Metal viscoplasticity with two-temperature thermodynamics and two dislocation densities

Abstract

Posed within the two-temperature theory of non-equilibrium thermodynamics, we propose a model for thermoviscoplastic deformation in metals. We incorporate the dynamics of dislocation densities–mobile and forest—that play the role of internal state variables in the formulation. The description based on two temperatures appears naturally when one recognizes that the thermodynamic system undergoing viscoplastic deformation is composed of two weakly interacting subsystems, viz. a kinetic-vibrational subsystem of the vibrating atomic lattices and a configurational subsystem of the slower degrees of freedom relating to defect motion, each with its own temperature. Starting with a basic model that involves only homogeneous deformation, a three-dimensional model for inhomogeneous viscoplasticity applicable to finite deformation is charted out in an overstress driven viscoplastic deformation framework. The model shows how the coupled evolutions of mobile and forest dislocation densities, which are critically influenced by the dynamics of configurational temperature, govern the strength and ductility of the metal. Unlike most contemporary models, the current proposal also affords a prediction of certain finer details as observed in the experimental data on stress–strain behaviour of metals and this in turn enhances the understanding of the evolving and interacting dislocation densities.