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.
Highlights
Amorphous carbon (a-C) has many industrial applications, from electrochemical sensors [1] to wear-resistant coatings [2]
A full R curve manifests three stages of crack growth: (i) The crack initiation regime provides us with KIc. (ii) The crack growth regime is characterized by the slope dKI /d a that drops toward zero when the crack enters (iii) the steady-state regime, where the stress intensity factor saturates to a constant fracture toughness value KIss
For a semi-infinite crack in a big enough sample loaded according to the elastic K field, unstable growth only happens if KI = KIss
Summary
Amorphous carbon (a-C) has many industrial applications, from electrochemical sensors [1] to wear-resistant coatings [2]. Mechanical processes, such as plasticity and fracture, play a crucial role in the performance of a-C in these applications [3]. Toughness values are commonly measured using nanoindentation tests [6,7,8,9]. The values reported for frac√ture toughness of a-C scatter between KI = 3 and 12 MPa m [6,7,8,9]. The differences between results highlight the fact that it is not straightforward to measure fracture properties using nanoindentation methods
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