Page 270 - Handbook of Properties of Textile and Technical Fibres

244 Handbook of Properties of Textile and Technical Fibres

7.11.5 Key points on the relationships between bundle strength
and single-fiber strength of cotton fibers
Covering the fundamental aspects of the fiber-bundle problem is outside the scope of
this chapter due to the immense contents of the subject. Nevertheless, it will be useful
to briefly point out some of the theoretical and experimental challenges associated with
the problem with the hope to encourage young researchers to work on this outstanding
subject. In an unpublished report by Dr. Elmogahzy, the essences of the fiber bundle
problem were simplified in the following points:
• A cotton fiber bundle (whether in parallel or twisted array) essentially consists of hundreds or
thousands of single fibers that are typically selected from a much larger population of fibers
that may amount to billions or trillions of fibers. When a characteristic of a single fiber is
compared to the corresponding characteristic in a fiber bundle, the biggest obstacle facing
the comparison is essentially a statistical one. The point here is that “variability represents
the primary challenge in dealing with the cotton fiber bundle model.”
• In fiber-bundle strength tests, the bundle or the fiber beard is typically weighed, and a standard
weight is used. This simple fact creates an automatic strength bias to fiber bundles consisting of
fine fibers as it will have higher number of fibers, more interfiber surface contact, higher fiber
entanglement, or cross-linking due to residual fiber crimp, and consequently, an increasing
contribution of the effect of interfiber friction. The point here is that “the validity of comparing
the bundle strength of fine fibers with that of coarse fibers often represents a hidden influential
factor in the relationship between bundle strength and single-fiber strength.”
• Depending on the sampling technique used and the population source, individual fibers in the
fiber bundle are likely to exhibit different values in all characteristics such as length, fineness,
maturity, inherent strength, and crimp level (particularly when different cotton varieties are
represented in the sample). The point here is “variability is multiplied by the interdependence
between fiber strength and other fiber characteristics.”
• Depending on the history of fiber processing (harvesting, ginning, opening, cleaning,
drawing, etc.), individual fibers in the bundle or the fiber assembly may exhibit hidden or
immeasurable mechanical and heat set imposed by the dynamic effects of the processing
machinery or the drying process. The point here is “there is a great deal of difficulty in
establishing a calibration reference for testing the single-fiber bundle strength and the
bundle-fiber elongation.” Indeed, the term “calibration samples” should be carefully viewed
as it often reflects what an instrument can recognize in a sample for computation purposes,
and not the physical reference of cotton fiber.
• Since the early work by Peirce (1926), it has been known that the way individual fibers share
the loading effects on a fiber bundle is quite complex. Fibers are assumed to be arranged in a
parallel array in the bundle; but fibers are also overlapping and may be entangled in such a
way that what is perceived as a contribution of a single fiber could be a contribution of a fiber
cluster. The point here is that “a single fiber automatically loses its independence once it is
placed in the bundle.”
• Although testing bundle strength at a zero or 1/8 in (3.175 mm) gauge length solves a great
deal of problems regarding the weak-link effect, it provides an artificial weak-link effect
represented by the random points between the two clamps, that may have little to do with
the true weak-link of the single fiber. The point here is that “in practice, a fiber breaks at
its true weak point along the fiber axis leading to random fragmentation of fibers during
processing, while the static loading of fibers applied during testing at a zero or 1/8 inch
(3.175 mm) gauge length represents a preinduced failure zone.”