Rate dependent shear bands in a shear transformation zone model of amorphous solids

TL;DR

This paper develops a shear transformation zone model for amorphous solids that predicts various deformation behaviors, including shear band formation and failure, based on shear rate and initial material conditions, emphasizing rate-dependent effects.

Contribution

It introduces a rate-dependent STZ model that captures diverse deformation regimes and predicts shear band characteristics and failure mechanisms in amorphous solids.

Findings

Homogeneous deformation at low shear rates and short quench times.

Inhomogeneous shear bands form at higher shear rates and longer quench times.

Material failure linked to runaway shear heating and disorder feedback.

Abstract

We use Shear Transformation Zone (STZ) theory to develop a deformation map for amorphous solids as a function of the imposed shear rate and initial material preparation. The STZ formulation incorporates recent simulation results [Haxton and Liu, PRL 99 195701 (2007)] showing that the steady state effective temperature is rate dependent. The resulting model predicts a wide range of deformation behavior as a function of the initial conditions, including homogeneous deformation, broad shear bands, extremely thin shear bands, and the onset of material failure. In particular, the STZ model predicts homogeneous deformation for shorter quench times and lower strain rates, and inhomogeneous deformation for longer quench times and higher strain rates. The location of the transition between homogeneous and inhomogeneous flow on the deformation map is determined in part by the steady state effective temperature, which is likely material dependent. This model also suggests that material failure occurs due to a runaway feedback between shear heating and the local disorder, and provides an explanation for the thickness of shear bands near the onset of material failure. We find that this model, which resolves dynamics within a sheared material interface, predicts that the stress weakens with strain much more rapidly than a similar model which uses a single state variable to specify internal dynamics on the interface.