Mode I crack analysis in single crystals with anisotropic discrete dislocation plasticity: II. Stationary crack-tip fields

Small-scale yielding around a stationary mode I crack in a cubic single crystal is analyzed in terms of plane-strain elastically anisotropic discrete dislocation plasticity (DDP). Two symmetric crack orientations are considered with two objectives in mind. First, we study the sensitivity to materials aspects such as dislocation source density and elastic anisotropy as well as orientation dependence. Plastic deformation around the crack tip in a single crystal is a patchy field due to the discreteness of the slip systems, as demonstrated in analytical solutions and experimental observations. While these solutions/observations have in common that the plastic zone is composed of sectors with specific slip system(s) active inside each sector, detailed comparisons-recapitulated in this paper-reveal a few, yet significant, discrepancies. In an attempt to resolve these issues, the second objective of this paper is to construct sector arrangements of active slip system(s) from the present DDP simulations and compare those with the analytical solutions. We find that the estimated sector arrangements are in best agreement with the hardening analytical solutions of Saeedvafa and Rice (1989 J. Mech. Phys. Solids 37 673-91); indeed, angular variations of stresses around the crack tip confirm this observation.