Characterizing the Stress Intensity Factor of Graphene Sheet with Central Crack

Abstract

This paper aims to characterize the stress intensity factor (SIF) of atomistic graphene sheet with central crack subjected to uniaxial loading. The equilibrium configuration of the defective graphene sheet with missing covalent bonds was generated through molecular dynamics (MD) simulation. Subsequently, the local stress distribution near the crack tip of atomistic structure was evaluated using the Hardy stress formulation as well as the non-local elasticity theory. Based on the local stress distributions, the SIF of the atomistic graphene sheet was determined through the projection process. In comparison, the graphene sheet was also treated as a continuum solid, and the stress distribution near the crack tip as well as the SIF were evaluated from the finite element method (FEM). In an attempt to understand the crack size effect, the crack length was assumed to vary from 3 lattice distance to around 80 lattice distance. Results revealed that the SIF calculated based on the nonlocal elasticity theory in conjunction with the projection process is quite sensitive to the selection of the projection point. However, for the Hardy stress distribution, when the projection position is 1 lattice distance away from the crack tip, the SIF is quite consistent and the result is compatible to that obtained from the FEM analysis. Moreover, the agreement is better as the crack size is increasing. Therefore, the SIF calculated based on the Hardy stress formulation together with the projection approach could be a physical quantity correlating the defective atomistic graphene sheet with its continuum counterpart.