The Capriccio method as a versatile tool for quantifying the fracture properties of glassy materials under complex loading conditions with chemical specificity

TL;DR

The Capriccio method enables concurrent FE–MD fracture simulations in amorphous silica, linking atomistic detail near cracks with macroscopic boundary conditions. By examining mode I–III loadings and multiple onset indicators (virial stress, bond count, kinetic energy, crack velocity, and COD), the study derives KIc, KIIc, and KIIIc and assesses the method’s accuracy and limitations. The results show reasonable KIc values (and plausible KIIc/KIIIc) with COD aligned to LEFM predictions in early loading, while highlighting motion-resistance and boundary-coupling effects as key sources of quantitative deviation, especially in non-tensile geometries. Overall, Capriccio offers a versatile pathway to integrate chemical specificity into fracture analyses at larger scales, with clear directions for improving coupling and extending to macroscopic applications and environments.

Abstract

Molecular dynamics (MD) simulations are widely used to provide insights into fracture mechanisms while maintaining chemical specificity. However, particle-based techniques such as MD are limited in terms of accessible length scales and applicable boundary conditions, which restricts the investigation of fracture phenomena in typical engineering settings. In an attempt to overcome these limitations, we apply the partitioned-domain Capriccio method to couple atomistic MD samples representing silica glass with the finite element (FE) method. With this approach, we perform mode I (rectangular panel under tension, three-, and four-point bending), mode II as well as mode III (rectangular panel under in-plane or out-of-plane shear) simulations. Thereby, we investigate multiple criteria to identify the onset of crack propagation based on the virial stress, the number of pair interactions, the kinetic energy/temperature, the crack velocity, and the crack opening displacement. The approach presented provides quantitatively plausible results for the critical stress intensity factors KIc, KIIc, and KIIIc. This contribution shows that the Capriccio method is a flexible means of performing fracture simulations that take into account boundary conditions typical of experimental test setups with atomistic specificity near the crack tip. While also pointing out the current limitations of the Capriccio method, we demonstrate its potential to integrate atomistic insights into FE models with significantly larger overall dimensions.

Figures (38)

• Figure 1: General setup of the fracture simulations: The samples are pre-notched with notch length $a$ as well as notch width $L_{x}^{\mathrm{crack}}$. While loading the specimens with surface tractions $\bar{\mathbf{t}}$, atomistic quantities are evaluated in an observation region of dimensions $L_{x}^{\mathrm{obs}} = L_{y}^{\mathrm{obs}}$ in front of the crack tip, whereas the crack opening displacement $\delta$ is measured as the change in the distance between the two purple points. The entire samples measure $b$ in width, $2c$ in length and $h$ in thickness.
• Figure 2: Setup of the three-point (blue) and four-point (red) bending tests: Applied force $P$ and distances between the supports $S_{\mathrm{o}}$ and the forces $S_{\mathrm{i}}$.
• Figure 3: Examples of deformed configurations of the strip simulations: a) Mode I, b) mode II, and c) mode III conditions.
• Figure 4: Effect of the region of interest: a) Virial stress $\sigma_{xx}$, b) number of bonds $n_{\mathrm{B}}$, c) kinetic energy $E^{\mathrm{k}}$, and d) crack velocity $v_{\mathrm{crack}}$ over the stress intensity factor $K_{\mathrm{I}}$ for different sizes of the observation region in front of the crack tip $L^{\mathrm{obs}}_{x} = L^{\mathrm{obs}}_{y}$. Since the number of bonds and the kinetic energy are extensive quantities, we normalize them to the average value over five systems after equilibration at $K_{\mathrm{I}} = 0$.
• Figure 5: Assessment of the overall deformation: a) Resulting crack opening displacement $\delta$ between the outermost finite element (FE) nodes of the notch over the stress intensity factor $K_{\mathrm{I}}$ compared to the theoretical reference curve given by Eq. \ref{['eq:CODModeI']} and b) snapshot of one of the samples at $K_{\mathrm{I}} = 1.03MPa\sqrt{m}$. For the present sample, the critical stress intensity factor, derived based on the virial stress as described in Section \ref{['ssec:Definition of the quantities of interest']}, is $K_{\mathrm{Ic}} = 0.75MPa\sqrt{m}$.