The effect of dislocation loop shape on emission from cracks

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Abstract
Recent experimental studies suggest that dislocation emission from crack tips occurs at stress intensities considerably lower than estimates from several theoretical models based on homogeneous nucleation. Despite complicated observed geometries of nucleating dislocations, many models are essentially restricted to a one-degree-of-freedom description of the loop shape. This work considers a Volterra description of a nucleating dislocation loop, which is rectangular with variable dimensions parallel and perpendicular to a straight crack front, i.e., it has two degrees of freedom. By studying the nature of the energetic forces on the dislocation loop during expansion, two criteria for dislocation nucleation are proposed. These criteria predict critical crack tip loadings that are 30-40% lower than the corresponding Rice-Thomson and Mason predictions, assuming a dislocation core cut-off equal to a Burgers vector. The critical loop sizes are predicted to be of the order of several Burgers vectors, and are much larger than previously predicted values. This analysis also addresses the shape of critical incipient loops as a function of the relative orientation of slip plane and crack plane and ledge energy, and eliminates the necessity of picking a loop shape a priori.