Application of micro-computed tomography (micro-CT) to study unevenness of the structure of yarns

Abstract

A study was conducted on the structure of a single cotton yarn using micro-computer tomography (micro-CT). This article describes two important parameters determining the unevenness of yarn structure, i.e. the migration of staple fibers and packing density of staple fibers in the yarn cross-section. Relationships were found between the variation of staple fiber migration characteristics and the relationship between yarn durability and twist. For the boundary value, the radius and range of migration are the highest, and the variation coefficient of the fiber migration range is the lowest. The number of fibers in the yarn cross-section decreases with twist. Above the boundary twist value, the number of fibers in the yarn cross-section stabilizes at the value corresponding to the number of fibers in the boundary twist.

Keywords

micro-CT uneveness tomography fiber yarn fabric formation fabrication spinning production

Introduction

The first and simplest approximation of yarn structure involves the assumption that fibers are arranged according to an ideal helix with a fixed turn and radius.^1–3 In 1947, Peirce³ described a phenomenon whereby fibers exchanged positions within the yarn cross-section. A later study by Morton and Yen in 1952 using trace analysis⁴ indicated that fibers are not aligned ideally along parallel helices. Rather, they form spirals with varying turn and radius, assuming that fiber packing density in the yarn cross-section is constant. However, Morton and Yen’s assumption is also purely theoretical. Fiber migration occurs when fibers are twisted into a yarn. The fibers travel along a spiral throughout the length of the yarn. The radius of the spiral may range from 0 to 2R, where R is the yarn radius. Fibers must always be twisted under a particular initial stress. Differences in stresses between fibers located at varying distances from the yarn axis cause yarns to change their position relative to the yarn axis throughout the length of the yarn. Stretching stress is the highest in fibers located closest to the outer twist of the yarn and the lowest in the fibers located closest to the yarn axis. At the same time, neighbouring fibers exert a lateral stress that prevents the fibers located closest to the axis from straightening, causing them to buckle. The differences in stress between fibers located at varying distances from the yarn axis mean that fibers in the outer twist of the yarn exert the highest radial forces on other fibers. Consequently, they penetrate the yarn, pushing outwards those fibers that were previously located close to the yarn axis and were exposed to a lower principal stress than the fibers in outer twists. Fiber migration occurring during fiber twisting causes all of the fibers in a yarn to interlock to a lesser or greater extent (depending on the twist length and the distribution of the fiber lengths in the fiber stream).

Migration of staple fibers in the yarn

In 1962, Hearle and Merchant⁵ determined the factors affecting the extent of fiber migration. These factors comprise twist, fiber stress during twisting, length of twisting area (twisting cone), and the degree of entanglement between fibers before they are introduced to the twisting area. The research found that the migration intensity decreases with the increase in fiber stress during twisting and increases with the increase in the length of the twisting area. Hearle’s research indicated that if fiber stress during twisting becomes low enough, the fiber located closest to the yarn axis will form a loop. Furthermore, the central fiber will never undergo migration if it is exposed to any stretching stress. Only a lack of stretching stress can cause the central fiber to migrate to other values of the cross-section radius. In 1965, Hearle et al.⁶ determined what is referred to as equivalent migration (i.e. migration with a constant turn and varying radius). They described the phenomenon through the following function Z representing the length of the migration cycle, under the assumption that the fiber packing density in the yarn cross-section is constant

Z = 2 Q / (1 + \sec α) [mm]

(1)

where Q is the fiber length corresponding to a single migration cycle [mm], and α is the tilt angle of fibers on the surface of the yarn [deg.], and sec α is a trigonometric function, secant of angle α.

In 1965, Treloar⁷ published a model for the migration of filaments during their twisting into a yarn. Treloar assumed that the fiber packing density is even throughout the cross-section of the yarn. A comparative analysis was conducted concerning whether two models describing the resistance to stretching of a multifilament yarn conformed to experimental results. One model assumed that the distance between the filament and the yarn axis varied along the entire filament length, and the other model assumed that the filament formed a helix with a constant turn and radius. Both models were designed using the energy method and were tested for their experimental viability. Treloar reached the conclusion that filament fiber migration had no significant effect on the results obtained from the theoretical model of multifilament yarn durability. However, subsequent publications on the subject took into account the effect of fiber migration. A description of fiber migration should involve determining its period and amplitude. Treloar expressed the period of migration (P) as a function of yarn shrinkage

P = \frac{2 z}{R} (\frac{1}{1 - Ψ})

(2)

where P is the migration coefficient [dimensionless], 2z is the period of migration of fibers [mm], R is the radius of the yarn [mm], and Ψ is the yarn shrinkage coefficient [dimensionless].

The migration path can be expressed as where z is the axial coordinate defined along the axis of the yarn [dimensionless], R is the yarn radius [mm], ρ is the parameter determining the location of a fiber in the radial direction [dimensionless], and ρ = r/R, where r is the radial position; Ψ = 2πnR and n is the number of twists per unit of length of the yarn.

Treloar also defined regular and irregular migration. Regular migration occurs when fibers in the yarn show a varying alignment along the yarn axis and a constant migration period. Irregular migration occurs when fibers are aligned along a helix with a varying turn and a varying radius.

In a later study, Treloar and Riding’s⁸ description of filament migration took into account the three-dimensional character of the phenomenon, and introduced into the equation the initial angle between a filament and the x- and z-axes, and a parameter characterizing filament migration rate, i.e. the number of turning points of the filament system along the vertical coordinate. In other words, irregular migration (i.e. migration with a varying helix turn) was assumed. Treloar described the path of the filament during irregular migration through the function where δ is the angle allowing positioning the fibers in the x,y plane [deg].

This approach to the fiber path was tested experimentally. The test found a significant conformity between the theoretical course of the path and actual changes in filament position relative to the yarn axis. In 1996, Önder and Baser⁹ proposed a theoretical solution to the problem of fiber migration in order to develop a mathematical model of yarn durability. They described spirals formed by staple fibers as conical helix paths with a constant turn and a constant radius, the latter of which changes from 0 (i.e. from the yarn axis) to R (i.e. the maximal radius of the yarn). The path of the staple fiber in a cylindrical coordinate system was expressed as

d s = [d r 2 + r 2 \sin 2 θ d ϕ 2] \frac{1}{2}

(5)

ϕ is the angle of the fiber in relation to the horizontal plane [deg.].

d r = \frac{d z}{\cos θ}

(6)

As a consequence the migration path (s) can be calculated using

s = {\frac{z}{2 \cos θ} \sqrt{1 + (2 π T \sin θ z) 2} + \frac{1}{2 \cos θ (2 π T \sin θ z)} \times \ln | 2 π T \sin θ z + \sqrt{1 + (2 π T \sin θ z) 2}}

(7)

where θ is half the cone angle is formed by the fiber, where

θ = \tan - 1 (R / Z) = const

, where R is the radius of the yarn [mm] and Z is Q/2 [mm], where Q is the period of migration of the fibers. T is the number of twists per unit of length of the yarn.

In 1996, Tao¹⁰ characterized the irregular migration of staple fibers by expressing the coordinates x,y,z using the equations

x = R (ϕ) \cos ϕ, y = R (ϕ) \sin ϕ, z = \frac{h}{2 π} ϕ

(8)

where h is the height of the helix [mm], ϕ is the angle of the fiber referred to the horizontal plane [deg.], and R(ϕ) [mm] is a plan view that staggers the radius of the fiber in the horizontal plane

R (ϕ) = R_{min} + \frac{R_{max} - R_{min}}{2} (\cos \frac{h ϕ}{2 π λ} + 1)

(9)

where R_min [mm] is the minimum radius and R_max [mm] is the maximum radius that the fiber may have when creating a helix in the yarn. In other words, R_min is the closest end of one of the ends of the fiber to the axis of the yarn and R_max is the most distant end of one of the ends of the fibers to the axis of the yarn. The difference between R_max and R_min defines the amplitude of the helix, and 1/λ determines the frequency of migration.

Fiber packing density in the yarn cross-section

In 1988, Postle et al.¹¹ made the simplifying assumption that the function of staple fiber packing density in the cross-section of a yarn exposed to an initial stress should constitute a square function, with the yarn radius as the independent variable. Subsequently, the authors analyzed fiber migration under increasing stretching stress applied to the yarn, and formulated the hypothesis of the ‘shortest path,’ whereby staple fibers migrate towards the yarn core in accordance with the principle of stress minimization. As a result, the tightness and durability of the yarn structure increases as stretching progresses.

In 1988, Lee and Lee¹² suggested that if dL is the sum of fiber section lengths, the orientation of which ranges between the azimuth angle θ and θ + dθ and between the polar angle ϕ and ϕ + dϕ, and if L is the length of the yarn, then the function of fiber packing density in the cross-section should be described by

Ω (θ, φ) \sin θ d θ = \frac{d L}{L}

(10)

Solving this equation leads to the following form of the distribution of density of staple fibers packing in the cross-section of the yarn where q is the angle of inclination of the helix that is formed by the staple fibers on the surface of the yarn. In 1992, Pan¹³ and Ute and Kadoglu¹⁴ confirmed that the structure of the yarn is uneven and the density of packing of staple fibers in the cross-section of the yarn is low. As a consequence, it is assumed that the function of density distribution of staple fibers in the cross-section can be described by the directional orientation of the fibers in the yarn, by azimuthal and pole angles assigned to the Cartesian coordinate system

Ω (θ, φ) \sin θ = Ω_{0} \sin θ

(12)

where φ is an azimuthal angle having a value from 0 to π and θ is a pole angle equal to the helix angle of inclination of the fibers with respect to the longitudinal axis of the yarn. It takes values from 0 to q, where q is the angle of inclination of the helix. Ω₀ is a constant value that can be calculated using the equation

\int_{0}^{q} d θ \int_{0}^{π} d φ θ (θ, φ) \sin θ = 1

(13)

Solving this equation allows the description of $Ω_{0}$ as

Ω_{0} = \frac{1}{π (1 - \cos q)}

(14)

Application of this type of yarn structure description, and taking into consideration a mutual sliding of staple fibers in the yarn under tension, Pan assessed a mean value of deformation of a staple fiber as a function of deformation of a whole yarn. In 1993, in the course of further studies, he compared a real change in the packing densities of staple fibers in the cross-sections using three assumptions:

The density of packing of staple fibers in the cross-section of the yarn is constant (based on Hearle’s work in 1958¹⁵);

The density of packing of staple fibers in the cross-section of the yarn characterized by Lee and Lee in 1988;¹²

The density of packing of staple fibers in the cross-section of the yarn characterized by Pan in 1992.¹³

The results of comparison of the density of staple fibers in the yarn’s cross-section plotted as a function of the angle of the helix made of the staple fibers on the surface of the yarn has shown that there are significant differences in the course of these curves, when it assumes a constant packing density of fibers in cross-section (according to Hearle) or a variable density of fibers (according to Lee and Pan). In the case of the assumption of a constant function of density of fibers in the yarn cross-section, it was found that the actual density decreases with an increase of the angle of the helix that forms the staple fibers on the surface of the yarn (analyzing the different angles of the fibers on the yarn surface).

It has been found that in the case of the density of the fibers in the outer twists of the yarn, it remains unchanged with the increase in the angle of the helix that forms the staple on the surface of the yarn. After exceeding 90°, the density decreases rapidly to zero. Only in the value of the angle of inclination of the helix that forms the fibers are there no significant differences in the course of the two functions that describe the variable density of fibers in the yarn cross-section. However, the verification of the models of the density distribution of fibers in the yarn cross-section proved the existence of significant differences between the experimental results and the implementation of the model.

Tandon et al.¹⁶ described a torsion model for yarn, applying the so-called “energetic method” to characterize the phenomenon of migration of staple fibers in the yarn (calculation of the work required to stretch the yarn, bend it, and twist) under conditions of uneven distribution of fibers in the yarn’s cross-section. They distinguished four regions in a cross-section of the deformed yarn. In the external region of the yarn (number 1), the fibers are not subject to meaningful deformations. They are a distance from region number 4, where the fibers are fully jammed. In region number 3, the closest to the core, staple fibers are subject to compression and are fully fixed. The core of the yarn remains empty; however, this case only appears if the length of the axis of the deformed yarn is shorter than the initial length of its axis (contraction forces). The density function for the distribution of staple fibers in the core was a quadratic function in relation to the radius of yarn and was described in the form

φ_{j 0} = φ_{0} {1 - (r_{j 0} / R) 2} φ_{0} = 2 \bar{φ} = 2 tex / (π R 2 ρ_{f} 105)

(15)

where φ_j₀ is the density of packing of staple fibers in any cross-section of the yarn [fibers/surface],

φ_{0}

and

\bar{φ}

are the maximum and average value of density of packing of staple fibers in any cross-section [fibers/surface], respectively,

ρ_{f}

is the density of the fiber (the substance) [kg/m³], and R is the radius of the yarn [mm].

This model has been verified experimentally. Yarn cross-sections were divided into 50 concentric regions.

Van Langenhove¹⁷ and Mouckova and Jiraskova¹⁸ accepted uneven distribution of the staple fibers in the yarn’s cross-section, having regard to the existence of voids between fibers with a predetermined density function – the lowest density in the core of the yarn and in the outer twists. As a function describing the distribution of the density of fibers in the cross-section, an exponential function of the radius of the yarn was adopted, which was elaborated by linear regression.

Well-designed studies on the migration of fibers taking into account the fiber density function were carried out by Jeon and Lee¹⁹ in 2000. According to them a dimensionless density function P(ß) describes the dependence of the rate of two angles: the angle β, which determines the actual fiber orientation with respect to the longitudinal axis of the yarn, and the angle α, which is the nominal specified angle relative to the radial direction of the yarn; and the angle is the angle determined from the yarn surface.

It takes into consideration the migration of the fibers in the radial direction and in the direction of the longitudinal axis of the yarn and, as a consequence, a function of the density of the fibers’ orientation can be described as

P (β) = \frac{M_{h}^{2}}{tan 2 α M_{r}^{2}} \tan β \sec 2 β {1 \pm \frac{1}{\sqrt{1 - \frac{M_{r}^{2} tan 4 α}{4 π 2 M_{h}^{4} tan 4 β}}}}

(16)

where M_h = h/H is a dimensionless variable that describes the period of migration in the direction of the yarn axis; h is the height of the helix and H is the pitch of one turn of the twist.

It was concluded that the yarns with a lower nominal twist value are more actively ordered in the direction of the longitudinal axis of the yarn under the influence of tensile stress than yarns with a higher nominal twist value. The density function of the orientation of the staple fibers in the yarn is strongly correlated with the migration of the fibers in the longitudinal and transverse directions.

The motivation for this research was to investigate the relationships between the effect of twist on the parameters of migration of the staple fibers in the yarn, e.g. the effect of twist on the migration radius and the effect of twist on the staple fiber packing density, and to prove it using the most up-to-date existing methodology, which is micro-computer tomography (micro-CT) of the yarns.

Materials and methods

In order to learn more about the migration of the staple fibers that takes place during their twisting, five cotton yarns were produced, each of 25% ± 2.5% tex, having different nominal twist values: D1: 700 tpm; D2: 800 tpm; D3: 900 tpm; D4: 1000 tpm; and D5: 1100 tpm. The diameter of a single fiber was 1.2 × 10⁶m; the average length of the fibers was 0.02 m. The maximum length of a single fiber in the yarns was 0.037 m, and the minimum length was 0.003 m. The linear density of the yarns was measured according to ASTM D1577 Standard test methods for linear density of textile fibers.²⁰ Next, all of the yarns were subjected to micro-CT imaging in order to investigate in detail the phenomena taking place during the twisting process.

Micro-CT measurements were conducted using a SKYSCAN X-ray machine, SkyScan, model 1272, X-ray machine, Bruker Corporation Company, US. The source of radiation was an X-ray lamp set to a voltage of 35 kV and a current of 200 µA. Two sections, 5 mm and 20 mm in length, were analyzed from five samples of plied yarns. CT measurements of the samples were taken at the highest possible resolution of 2.5 µm (the size of a single pixel). Figure 1 presents the measurement setup (the yarn is held with a polymer foam clamp). Each measurement comprised nine partial scans that were later digitally combined.

Figure 1.

Photograph of the measurement setup for CT scans.

The micro-CT measurements were performed as a series of X-ray photographs taken at different angles ranging from 0° to 180°. The cross-sections of yarns were reconstructed based on the obtained images using the SkyScan NRecon computer program, Bruker Corporation Company, US. The reconstructed cross-sections (in 8-bit grayscale BMP images) were the basis for further processing and creating the 3D models. Table 1 shows detailed data concerning the number of scans performed for each sample with 5 mm and 20 mm sections.

Table 1.

Results obtained for the 5 mm and 20 mm cross-sections.

Sample no.	Number of pictures taken		Resolution (µm)
Sample no.	5 mm cross- section	20 mm cross- section	Resolution (µm)
D1_700	2000	7950	2.5
D2_800	2050	8000	2.5
D3_900	2010	8000	2.5
D4_1000	2100	8000	2.5
D5_1100	2070	8000	2.5

The reconstructed cross-sections were filtered and converted to binary format to allow the samples to be visualized in three dimensions. The Computed Tomography scan Analyser 1.13 (CTAn), Bruker Corporation Company, US, software program was used to create 3D models of the samples.

Figure 2 presents a cross-section of a cotton yarn, and Figures 3, 4, and 5 present longitudinal sections of the yarn with a linear density of 25 tex. The images were obtained using micro-CT followed by image reconstruction. Figure 6 presents the 3D model of an analyzed yarn that was generated based on the scans.

Figure 2.

Cross-section of an analyzed yarn.

Figure 3.

A longitudinal section of the yarn (YZ plane).

Figure 4.

A longitudinal section of the yarn (XZ plane).

Figure 5.

Cross-section of the yarn together with longitudinal sections of the yarn in two planes.

Figure 6.

Visualization of the 3D model of a single analyzed yarn.

Effect of twist on staple fiber migration

Characteristics of migration

Seven characteristics of fiber migration were used:

mean fiber migration radius;

mean fiber migration amplitude (migration parameter);

mean radial position of a fiber relative to the radius of a single yarn (migration range);

standard deviation (D) from the mean radial position (Y) of a fiber;

coefficient of variation of the radial position of fibers;

mean migration intensity measured as the ratio between the radial position of a fiber to its migration period;

mean migration period.

Effect of twist on staple fiber packing density in a yarn

Three selected characteristics of the yarns utilized were:

number of staple fibers in the cross-section of a single yarn;

diameter of a single yarn;

staple fiber packing density in a single yarn.

Selected exemplary calculation scheme for yarn D1 (700 twists/m)

Mean fiber migration radius, r_im (column 3 in Table 2):

r_{im} = (x_{i}^{2} + y_{i}^{2}) 0.5 = 8.03479 \times 10 - 5 m

where x,y are the fibers’ coordinates.

Mean fiber migration amplitude m_am (column 4 in Table 2): m_am = d_rm/r; m_am = 2.01893; where d_rm is the absolute change in fiber migration range, d_rm = 3.21011 × 10⁻⁵ m, and r is the yarn radius; r = 0.000159 m.

Mean radial position of a fiber relative to the radius of a single stand (migration range) (column 5 in Table 2):

Y = \sum \frac{(\frac{r_{i}}{r})}{n_{i}} = 0.502174

where r_i_m is the mean fiber migration radius, n_i is a number of fibers and r is the yarn radius.

Standard deviation (D) from the mean radial position (Y) of a fiber (column 6 in Table 2)

D = [\sum \frac{(Y_{i} - Y) 2}{n_{i}}] \frac{1}{2} = 0.248794

where Y_i is the observed values of a radical position of staple fibers.

Coefficient of variation (CV) of the migration range of fiber: (column 7 in Table 2)

CV = D / Y * 100 % = 49.75 %

Migration intensity (I) measured as the ratio between the radial position of a fiber to its migration period (column 8 in Table 2)

I = [\sum \frac{(\frac{d Y_{i}}{d z}) 2}{n_{i}}] \frac{1}{2} = 439.7594175 / m = 4.39 / cm

Mean fiber migration period (z) (column 9 in Table 2): z = 0.002273971 m

Table 2.

Parameters defining staple migration in single yarns.

1		2	3	4	5	6	7	8	9
Yarn	tpm	Radius of the yarn [m]	Mean fiber migration radius [m]	Mean fiber migration amplitude	Mean migration range $Y = \sum \frac{(\frac{r_{i}}{r})}{n_{i}}$	SD of Y	CV of Y [%]	Migration intensity I [per meter]	Migration period [m]
D1	700	0.000159	8.0348 × 10⁻⁵	0.2020	0.5020	0.24	49.75	440	0.002270
D2	800	0.000111	1.0665 × 10⁻⁴	0.1524	0.95908788	0.21	22.64	522	0.001910
D3	900	0.000110	2.0685 × 10⁻⁴	0.060125	1	0.09	4.93	1237	0.000800
D4	1000	0.000104	3.96728 × 10⁻⁵	0.09800	0.3800	0.1312	34.42	1805	0.000550
D5	1100	0.000079	3.50234 × 10⁻⁵	0.0576	0.439	0.1366	31.05	1680	0.000590

Table 2 shows an overview of the results for the parameters of yarns D1 to D5, which allow the measurement of fiber migration in yarns. The data collected in Table 2 are the numerical values characterizing the migration of the staple fibers in specific yarns, and the positioning of these staple fibers in yarns is presented in Figures 7 –11.

Figure 7.

The trajectory of a single staple fiber obtained for yarn D1 in the Cartesian coordinate system: (a) 3D position of the fiber; (b) position of the fiber in the XY plane; (c) position of the fiber in the YZ plane; (d) position of the fiber in the XZ plane.

Figure 8.

The trajectory of a single staple fiber obtained for yarn D2 in the Cartesian coordinate system: (a) 3D position of the fiber; (b) position of the fiber in the XY plane; (c) position of the fiber in the YZ plane; (d) position of the fiber in the XZ plane.

Figure 9.

The trajectory of a single staple fiber obtained for yarn D3 in the Cartesian coordinate system: (a) 3D position of the fiber; (b) position of the fiber in the XY plane; (c) position of the fiber in the YZ plane; (d) position of the fiber in the XZ plane.

Figure 10.

The trajectory of a single staple fiber obtained for yarn D4 in the Cartesian coordinate system: (a) 3D position of the fiber; (b) position of the fiber in the XY plane; (c) position of the fiber in the YZ plane; (d) position of the fiber in the XZ plane.

Figure 11.

The trajectory of a single staple fiber obtained foryarn D5 in the Cartesian coordinate system: (a) 3D position of the fiber; (b) position of the fiber in the XY plane; (c) position of the fiber in the YZ plane; (d) position of the fiber in the XZ plane.

Results

The migration intensity increases with an increase in yarn twist, which is presented in Figure 12.

Figure 12.

Effect of twist on migration intensity.

The migration period of staple fibers decreases with an increase in twist for twists lower than the boundary twist (boundary twist is defined here as the value of the twist corresponding to the twist coefficient for which the yarn durability is the highest). The migration period is constant above the boundary twist, which is presented in Figure 13.

Figure 13.

Effect of twist on migration period.

The migration amplitude decreases for twists lower than the boundary twist. For twists greater than the boundary twist, the migration amplitude of fibers remains close to the boundary twist. It is depicted in Figure 14.

Figure 14.

Effect of twist on migration amplitude.

The migration radius of fibers increases with an increase in yarn twist until it reaches the maximal value, i.e. the value of the twist corresponding to the highest yarn durability. The migration radius decreases above the value of the boundary twist, which is presented in Figure 15.

Figure 15.

Effect of twist on migration radius.

The relationship between the migration range of fibers measured through the radial position of a fiber and twist shows a similar variability to the relationship between yarn durability and twist, i.e. the highest migration range corresponds to the value of the twist for which yarn durability is the highest (the migration range increases for twists lower than the boundary twist). The migration range decreases for twist values lower than the boundary twist, which is presented in Figure 16.

Figure 16.

Effect of twist on migration range.

The coefficient of variation of the migration range is lowest for the boundary twist, which is presented in Figure 17. The coefficient decreases with an increase in twist up to the boundary twist and increases above the boundary twist.

Figure 17.

Effect of twist on the coefficient of variation of the migration range.

Effect of twist on staple fiber packing density in a yarn

The number of fibers in the cross-section of a yarn decreases with the twist. Above the boundary twist, the number of fibers in the cross-section of a yarn is constant and equal to the number of fibers for the boundary twist (Figure 18).

Figure 18.

Effect of twist on the number of staple fibers in the cross-section of a single yarn.

The diameter of a yarn also decreases with an increase in the twist (Figure 19).

Figure 19.

Effect of twist on the diameter of a single yarn.

Consequently, the staple fiber packing density in the cross-section of a yarn increases with an increase in the twist, which is presented in Figure 20.

Figure 20.

Effect of twist on the staple fiber packing density in a single yarn.

Analysis of the CT scans of a cotton yarn found that the fibers within the yarn become less regularly distributed as the yarn twist increases. The fiber packing density varies throughout the yarn cross-section, being lower on the outer surface. Taking into account the spiral alignment of fibers in the yarn, it was found that the fibers within the core are straight or twisted along a helix with a low radius. Fibers located farther from the yarn axis travel towards the outer surface along a helix with an increasing radius (r).

The cross-section of the yarn was divided into three areas located at different distances from the yarn axis in order to determine the number of fibers (Figure 21). In addition, the migration of single fibers between the three areas was observed.

Figure 21.

Division of the yarn cross-section into three areas in order to analyze the number of fibers at appropriate distances from the yarn axis.

Scanned samples of the yarns composed of staple fibers indicated that fibers in the yarn cross-section became more regularly distributed with an increase in twist. Fiber packing density in the yarn differs between longitudinal sections depending on the distance between each longitudinal section and the yarn axis. Taking into account the spiral alignment of fibers in the yarn, it was observed that fibers within the core are straight or twisted along a helix with a low radius and even fiber distribution. Fibers located farther from the yarn axis twist along a helix with an increasing radius and are pushed towards the outer surface of the yarn. The number of fibers in the cross-section decreases with an increase in twist. Furthermore, fiber packing density becomes more regular with an increase in twist (Table 3).

Table 3.

Fiber packing density according to twist for samples D1, D3, and D5.

	tpm	l	l ₁	l ₂	l ₃
D1	700	105	11	58	37
D3	900	94	10	56	28
D5	1100	85	8	53	25

The highest number of fibers was found in the ring located between one-third and two-thirds of the yarn radius. The lowest number of fibers was found in the center of the yarn, which was partly congruent with other findings,^21–23 where it was stated that the greatest migration of staple fibers takes place in a quarter of the radius of the single component thread. The calculated intensity of migration is 2.19/cm, and even the shortest fibers in this layer migrate to other layers, keeping the migration in the center of the yarn at a minimum level.

Conclusions

Analogies were found between the variability of the characteristics of staple fiber migration and twist, and between the the variability of yarn durability and twist.

For the boundary twist, the migration radius and the migration range are the highest, while the coefficient of variation of the migration range is the lowest.

The migration period and migration amplitude decrease with an increase in twist up to the boundary twist. Above the boundary twist, the migration period and migration amplitude remain close to the boundary twist.

The migration intensity increases with an increase in twist.

The number of fibers in the yarn cross-section decreases with the twist. Above the boundary twist, the number of fibers in the cross-section of a yarn is constant and equal to the number of fibers for the boundary twist.

Staple fiber packing density in the cross-section of a yarn increases with twist.

The highest number of fibers was found in the ring located between one-third and two-thirds of the yarn radius. The lowest number of fibers was found in the center of the yarn.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Centre of Science, ‘Basic Researches on Construction of Space Cable’ ID: 147886 (grant number 2011/01/B/ST8/03848). The last author’s work was supported by the European Union, 7th European Framework, Marie Curie International Outgoing, Magnum Bonum project (grant number 622043).

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