Chemistry Reference
In-Depth Information
8.4.5
Flexibility in conductive fibres and yarns
Unlike textile fibres, many conductive fibres have a clear Young's modulus.
Consequently, Finlayson's equation for the flexibility of fibres can be essen-
tial in understanding the sewability of yarns made from conductive fibres
67
.
For instance, metal fibres in yarns may have a Young's modulus between 80
GPa (Au) and 200 GPa (steel). In contrast, a spider's dragline has a modulus
of 2.7-4.4 GPa and nylon a modulus of 3 GPa
67
.Finlayson makes an impor-
tant comparison between flexibility in fibres and the standard physics of
both the deflection of a cantilever beam under stress, and the bending
modulus of a beam supported in the center with deflected ends. Finlayson
derives this equation for inherent filament and fibre flexibility from the
equation for deflection in a cantilever beam loaded at the end. Note that
this equation has some unusual notation:
FlR
W
3
=
()
f
f
[8.1]
E
4
where
f
is the deflexion,
l
is the length of cantilever, E is Young's modulus
of fibre (isotropic material),
F
is the applied load modulus,
R
is the
eccentricity of cross section, or major axis width/minor axis width, and
W
is the average diameter.
According to Finlayson, this demonstrated that the flexibility of a
filament is directly proportional to its flatness, as measured by the ratio of
major to minor axis of the elliptical cross section, and is inversely propor-
tional to its elasticity and the fourth power of its diameter. Although the
equation describes the flexibility of individual fibres, it can also be relevant
for yarns. Yarns are composite materials made from the twisting of fibres,
which are held together by the forces between these fibres. As a yarn is
tensioned, these fibres slide past each other allowing strain in the yarn to
occur. This strain is non-Hookian and anisotropic. The twist of most yarns
imparts a far more complex geometric and mechanical relationship
between fibres. The movement of fibres during the straining of a yarn may
render the stiffness of the individual fibres irrelevant to overall fabric and
yarn stiffness
68
.
The width and shape of non-textile fibres is also significant to its flexi-
bility. In general, textile fibre widths can vary from 15 mm in fine cotton, to
50 mm for ramie. Wool fibres, which possess a width of 25 mm, a low tensile
strength, and a circular cross-section are far less flexible than cotton and
are therefore never used for machine sewing thread. Comparing wool with
the drawn stainless-steel fibres that are incorporated into yarns, stainless-
steel fibres have a diameter larger than 35 mm, and a generally circular cross
section. Thus, looking at the diameter, cross-sectional shape and Young's
modulus of stainless-steel fibres may lead to the assumption that these
