Page 255 - Handbook of Properties of Textile and Technical Fibres

Tensile properties of cotton fibers: importance, research, and limitations 229

the extension of a cotton fiber at low stresses. Nevertheless, the authors indicated that a
full mechanical analysis of a convoluted ribbon, with fibrils following distorted and
flattened helical paths, would be difficult. To simplify the problem, they separated fiber
extension into two parts: (1) the strain due to deconvolution; and (2) the strain due to
the extension of a freely untwisting helical assembly, assumed for simplicity to be
circularly cylindrical, solid, and of constant helix angle. Obviously, the cotton fiber
is never circular as it always exhibits a flattened geometry. The authors admitted
this gross assumption. They also indicated that their analysis ignores several factors
due to their insignificant effect on the extension behavior. These factors include: (1)
any contribution from the primary wall; (2) any effect of the changes in helix angle,
which occurs through the secondary wall; (3) any specific localized strains at the
reversal points; (4) any effect of the residual lumen; (5) any effect of the disturbance
of the fine structure on collapse of the fiber; (6) and any differences from a fine
structure, which is assumed to consist of crystalline cellulose oriented perfectly along
the helical lines. Considering this study, the total fiber strain, ε T , at the time of fracture
is represented by the following simple equation:
ε T ¼ ε s þ ε c

where ε s is the strain resulting from changes in the fibrillar structure, and ε c is the strain
from the deconvolution effect. The strain from the deconvolution effect was expressed
by the following equation:
2
ε c ¼ X tan u o
where u o is the convolution angle, and X is a geometrical factor ranging from 0.5 to
1.0. This equation describes the increase in the strain from the deconvolution due to the
increase in the convolution angle.
As indicated earlier, cotton fiber is tapered on one end and fibrillated on the other
end where it is joined to the seed. A lower convolution angle can be seen at the tip than
at the root of the fiber (a difference reaching 175% within a fiber), and a lower surface
area at the tip than at the root. The differential surface effect resulting from this feature
is likely to influence the single-fiber strength, as it will result in a failure point along the
single fiber that is largely unpredictable. To the knowledge of the author, this point was
never addressed in previous studies. In the case of bundle strength testing, the differ-
ential surface effect may be reduced by the random pick of the bundle sample. It was
also indicated that within a given fiber, the birefringence index increases from the tip
(0e0.008) to the root of the fiber (above 0.04). This change in molecular orientation
from the tip to the fiber root suggests that when a fiber is broken during processing at
some points along its length, we could have two fiber fragments with substantially
different tensile behaviors, with the fragment closer to the fiber root being stronger
than the one near the fiber tip. The relationship between birefringence and fiber
tenacity has been examined in many studies. One investigation (Foullc and McAlister,
2002) revealed a significant correlation between tenacity and birefringence with an
increase from 20 cN/tex at a birefringence of 0.04 to 37 cN/tex at 0.05. The definitions
of tex and tenacity are given later in this chapter.