Deformation and flow in bulk metallic glasses and deeply undercooled glass forming liquids—a self consistent dynamic free volume model

Bulk glass forming metallic liquids such as those of the Zr–Ti–Ni–Cu–Be Vitreloy alloy family have been shown to have Newtonian Viscosity which is well described by the Vogel–Fulcher–Tamann (VFT) equation over roughly 15 orders of magnitude from the high temperature equilibrium melt to the deeply undercooled liquid near and below the experimentally observed glass transition. Experiments have also shown flow becomes non-Newtonian and ultimately unstable against spatial localization into shear bands as the strain rate at a given temperature is increased. This transition from homogeneous to inhomogeneous flow and flow localization has been discussed by several authors and attributed to the influence of strain softening, strain rate sensitivity, and thermal softening.which collectively result in the destabilization of the uniform flow field. The present paper presents a simple self consistent model of uniform steady state flow which is based on the tradition Free Volume Model of the glass transition, the VFT-equation, and a simple treatment of free volume production and annihilation during flow. The model is used to analyze the flow data and shown to give a simple one-parameter fit to experimental steady state Newtonian and non-Newtonian flow data over a broad range of temperatures and strain rates. The model gives simple analytic expressions for the steady state constitutive flow law, the strain rate sensitivity exponent (SRSE), and an implicit equation for the strain rate and temperature dependent viscosity, which is solved numerically. An approximate analytic expression for the non-Newtonian effects is proposed. Generalizing the model to time dependent flow, it is argued that observed shear localization and serrated flow in bulk glass forming liquids arises primarily from transient response phenomena.