The anomalous yield behavior of fused silica glass

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 wellcaptured 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 criticalstate line. Despite this lack of convexity, the effective macroscopic model is stable against microstructure formation and defines well-posed boundaryvalue problems.

Pressure effects on shear deformation of borosilicate glasses

“…These alkali‐rich regions tend to densify preferentially under pressure, 26 but the densification of these regions does not affect the number of constraints (rigidity) in the sample 38 . For Boro33, its minimum in modulus is in agreement with the elastic moduli anomaly found in silica 39‐41 and also silicate glasses 26 . It has been shown that the critical composition at which the transition between anomalous and normal behavior happens is located at 15% Na 2 O 42 and the anomalous behavior mainly results from the isotropic collapse of glass's network due to more free volume in the structure 23,26 rather than the coordination change 40 This anomaly is thus not observed in N‐BK7 because of more alkali amount.…”

Mechanical and microstructural response of densified silica glass under uniaxial compression: Atomistic simulations*

“…Nowadays, molecular dynamics (MD) simulations have been widely used to study structures and dynamic response of silica glass. [17][18][19][20][21][22][23][24][25][26] Zeidler et al [17] used MD and experiments to establish the relationship between the ring size and Si-O coordination number of silica glass under cold compression conditions, which is helpful for understanding the densification process. Huang et al [18] simulated the cold and hot compression of silica glass.…”

Symmetric Div-Quasiconvexity and the Relaxation of Static Problems

“…1a, resulting in a strongly non-convex elastic domain in the pressure-shear stress plane. Several authors [MR08,SHCO18] have performed molecular dynamics calculations of amorphous solids deforming in pressure-shear and have found that the resulting deformation field forms distinctive patterns to accommodate permanent macroscopic deformations, Fig. 1b.…”