A method was developed for deriving analytical expressions for the elastic interaction between a screw dislocation dipole or a concentrated force and a crack cutting perpendicularly across the interface of a bimaterial. The crossing-line composed of the interface and the crack was mapped into a line, and then the complex potentials were deduced. The Muskhelishvili method was extended by creating a Plemelj function that matched the singularity of the real crack tips, and eliminated the pseudo-tip singularity induced by the conformal mapping. The stress field was obtained after solving the Riemann–Hilbert boundary value problem. Based upon the stress-field expressions, crack-tip stress intensity factors, dislocation dipole image forces and image torque were formulated. Numerical curves showed that both translation and rotation had to be considered in the static equilibrium of the dipole system. The crack-tip stress intensity factor introduced by the dipole could rise or fall, and the crack could attract or reject the dipole. These trends depended not only upon the crack length, but also upon the dipole location, the length and the angle of the dipole span. Generally, the horizontal image force exerted at the centre of the dislocation dipole was much smaller than the vertical one. Whether the dipole was subjected to clockwise torque or anticlockwise torque was determined by whether the Burgers vector of the crack near the dislocation of the dipole was positive or negative. A concentrated load introduced no singularity into crack-tip stress fields, as the load was located at the crack line. However, as the concentrated force was not located on the crack line, but approached the crack tip, the nearby crack tip stress-intensity factor, KIIIu, increased steeply to infinity.

A Technique for Studying Interaction Between a Screw Dislocation Dipole or a Concentrated Load and a Mode III Crack Crossing an Interface. W.Xiao, C.Xie: International Journal of Solids and Structures, 2008, 45[22-23], 5705-15