13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- Figure 2. Effective critical stress intensity factors Keff c of graphene cracks, ZZ in blue and AC in red, changing with phase angles φ of far-field loading. KI and KII are opening and shear components of Keff c. Up to now, no single criterion in classical continuum mechanics can give satisfactory predictions for crack initiation direction under all loading conditions. All existing criteria predict that a crack under mode II (in-pane shear, φ = 0°) loading propagates along about a 70°direction with respect to the original crack line. However, a mode II crack either propagates in mode I (opening, φ = 90°) or mode II, depending on material properties and load magnitudes [31]. Continuum criteria seem to lose efficacy in predicting direction of crack initiation in graphene. In Figure 3a-f, our results show that ZZ cracks initiate in the direction of an angle β = 120°deviating from the original edge when in-plane shear loading is prevailing, β maintains unchanged till φ = 60 ° and fresh edges are in zigzag (blue). Further increasing φ will induce the transition of β. At φ = 65°, β changes to 150°, and fresh edges are in armchair (red). This configuration coincides with the prediction that zigzag-armchair junctions with an angle of 150°would be more stable [32, 5]. Once φ > 65°, opening loading becomes dominant, crack grows self-similarly along original direction and fresh edges are in zigzag again. For AC cracks in Figure 3g-l, initiation angle β = 90°at φ = 0°, new crack tips nucleate prior to initial tip, and fresh edges are in zigzag. At φ = 26.5°, propagating direction changes to β = 120°, and fresh edges are in armchair. When φ> 26.5°, β transforms to 150°and keeps unchanged till φ = 90°, and fresh edges are in zigzag again.
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