Confinement-deconfinement transitions in a model of interacting dislocations

An exact solution is found for the equilibrium dislocation distribution in a continuum model of interacting parallel dislocations moving in a common slip plane, under an external shear and a realistic internal stress barrier that is finite everywhere on the slip plane. As functions of and the total populations, we find regions of two-component confinement (a compact distribution of dislocations of both signs), stable single-component confinement, and breakaway. Stability properties are summarized and critical lines on the bifurcation surface are identified. © 1986 The American Physical Society.