Interaction of an edge dislocation with a wedge crack

The elastic interaction of an edge dislocation with a wedge crack is investigated using Muskhelishvili's complex potential treatment of elasticity. The stress intensity factors induced by the dislocation, the strain energy, and the image force acting on the dislocation are formulated, calculated, and plotted. Especially, the influence of wedge angle on the shielding effects and on image forces is investigated. The results show that the radial component of the image force is inversely proportional to the distance from the crack tip to the dislocation and the tangential image force increases with increasing wedge angle as the dislocation position is kept unchanged. When the slip plane passes the crack tip, whether the edge dislocation shields or antishields the crack tip depends on its Burgers vector. In this case, the slip plane of the edge dislocation of Burgers vector b₁+ib₂=be ⁱθ_max inclined at an angle θ_max with respect to the positive real axis corresponding to the maximum mode I crack shielding increases slightly to a maximum and then decreases with increasing wedge angle. Regardless of wedge angle, the maximum mode II shielding (or anti-shielding) occurs when the dislocation is located at the positive real axis.