Yarn structure plays a key role in determining the yarn physical properties and the performance characteristics of yarns and fabrics. The best way to study the internal structure of the yarns is to examine the arrangement of single fibers in the yarn body, and analyze their migration in crosswise and lengthwise fashions. This requires visual observation of the path of a single fiber in the yarn. Since a fiber is relatively a small element some specific techniques have to be utilized for its observation. In order to perform this task, two different experimental techniques have been developed by previous researchers.
a. Tracer fiber technique: This technique involves immersing a yarn, which contains a very small percentage of dyed fibers, in a liquid whose refractive index is the same as that of the original undyed fibers. This causes the undyed fibers to almost disappear from view and enables the observation of the path of a black dyed tracer fiber under a microscope. Dyed fibers are added to the raw stock before spinning to act as tracers. This technique was introduced by Morton and Yen .
b. Cross sectional method: In this method first the fibers in the yarn are locked in their original position by means of a suitable embedding medium, then the yarn is cut into thin sections, and these sections are studied under microscope. As in the tracer fiber technique, the yarn consists of mostly undyed fibers and a small proportion of dyed fibers such that there is no more than one dyed fiber in any yarn cross-section.
Fiber migration can be defined as the variation in fiber position within the yarn. Migration and twist are two necessary components to generate strength and cohesion in spun yarns. Twist increases the frictional forces between fibers and prevents fibers from slipping over one another by creating radial forces directed toward the yarn interior while fiber migration ensures that some parts of the all fibers were locked in the structure.
It was first recognized by Pierce that there is a need for the interchange of the fiber position inside a yarn since if a yarn consisted of a core fiber surrounded by coaxial cylindrical layers of other fibers, each forming a perfect helix of constant radius, discrete layers of the yarn could easily separate. Morton and Yen discovered that the fibers migrate among imaginary cylindrical zones in the yarn and named this phenomenon “fiber migration.”
Mechanisms Causing Fiber Migration
Morton  proposed that one of the mechanisms which cause fiber migration is the tension differences between fibers at different radial positions in a twisted yarn. During the twist insertion, fibers are subjected to different tensions depending on their radial positions. Fibers at the core will be under minimum tension due to shorter fiber path while fibers on the surface will be exposed to the maximum tension. According to the principle of the minimum energy of deformation, fibers lying near the yarn surface will try to migrate into inner zones where the energy is lower. This will lead to a cyclic interchange of fiber position. Later Hearle and Bose gave another mechanism which causes migration. They suggested that when the ribbon-like fiber bundle is turned into the
Apart from the theoretical work cited above, several experimental investigations have been carried out during 1960’s to find out the possible factors affecting fiber migration. Results showed that the fiber migration can be influenced mainly by three groups of factors:
q fiber related factors such as fiber type, fiber length, fiber fineness, fiber initial modulus, fiber bending modulus and torsional rigidity;
q yarn related factors, such as yarn count and yarn twist ; and
q processing factors such as twisting tension, drafting system and number of doubling.
Methods for Assessing Fiber Migration
To study fiber migration Morton and Yen introduced the tracer fiber method. As explained in the previous section, this method enables the observation of the path of a single tracer fiber under a microscope. In order to draw the paths of the tracer fibers in the horizontal plane, Morton and Yen made measurements at successive peaks and troughs of the tracer images. Each peak and trough was in turn brought to register with the hairline of a micrometer eyepiece and scale readings were taken at a, b, and c as seen in Figure 22. The yarn diameter in scale units was given by c-a, while the offset of the
peak or trough, the fiber helix radii, was given by
The distance between
adjacent peaks and troughs was denoted by d. The overall extent of the tracer fiber was obtained from the images, as well. Morton and Yen concluded that in one complete cycle of migration, the fiber rarely crosses through all zones of the structure, from the surface of the yarn to the core and back again, which was considered as ideal migration.
Later Morton  used the tracer fiber method to characterize the migration quantitatively by means of a coefficient so called “the coefficient of migration.” He proposed that the intensity of migration i.e., completeness of the migration, or otherwise, of any migratory traverse could be evaluated by the change in helix radius between successive inflections of the helix envelope expressed as the fraction of yarn radius. For example intensity of migration in Figure 23 from A to B was stated as
where rA and rB are helix radius at A and B, respectively and R is yarn radius.
In order to express the intensity of migration for a whole fiber, Morton used the coefficient of migration, which is the ratio of actual migration amplitude to the ideal case. The coefficient of migration was given by
Merchant [ 1 ] modified the helix envelope by expressing the radial position in terms of (r / R) in order avoid any effects due to the irregularities in yarn diameter. The plot of (r / R) along the yarn axis gives a cylindrical envelope of varying radi
us around which the fiber follows a helical path. This plot is called a helix envelope profile. Expression of the radial position in terms of (r / R) involves the division of yarn cross sections into zones of equal radial spacing, which means fibers present longer lengths in the outer zones. Hearle et al.  suggested that it is more convenient to divide the yarn cross sections into zones of equal area so that the fibers are equally distributed between all zones. This was achieved by expressing the radial position in terms of (r / R)2, and the plot of (r / R)2against the length along the yarn is called a corrected helix envelope profile which presents a linear envelope for the ideal migration if the fiber packing density is uniform (Figure 24). The corrected helix envelope profile is much easier to manage analytically.
In 1964 Riding  worked on filament yarns, and expanded the tracer fiber technique by observing the fiber from two directions at right angles by placing a plane mirror near the yarn in the liquid with the plane of the mirror at 45° to the direction of observation. The radial position of the tracer fiber along the yarn was calculated by the following equation:
where x and y are the distances of the fiber from the yarn axis by the x and y coordinates; and dx and dy are the corresponding diameter measurements.
Riding also argued that it is unlikely that any single parameter, such as the coefficient of migration will completely characterize the migration behavior due to its statistical nature. He analyzed the migration patterns using the correlogram, or Auto-correlation Function and suggested that this analysis gives an overall statistical picture of the migration. Riding calculated the auto-correlation coefficient, rs from a series of
values of r / R for a separation of s intervals and obtained the correlogram for each experiment by plotting rs against s. Later a detailed theoretical study by Hearle and Goswami showed that the correlogram method should be used with caution because it tends to pick up only the regular migration.
Hearle and his co-researchers worked on a comprehensive theoretical and experimental analysis of fiber migration in the mid 1960’s. In Part I of the series Hearle, Gupta and Merchant came up with four parameters using an analogy with the method of describing an electric current to characterize the migration behaviors of fibers.
These parameters are:
i. the mean fiber position, which is the overall tendency of a fiber to be near the yarn surface or the yarn center.
ii. r.m.s deviation, which is the degree of the deviation from the mean fiber position
iii. mean migration intensity, which is the rate of change in radial position of a fiber.
iv. equivalent migration frequency, which is the value of migration frequency when an ideal migration cycle is formed from the calculated values of I and D.
r is the current radial position of the fiber with respect to the yarn axis;
R is the yarn radius;
n is the number of the observations; and
Zn is the length of the yarn under consideration
By expressing the migration behavior in terms of these parameters, Hearle et al. replaced an actual migration behavior with a partial ideal migration which is linear with z (length along the fiber axis) but has the same mean fiber position, same r.m.s deviation, and the same mean migration intensity.
Later Hearle and Gupta  studied the fiber migration experimentally by using the tracer fiber technique. By taking into consideration the problem of asymmetry in the yarn cross section they came up with the following equation:
r1 and r2 are the helix radii
R1 and R2 are the yarn radii at position z1 and z2 along the yarn.
In 1972 Hearle et al. carried some experimental work on the migration in open-end spun yarns, and they observed that migration pattern in open-end yarns was considerably different from that of ring spun yarns. They suggested that this difference was the reason for the dissimilarity between mechanical and structural parameters of these two yarns.
Among numerous investigations of migration, there have been some attempts to develop a numerical algorithm to simulate yarn behavior. Possibly the most promising
and powerful approach was to apply a finite element analysis method to the mechanics of yarns.
One of the most recently published researches on the mathematical modeling of fiber migration in staple yarns was carried out by Grishanov, et al. They developed a new method to model the fiber migration using a Markov process, and claimed that all the main features of yarn structure could be modeled with this new method. In this approach the process of fiber migration was considered as a Poisson’s flow of events, and the fiber migration characteristics were expressed in terms of a transition matrix.
Another recent study was done by Primentas and Iype. They utilized the level of the focusing depth of a projection microscope as a measure of the fiber position along the z-axis with respect to the body of the yarn. Using a suitable reference depth they plotted the possible 3-dimensional configuration of the tracer fiber. In this study they assumed that yarn had a circular cross section and the difference between minimum and maximum values in depth represented the value of the vertical diameter, which was also equal to horizontal diameter. However, the yarn is irregular along its axis, and its cross section deviates from a circle. Besides, it is questionable that the difference between minimum and maximum values in depth would give the value of the vertical diameter. As these researchers stated this technique is in the “embryonic stage of development.”