The interaction between a screw dislocation and an elastic elliptical inhomogeneity which contains a confocal rigid line was investigated. The screw dislocation was located inside either the elliptical inhomogeneity or the infinite matrix. By using the complex potential method, explicit series solutions of complex potentials were obtained. The image force acting on the screw dislocation and the stress intensity factor at the tip of the rigid line were derived. As a result, the analysis and discussion show that the influence of the rigid line on the interaction effects between a screw dislocation and an elliptical inhomogeneity was significant. The rigid line enhances the repulsive force exerted on the dislocation produced by the stiff inhomogeneity and abates the attractive force produced by the soft inhomogeneity. For the soft inhomogeneity, there was an unstable equilibrium position when the dislocation was inside the matrix and there was a stable equilibrium position when the dislocation was inside the inhomogeneity. The stress intensity factor contour around the rigid line tip showed that when a dislocation with positive burgers vector was in the upper half-plane, stress intensity factor will be positive; while in the lower half-plane, stress intensity factor will be negative; and in the x-axis, it will be zero. The absolute value of the stress intensity factor will increase when the dislocation approaches the tip of the rigid line. The stress intensity factor at the rigid line tip was enhanced by a harder matrix and abated by a softer matrix.

The Interaction between a Screw Dislocation and a Rigid Line in a Confocal Elliptical Inhomogeneity. Q.H.Fang, J.M.Chen, Z.D.Luo, H.P.Song, Y.W.Liu: Applied Mathematical Modelling, 2011, 35[3], 985-95