Atomistic-Continuum theory of graphene fracture for opening mode crack

Abstract

Although atomic calculations and experiments have demonstrated that the fracture of graphene and single-walled carbon nanotubes (SWCNTs) is brittle, it is still an open question how to explain the fracture’s mechanism. We established an atomic-continuum theory in the present paper to explore this question for the opening mode crack (mode Ι crack). In the new theory, the stress-intensity factor and the interatomic Morse potential are coupled in the equation of motion of a crack-tip carbon atom for the fracture along the zigzag direction. This theory reveals that the brittle fracture in graphene arises from the static bifurcation of the bond length with the stress-intensity factor. There are two thresholds corresponding to the carbon–carbon bond rupture or re-bonding under the opposite load sequences. When the stress-intensity factor increases from zero to the critical valueKcrD, the bond length at the crack tip suddenly increases and then induces the bond rupture. On the contrary, when the stress-intensity factor gradually decreases from a large value to another critical value KcrC (KcrC<KcrD), the bond length will suddenly drop, and then the broken bond will re-bond. The new theory also discovers that the rupture and re-bonding of the carbon–carbon bond are sensitive to parameters of Morse potential, initial conditions, and harmonic exciting forces. This study may imply that it is feasible to model the failure of monolayer nanostructures through modifying classical continuum mechanics.