The chirality-dependent fracture properties of single-layer graphene sheets: Molecular dynamics simulations and finite element method

Abstract

The chirality-dependent mixed-mode I-II fracture toughness and crack growth angles of single-layer graphene sheets are determined using molecular dynamics (MD) simulations and the finite element (FE) method based on the boundary layer model, respectively. The carbon–carbon bond in the FE method is equivalent to a nonlinear Timoshenko beam based on the Tersoff–Brenner potential. All the results of the present FE method agree well with those of our MD simulations performed using the REBO potential. The chiral crack angles of α = 0° (zigzag), 15°, 30° (or 90°, armchair), and 45° at different loading angles from 0° ≤ φ ≤ 90° (φ = 90° for mode I and φ = 0° for mode II) are studied. The present results show that both critical stress intensity factors (SIFs) and crack growth angles strongly depend on the chiral angle α, the dimensions [in two-dimensional (2D) or three-dimensional (3D) states], as well as the temperature, for a given loading angle φ. The critical equivalent SIFs change from 2.52 to 4.07 nN Å−3/2 in the 2D state and from 2.46 to 5.06 nN Å−3/2 in the 3D state at different loading angles. The SIFs are around one order of magnitude smaller than those of ordinary steel, which indicates that chiral graphene is remarkably brittle in contrast to its ultrahigh strength. These findings should be of great help in understanding the chirality-dependent fracture properties of graphene sheets and designing graphene-based nanodevices.