Effect of grain boundary ledges on mode III fracture

Abstract

Dislocations piled up between a finite crack tip and a grain boundary ledge with a dislocation-free zone are investigated by a continuous dislocation modelling method. The dislocation distribution function to simulate the crack and plastic zone is analytically derived. A closed form for the number of dislocations in the plastic zone is analytically derived. A closed form for the number of dislocations in the plastic zone and stress field is obtained. From the stress field, the stress intensity factor K _m and stress concentration at the grain boundary are obtained. When there is no dislocation-free zone in front of crack tip, the stress intensity factor K _m is zero, no matter whether the grain boundary exists or not. The effect of the grain boundary ledge on the fracture toughness and the effect of the crack on the strength of the grain boundary, such as described by the Hall-Petch equation, are discussed. Finally, our results can reduce to several special cases, and these are discussed.