A Self-Consistent Model For Directional Dependence Of Crack Growth

Fracture growth is considered as the competition between cleavage and dislocation self-organization in elastic-plastic solids. A self-consistent model is proposed to bridge the responses at relevant length scales, an elastic enclave in the immediate vicinity of crack tip, an array of disclination dipoles and macroscopic plastic deformation. The directional dependence of crack growth is studied. In the continuum limit, the flow stress is expressed by a spatial coupling in terms of a second-order gradient of the rotation strength of disclination dipoles. An estimate of the core size and the crack-tip shielding ratio is given by identification of the macroscopic plastic fields, the elastic field and the constitutive flow stress from the micromechanics consideration, on the boundary of elastic core. Strong dependence of apparent fracture toughness on the intrinsic surface energy and the ductile-to-brittle transition are examined