Page 199 - Carbon Nanotube Fibres and Yarns

Mechanics modeling of carbon nanotube yarns 189

yarn strength should be proportional to the length of the staple fiber, the
coefficient of static friction between staples, and the surface area of contact
between them [85,86].
Vilatela et al. pointed out that the contact area between adjacent CNTs
is determined by their degree of polygonization or collapse, which in turn
depends on their diameter and number of layers. Therefore, larger diameter
and thin-walled CNTs have a greater degree of contact, as determined by
continuum elasticity theory, MM, and image analysis of transmission elec-
tron micrographs. A direct experimental comparison study has also shown
that the double-walled (or few-walled, i.e., two- to four-walled) CNT yarns
exhibited the best mechanical properties [30]. The axial stress in the CNTs
is built up by stress transfer between adjacent CNTs through shear and is
thus proportional to CNT length, as supported by data in the literature for
CNT fibers produced by different methods and research groups. A tensile
strength of 3.54 N/tex was predicted for an aerogel-spun CNT yarn, and
higher values (~5 N/tex) can be expected by more precise process con-
trol and the possibility of post-processing operations to enhance the shear
strength of the intertube contacts.

8.2.4 Monte Carlo model
There have been other theoretical models to exhibit the predominant
mechanisms of yarn failure, including Daniels’ model [84] that treated the
yarn as a bundle of parallel fibers and Hearle’s model [77] that included
the effects of fiber length, twist angle, and fiber migration. Porwal et al.
extended Daniels’ model and developed a Monte Carlo (MC) model to
predict the statistical strength of a twisted yarn using a twist-modified equal
load sharing rule [87]. Such model took into account the statistical distri-
bution of fiber strength and simulated fiber break initiation and progression
for a yarn under tension. Later, this model was adopted to predict the me-
chanical strength of CNT yarns by designing the load sharing rule [88,89].
These models usually simplify the interfacial interactions into a static fric-
tion law that requires a transverse pressure on fibers to cause load transfer.
However, there also exists inconsistency between the model prediction and
experimental observation, especially the load-transfer capability is misde-
scribed in the model as it always increases linearly when the overlap distance
increases [90]. To solve this problem, Wei et al. suggested a new MC model
for predicting the yarn mechanical properties [91].
Fig. 8.3 shows the schematics of a twisted yarn consisting of fibers in
a hexagonal close-packing structure [91]. Here a fiber refers to a bundle
consisting of 60–100 CNTs, and the axial positions of individual fibers