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-controlled tensile loading of SWNTs (applied
through moving the outermost layer of atoms at one end at constant strain rate of
9.4 × 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 Å long. The fracture resistance,
Gc, is determined as a function of crack length for each tube at three
different temperatures (1, 300 and 500 K). A significant dependence of
Gc
on crack length is observed, reminiscent of the rising
R
curve behaviour 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 K,
Gc
for the (35, 0) tube with aspect ratio 4 converges to
6 J m−2 as the crack
length exceeds 20 Å. 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 1 K. The fracture resistances of the
longer nanotubes are found to be comparable to those of the shorter nanotubes.