Graphene as a model system for 2D fracture behavior of perfect and defective solids

A 2D bond-breaking model is presented that allows the extraction of the intrinsic line or edge energy, fracture toughness, and strain energy release rate of graphene from measured and calculated 2D Young’s moduli and 2D pristine strengths. The ideal fracture stress of perfect graphene is compared with the critical fracture stresses of defective graphene sheets containing different types of imperfections. This includes (multiple) vacancies in the subnanometer range, grain boundaries, slits in the nanometer region, and artificial pre-cracks with sizes of 30 nm to 1 ?m. Independent of the type of defect, a common dependence of the critical fracture strength on the square root of half defect size is observed. Furthermore, the results suggest the applicability of the Griffith relation at length scales of several nanometers. This observation is not consistent with simulations pointing to the existence of a flaw tolerance for defects with nanometer size. According to simulations for quasi-static growth of pre-existing cracks, the atomic mechanism may also consist of an alternating sequence of bond-breaking and bond-rotation steps with a straight extension of the crack path. Independent of the exact atomic failure mechanism brittle fracture of graphene is generally assumed at low temperatures.