Influence of dislocation on interaction between a crack and a circular inhomogeneity

• Interaction among a crack, an edge dislocation and a circular inhomogeneity.
• Expression for the SIF at the crack tip is determined.
• There is competition between the effects of inhomogeneity and dislocation on SIF.
• Analyze effect of crack position and elastic modulus of inhomogeneity on SIF.
• Consider effect of remote load, inhomogeneity size and dislocation position on SIF.

The investigation for the interaction problem between a Griffith crack and a circular inhomogeneity in the presence of an edge dislocation under the remote load is carried out. The expressions for the stress intensity factors (SIFs) at the crack tip are determined for different sets of geometric and material parameters with the distributed dislocation technique. The formulated singular integral equations are then solved numerically. The numerical results show that the edge dislocation can reduce the SIF or increase it, depending on the position of edge dislocation. When the distance between the edge dislocation and the inhomogeneity is fixed, there is competition between the effects of the inhomogeneity and the edge dislocation on the SIF. When the distance between the edge dislocation and the crack is less than a certain value, the edge dislocation is more distinct factor that influences the crack propagation. When the distance between the edge dislocation and the crack is equal to the certain value, the edge dislocation and the inhomogeneity counteract each other's efforts. When the distance between the edge dislocation and the crack tip is more than the certain value, the effect of the inhomogeneity is more dominant. As the remote load increases, the influence of the edge dislocation on SIF decreases, while the effect of the inhomogeneity on it keeps unchanged.