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.