Effects of lattice incompatibility-induced hardening on the fracture behavior of ductile single crystals

Plane-strain mode-I cracks in a ductile single crystal are studied under conditions of small scale yielding. The specific case of a (0 1 0) crack growing in the 1 0 1] direction for an FCC crystal is considered. Crack initiation and its subsequent growth are computed by specifying a traction-separation relation in the crack plane ahead of the crack tip. The crystal is characterized by a hardening model that incorporates physically motivated gradient effects. Significant traction elevation ahead of the crack tip is obtained by incorporating such effects, allowing a better basis for the explanation of experimentally observed cleavage in the presence of substantial plastic flow in slowly deforming ductile materials. Resistance curves based on parameters characterizing the fracture process and the continuum properties of the crystal are computed. Simulation results indicate that the length-scale of the lattice incompatibility-dominated region has to be comparable or larger than the length of the fracture process zone for gradient effects to have a significant effect on fracture resistance. Both the work of separation and the peak separation stress also play important roles in determining the fracture resistance of the crystal.