The anomalous yield behavior of fused silica glass
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 defines 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.
© 2018 Elsevier Ltd. Received 13 October 2017, Revised 21 December 2017, Accepted 8 January 2018, Available online 1 February 2018. WS, SH and MO gratefully acknowledge support from the US Office of Naval Research, Naval Materials Div., Dr. R. Barsoum Program Officer, through grant N000141512453. SH gratefully acknowledges support from the Alexander von Humboldt Stiftung through a Research Fellowship for Postdoctoral Researchers. SC is grateful for the support of the Deutsche Forschungsgemeinschaft through the Sonderforschungsbereich 1060 "The mathematics of emergent effects". The visualization of atomistic simultions were generated using the OVITO software package (Stukowski, 2010).
Submitted - 1710.05077.pdf