Page 261 - Handbook of Properties of Textile and Technical Fibres

Tensile properties of cotton fibers: importance, research, and limitations 235

7.6 Tenacity or specific stress of cotton fibers

This is the breaking load in cN divided by the linear density of fiber expressed in tex.
The tex is the mass of 1000 m of the fiber expressed in grams.

Load at break
Tenacity ¼ s s ¼ cN=tex
Linear density ðtexÞ

Typical values of cotton fiber linear density or what is commonly known as fiber
fineness may range from about 130 mtex for very fine fibers to more than 230 mtex
for coarse fibers.
In fiber research, the term “tenacity” is replaced by the term “specific stress, s s .”
This is a unique term that material engineers are not commonly familiar with. Indeed,
many engineers outside the fiber and polymer research area are unaware of the
possibility that tensile stress can be expressed in terms of load per unit of linear density
(or mass per unit length). The engineering stress (cN/cm (Elmogahzy, December,
2015)) is expressed by the following equation:

Load at break F 2
Engineering stress ¼ s e ¼ ¼ cN=cm
Cross sectional area A o
The principle, underlying the use of specific stress instead of the engineering stress,
stems from the difficulty of determining the area of fiber cross section, A o , required to
calculate the engineering stress. A typical textile fiber is not a solid cylinder as shown
in Fig. 7.6, and the cotton fiber is certainly far from taking a cylindrical shape because
of its twisted ribbon shape along the length of the fiber and the kidney-shaped cross
section. Furthermore, the tapered geometry of the cotton fiber clearly indicates that
the fiber thickness varies along the fiber length. These factors make it difficult to
use engineering stress to determine cotton fiber tensile strength. It should be pointed
out, however, that the engineering stress can be roughly estimated from the specific
stress for any fiber if the volumetric density of fiber, r, is constant and of a known
value.
Table 7.1 provides some useful terms and conversion constants of fiber tenacity. A
typical value of cotton fiber strength may range from 20 to 40 cN/tex. These values are
significantly higher than those for wool fibers which are typically in the range
12e20 cN/tex and substantially lower than polyester fibers which are typically in
the range 35e60 cN/tex.

7.7 Breaking elongation (strain)

Breaking elongation (or breaking strain) is the percentage of elongation at break:

E at break ¼ 100ðDL break =L o Þ