Modeling the transient flow of undercooled glass-forming liquids

In a recent experimental study on flow behavior of Vitreloy-1 (Zr41.25Ti13.75Cu12.5Ni10Be22.5), three distinct modes of flow are suggested: Newtonian, non-Newtonian, and localized flow. In a subsequent study, the experimental flow data is utilized in a self-consistent manner to develop a rate equation to govern local free volume production. In the present study the production-rate equation is transformed into a transport equation that can be coupled with momentum and energy transport via viscosity to formulate a model capable to govern the flow of undercooled glass forming liquids. The model is implemented to study the flow behavior of undercooled Vitreloy-1 melt. For a temperature of 700 K and shear loading of 1.0 MPa, the model predicts that the flow profile gradually stabilizes to its Newtonian limit while the liquid is maintained in structural and thermal equilibrium. For the conditions of 675 K and 100 MPa, the model predicts that the flow profile departs from its Newtonian limit and gradually stabilizes to a non-Newtonian limit. The non-Newtonian profile is evaluated independently by considering structurally quasistatic conditions, which yield the shear-rate dependency of flow. For the conditions of 650 K and 2.0 GPa, the model predicts that the flow continuously localizes and ultimately accelerates unconstrained, while the system is driven out of structural and thermal equilibration towards an unstable state associated with free volume generation, viscosity degradation, and temperature rise. The computed temperature and shear rate evolutions for the three distinct flow modes are superimposed on a temperature-shear rate diagram and appear to computationally reproduce the experimental flow map. The system's structural state that appears to dictate flow behavior is quantified by a dimensionless number, which results from a time scale analysis of the free volume production equation. (C) 2004 American Institute of Physics.