A kinetic model for time-dependent fracture of carbon nanotubes

Based on the classical kinetic concept of solid fracture and a strain concentration concept, a model is proposed for predicting time-dependent fracture of carbon nanotubes. The time-dependent fracture behavior of a zigzag type single-walled carbon nanotube with a range of preexisting cracks under tension is studied by molecular mechanics simulations and a numerical scheme using crack front strain energy concentration. Results of the study quantitatively agree with a recent study on fatigue of aligned single-walled carbon nanotube bundles. It is found that the coefficient of strain energy concentration increases as a crack grows and the time-to-failure of the carbon nanotube is dominated by the lifetimes of a few bonds after initial bond dissociation when load is large while more bonds contribute to the overall lifetime when applied load is small, resulting in the logarithm of time-to-failure of carbon nanotubes being approximately linearly related to applied stress.