A dislocation-based flow rule with succinct power-law form suitable for crystal plasticity finite element simulations

Abstract

The physical interpretation of the power-law flow rule from the classic Kocks model suggests that strain rate sensitivity is determined by an empirical parameter that differs from the zero-stress activation energy. This paper proposes a dislocation bow-out model that seeks to further interpret the physical significance of strain rate sensitivity of face-centered cubic (fcc) metals without involving empirical terms. Interestingly, strain rate sensitivity is found to rely on the ratio of the obstacle strength to the zero-stress activation energy. The values of strain rate sensitivity obtained from our calculations match well with the experimental data for pure fcc metals. The resulting flow rule maintains a mathematically concise power-law form with parameters having clear physical meanings and sufficient accuracy. The concise power-law form of the present model enables its easy implementation in the crystal plasticity finite element method and offers flexibility to simulate stress-strain curves of fcc metals deformed at a wide range of temperatures and strain rates.