Fiber Bending and Torque in a Yarn
For textile structures, bending is involved not
only in their forming processes, but actual use
conditions may include various modes of bending
motion. For instance, when a rope is stretched,
the yarn deformation not only includes tensile,
but also bending and torsional deformations because
of the helical orientation of the fibers. Thus,
bending effects have been an active research area
for many years and good progress has been
achieved in several studies; for instance, early
work by Backer in yarn bending geometry,
Platt in calculating yarn bending rigidity, and
Zorowski and Chen in frictional constraints.
Kim and coworkers investigated the bending
properties of monofilaments at large bending deformation
(beyond yielding) and considered the
filaments to be elastic–plastic. Wu et al.13 studied
the rope behavior as a bending field superimposed
on a tension strain field. Marine ropes are usually
subjected to bending by virtue of geometric constraints
such as eye splice terminations or looping
on a pin, or running through pulleys and blocks.
Twisting a yarn is very different from twisting
a solid shaft. “The linear elastic analysis of twisting
a rod to a small strain reveals that the primary
mode of deformation of the rod material is
that of pure shear. However, when a yarn is
twisted, there is no significant resistance to the
fibers that lie parallel in the yarn simply sliding
past each other in the direction of the fibers. In
other words, there is virtually no resistance to
immediate and catastrophic shear failure. Resistance
to twisting is very low in any case and it
only builds up significantly at large strains.”