Page 23 - Handbook of Properties of Textile and Technical Fibres

4 Handbook of Properties of Textile and Technical Fibres

As force/(cross-section) is the engineering definition of stress, it can be seen that
strengths given in textile units are related to engineering units through the density
of the fibers.

1.3 Fineness and flexibility

An obvious characteristic of fibers is their flexibility. Their ability to bend is the basis
of the drapeability of cloth and this is important not only in textile applications but also
in many other manufacturing processes involving fibers. Most fibers are stiff in ten-
sion; some synthetic fibers are several times stiffer than steel and some natural fibers
can be half as stiff as glass, yet they can still be flexible. That means that they can be
woven, knitted, or transformed in any number of the ways that the textile industry has
developed. In order to understand this characteristic, consider the factors that govern
stiffness in bending. For that consider a simple elastic beam, fixed horizontally at one
end, as shown in Fig. 1.1. If it is thin enough we will be able to see it bending under its
own weight. Alternatively we could apply a load to make it deflect from the horizontal.
The question is how does the flexibility of the beam vary when we alter its thickness?
As the beam bends, its lower concave side is being put into compression whereas
the upper convex side is being stretched and experiences tension. There is a neutral
axis where the stresses are zero. If the beam is made of an elastic material this neutral
0
axis will be at the midsection C C. If we consider a small deflection, we can write

C C ¼ rq
0
0
Consider the line D D, parallel to but some way from the neutral axis. As is depicted
in Fig. 1.1, the material is being stretched and its length is
0
D D ¼ðr þ SÞq

D'
C'
D
C
S
ρ
θ

Figure 1.1 Consider a horizontal beam, representing a fiber, fixed at one end. It bends under its
own weight.