  Brittle fracture is one of the important failure modes of Single-Walled
Carbon Nanotube (SWNT) due to mechanical loading. In this paper, the fracture
resistance of zigzag SWNTs with preexisting defects is calculated using
fracture mechanics concepts based on atomistic simulations. The problem of
unstable crack growth at finite temperature, presumably caused by lattice
trapping effect, is circumvented by computing the strain energy release rate
through a series of displacement-controlled tensile loading of SWNTs (applied
through moving the outermost layer of atoms at one end at constant strain rate
of 9.4x10-4/ps) 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{\AA} long. The
fracture resistance, Gc, is determined as a function of crack length for each
tube at three different temperatures (1K, 300K and 500K). A significant
dependence of Gc on crack length is observed reminiscent of the rising R curve
behavior of metals at the macroscale: for the zigzag nanotubes Gc 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
Kelvin, Gc for the (35,0) tube with aspect ratio 4 converges to 6 Joule/m2 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 1K.
