DYNAMICAL DISLOCATION MODELS OF CRYSTAL PLASTICITY.

For glide occurring in a single system, a general relation is established between the rate of plastic strain, and the configuration and velocity distribution of dislocations in a monocrystal. This relation is applied to various idealized configurations, and the concept of dislocation density is defined for the case of parallel, straight dislocation lines. An elementary model of mechanical behavior is developed, assuming that the average velocity of dislocations is represented by a quasiviscous relation, and that the time rate of increase of dislocations is proportional to the number of dislocations and their average velocity. This model is investigated under three loading conditions, both by analytic and digital computer techniques. An improved model is derived by additionally assuming a dislocation stalemating rate proportional to the square of the number of dislocations and their average velocity. Finally, models are proposed which exhibit strain-hardening. The hardening mechanisms considered are effect of strain on dislocation mobility the reduction of average velocity caused by spatial fluctuations in the stress field and stalemating interactions between fixed and mobile dislocations. Stress-strain curves are calculated based upon these models, and for one model the constant load strain-time problem is solved in closed form. Author