Fracture Nucleation in Single-Wall Carbon Nanotubes Under Tension: A Continuum Analysis Incorporating Interatomic Potentials

Carbon nanotubes show great promise for applications ranging from nanocomposites, nanoelectronic components, nanosensors, to nanoscale mechanical probes. These materials exhibit very attractive mechanical properties with extraordinarily high stiffness and strength, and are of great interest to researchers from both atomistic and continuum points of view. In this paper, we intend to develop a continuum theory of fracture nucleation in single-walled carbon nanotubes by incorporating interatomic potentials between carbon atoms into a continuum constitutive model for the nanotube wall. In this theory, the fracture nucleation is viewed as a bifurcation instability of a homogeneously deformed nanotube at a critical strain. An eigenvalue problem is set up to determine the onset of fracture, with results in good agreement with those from atomistic studies.