Mathematical Model of Formation of a Crystallographic Shear Zone in the Representation of a Piecewise-Continuous Closed Dislocation Loop

A mathematical model is devised for the formation of a crystallographic shear zone for a closed piecewisecontinuous dislocation loop which is represented in its initial configuration by a regular polygon with sides that are as small as desired and which preserves its polygonal shape as it expands. The model takes into account the orientational dependence of the line tension of the dislocation loop, and of the resistance from a dislocation pileup and generation of point defects on the orientation of the Burgers vector relative to the dislocation line.