Small-scale yielding around a stationary plane-strain mode-I crack was analyzed by using discrete dislocation plasticity methods. The dislocations were all of edge-type and were modelled as being line singularities within a linear-elastic material. Superposition techniques were used to present the solution in terms of analytical fields for edge dislocations in a half-space, and a numerical image solution which enforced the boundary conditions. The dislocation dynamics description included the lattice resistance to dislocation motion, dislocation nucleation, interaction with obstacles and annihilation. A model planar crystal, with 3 slip systems was considered. Two slip-system orientations were analyzed, which differed by a 90º rotation. The Rice non-hardening single-crystal plasticity continuum slip solution for this model crystal predicted that slip and kink bands would appear for both crystal geometries. For a given set of parameters, kink band-free solutions were found for one orientation, while the kink bands were found for the other orientation. However, lowering the dislocation-source density suppressed the formation of kink bands in this orientation as well. In all of the calculations, the opening stress in the immediate vicinity of the crack tip was much greater than that predicted by continuum slip theory.

Discrete Dislocation Plasticity and Crack Tip Fields in Single Crystals. E.Van der Giessen, V.S.Deshpande, H.H.M.Cleveringa, A.Needleman: Journal of the Mechanics and Physics of Solids, 2001, 49[9], 2133-53