A new continuum model for viscoplasticity in metallic glasses based on thermodynamics and its application to creep tests

Abstract

In this study, we developed a new continuum model for the time-dependent plasticity of metallic glasses based on the laws of thermodynamics. In this model, the free energy of a material point is formulated as not only the local strain state but also the local atomic concentration (or the free volume). Atomic kinetics, controlled by the gradient of the chemical potential, is linked directly with the plastic deformation by a new plastic flow rule. Finite element implementation of our model is validated through the classical uniaxial tension and simple shear tests in which the shear band instability and shear-dilatation phenomena are reproduced. Applied to the creep of Cu-Zr metallic glass, our model captures the transition of two distinct power laws for the creep strain rate vs. applied stress relations around a critical stress. These two power laws, below and above the critical stress, correspond to two different diffusion mechanisms activated by the thermal energy gradient and strain energy gradient, respectively. At last, we carry out a linear perturbation analysis to explain the origin of the critical stress as well as its dependence on the sample size.