A fictive stress model and nonlinear viscoelastic behaviors in metallic glasses

Abstract

Transition behaviors from linear to nonlinear viscoelasticity under constant strain-rate deformation near the glass transition have been investigated for Pd- and Zr-based alloy glasses. The transition occurs at critical strain-rate, and the steady-state viscosity may decrease by many orders of magnitude above the critical strain-rate. Concurrently with the transition, the growth of the stress shows a stress-overshoot: the stress increases initially attaining a maximum, then decreases and attains a steady-state flow. The transition between steady-state Newtonian and non-Newtonian flows can be analyzed by a stretched exponent relaxation function, and both the normalized viscosity and the flow stress can be represented by a master curve in terms of the product of the strain-rate and the Newtonian viscosity. These results imply that the occurrence of the transition from the Newtonian to non-Newtonian is explicitly determined by the flow stress. A model, based on the hypothesis of stress-induced structural relaxation and the concept of fictive stress for the nonlinear viscoelastic behaviors has been proposed. The model calculation has reproduced fairly well the experimental results of the Pd- and Zr-based glasses, in particular, the development of the stress-overshoot behavior. In addition, the model reveals a stress-overshoot and under-shoot oscillation at very high strain-rate. This oscillatory nonlinear behavior has been observed in many polymer solutions, and also the latest study in metallic glasses. The model calculations of other nonlinear viscoelastic behaviors, such as stress relaxation during stress growth after abrupt cessation of steady-state flow, and a stress regrowth after a brief interval of relaxation, are also presented.