A dual-scale elasto-viscoplastic constitutive model of metallic materials to describe thermo-mechanically coupled monotonic and cyclic deformations

Abstract

Thermo-mechanical coupling effect often occurs during the deformation of the metallic materials, especially when they are subjected to cyclic loadings at a high loading rate. On one hand, the internal heat generation and accumulation originated from the energy dissipation during plastic deformation lead to the change of temperature field in the material. On the other hand, the variation of temperature field further changes the dissipation property of the material, since the stress-strain response depends on the temperature. These two factors influence with each other and result in a complex thermo-mechanical coupling effect. In this work, a dual-scale thermo-mechanically coupled elasto-viscoplastic constitutive model is developed to predict the monotonic, cyclic deformation and temperature field evolution of metallic materials under monotonic and cyclic loadings. At the mesoscopic scale, the polycrystalline representative volume element (RVE) is considered as an aggregation of individual grains. For an individual grain, a crystal plasticity model accounting for the internal heat generation is developed based on the fundamental laws of irreversible thermodynamics. A nonlinear kinematic hardening rule extended from the Ohno-Abdel-Karim model is adopted to capture the evolution of resolved shear back stress for each slip system, and the classical Bassani-Wu latent hardening rule is utilized to describe the interaction of dislocation slipping. To calculate the thermo-mechanical interactions among the grains, and obtain the overall responses of the polycrystalline RVE, a self-consistent (SC) homogenization scheme accounting for material nonlinearity and thermo-mechanical coupling effect is developed. At the macroscopic scale, the thermo-mechanical responses for the specimen are obtained by solving the equations of force balance, deformation compatibility, thermodynamic equilibrium and constitutive relationship through an approximation method. Finally, the proposed model is validated by predicting the monotonic, cyclic stress-strain responses and temperature evolution of 316L stainless steel.