Prediction of fracture toughness for carbon nanotubes

A modified molecular-continuum model is employed to predict fracture toughness of carbon nanotubes. In this model, the modified Morse potential function is used to evaluate the potential energy, and the near tip solution of linear elastic fracture mechanics is used to locate the atoms of the cracked specimen under tensile or shear loads. The representative volume is selected to be a circular region with center at the crack tip and radius determined from the equivalence of strain energy and virtual work for crack advancement. Using the relation between strain energy release rate and stress intensity factor, a nonlinear generalized stress-strain diagram is generated and the fracture toughness is then estimated to be the maximum point of this diagram. Through proper choice of representative volume and crack simulation, a vast of computational time can be saved and the results predicted by this model are shown to be consistent with those predicted by the other experimental or numerical methods.