13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- Figure 3. Insets (r = 30Å, cut from the whole models in Figure 1) of crack initiation in flawed graphene (green) under I/II mixed-mode loading. (a)-(f) ZZ cracks initiation at phase angle φ = 0°, 30°, 45°, 60°, 65°, 90°, and (g)-(l) AC cracks at φ = 0°, 26.5°, 30°, 45°, 60°, 90°, correspondingly. Fresh edges exhibit mostly in zigzag, and armchair edges are formed during the transition of propagating direction. Under loading Keff app = 3.21 nN Å-3/2 at φ = 65°in Figure 3e, zigzag crack (blue) kinks and armchair edge (red) is formed. In Figure 3h, armchair crack (red) turns its direction with 120°followed by armchair edge (red) under Keff app = 3.25 nN Å-3/2 at φ = 26.5°. This is similar to experimental tears kinking within graphene membrane under complex mechanical stress applied by circular boundary of the Quantifoil holey carbon TEM grid [13]. With the increasing of complex loading, the stress concentrated around crack tip morphs the hexagonal carbon rings into deformed shapes. Once the bonds at the tip rotated or broken, the hexagonal symmetry of the graphene lattice is destroyed with the formation and motion of topological defects, which leads to crack kinking. The dynamic effect of a fast fracture in MD simulations can also cause kinking, while branching is not observed. Further crack extension would proceed by alternating sequence of bond breaking or rotation. Graphene edges are of particular interest since their orientation determines the electronic properties. Crack extension with the formation of fresh edges is mainly caused by local high strain concentrated around crack tips. Our simulations demonstrate that torn edges maintain straightness and clean in either zigzag or armchair direction, in Figure 3, and can change directions by 30°or multiples of 30°, in Figure 3, coincided with experiments [13]. Under pure opening loading (φ = 90°), the growth of zigzag cracks is self-similar whereas armchair cracks advance in an irregular manner, consistent with previous reports [6]. The direction of crack growth changes definitely under coupled opening and shearing stresses and edges interconvert between ZZ and AC. Cracks preferably grow along zigzag directions in agreement with previous theoretical simulations [9, 12]. By Griffith criterion, this suggests lower edge energy in ZZ opposed to AC, which is coincided with simulations by empirical potentials [28, 29, 33]. More abundant ZZ edges appeared may be due to lower edge energy, somewhat local residual stresses and dynamic fracture effects. Experiments also showed long-term stability [34] of ZZ edges, and more ZZ edges were initially formed at high temperatures [35]. In [13], the initial torn edges were along ZZ direction under pure mechanical stress during the graphene transfer process, while heating and chemical effects, knock-on sputtering induced by electron irradiation in TEM inevitably influenced crack extension stimulated afterwards.
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