The stress-driven diffusion of point defects to a slowly moving crack

The stress-driven diffusion of point defects to a slowly moving brittle crack is studied under the condition of pure drift. In the pure-drift approximation it is assumed that the point defect flow in the vicinity of a crack tip is dominated by the elastic interaction between the stress field of the crack and a point defect and that concentration gradient effects can be neglected. The first-order drift-diffusion equation for a slowly moving crack at uniform velocity is solved. This yields the flow lines of the point defects and the impurity segregation rate directly in terms of the crack growth rate. The flow line patterns reveal important insights with respect to the point defect migration kinetics near a steadily advancing crack.