13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- avoid self sealing, especially in pure shear case. The length of crack is more than 10 times lattice spacing to avoid unphysical Griffith fracture stress and flaw insensitiveness [22]. A total of around 4000 carbon atoms in our disk models with a radius r = 60Å are initially relaxed until the energy of the system is fully minimized for a specified temperature. The thickness of graphene is assumed to be 3.335Å under plane stress condition. Hereafter our results are divided by 3.335Å to make connection of a two-dimensional lattice with a three-dimensional solid. Figure 1. Boundary layer MD model and coordinates. A pre-existing straight crack along zigzag edge is embedded in a two-dimensional graphene lattice (green). The outer boundary layer (pink atoms) is subject to displacement loadings. Williams [23] has given the asymptotic expansion of the displacement field around the crack tip in an isotropic linear elastic body. At a given SIF Kapp applied by far-field loadings, the crack-tip asymptotic solution is as [24] 2 1 2cos 2 sin 2 1 2sin 2 cos 2 1 2 II 2 I x k K k K r E v u app app , (1) 2 1 2sin 2 cos 2 1 2cos 2 sin 2 1 2 II 2 I y k K k K r E v u app app . (2) where radius r and polar angle θ are defined in Figure 1, ux and uy are displacements in X and Y directions, respectively. Young’s modulus E is 1.0 TPa [2], and Poisson’s ratio v is 0.165 [25], and k = (3-v)/(1+v) for plane stress here. KI app and KII app are SIF components specified by opening and shear stresses. Phase angle φ (loading mixed parameter or equivalent crack angle) is defined as φ = tan-1(KI app/KII app), and an effective SIF at the initial crack length is evaluated as (Keff app) 2 = (KI app )2 + (KII app )2, see Figure 1. Therefore the far field behavior of pristine graphene is assumed to be well-represented by the solution since the singularity decreases apart from the crack tip. The boundary condition is similar to a suspended graphene spanning a hole in the TEM grid. KI φ KII Keff Y X Z r θ
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