Quantitative prediction of the fracture toughness of amorphous carbon from atomic-scale simulations
S. Mostafa Khosrownejad, James R. Kermode, Lars Pastewka
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 nanoindentation tests, and results of reported experiments are not consistent. Here, we use atomic-scale simulations to make quantitative and mechanistic predictions of 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 $\ensuremath{\rho}=2.5$, 3.0, and $3.5\phantom{\rule{0.28em}{0ex}}{\text{g/cm}}^{3}$ created by liquid quenches for a range of quench rates ${\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{T}}_{q}=10--1000\phantom{\rule{0.28em}{0ex}}\text{K/ps}$. The simulations show that the crack propagates by nucleation, growth, and coalescence of voids. Distances of $\ensuremath{\approx}1\phantom{\rule{0.28em}{0ex}}\text{nm}$ between nucleated voids result in a brittlelike fracture toughness. We use a crack growth criterion proposed by Drugan, Rice, and Sham [J. Mech. Phys. Solids 30, 447 (1982)] to estimate steady-state fracture toughness based on our short crack-length fracture simulations. Fracture toughness values of $2.4--6.0\phantom{\rule{0.28em}{0ex}}\text{MPa}\phantom{\rule{0.16em}{0ex}}\sqrt{\text{m}}$ for initiation and $3--10\phantom{\rule{0.28em}{0ex}}\text{MPa}\phantom{\rule{0.16em}{0ex}}\sqrt{\text{m}}$ 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.