Quantitative prediction of the fracture toughness of amorphous carbon from atomic-scale simulations

TL;DR

This study uses atomic-scale simulations to quantitatively predict the fracture toughness of amorphous carbon, revealing mechanisms of crack propagation and providing results consistent with experimental data.

Contribution

First to systematically simulate and predict fracture toughness of amorphous carbon at atomic scale using large-scale crack propagation models.

Findings

Fracture occurs via void nucleation, growth, and coalescence.

Predicted fracture toughness ranges align with experimental reports.

Void spacing of about 1 nm leads to brittle-like fracture.

Abstract

Fracture is the ultimate source of failure of amorphous carbon (a-C) films, however it is challenging to measure fracture properties of a-C from nano-indentation tests and results of reported experiments are not consistent. Here, we use atomic-scale simulations to make quantitative and mechanistic predictions on fracture of a-C. Systematic large-scale K-field controlled atomic-scale simulations of crack propagation are performed for a-C samples with densities of $\rho=2.5, \, 3.0 \, \text{ and } 3.5~\text{g/cm}^{3}$ created by liquid quenches for a range of quench rates $\dot{T}_q = 10 - 1000~\text{K/ps}$. The simulations show that the crack propagates by nucleation, growth, and coalescence of voids. Distances of $ \approx 1\, \text{nm}$ between nucleated voids result in a brittle-like fracture toughness. We use a crack growth criterion proposed by Drugan, Rice \& Sham to estimate steady-state fracture toughness based on our short crack-length fracture simulations. Fracture toughness values of $2.4-6.0\,\text{MPa}\sqrt{\text{m}}$ for initiation and $3-10\,\text{MPa}\sqrt{\text{m}}$ for the steady-state crack growth are within the experimentally reported range. These findings demonstrate that atomic-scale simulations can provide quantitatively predictive results even for fracture of materials with a ductile crack propagation mechanism.