Crack tip fields at a ductile single crystal-rigid material interface

Small-scale yielding around a stationary crack along a ductile single crystal - rigid material interface is analyzed. Plane strain conditions are assumed to prevail and geometry changes are neglected. The analyses are carried out using both continuum slip and discrete dislocation plasticity theory for model fcc and bcc crystal geometries having either two or three slip systems. Numerical and analytical asymptotic solutions are presented for continuum slip plasticity theory. Solutions exhibiting both slip bands and kink bands are obtained. The addition of a third slip system to ductile single crystals having two slip systems is found to have a significant effect on the interface crack-tip fields. The results illustrate the role that each of the formulations considered can play in elucidating crack tip fields in single crystals.