Theoretical and numerical studies on the fracture properties of pre-cracked single-layer graphene

Abstract

Based on the theories of solid state physics and quantum fracture mechanics, a theoretical model is proposed to investigate the fracture properties of pre-cracked single-layer graphene, and the analytical expressions of failure strength and fracture toughness of pre-cracked graphene are derived. Simultaneously, the failure strength of pre-cracked graphene is calculated by finite element method (FEM) based on molecular structure mechanics. The results of FEM are in good agreement with the theoretical counterparts. Via the theoretical analyses and numerical calculations, the effects of crack length, crack tip radius and domain size of graphene on the failure strength and fracture toughness of pre-cracked graphene are systematically studied. It is found that the failure strength of pre-cracked graphene gradually decreases with increasing crack length and domain size of graphene. However, as the crack tip radius increases, the failure strength gradually increases. In addition, it is also found that the crack length and domain size of graphene have little impact on the fracture toughness of graphene. The fracture toughness is significantly affected by crack tip radius.