Investigation of the Crack-Dislocation Interaction Effects

The objective of the current work is to investigate the interaction effects between a crack and an array of dislocations under various configurations using the elasticity theory. By treating the crack and dislocations as singularities in the elastic field of a material, we examine their collective stress and displacement responses near the crack tip at the micromechanical level. First, the stationary formulation for a crack interacting with a single dislocation is presented, and the effects of dislocation upon the crack tip field are systematically assessed under different spatial configurations. This stress—displacement analysis shows that the crack remains open at all times for the blunting dislocations, while the crack closure is observed at the tip for wake dislocations. Subsequently, the elastic theory of crack-multiple dislocations interaction is rigorously studied by considering three types of forces exerted on the dislocations along different slip planes. Specifically, the slip forces exerted on a typical dislocation are due to the influences from the external loading, its own image dislocations, and other interacting dislocations as well as all their image dislocations. Furthermore, the dislocation emission criterion defined by Lin and Thomson is employed, and the behavior of multiple dislocations is systematically investigated. Finally, the effective stress intensity factor, the shielding of the crack tip from the dislocation array, the geometric dislocation distributions, and the dislocation-free zone are explored in detail.