Mode I fracture toughness analysis of a single-layer grapheme sheet
MN Ky and YJ Yum, JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY, 28, 3645-3652 (2014).
To predict the fracture toughness of a single-layer graphene sheet (SLGS), analytical formulations were devised for the hexagonal honeycomb lattice using a linkage equivalent discrete frame structure. Broken bonds were identified by a sharp increase in the position of the atoms. As crack propagation progressed, the crack tip position and crack path were updated from broken bonds in the molecular dynamics (MD) model. At each step in the simulation, the atomic model was centered on the crack tip to adaptively follow its path. A new formula was derived analytically from the deformation and bending mechanism of solid-state carbon-carbon bonds so as to describe the mode I fracture of SLGS. The fracture toughness of single-layer graphene is governed by a competition between bond breaking and bond rotation at a crack tip. K-field based displacements were applied on the boundary of the micromechanical model, and FEM results were obtained and compared with theoretical findings. The critical stress intensity factor for a graphene sheet was found to be K (IC) = 2.63 - 3.2MPa root m for the case of a zigzag crack.
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