Toughness and ultimate strength of amorphous silica identified through a combined microbeam and phase-field approach

This work presents a new approach to evaluating the toughness, described by the critical energy release rate ( ), and ultimate tensile strength ( ) of amorphous silica (SiO 2 glass), combining microbeam tests and phase-field calculations. The latter provides a numerical route to brittle fracture without prescribing explicit fracture surfaces a priori , enabling crack initiation and propagation to be tracked. Single-notched microbeams and newly designed bone-shaped microbeams with a notch-free gauge section were fabricated by Focused Ion Beam (FIB) milling and tested under bending in air, probing the brittle-fracture and strength-controlled regimes, respectively. Both geometries were modeled by Finite Element Analysis (FEA) coupled with a phase-field formulation. We found J/m 2 (critical stress intensity factor MPa m ), an intrinsic material length scale nm, and GPa, consistent with previously reported brittle properties of silica glass. Through a parametric study, we quantified the impact of dimensional measurement error on the determined toughness. Unlike conventional micromechanical methods that yield only , our combined microbeam geometries and phase-field approach simultaneously deliver and , bridging brittle-fracture characterization and the strength-controlled regime inaccessible to toughness-only techniques.