13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- 2. Molecular Dynamics Simulations Adaptive intermolecular reactive empirical bond order (AIREBO) potential [10], implemented in LAMMPS MD simulation package [11] is used in this study. Cut-off radius of AIREBO potential is set to be 2 Å to eliminate the non-physical strain hardening of the stress-strain curve [12]. Length and width of the simulation box are selected to be greater than 10 times of the crack length in order to avoid finite-size effects [13]. Strain rate and time step are 0.001 ps-1 and 0.5 fs, respectively. MD simulations are performed at 1K and 300K on armchair and zigzag sheets with crack lengths ranging from 4 Å to 29 Å to investigate the effect of crack length and temperature on the tensile strength (σult). The crack lengths are defined as shown in Fig. 1. Figure 1: Crack length (2a) and crack tip radius (ρ) of armchair and zigzag graphene sheets. Arrows indicate the straining direction. It is noticed during MD simulations that crack tips come out of the plane of graphene sheet at unstrained state. The crack tips are free edges. Deformation of free edges of graphene could be explained by considering an edge force, which arises from the difference in the energy stored in edge atoms and interior atoms [14]. As shown in Fig. 2, the out-of-plane deformation of a crack tip at equilibrium configuration is localized around the tip. However, as strain increases up to 0.018, the shape of the crack tip changes, and it acts as a localized ripple. As strain further increases up to 0.0235, this localized ripple spreads throughout the sheet. Figure 2: Ripples in 27 nm x 27 nm sheet with central crack. Strain is applied along y-direction.
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