13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- of fact, mixed-mode fracture inevitably occurred during the tearing of graphene sheets from graphite or other substrates to obtain free-standing sheets or narrow ribbons [12]. In [5], multiple crack branched sprouting off the primary crack front, thus tilted cracks were actually under mixed tensile and shear loading. Besides theoretical studies, Kim et al. [13] presented investigations on tears in suspended monolayer graphene membranes by high-resolution transmission electron microscopy (HRTEM). However, radiation damage by electron-beam energy and applied dose cannot be neglected for light element materials due to the limitations of HRTEM [14]. It is still a challenge to observe experimentally the cracking of graphene under pure mechanical loading without electromechanical coupling effects. Thus far, complex mechanical loading is rarely considered in previous works on fracture in graphene. Here we will show our extensive molecular dynamics (MD) simulations on nanoscale fracture of graphene under coupled opening and in-plane shear loading of far-field (I/II mixed-mode fracture). A boundary layer model embedded with a straight crack along either zigzag (ZZ) or armchair (AC) edge is applied with complex stresses by a displacement boundary governed by crack-tip asymptotic solution. The modified second-generation reactive empirical bond-order (REBO) potential [15] is used by shifting the cut-off distance and removing cut-off function to avoid unphysical dramatic increase in the interatomic force. The evolution of atomically cleaving of graphene is then revealed without manually specified direction of crack propagation. 2. Methodology and model The well established REBO potential for hydrocarbons has been widely used [5, 9, 16-18] to specifically describe the interatomic interaction of carbon atoms lattices and nonlocal effects via an analytic function, Lennard-Jones 6-12 potential was used to mimic the nonbonding interatomic interaction, and the potential can correctly describe the bond breaking and switching between carbon atoms. In REBO potential, two cutoff distances 1.7 Å and 2.0 Å are initially set for a smooth transition of cutoff function from 1 to 0 to limit the range of covalent interactions as the interatomic distance increases. However, as noted in several previous studies [19, 20], such a cutoff function generates spurious bond forces near the cutoff distance, which will lead to unphysical results due to discontinuity in the second derivative of the cutoff function. This artifact defect shall be avoided in the study of graphene fracture. In this study, the cutoff function is taken to be 1.0 within a cutoff distance of 1.92 Å [21] and zero otherwise, as suggested by the developers [19]. It was found that the numerical results up to fracture of GNRs are unaffected if the cutoff distance is within 1.9 Å to 2.2 Å [9]. A size-reduced model containing a small circular-shaped domain cut from the crack tip is utilized to model semi-infinite cracks in real graphene. A reasonable domain size is chosen so that its outer boundary falls in the K-dominant zone, which can make all-atom simulations computationally efficient. We consider an initially straight crack subject to in-plane opening and shear loading characterized by the local stress intensity factor (SIF) K field. Two prevalent cracks with orientations along ZZ or AC edges are chosen in Figure 1. Two or three rows of atoms are removed to generate cracks in our models, and the distance between two crack surfaces is big enough to
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