Kinetics of plastic flow in polycrystal plasticity.

摘要

An elasto-viscoplastic polycrystal plasticity model is developed that considers the kinetics of plastic flow. Strain rate and temperature dependencies, included in the single crystal constitutive response, are based on the isotropic mechanical threshold stress continuum model. A modified power law is used to determine slip system activity without introducing artificial strain rate sensitivity. In addition, a slip system hardening law is introduced that is capable of modeling stage IV hardening. The evolution law uses two state variables and includes a hardening contribution from geometrically necessary dislocations (net/excess dislocations). To perform the computations a novel lattice rotation integration algorithm, based on an analytical solution, has been developed. Implicit and explicit formulations are presented, and both have superior accuracy in comparison to standard integration methods. The flexibility of the modified power law allows the highly nonlinear constitutive description of the Portevin - Le Chatelier (PLC) effect to be included in the model. Finite element simulations of this phenomenon show the transition from continuous to discontinuous shear band propagation as the applied strain rate is decreased. Across this transition the stress drop magnitude and duration distributions are characterized by a shift away from power law relations towards peaked distributions. These shifts are consistent with experimental observations.