Discrete dislocation plasticity and crack tip fields in single crystals

Small-scale yielding around a stationary plane strain mode I crack is analy zed using discrete dislocation plasticity. The dislocations are all of edge character, and are modeled as line singularities in a linear elastic mater ial. Superposition is used to represent the solution in terms of analytical fields for edge dislocations in a half-space and a numerical image solutio n that enforces the boundary conditions. The description of the dislocation dynamics includes the lattice resistance to dislocation motion, dislocatio n nucleation, interaction with obstacles and annihilation. A model planar c rystal with three slip systems is considered. Two slip system orientations are analyzed that differ by a 90 degrees rotation. The non-hardening, singl e crystal plasticity continuum slip solution of Rice (Mech. Mater. 6 (1987) 317) for this model crystal predicts that slip and kink bands emerge for b oth crystal geometries, while Drugan (J. Mech. Phys. Solids 49 (2001) 2155) has obtained kink band free solutions. For a reference set of parameter va lues, kink band free solutions are found in one orientation while the emerg ence of kink bands is seen in the other orientation. However, lowering the dislocation source density suppresses the formation of kink bands in this o rientation as well. In all calculations, the opening stress in the immediat e vicinity of the crack tip is much larger than predicted by continuum slip theory. (C) 2001 Elsevier Science Ltd. All rights reserved.