Page 197 - Carbon Nanotube Fibres and Yarns

Mechanics modeling of carbon nanotube yarns 187

critical value. Such treatment led to the prediction of two strength peaks at
α ≈ 15–20 degrees and >30 degrees, in agreement with their experimental
results [29]. This model can be used to calculate the contribution of each
layer of CNTs to the yarn strength. The radial pressure deep inside a CNT
yarn is usually smaller than that near the yarn surface, in other words, the
outer layers shield the yarn interior (“arch effect”). This was also substanti-
ated by evidences from the yarn forming process [81].

8.2.2 Two-scale damage mechanics model
The above treatment is a rough model as it only extends the basic yarn ge-
ometry to include the radial compression inside the yarn. The model cannot
be used easily to predict the tensile behaviors of CNT yarn, such as the
plastic deformation and failure elongation. Rong et al. [82] used a two-scale
damage mechanics model to quantitatively investigate the effects of twisting
on the mechanical properties of CNT yarns. They divided the component
CNTs into two scale levels: CNT bundles that are twisted to form the yarn
and amorphous CNT “threads” that exist in the spaces between the bundles.
CNT threads refer to CNT groups that are much smaller than the CNT
bundles. Upon tensioning, the CNT bundles bear most of the loads, while
the amorphous CNT threads act as imperfect interfaces between the bundles
for transferring shear stresses. Such treatment is reminiscent of the model
used to describe dry-drawing of CNT sheet from a CNT forest, where the
large-sized bundles are connected by smaller bundles or individual nano-
tubes [83]. In the forest, the density of the small bundles plays a key role in
determining the spinnability of a CNT forest. With increasing strain, more
and more CNT threads are stretched and thus start to bear tensile stress. In
the two-scale model, a CNT yarn is assumed to consist of N CNT bundles
with a twist angle θ, in which n bundles have initiated damage. By summing
up the contributions of these different bundles and adjusting the fractions of
damaged bundles during tensioning, the elastic- and plastic-like behaviors of
CNT yarns can be obtained. This treatment, although rather complicated,
can reasonably well describe the tensioning process with the introduction of
damage to CNT bundles.

8.2.3 Fracture model based on intertube contacts

The above two-scale damage mechanics model does not fully consider the
intertube contact and shear strength, which are the most important factors
in determining the yarn’s mechanical properties. Vilatela et al. [21] proposed