Statistical Modeling of a Dislocation Phase-Field in Ductile Single Crystals

Abstract

ABSTRACTA model for the description of strain hardening and hysteresis at different temperatures and strain rates in ductile single crystals is introduced. The theory accounts for: and arbitrary number and arrangement of dislocation lines over a slip plane; the long-range elastic interactions between dislocation lines; the core structure of the dislocations; the interaction between the dislocations and applied resolved shear stress field; and the dissipative in teractions with short-range obstacles and lattice friction, resulting in hardening, path dependency and hysteresis. We introduce a variational formulation for the statistical mechanics of dissipative systems. The influence of finite temperature as well as the mechanics are modeled with Metropolis Monte Carlo simulations and a mean field approximation. The theory predicts a range of behaviors which are in qualitative agreement with observation, including: hardening and dislocation multiplication under monotonic loading and hysteresis loops under under cyclic loading. The flow stress was found to be dependent on the temperature and on the strain rate only at finite temperature.