The interaction between an edge dislocation and a semi-infinite long crack penetrating a circular inhomogeneity

• Study the interaction among edge dislocation, inhomogeneity and crack.
• Obtained the analytical solutions of problem by the analysis method of singularity.
• Crack strongly influences the interaction between edge dislocation and inhomogeneity.
• Edge dislocation has a stable equilibrium position in the matrix.
• Edge dislocation can reduce the stress intensity factor at the crack tip.

The interaction between an edge dislocation and a semi-infinite long crack penetrating a circular inhomogeneity is investigated. Using Riemann–Schwartz’s symmetry principle integrated with the analysis of singularity of complex function, the closed form solutions of complex potentials and stress field are obtained. Stress intensity factor at the crack tip and image force acting on edge dislocation are calculated. As a result, the crack penetrating inhomogeneity and interface has a strong influence on the interaction between an edge dislocation and an elastic circular inhomogeneity. It attracts the edge dislocation evidently and because of the influence of crack, the edge dislocation has a stable equilibrium position in matrix. Under a certain condition, the edge dislocation can reduce the stress intensity factor near crack tip. If the distance between the edge dislocation and crack tip is fixed, there always exists a critical value of position angle of edge dislocation at which the shielding or anti-shielding effect is maximal. Shielding effect to the stress intensity factor increases when edge dislocation approaches the tip of crack. In addition, the material mismatch also has a great influence on image force, shielding and anti-shielding effects.