A non-equilibrium thermodynamic framework for viscoplasticity incorporating dynamic recrystallization at large strains

Microstructure evolution due to thermomechanical processing severely affects the macroscopic material properties for various steels. This effect includes viscoplastic deformation and re crystallization. In order to account for a non-equilibrium state of the crystalline material a non-equilibrium thermodynamic framework for multi-systems is presented. Regarding the constitutive modeling of recrystallization, we present several modifications for a model originally proposed by Brown and Bammann (2012) with the following key objectives: to consider microscopic quantities dependent on time varying recrystallized volume fractions, thus resulting into explicit and convective parts of their time derivatives, to derive (rather than to assume) evolution equations for the microscopic stresses in the unrecrystallized phase, to explicitly derive the constitutive relations for macroscopic and microscopic quantities for recrystallized media combined to viscoplasticity based on thermodynamic arguments and to clarify the relation between macroscopic flow stress and microscopic hardening stresses for recrystallized media based on thermodynamic arguments. On the numerical side we propose an efficient explicit/implicit algorithm suitable for the finite-element-method (FEM). In the numerical examples for homogeneous and inhomogeneous test specimen, the characteristic effects of our model, such as strain softening due to recrystallization, are illustrated.