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Boundary layer MD models and coordinates. A pre-existing straight crack along (a) zigzag or (b) armchair edge is embedded in a two-dimensional graphene lattice (green). The outer boundary layer (pink atoms) is subject to displacement loadings, (a) opening and/or (b) in-plane shear. Origins are at the concave crack tips located either at (a) a bond or (b) an atom.
Critical effective stress intensity factors of graphene cracks (ZZ in blue and AC in red) varying with phase angles φ of far-field loading. K I and K II are opening and shear components of .
Snapshots (r = 20 Å insets from the whole model in Figure 1) of crack initiations in graphene lattices (green) under critical loads , overlapped with previous configurations (grey lattices) to depict the local bond breaking. (a)–(f) ZZ crack models at φ = 0°, 30°, 45°, 60°, 65°, and 90°; (g)–(l) AC crack models at φ = 0°, 26.5°, 30°, 45°, 60°, and 90°, respectively. The atoms where the first bond is broke are marked in orange.
Snapshots (r = 30 Å) of crack propagation after initiation in Figure 3 under complex mechanical stress. The angle of crack propagation β orienting to primary crack is depicted correspondingly. ZZ crack edges are rendered in blue, AC in red.
Images of crack kinking in graphene lattices (green) after propagation in Figure 4 (after breakdown of the first bond in Figure 3, the crack-tip moves, the applied displacement loads are not precisely of the crack-tip asymptotic solution, stresses become more complex), ZZ (blue), or AC (red) edges appear alternatively changing direction of growth (enhanced online). [URL: http://dx.doi.org/10.1063/1.4754115.1] [URL: http://dx.doi.org/10.1063/1.4754115.2]10.1063/1.4754115.110.1063/1.4754115.2
Critical effective stress intensity factors (nN Å−3/2) of ZZ and AC cracks in graphene under mixed-mode far-field loading at various phase angles φ.
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