Page 49 - Fiber Fracture

34 M. Elices and J. Llorca

the basic structural unit. They are the building blocks of multi-wall nanotubes, contain-
ing several coaxial cylinders of increasing diameter about a common axis, and nanotube
ropes, consisting of ordered arrays of single-wall nanotubes.
Carbon nanotubes are dealt with in detail in the final paper of this book. It suffices
to underline that experimental measurements of fracture loads agree quite well with
theoretical predictions. Large-scale molecular dynamic simulations were used by J.
Bernholc and collaborators (Bernholc, 1999, and references in paper by Bernholc et
al., this volume) to study the response of carbon nanotubes to a tensile load. Plastic or
brittle behaviours can occur depending upon the external conditions and tube symmetry.
These simulations uncovered the dominant strain release mechanisms as well as their
energetics; beyond a critical value of the tension, the nanotube releases part of its stored
energy via formation of defects. Static calculations show that such defects should appear
at strains of about 0.05 and act as nucleation centres for the formation of dislocations
in the ideal graphite network and can lead to plastic behaviour. Nevertheless, if brittle
fracture is triggered, nanotube rupture at this strain may occur at a tensile stress of 62
GPa, a value assuming a linear stress-strain behaviour with a Young modulus of 1250
GPa for single-walled nanotubes (Krishnan et a]., 1998).
Recently R.S. Ruoff and collaborators (Yu et al., 2000) measured the mechanical
response of 15 single-wall carbon nanotube fibres under tensile load. In 8 of these
fibres, strain data were obtained; they broke at strain values of 0.053 or lower. Assuming
that the load acting on the nanotube (ranging from 400 to 1300 nN) is carried on the
perimeter, tensile stresses ranging from 13 to 52 GPa were obtained. These results add
confidence in atomic models of fibre fracture although in this particular example a great
part of the success is due to its being simpler to model a perfect nanotube than a bundle
of polymer fibres with defects.
Similar results apply to BN nanotubes (Chopra and Zettl, 1998) where Young’s
modulus has been measured at 1200 GPa, consistent with theoretical estimates. These
values suggest maximum tensile stresses of about 60 GPa for single-wall boron nitride
nanotubes.
Graphite whiskers can also be considered another example of a two-dimensional
strong bonded structure, because they consist of concentric tubes, or rolled-up sheets of
graphite layers, extending along the length of the whisker. The degree of alignment of
these graphitic layers depends on the precursor used and on the processing technique.
The highest stress recorded for a graphite whisker in tension appears to be 20 GPa
(Bacon, 1960), whereas tensile stresses for commercial high-performance fibres are
about 3 or 4 GPa. Only the polyacrylonitride (PAN)-based fibre, designated T-1000 by
Toray, exhibits a tensile stress of 7 GPa (Fitzer and Frohs, 1990). These discrepancies
are due to lack of alignment of the graphite layers and the presence of bubbles, holes and
other defects that initiate tensile failure. Fig. 4 adds further support to this reasoning,
showing a large increase in tensile stress as defects are reduced, when fibre diameters
decrease, or gauge length decreases. Carbon fibres are considered in detail in the paper
by Lavin in this volume.