Dislocation emission from crack tips

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Abstract
The emission of a dislocation from a crack tip is described in two dimensions by the build-up of a continuous distribution of infinitesimal dislocations ahead of the crack tip. The shape of the incipient dislocation is actually determined by the atomic potential in the glide plane but is approximated here by a truncated arctan (x/w) function with ‘dislocation width’ w as adjustable parameter. The elastic self-stress in the glide plane balanced by the atomic interaction across the glide plane and the image stress due to the crack surface can be calculated and the energy of the configuration as a function of the stress intensity K caused by an externally applied stress can be determined. For small K there exists an energy minimum where the incipient dislocation is partially emitted, its complete emission occurring across an energy barrier. When K increases, the energy barrier decreases and vanishes at a critical K = K e. This situation corresponds to spontaneous emission in two dimensions. The realistic emission process occurs in three dimensions and can be formulated along similar lines.