Discrete dislocation plasticity modeling of short cracks in single crystals

Abstract

The mode-I crack growth behavior of geometrically similar edge-cracked single crystal specimens of varying size subject to both monotonic and cyclic axial loading is analyzed using discrete dislocation dynamics. Plastic deformation is modeled through the motion of edge dislocations in an elastic solid with the lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation incorporated through a set of constitutive rules. The fracture properties are specified through an irreversible cohesive relation. Under monotonic loading conditions, with the applied stress below the yield strength of the uncracked specimen, the initiation of crack growth is found to be governed by the mode-I stress intensity factor, calculated from the applied stress, with the value of K init decreasing slightly with crack size due to the reduction in shielding associated with dislocations near a free surface. Under cyclic loading, the fatigue threshold is ΔK-governed for sufficiently long cracks. Below a critical crack size the value of ΔK I at the fatigue threshold is found to decrease substantially with crack size and progressive cyclic crack growth occurs even when K max is less than that required for the initiation of crack crack growth in an elastic solid. The reduction in the fatigue threshold with crack size is associated with a progressive increase in internal stress under cyclic loading. However, for sufficiently small cracks, the dislocation structure generated is sparse and the internal stresses and plastic dissipation associated with this structure alone are not sufficient to drive fatigue crack growth.