Page 284 - Carbon Nanotube Fibres and Yarns

Carbon nanotube yarn-based actuators 273

(Q t ) is an extremely large component of the yarn torque that can amount
to more than 90% of the total torque of the yarn [25]. The yarn torque due
to fiber tension can be expressed as
r π 3
Q = E ε tan θ (11.3)
t
2 f y
where E f is the tensile modulus of the fiber, ε y is the tensile strain of the
yarn, θ is the surface helix angle of the yarn (twist angle), and r is the yarn
radius. In the case of CNT yarns, the nanotube diameter is about three or-
ders of magnitude smaller than the yarn diameter, so the yarn torque may be
considered to be derived totally from the tension of the nanotubes.

11.2.3 Cylindrical coils or snarls formed from excessively
twisted yarns
Under the twist level commonly encountered in textile processes, the yarn
axis maintains a straight line. When the twist in the yarn is increased and
thus yarn torque becomes excessively high in relation with the tension ap-
plied to the yarn, local instability occurs, thereby the straight yarn axis jumps
to assume a curved shape, a phenomenon known as localized writhing [26].
This distorted yarn structure is known as a snarl in the textile industry.
Depending on the twist introduced to the yarn and the tension applied
to the yarn, two types of snarls can be formed. The more common type of
snarl, which is formed at relatively low twist and tension, is the side snarl
in the form of a two-ply yarn loop standing perpendicular to the original
yarn axis (Fig. 11.1A). The other type of yarn snarl assumes a spring-like
cylindrical coil parallel to the direction of the original yarn axis, as shown
in Fig. 11.1B. The cylindrical snarl is formed at much higher twist and ten-
sion than the side snarl. Snarls are normally considered to be faults in textile
processing as they block the smooth passage of the yarn through processing
machines, although purposely produced snarls can be made into a visual
feature for fashion garments [27] and have also been utilized to provide
stretch in false-twist texturized thermoplastic filament yarns [28].
The conditions for the onset of side snarling of twisted elstatic rods and
yarns, known as torsional instability in mechanics of materials or writhing
in knot theory, have been studied by many researchers [26, 29–36]. The
mechanical conditions to form the cylindrically coiled snarls, which are
particularly relevant to the artificial muscles reviewed hereafter, were stud-
ied by Hearle and Yegin [37] and Ghatak and Mahadevan [38]. These studies
focused on predicting the onset of snarling, that is, conditions triggering a