A comparative discrete-dislocation/nonlocal crystal-plasticity analysis of plane-strain mode I fracture

Crack growth associated with plane-strain mode I loading is studied computationally using both a discrete-dislocation approach and a nonlocal crystal-plasticity formulation. Within the discrete-dislocation approach, the material is modeled as a linear elastic solid which contains discrete dislocations capable of moving and interacting with each other and with other lattice defects either at a distance through their stress fields, or through direct contact. In the case of nonlocal crystal-plasticity, the effect of the plastic strain gradient on the materials’ behavior is incorporated through the contribution that the geometrically necessary dislocations make to the rate of strain hardening. In both formulations, the behavior of the crack is modeled using a cohesive zone approach. The results show that while both approaches yield comparable stress and strain fields around the crack tip, the global (stress intensity versus crack extension) responses as well as the crack tip profiles can be significantly different in the two cases. These differences are related to the ways crystallographic slip is modeled in the two approaches.