Carbon nanotubes (CNTs) are known to possess extraordinary strength, stiffness and ductility properties. Their fracture resistance is an important issue from the perspective of durability and reliability of CNT-based materials and devices. According to existing studies, brittle fracture is one of the important failure modes of single-walled carbon nanotube (SWNT) failure due to mechanical loading. However, based on the authors' knowledge, the fracture resistance of CNTs has not been quantified so far. In this paper, the fracture resistance of zigzag SWNTs with preexisting defects is calculated using fracture mechanics concepts based on atomistic simulations. The interatomic forces are modelled with a modified Morse potential; the Anderson thermostat is used for temperature control. The problem of unstable crack growth at finite temperature, presumably caused by the lattice trapping effect, is circumvented by computing the strain energy release rate through a series of displacement-control led tensile loading of SWNTs (applied through moving the outermost layer of atoms at one end at constant strain rate of 9.4 x 10(-4) ps(-1)) with pre-existing crack-like defects of various lengths. The strain energy release rate, G, is computed for (17, 0), (28, 0) and (35, 0) SWNTs (each with aspect ratio 4) with pre-existing cracks up to 29.5 angstrom long. The fracture resistance, G(c) is determined as a function of crack length for each tube at three different temperatures (1, 300 and 500 K). A significant dependence of G(c) on crack length is observed, reminiscent of the rising R curve behaviour of metals at the macroscale: for the zigzag nanotubes G(c) increases with crack length at small length, and tends to reach a constant value if the tube diameter is large enough. We suspect that the lattice trapping effect plays the role of crack tip plasticity at the atomic scale. For example, at 300 K, G(c) for the (35, 0) tube with aspect ratio 4 converges to 6 J m(-2) as the crack length exceeds 20 angstrom. This value is comparable with the fracture toughness of graphite and silicon. The fracture resistance of the tubes is found to decrease significantly as the temperature increases. To study the length effects, the computations are repeated for zigzag nanotubes with the same three chiralities but with aspect ratio 8 at I K. The fracture resistances of the longer nanotubes are found to be comparable to those of the shorter nanotubes.
