Nonlinear visco-elasto-plastic model for the stress-strain and stress-relaxation in metallic glass

Abstract

We develop a nonlinear visco-elasto-plastic (VEP) model for the stress-strain response of metallic glasses by connecting the deformation dynamics with the material relaxation time obtained from independent stress-relaxation measurements. The material is modeled as a Maxwell-type element, with a nonlinear elastic spring and a stretched-exponential dashpot whose behavior is determined from the separate stress-relaxation data. The model captures the effects of temperature and strain rate on the initial elastic response, stress overshoot, post-yield softening, and steady flow. We independently determine the reference material-time function $X_0(\varepsilon)$ from the stress-relaxation response and the nonlinear material-time variable $X(\varepsilon)$ from the elastic-viscoplastic strain decomposition based on the stress-strain response. We introduce an Eyring-type function or material-time ratio $\phi(\varepsilon)=X(\varepsilon)/X_0(\varepsilon)$ which quantifies the change of relaxation dynamics during nonlinear deformation. Our model provides a simple connection between structural relaxation and yielding in metallic glasses.