Tensile behaviors of graphene sheets and carbon nanotubes with multiple Stone-Wales defects

An atomistic based finite bond element model has been developed to study the effects of multiple Stone-Wales (5-7-7-5) defects on mechanical properties of graphene sheets and carbon nanotubes. The element formulation includes 8 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 uses the modified Morse potential to predict the Young's modulus and stress-strain relationship of perfect and defective nanotubes and graphene sheets. The variation of ultimate stress, strain at failure, and Young's modulus values of carbon nanotubes and graphene sheets have been examined as a function of the distance between two defects aligned in the axial and hoop directions. The mechanical properties as a function of the number of defects in the hoop direction are also studied. It is found that the moduli are sensitive to the tube lengths when the total tube length is used to compute the strain. If one uses a local defective length to define the strain, a size independent modulus can be obtained for the defective region. The diameter of the affected region (2 nm) from a single defect is defined as the defective length and is used for all different tube lengths examined in the present study. The effects of defect density on mechanical properties of tubes of any lengths are also discussed.