and the crack may attract or reject the dipole. These trends depend not only on the crack length, but also on the dipole location, the length and the angle of the dipole span. Generally, the horizontal image force exerted at the center of the dislocation dipole is much smaller than the vertical one. Whether the dipole subjected to clockwise torque or anticlockwise torque is determined by whether the Burgers vector of the crack-nearby dislocation of the dipole is positive or negative. A concentrated load induces no singularity to crack tip stress fields as the load is located at the crack line. However, as the concentrated force is not located on the crack line but approaches the crack tip, the nearby crack tip stress intensity factor K_IIIu increases steeply to infinity.