Fracture and progressive failure of defective graphene sheets and carbon nanotubes

An atomistic based finite bond element model for the prediction of fracture and progressive failure of graphene sheets and carbon nanotubes is developed by incorporating the modified Morse potential. The element formulation includes eight degrees of freedom reducing computational cost compared to the 12 degrees of freedom used in other FE type models. The coefficients of the elements are determined based on the analytical molecular structural mechanics model developed by the authors. The model is capable of predicting the mechanical properties (Young’s moduli, Poisson’s ratios and force–strain relationships) of both defect-free and defective carbon nanotubes under different loading conditions. In particular our approach is shown to more accurately predict Poisson’s ratio. The numerical prediction of nonlinear stress–strain relationships for defect-free nanotubes including ultimate strength and strain to failure of nanotubes is identical to our analytical molecular structural mechanics solution. An interaction based mechanics approach is introduced to model the formation of Stone–Wales (5-7-7-5) topological defect. The predicted formation energy is compared with ab initio calculations. The progressive failure of defective graphene sheets and nanotubes containing a 5-7-7-5 defect is studied, and the degradation of Young’s moduli, ultimate strength and failure strains of defective nanotubes is predicted.