Page 267 - Handbook of Properties of Textile and Technical Fibres

Tensile properties of cotton fibers: importance, research, and limitations 241

cylindrical wire or a circular fiber of known dimensions. However, this kind of
calibration sample is far from simulating the ribbonlike cotton fiber, and there is no
easy way to calibrate for initial crimp in the sample.
In light of the above discussion, it follows that the two methods of testing cotton
fiber strength, namely the beard test and the single-fiber test will remain equally impor-
tant, but incomparably performed. This issue raises a great deal of questions about the
type of information provided by each method and the possible relationship between
them. On one side, many researchers agree on the fact that single-fiber strength test
is more descriptive of the inherent tensile behavior of cotton fiber than the bundle
strength. On the other side, beard strength test seems to receive wide acceptance in
the cotton market. The logical question at this point is that if the single-fiber strength
indeed describes the inherent tensile behavior of cotton fiber, how is this behavior is
manifested in the bundle strength? And what is the relationship between single-fiber
strength and bundle strength? These questions were addressed in many studies; unfor-
tunately, with limited success, and with few relationships developed in these studies,
that cannot be generalized because of their poor reliability and their overlooking of key
parameters. This is not, by any means, the fault of the researcher; it is largely because
of the fact that the relationship between single-fiber strength and bundle (or fiber
assembly) strength can be best described as “physical, geometrical, structural, and
stochastic relationship.”
Since the original work by Peirce in 1926 on the strength of fiber assemblies, and
the outstanding follow-up seminal review-cum-research article on the statistical theory
of fiber-bundle strength, by Daniels in 1945, the comparison between single-fiber
strength and bundle strength has been in the center of research interest by many inves-
tigators. Indeed, the problem of integrating the strength of individual fibers to yield a
total bundle strength is known as the “fiber bundle model theory,” and it is often
referred to as one of the complex problems in physics. In a recent book by Hansen
et al. (2015) titled: The Fiber Bundle Model: Modeling Failure in Material and
published in 2015, the authors explained the reasons for the high interest in fiber
bundle models in the field of physics as being a result of “their deceivingly simple
appearance coupled with an extraordinary richness of behaviors.” Indeed, a first
look at the problem would provide a sense of simplicity as it would seem like a
problem of parallel rods being gripped at their two ends and pulled to breakage,
leading to a simple distribution of load sharing by the individual rods. Unfortunately,
the problem is far more complex than this simple view, and when cotton is the fiber
of interest, the fiber bundle model will represent the ultimate challenge even by a
combined effort of engineers, physicists, and statisticians.
In cotton research, the common approach to developing relationships between
single-fiber strength and bundle strength of cotton fibers has been to develop empirical
relationships based on actual values of fiber strength. Unfortunately, textile and fiber
researchers are not necessarily statisticians; you add this fact to the widespread
availability of advanced computation techniques and commercial statistics software
programs, and you may have a serious problem in hand. Most empirical relationships
between bundle strength and single-fiber strength have been performed using simple or
multiple regression analysis. These are valid techniques for developing empirical