Fracture of perfect and defective graphene at the nanometer scale: Is graphene the strongest material?

Abstract

The basic relationships between the linear elastic and nonlinear fracture properties given by a local bond-breaking model and Griffith's criterion are used to characterize the two-dimensional (2D) mechanical properties of an intrinsic and a defective graphene, respectively. The analytical 2D models describe the localized bond-breaking in perfect monolayers and the failure of defective graphene by the global energy balance concept. From the experimental data, density functional theory calculations, molecular dynamics simulations, and continuum 2D models, a consistent set of 2D mechanical properties consisting of Young's modulus, fracture strength, fracture toughness, line (edge) energy, and critical strain energy release rate can be obtained. The critical fracture stress shows a linear dependence on the square root of the effective defect length from the subnanometer to the micrometer scale. The lower limit of fracture toughness and strain energy release rate is essentially independent of the defect size for vacancies, slits, and pre-cracks in the nanometer range. In the subnanometer range, the direct bond breaking and Griffith models deliver a consistent description of mode I fracture by a uniaxial tension. The promising results suggest an extension of the continuum models to other fracture modes such as the failure by shear load.