The Anomalous Yield Behavior of Fused Silica Glass

TL;DR

This paper introduces a critical-state plasticity model for fused silica glass based on molecular dynamics data, capturing its anomalous non-convex yield behavior and explaining patterning phenomena during deformation.

Contribution

It develops a novel critical-state model that accounts for the non-convex yield surface of fused silica, linking microscopic MD data to macroscopic stability.

Findings

The yield surface of fused silica is strongly non-convex due to two distinct phases.

The model captures irreversible densification and constant-volume critical states.

Despite non-convexity, the model remains stable and well-posed.

Abstract

We develop a critical-state model of fused silica plasticity on the basis of data mined from molecular dynamics (MD) calculations. The MD data is suggestive of an irreversible densification transition in volumetric compression resulting in permanent, or plastic, densification upon unloading. The MD data also reveals an evolution towards a critical state of constant volume under pressure-shear deformation. The trend towards constant volume is from above, when the glass is overconsolidated, or from below, when it is underconsolidated. We show that these characteristic behaviors are well-captured by a critical state model of plasticity, where the densification law for glass takes the place of the classical consolidation law of granular media and the locus of constant volume states denotes the critical-state line. A salient feature of the critical-state line of fused silica, as identified from the MD data, that renders its yield behavior anomalous is that it is strongly non-convex, owing to the existence of two well-differentiated phases at low and high pressures. We argue that this strong non-convexity of yield explains the patterning that is observed in molecular dynamics calculations of amorphous solids deforming in shear. We employ an explicit and exact rank-2 envelope construction to upscale the microscopic critical-state model to the macroscale. Remarkably, owing to the equilibrium constraint the resulting effective macroscopic behavior is still characterized by a non-convex critical-state line. Despite this lack of convexity, the effective macroscopic model is stable against microstructure formation and defines well-posed boundary-value problems.