AN ANALYSIS OF CRACKS IN DUCTILE SINGLE-CRYSTALS .1. ANTIPLANE SHEAR

THE PROBLEM of a stationary mathematically sharp semi-infinite crack in an FCC crystal is considered. We adopt a geometrically rigorous formulation of crystalline plasticity accounting for finite deformations and finite lattice rotations, as well as for the full three-dimensional crystallographic geometry of the crystal. A comparison of results with earlier small-strain solutions reveals some notable differences. These include the expected development of finite deformations and rotations near the crack tip, but also discrepancies such as a considerable spread of the plastic zones. In addition, nearly self-similar, square-root singular fields are obtained within the portion of the plastic zone where the crystal is in a state of high positive hardening. The results suggest that both finite-deformation and lattice rotation effects, as well as the details of the hardening law, strongly influence the structure of the solution.