Thermo-visco-plasticity under high strain rates: a micro-inertia driven dynamic flow rule

Built on the tenets of rational thermodynamics, this article proposes a theory of strain gradient thermo-visco-plasticity for isotropic polycrystalline materials under high strain rates. The effect of micro-inertia, which arises due to dynamically evolving microstructural defects, is brought to bear on the macro-continuum through a micro-force balance. Constitutive modelling of dissipative micro-stresses incorporates relaxation time parameters to account for the time lags of the dissipative fluxes in attaining a steady state. Augmentation of the micro-force balance with constitutive relations for the micro-stresses yields a non-local flow rule that reflects the effect of micro-inertia on the evolution of the plastic strain. A thermodynamically consistent derivation of temperature evolution is provided, thus replacing an empirical route. Numerical implementation of the proposal does not demand a computationally intensive return mapping algorithm. A two dimensional plane strain model of impact between two 4340 steel plates is used to numerically assess the influence that micro-inertial and relaxation time parameters as well as various length scales may have on the macro-continuum response.