2D microscopic model of graphene fracture properties

An analytical two-dimensional (2D) microscopic fracture model based on Morse-type interaction is derived containing no adjustable parameter. From the 2D Young's moduli and 2D intrinsic strengths of graphene measured by nanoindentation based on biaxial tension and calculated by density functional theory for uniaxial tension the widely unknown breaking force, line or edge energy, surface energy, fracture toughness, and strain energy release rate were determined. The simulated line energy agrees well with ab initio calculations and the fracture toughness of perfect graphene sheets is in good agreement with molecular dynamics simulations and the fracture toughness evaluated for defective graphene using the Griffith relation. Similarly, the estimated critical strain energy release rate agrees well with result of various theoretical approaches based on the J-integral and surface energy. The 2D microscopic model, connecting 2D and three-dimensional mechanical properties in a consistent way, provides a versatile relationship to easily access all relevant fracture properties of pristine 2D solids. (paper)