  While CNTs are found to have ultra high stiffness and strength, an enormous
scatter is also observed in available laboratory results. This paper studies
the effects of randomly distributed Stone Wales (SW or 5 7 7 5) defects on the
mechanical properties of single walled nanotubes (SWNTs) using the technique of
atomistic simulation (AS). A Matern hard core random field applied on a finite
cylindrical surface is used to describe the spatial distribution of the Stone
Wales defects. We simulate a set of displacement controlled tensile loading up
to fracture of SWNTs with (6,6) armchair and (10, 0) zigzag configurations and
aspect ratio around 6. A modified Morse potential is adopted to model the
interatomic forces. We found that fracture invariably initiates from a defect
if one is present; for a defect-free tube the crack initiates at quite random
locations. The force-displacement curve typically behaves almost linearly up to
about half way, although there is no obvious yield point. Three mechanical
properties - stiffness, ultimate strength and ultimate strain - are calculated
from the simulated force and displacement time histories. The randomness in
mechanical behavior resulting only from initial velocity distribution was found
to be insignificant at room temperature. The mean values of stiffness, ultimate
strength and ultimate strain of the tube decrease as the average number of
defects increases although the coefficients of variation do not show such
monotonic trend. The introduction of an additional defect has the most
pronounced effect on the randomness in mechanical properties when the tube is
originally defect free. We also found that, for a given mean number of defects
in the tube, the zigzag configuration has less strength and less ultimate
strain on the average, but more uncertainty in its stiffness and ultimate
strain, compared with the armchair tube.
