Abstract
This research contributes to the study of prickle sensation in terms of single fiber bending modulus and flexural rigidity, which are important factors for fabric-evoked prickle for garment tactile comfort. In this study, a novel technique was used to study the flexural buckling behavior of single fibers using an axial fiber-compression-bending analyzer (FICBA). The bending behavior and bending equivalent modulus of different single fibers were measured and analyzed. The bending properties of single fibers were quantified by calculating the equivalent bending modulus, and the flexural rigidity via measurement of the protruding length (l), diameter (d) of single fiber, and its critical force (Pcr), obtained from the peak point of the force–displacement curve. The experimental results indicate that ramie single fiber has the highest bending modulus, while cotton has the lowest bending modulus. However, hemp, jute, wool, flax, and cashmere fiber have bending modulus values lower than ramie but higher than cotton. On the other hand, the flexural rigidity of jute fiber is higher than that of wool followed by ramie, hemp, flax, cashmere, and cotton consecutively. Therefore, jute, wool, and ramie are stiffer than the other fibers, especially jute fiber. Thus, jute, wool, and ramie are uncomfortable single fibers because the fabric-evoked prickle, which is caused by short, coarse, and stiff fibers protruding from the fabric surface, generate sufficient force to evoke a low level of activity on a human nociceptors, but insufficient to penetrate the human skin so as to cause itchiness.
Keywords
Introduction
The principal criteria for the purchase of clothing fabrics are comfort, fashion, maintenance, and aesthetics. More specifically, comfort is considered to be a fundamental property of clothing fabrics when a textile product is valued.1,2 Therefore, sensations perceived from the contact of fabric with the human skin can greatly influence our overall state of comfort, especially tactile comfort. 3 When a garment is worn next to the skin, an unpleasant sensation known as fabric-evoked prickle can sometimes arise. This sensation results from the mechanical stimulation of specific nerve endings in the skin rather than an allergic reaction.4–7 Researchers have explained that the specific nerve endings associated with prickle sensation are triggered by a force applied vertically to the skin surface that is greater than a critical load level, typically 0.75 mN. This is present at a relatively small number of such stimuli per unit area of the skin surface, i.e. sufficient to trigger the prickle sensation. 4 A large number of studies dealing with fabric-evoked prickle have led to the conclusion that stiff fiber needles protruding from a fabric surface, and in contact with the human skin when worn, act mechanically as simple Euler’s rods.8–14 If they are able to sustain the sufficient forces before buckling, they can trigger the nerve endings, resulting in the pain prickle sensation on the human body. 15 These published studies include experiments where fabrics manufactured from blended acrylic fiber, engineered to give a broad fiber diameter distribution, exhibited a prickle response, thus demonstrating that prickle is not only specific to wool. 10 Naylor et al. have studied extensively the characterization of fabric-evoked prickle in wool worsted spun single jersey fabrics.11–14
Theoretically, we know that fiber ends act as simple columns under compression that will buckle at a particular threshold force, applied to the top of the fiber and parallel to the fiber axis, which is proportional to Ed4/L2 (where E is the Young’s modulus of the material, d is the fiber diameter, and L is the length of the fiber end protruding from the fabric surface).16,17 From this perspective, researchers at the Textile Materials and Technology (TMT) lab at Donghua University have performed a number of studies to evaluate and test this phenomenon.17–20 In this regard, Qi and Yu, 18 based on neurophysiologist studies of the prickly sensation, discussed the causes of the prickle sense evoked by the contact between skin and fabrics. The results show that it is necessary to adopt a single-fiber stinging measurement to characterize the prickle sensation of human skin. Moreover, Liu and Yu evaluated the softness of wool and alpaca fibers based on a single-fiber bending test. 20 They concluded that alpaca fibers have a much higher resistance to bending, i.e. higher bending stiffness, than wool and that the softer feel of alpaca fibers is mainly due to the lower surface frictional resistance that makes slip between fibers more easy. Therefore, testing and evaluation of the prickle characterization caused by a needle of fiber protruding from a fabric surface is a difficult task with the primary assessment being subjective (sensory) responses from wearers. This evaluation is time-consuming, less reliable, and non-reproducible method because high variability occurs between the human sensitivity to prickle, skin mechanical properties, effective density of nociceptors, and the mood state of the individual. Also, research work on comparing prickle sensation of different important textile single fiber has been minimal.
For the above reasons, there is a need to find an objective method to measure single fiber stimulation on human skin and to predict the prickle caused by stiff or thick needle fiber ends protruding from the fabric surface. A type of axial fiber-compression-bending analyzer (FICBA) for single fibers has been used to investigate the characteristics of prickle tactile discomfort in wearing fabrics, based on the mechanical and physical properties of cotton, cashmere, flax, hemp, ramie, wool, and jute single fibers.
Theoretical considerations
The buckling properties of a single fiber protruding from the fabric wear surface when in contact with human skin can be mimicked theoretically by deriving Euler’s formula for the critical load of an axially compressed column with pinned ends.
21
Consequently, the buckling theory of a thin rod was applied to uniform fibers. The buckling column theory of the axial-compression-bending analyzer is shown schematically in Figure 1. A compression force, Pcr, is applied to a single fiber of length l. The critical force and buckled mode shape are those for a single fiber that is fixed at the base and pinned at the top.
22
Hence, the differential equation was solved to find Pcr, according to the model shown in Figure 1. When the single fiber buckles, horizontal reactive forces, R, develop at the supports and a reactive couple of hM0 develops at the base.
Buckled column theory of an axial-compression-bending analyzer of a single fiber.
The bending moment in the buckled fiber at distance x from the base is given by
From equation (1), the differential equation can be evaluated as
Thus, the general solution of the differential equation is
From equation (3) we found the buckling equation:
Experimental details
Single-fiber axial-compression-bending test
The axial
Sample preparation and conditioning
Single fiber samples, including cotton, cashmere, flax, hemp, ramie, jute, and wool, were collected for the single fiber axial compression bending test. The fiber was conditioned for 24 h under a standard temperature of 20 ± 2℃ and relative humidity of 65 ± 2%; then all fiber samples were prepared into single-fiber needles to simulate the fiber in contact with the human skin, when wearing fabric.
Single fiber preparation and test procedure
The single fiber samples were then prepared into single fiber. The steps used to prepare a protruding single-fiber sample for the test are shown in detail in Figure 2. A paper window (A) of sufficient thickness, with a width of 5 mm and a length of 25 mm, was prepared. Further, straightening and pasting of the single fibers on the paper window with glutinous resin was done before covering the window with adhesive tape (B). The window was cut into three independent paper windows and the straightened fiber snipped at different angles to obtain suitable slenderness (C). Finally, scissors were used to cut the card into a single-fiber sample (D) and the sample was inserted in between a metal clamp on the FICBA machine (E); at this point the sample was ready for the test. The level of error percentage of the machine was about ± 0.01 (on x, y, z axes).
The approach used to prepare a protruding single-fiber sample.
The single-fiber sample with certain protruding length was clamped by two metal grooves. The protruding length of each single fiber was determined by fiber thickness (diameter). Hence, the single-fiber slenderness (length/thickness) was suitable because the slenderness ratio served as a measure of single-fiber stiffness. The single fiber was neither short enough to be compressed directly to yield, nor long enough to detect the small load of the critical force.
Diameter and slenderness of protruding fibers
The protruding lengths (L) of cotton, cashmere, flax, hemp, ramie, jute, and wool were directly measured using an optical microscope with CCD camera on the FICBA. The diameters of the single fibers were also measured by fiber detection microscopy (YG002C), but with different angles perpendicular to the fiber. Table 1 shows the diameters (D), slenderness (L/D), and fineness of the different single fibers for diameters used in the experiments. Therefore, from the mean diameter The relationship between mean diameter Diameters, slenderness, and fineness of single-fiber samples
The relationships between The relationships between slenderness The diameter and protruding length of all single fibers (a). Loading and unloading curves of force–displacement of axial compression bending test on all single fibers (b–h), with maximum critical force point and displacement distance.

Result and discussion
Force–displacement curves of axial-compression-bending
Typical load–displacement plots recording single fiber bending and recovery are shown in Figure 5(b) to (h). The critical force, Pcr, illustrates the maximum loading force capability of the axial single fiber, when pressed in a fixed position; it is comparable to a human wearing the fabrics and the fibers protruding from the surface of the worn fabrics. Accordingly, textile fibers have a lower proportional limit than other fibers when the stresses in outer fibrils exceed the proportional limit, and the fiber needle no longer follows Hooke’s law. Naturally, the inclination of the force–displacement curve is unchanged up to the level of force at which the proportional limit is reached. Then, the curve continues upward, it reaches a maximum point, the critical force Pcr, after which the stresses in the outer layer result in the yield of the fibrils, and the curve turns downward.
When fibers that protrude above the fabric surface are in contact with human skin, a certain pressure force is incurred at the point at which Pcr is reached and starts to prickle human skin, making the fabric become uncomfortable. The detailed shapes of force–displacement curves of fabric wear fibers depend on the fiber material bending properties (bending rigidity, stiffness or fineness, and Young’s modulus, etc.) and the fiber slenderness (fiber length divided by fiber diameter). Force–displacement curves of different single fibers appear in Figure 5 for each type of single fiber, but Figure 6 shows a comparison of the curves for all fibers. This illustrates two important prickle characteristics of the uncomfortable nature of worn fabrics. Firstly, the critical force of jute fiber with 35.28 µm diameter and 1.33 mm protruding lengths is the highest among the seven single fibers, as shown in Figure 5(g), despite having the same specific single fiber slenderness, as shown in Table 2.
The critical force–displacement curves of all single-fiber samples. Characteristics of different single fibers
This means that jute fibers have a higher tensile modulus and stiffness than other fibers, followed by wool, ramie, hemp, flax, cashmere, and cotton fibers in that order, as shown in Figure 6. Secondly, the similar force–displacement curves and hysteresis loops (Figure 5) are due to a close structure with relatively similar slenderness. As can be seen from the above results, fibers with high critical force needed more force to become bent, which means they can more easily prickle the human skin and make fabrics manufactured from these fibers uncomfortable when worn.
The unloading curves after loading in Figure 5 did not follow the bending curve under loading, and a relatively big bending hysteresis loop was produced. The possible explanation for this behavior is the internal friction and slippage between the fibrils and the molecular chains. In addition, the hysteresis loss would be partially attributed to the compression hysteresis of the whole assembly. Therefore, cotton, cashmere, and flax (Figure 5(b) to (d)) single fibers had less hysteresis loss despite their lower bending modulus compared to ramie, wool, and jute which had high hysteresis loss, as shown in Figure 5(f) to (h).
The fiber discomfort characterization in this study shows that jute has extreme discomfort, as indicated in Figure 5(g), followed by wool, ramie, hemp, flax, cashmere, and cotton with the lowest critical force being extremely comfortable, as shown in Figure 5(b). Thus, jute, wool, and ramie are uncomfortable single fibers because the fabric-evoked prickle caused by short, coarse, and stiff protruding fibers from the fabric surface, which generate sufficient force to evoke a low level of activity on a human nociceptor, but insufficient to penetrate the human skin so as to cause itchiness.
Therefore, when a vertical force was applied on the different macro-structure of all single fibers, we found that the critical force increased when fiber length decreased. In addition, the lower bending modulus of single fiber is another factor that makes fiber assemblies compress easily when bent. Moreover, the bending load factor and its relationship with fiber cross-section, fineness, and length properties is very important for prickle sensation. Thus, when the cross-section and fineness becomes high, the bending load increases, but fiber length plays the main role in prickle sensations. From the results it has been found that wool, ramie, and jute have single-fiber protruding lengths of 1.1, 0.68, and 1.33 mm, respectively, above the fabric surface with fiber diameters of 28.39, 18.78, and 35.28 µm in that order. This would give a maximum buckling force that is sufficient to trigger the human stimulus and prickle, which occurs immediately.
Calculation of the equivalent bending modulus
The uncomfortable sensation of worn fabrics, especially fabric-evoked prickle, depends on the fineness (fiber diameter), stiffness, length (long or short fiber), and numbers of single fibers protruding from the surface of worn fabrics.
27
As a result, the flexural rigidity of the single fibers, i.e. the resistance to bending when compressed, represents the fineness or stiffness of the single fibers.28,29 Thus, two factors influence it, the first being a single fiber bending property denoted by equivalent bending modulus, and the second the cross-section of single fiber denoted by diameter and shape factor.
23
Therefore, there is a need for the equivalent bending modulus to be calculated. Since the cross-sections of single fibers are not exactly circular, a fiber will always bend at the thinnest side and in the easiest direction. The shape factor ηf is the ratio of the moment of inertia for a given cross-sectional area. Consequently, the shape factor of all single fibers is different because they have different cross-sections, as shown in Table 2. The shape factors of different cross
To arrive at the critical load, equation (5) can be modified by considering the effect of shape factor Statistical analysis of relationship between critical load (Pcr) and D4/L2 of cotton, cashmere, flax, hemp, ramie, wool, and jute single-fiber samples. Regressive equation and the coefficient of correlation (R2) for different single fibers

Consequently, the critical force can be simplified as
Thus, the equivalent bending modulus is
Bending characteristics of single needle-fiber samples
The fundamental characteristic value of single fiber bending and buckling is reflected by the equivalent bending modulus, which is independent of fiber diameter and determined only by fiber tensile modulus and compression modulus. This depends on fiber structure and components. From all the experiments, the equivalent bending modulus of ramie was larger than that of other single fibers, while for cotton it is lowest. From these results it can be seen that the uncomfortable fibers almost always have a higher equivalent bending modulus, as is apparent in the ramie, hemp, and jute results because both bast and leaf fibers are multicellular. Helix angles of fibrils in the cells are less than that of cotton, thus giving them higher tensile modulus, as shown in Figure 5(e) to (g). The tendency of cellulose fibers to bend suddenly is different in protein fibers like wool and cashmere, for which curves slowly inclined, as shown in Figure 5(c) and (h), and the reason is probably due to the more flexible protein molecule of α helical and β sheet structures than cellulose molecular structure.
As is known, the prickle feeling depends on Pcr, which is determined by the bending rigidity BR, but BR = EI, where E is the equivalent modulus and I is = (S/L)2. Therefore, E is one of the most important factors that affect Pcr properties. The softness or stiffness of single fibers should combine the equivalent bending modulus with fiber diameter or cross-section shape. A comparison of prickle characteristics depends on bending properties of cotton, cashmere, flax, hemp, ramie, wool and jute. Table 4 shows that value of the equivalent bending modulus are close between the protein fibers (wool and cashmere), but different in seed fibers (cotton) and bast fibers (flax, hemp, ramie, and jute). Furthermore, the flexural rigidity of jute is greater than wool, ramie, hemp, flax, cashmere, and cotton, respectively, which is caused by the fiber diameter and fineness, as shown in Table 4. These results indicate that the single jute fiber is stiffer than wool followed by ramie, cashmere, hemp, flax, and cotton. Therefore, yarns and fabrics made of jute fibers are stiffer. This makes them uncomfortable and prickly to wear because the fibers with high flexural rigidity will be difficult to bend when in contact with human skin, which causes the discomfort.
Conclusion
This study has significantly extended the knowledge of single fiber and prickle tactile discomfort sensation that is observed in some single fiber situations. The bending modulus and flexural rigidity of cotton, cashmere, flax, hemp, ramie, wool, and jute single fibers have been objectively investigated based on the axial FICBA. The bending properties of single fibers were quantified by calculating the equivalent bending modulus and the flexural rigidity by measuring the protruding length, diameter, and the critical load, Pcr, of the single fibers. The equivalent bending modulus and flexural rigidity are obtained from the relationship between a critical load (Pcr), diameter (D), and length (l) of single fibers. Consequently, the measured line of Pcr = D4/l2 has been regressed, and the fiber modulus and flexural rigidity obtained. The experiments and analysis results indicate that ramie single fiber has the biggest equivalent bending modulus, followed by hemp, jute, wool, flax, cashmere, and cotton in that order. Flexural rigidity of jute fiber has higher value than wool and ramie. Therefore, jute, wool, and ramie are stiffer single fibers than other fibers, but in particular jute fiber is the stiffest because it has high single-fiber fineness. Thus, jute, wool, and ramie are uncomfortable single fibers because the fabric-evoked prickle caused by short, coarse, and stiff protruding fibers comes from the fabric surface.
This technique and device based on bending modulus/flexural rigidity of single fiber can be used to characterize tactile comfort of fabric-evoked prickle. This study further gives resourceful insight relevant to subject selection and the general research trend on clothing wear tactile comfort. For garment manufacturers, the compiled consumer feedbacks by wearers of particular clothing are tools for product improvement to enhance utility. Finally, this research informs consumers about fabric clothing comfort, which will contribute to informed decision-making during purchase.
Footnotes
Funding
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.
