Modelling temperature-dependent fracture nucleation of SWCNTs using atomistic-based continuum theory

The fracture behaviour of carbon nanotubes depends largely on temperature, defect distribution, and geometric features. In this paper, the effect of temperature upon fracture nucleation of single-walled carbon nanotubes (SWCNTs) is investigated using an atomistic-based continuum theory. The temperature effects are described in terms of a modified Cauchy– Born rule based on the assumptions that the deformation is sufficiently small and locally homogeneous. Furthermore, it is assumed that the atoms have the same local vibration mode at a given temperature. The first derivative of the free energy density, which is a function of both the deformation gradient and the temperature, enables the determination of the second Piola–Kirchhoff stress. In the present study, the fracture nucleation is modelled as a bifurcation of a homogeneously deformed nanotube at a critical strain. The model predictions show that the fracture strain decreases with increasing temperature, while the elastic stiffness remains largely unchanged.