Finite-strain thermo-viscoplasticity for case-hardening steels over a wide temperature range

The aim of this work is the development of a thermodynamically consistent fully coupled thermo-viscoplastic material model for metals undergoing finite deformations. A multiplicative split of the deformation gradient into a thermal, an elastic and a plastic part is introduced, where isotropic thermal expansion and isochoric plastic deformation are assumed. The model is based on a decomposition of the free energy into a thermo-elastic and a plastic part and covers non-linear cold-work hardening and thermal softening. The model incorporates non-linear temperature dependent effects for the elastic moduli, thermal expansion, heat capacity, and heat conductivity. Furthermore, the temperature and strainrate dependency of the yield stress is realised using a Perzyna-type viscoplastic model incorporating a von Mises yield function, both enhanced by thermal softening. Special care has been taken for the time integration of the plastic deformation gradient to comply with the incompressibility constraint. The
model and its parameters have been fitted against experimental data for case hardening steel 16MnCr5 (1.7131). We discuss the consistent linearisation of the proposed model and its implementation in a monolithic fully coupled finite element framework. Finally, we present results for selected boundary value problems. They show the localisation and regularization behaviour of
the proposed model.