An analysis of cracks in ductile single crystals—II. Mode I loading

A geometrically rigorous formulation of crystalline plasticity is used to analyze the crack-tip deformation and stress fields in ductile single crystals subjected to mode I loading. The theory accounts for finite deformations and finite lattice rotations, as well as for the full three-dimensional crystallographic geometry of the crystal. An experimentally based self-hardening rule exhibiting an initial stage of rapid hardening followed by a saturation stage is also adopted. The problem of a stationary semi-infinite crack in FCC and BCC crystals is considered. As regards the dominant modes of deformation, the results are in partial agreement with earlier analytical and numerical solutions, but in excellent qualitative agreement with recent experimental observations. 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.