How glass breaks -- Damage explains the difference between surface and fracture energies in amorphous silica

TL;DR

The paper addresses why fracture energy in amorphous silica exceeds the free surface energy by separating surface formation energy from a diffuse damage contribution that spans roughly $l\approx$16–23 Å. It combines atomistic simulations with a phase-field fracture model and calibrates a FEMU approach to quantify damage-driven energy dissipation, yielding a fracture toughness consistent with experiments (notably $2\gamma/g_c \approx 0.23$). The results reveal a nonlocal damage zone around cracks that dominates energy loss, while plasticity is negligible, bridging atomic-scale mechanisms with continuum fracture concepts. This work enhances understanding of brittle fracture in glasses and suggests broader applicability of phase-field damage descriptions to other brittle amorphous materials and possibly metallic glasses under fatigue or dynamic loading.

Abstract

The difference between free surface energy and fracture toughness in amorphous silica is studied via multi-scale simulations. We combine the homogenization of a molecular dynamics fracture model with a phase-field approach to track and quantify the various energy contributions. We clearly separate free surface energy localized as potential energy on the surface and damage diffusion over a 16-23 A range around the crack path. The plastic contribution is negligible. These findings, which clarify brittle fracture mechanisms in amorphous materials, align with toughness measurements in silica.

Figures (10)

• Figure 1: (a) A cut of the atomic-scale model displaying atoms of a 5 Å thickness. (b) Deformed configuration with the same cut with $K_I=2.2$ MPa$\sqrt{m}$. (c) Coarse-grained displacement field in the Lagrangian configuration, obtained via convolution, at the same loading state as in (b).
• Figure 2: Damage field obtained from molecular simulations: (a) Distribution of damage in the middle plane of the sample. (b) Circles represent the damage profile along the $y$ direction at $x = 125$ Å, fitted with a Gaussian function of maximum height $d_{\rm{max}}$ and width $l$. (c) Variation of the fitted width $l$ along the crack and under different global loading states, color-coded by $d_{\rm{max}}$ according to the colorbar. The blue region indicates $l_c$ identified using the Finite Element Update (FEMU) scheme based on the phase-field formulation (see eq. \ref{['eq:PFSurf']}).
• Figure 3: (a) Principal difference between damaging and plastic response. (b) Maximum stress ratio at $K_I=2.2$ MPa$\sqrt{m}$.
• Figure 4: Distribution of free surface energy as a function of coarse-graining width. (a) Profiles of free surface energy along the $y$ axis for various coarse-graining widths. (b) Mean value and standard deviation of the local free surface energy $\gamma$, normalized by the global value.
• Figure 5: (a) Profiles of free surface energy for different models. In red, values for the dissected sample are shown with a CG width of 8 Å. In black, results from the cracked and coarse-grained sample are shown at $x=75$ Å. (b) Free surface energy distribution at $K_I=2.2$ MPa$\sqrt{m}$. (c) Crack surface as a function of loading derived from $\Psi_{\rm{FSE}}$ and from phase-field calculations.