Dynamical Dislocation Theory of Crystal Plasticity. II. Easy Glide and Strain Hardening

Mathematical descriptions of the stress-strain-time behavior of plastic crystals are developed using a statistical approach to dislocation dynamics. First, the ``easy-glide'' portions of stress-strain curves are described in terms of glide band propagation. Then, three models of strain hardening are developed and used in numerical calculations of stress-strain curves. In one model, the mean density of mobile dislocations first increases and then decreases with increasing plastic strain. In another, strain introduces internal stress fluctuations which decrease the mean velocities of mobile dislocations. In the third (and preferred) model, strain increases the mean viscous drag acting on moving dislocations, thereby decreasing the mean velocity at a given stress. The numerically calculated curves show that the dynamical models provide realistic descriptions.