A non-equilibrium thermodynamic model for viscoplasticity and damage: Two temperatures and a generalized fluctuation relation

Abstract

Utilizing a non-equilibrium thermodynamic setting that involves two temperatures, we present a model for ductile and brittle damage. The thermodynamic system consists of two interacting subsystems– configurational and kinetic-vibrational. While the kinetic-vibrational subsystem describes fast degrees-of-freedom (DOFs) of ordinary thermal vibration, the configurational subsystem includes the slower DOFs pertaining to a slew of configurational rearrangements that characterize elasto-visco-plasticity and damage, e.g. dislocation motion, lattice stretching, void nucleation, void growth and micro-crack formation. Following statistical mechanics, an expression for the entropy of a plastically deforming metal with growing voids and micro-cracks is derived. Subsequent application of the first and second laws of thermodynamics, suitably modified for the two-temperature system, yields coupled evolution rules for dislocation density, void volume fraction, micro-crack density etc. A modified flow rule for dilatant plasticity and evolution equations for the two temperatures are also derived. Even when the two subsystems are strongly coupled, we show that a splitting of energy and entropy is feasible and that the notion of two temperatures conforms with such splitting. We conduct numerical experiments on both brittle and ductile damage to assess the predictive features of the model and validate the results against available experimental evidence. Finally, a generalized fluctuation relation is put forth for deformations with extremely high strain rates. This leads to an entirely new procedure for constitutive closure, providing valuable insights into the emergent pseudo-inertial aspects of the evolving thermodynamic states.