A large strain thermoplasticity model including recovery, recrystallisation and grain size effects

Abstract

In manufacturing, thermomechanical processes such as static annealing and hot working are commonly used to tailor the microstructure of metals to achieve favourable macroscopic material properties that meet specific application requirements. To improve sequential manufacturing processes and to accurately predict the microstructural changes of the material along the process chain, physically motivated constitutive models are required that simultaneously account for the effects of recovery and recrystallisation, as well as grain size dependencies. To this end, Cho et al. [Int. J. Plasticity 112, 123–157 (2019)] proposed a macroscopic hypo-elasticity based large strain thermoplasticity model that aims at the unification of the effects of static and dynamic recovery and recrystallisation, as well as grain growth and refinement. In the present contribution, the hypo-elasticity based large strain recrystallisation formulation proposed by Cho et al. is transferred to a hyper-elasticity based large strain thermoplasticity framework to overcome the limitations typically accompanied with hypo-elasticity based formulations. For this purpose, an isotropic temperature dependent hyper-elastic Hencky type formulation defined in logarithmic strains is combined with a temperature dependent von Mises yield criterion. The recrystallisation modelling approach by Cho et al. is adopted, assuming a non-associated temperature dependent proportional hardening rate in the form of an Armstrong-Frederick type hardening minus recovery format, wherein the proportional hardening related internal variable is interpreted as a measure of dislocation density. It is shown that the hyper-elasticity based format results in a thermodynamical consistency condition that effectively constrains the physically motivated evolutions of recrystallised volume fraction and average grain size. To investigate the capability of the model to predict the material response of unified recrystallisation thermodynamically consistently, representative thermomechanical sequential loading conditions including static annealing and hot working are studied.