PREDICTING AIR PERMEABILITY AND FRICTIONAL BEHAVIOR OF SHIRTING FABRICS BASED ON PHASE STRUCTURE AND FIBER COMPOSITION

УДК 677.017.4

Abstract

This study investigates the influence of fabric phase structure and weft fiber composition on the air permeability and inter-yarn frictional behavior of shirting fabrics. Nine phase structures of plain weave fabrics are analyzed geometrically, and the friction angle between warp and weft yarns is calculated for each phase. Experimental data from 5-level single-factor active experiments (modal content in weft: 20–100%) with 5 repetitions each are statistically processed using Smirnov–Grubbs, Shapiro–Wilk, Cochran, Fisher, and Student’s tests. A linear regression model is obtained: Y = 144 + 0.55X, where Y is air permeability (dm³/m²·s) and X is modal content (%). Friction coefficients for cotton–cotton (0.33), cotton–modal (0.35), modal–modal (0.37), and cotton–polyester (0.21) pairs are determined. The friction force increases with phase number (I to IX) due to increasing friction angle (0.46 to 1.57 rad). Results enable prediction of fabric performance and optimized raw material selection for seasonal shirting fabrics.

Аннотация

В данном исследовании изучается влияние фазовой структуры ткани и состава волокон утка на воздухопроницаемость и межниточное фрикционное поведение рубашечных тканей. Геометрически проанализированы девять фазовых структур полотняного переплетения, и для каждой фазы рассчитан угол трения между нитями основы и утка. Экспериментальные данные, полученные в результате 5-уровневых однофакторных активных экспериментов (содержание модального волокна в утке: 20–100%) с пятикратной повторностью, были статистически обработаны с использованием критериев Смирнова–Граббса, Шапиро–Уилка, Кокрена, Фишера и Стьюдента. Получена линейная регрессионная модель: Y = 144 + 0,55X, где Y – воздухопроницаемость (дм³/м²·с), X – содержание модального волокна (%). Определены коэффициенты трения для пар: хлопок–хлопок (0,33), хлопок–модал (0,35), модал–модал (0,37) и хлопок–полиэстер (0,21). Сила трения возрастает с увеличением номера фазы (от I до IX) вследствие увеличения угла трения (от 0,46 до 1,57 рад). Полученные результаты позволяют прогнозировать эксплуатационные свойства ткани и оптимизировать выбор сырья для сезонных рубашечных тканей.

Keywords: fabric phase structure, air permeability, regression model, modal fiber.

Ключевые слова: фазовая структура ткани, воздухопроницаемость, регрессионная модель, модальное волокно.

Introduction

The quality of modern shirting fabrics is determined by a complex interplay of aesthetic, hygienic, and mechanical properties. Among these, air permeability directly affects thermal comfort, while inter-yarn friction influences fabric stiffness, dimensional stability, and resistance to seam slippage [1, 2]. Both properties are strongly dependent on two fundamental factors: the phase structure of the fabric (the relative bending wave heights of warp and weft yarns) and the fiber composition of the yarns [3].

Nine distinct phases for plain weave fabrics when warp and weft have equal diameters. In Phase I, warp yarns are completely straight (bending wave height h_warp = 0) and weft yarns are maximally bent (h_weft = 4r, where r is yarn radius). In Phase IX, the opposite occurs: weft straight (h_weft = 0), warp maximally bent (h_warp = 4r). Between these extremes, as the phase number increases, h_warp increases in steps of 0.5r while h_weft decreases by the same amount. Phase V represents a balanced structure where h_warp = h_weft = 2r [4, 5].

Recent studies have applied this geometric model to calculate the friction angle A at the intersection of warp and weft yarns [6, 7]. The tangent of this angle is given by the ratio of the bending wave heights (tan A = h_weft / h_warp or h_warp / h_weft depending on the phase). This friction angle directly determines the force required to slide one yarn system over the other, which affects fabric handle, wear resistance, and tailoring performance.

Simultaneously, the choice of fiber material has undergone significant diversification. Traditional cotton remains valued for its high moisture absorption (7–8% at 65% RH, 24–27% at 95% RH), breathability, and natural origin. However, modal—a high-wet-modulus viscose fiber derived from beech or eucalyptus wood—offers even higher moisture absorption (11% at 65% RH, 34–37% at 95% RH), superior softness, and excellent dimensional stability. Polyester (Lavsan) provides maximum tensile strength and abrasion resistance but minimal moisture uptake (0.4–0.5% at 65% RH).

The phase structure analysis of fiber composition effects has not been systematically addressed for shirting fabrics. This study aims to:

1. Develop a statistical regression model linking weft modal content to fabric air permeability.
2. Quantify friction coefficients for different yarn pairs across the nine phase structures.
3. Provide practical recommendations for selecting raw materials for summer and autumn-winter shirting fabrics.

Materials and methods

Materials

Three fiber types were studied:

• Cotton (100% natural, linear density 11.8×2 tex, staple length 16.5–43 mm).
• Modal (regenerated cellulose from eucalyptus wood, linear density 11.8×2 tex, staple length ~40 mm).
• Lavsan (polyester, linear density 23.6×2 tex).

Warp yarns were always cotton (11.8×2 tex). Weft yarns were prepared with modal content of 20%, 40%, 60%, 80%, and 100% (X factor). Fabric weave: plain 1/1.

Phase Structure Analysis

According to the theory of fabric phase structure (Novikov, 1946), the bending wave height of warp (h_warp) and weft (h_weft) varies in steps of 0.5 r (r = yarn radius). Nine phases (I to IX) are defined. The friction angle A between warp and weft at their crossing point is calculated geometrically from the right triangle formed by the bending wave heights:

 (or vice versa depending on phase).

For each phase, A (radians and degrees) is computed (Table 1, derived from [6]).

Single-Factor Active Experiment

A 5-level single-factor experiment was conducted with N = 5 factor levels (modal %: 20, 40, 60, 80, 100) and m = 5 repetitions per level. Air permeability Y (dm³/m²·s) was measured according to ISO 9237:2002.

Statistical processing included:

• Outlier detection (Smirnov–Grubbs test, PD = 0.95).
• Normality check (Shapiro–Wilk test).
• Homogeneity of variances (Cochran’s test).
• Regression model adequacy (Fisher’s F-test).
• Coefficient significance (Student’s t-test).

Friction Force Calculation

The friction force F between warp and weft is given by:

Where  is weft tension (assumed 10 cN), A is friction angle (rad), and f is friction coefficient determined experimentally for four friction pairs: cotton–cotton, cotton–modal, modal–modal, cotton–Lavsan.

Results and Discussion

Statistical Analysis of Air Permeability

Table 1. Experimental air permeability values (Y, dm³/m²·s) for different modal content in weft

Source: adapted from [8]

Smirnov–Grubbs test revealed no outliers (VRmax = 1.35 < VT = 1.869). Shapiro–Wilk test confirmed normal distribution (WR = 1.66 > WT = 0.762). Cochran’s test gave GR = 0.46 < GT = 0.544, confirming homogeneity of variances.

Regression equation:  (where X = modal content in weft, %).

Fisher’s test: F_R = 3.6 < F_T = 8.66 → model adequate. Student’s test: t_R{d₀}=122 > 2.07, t_R{d₁}=13.1 > 2.07 → both coefficients significant at P_D = 0.95.

Figure 1. Experimental (points) and predicted (line) air permeability vs. modal content in weft. Error bars show ± standard deviation.

Friction Angle Across Phase Structures

Table 2. Friction angle A (radians) for nine phase structures (plain weave, equal yarn diameters)

Calculated from geometric models in [9]

Figure 2. Geometric model for fabric phase V (h_weft = h_warp = 2r). The friction angle A is shown between the hypotenuse and the weft bending wave height.

Friction Force for Different Fiber Pairs

Table 3. Friction force F (cN) at Tweft = 10 cN for different phase structures and fiber pairs

Calculated from [7] Tables 4–6

Figure 3. Friction force vs. phase number for three fiber pairs (cotton–cotton, cotton–modal, modal–modal)

Comparative Physical–Mechanical Properties

Table 4. Key properties of cotton, modal, and polyester (Lavsan) fibers

Source: [10, p. 7–11)

Figure 4. Stress–strain curves for cotton, modal, and Lavsan yarns (single twist, N=40/1)

The linear regression model Y = 144 + 0.55X demonstrates that air permeability increases by 5.5 dm³/m²·s for every 10% increase in modal content. This is attributed to modal’s lower density and smoother surface compared to cotton, which creates more uniform inter-yarn channels. The model’s adequacy (FR < FT) confirms that a simple linear relationship sufficiently describes the process within the studied range (20–100% modal). These results align with earlier findings that modal fibers improve fabric breathability due to their high moisture transport capacity [8].

The friction angle A increases from 0.46 rad (Phase I) to 1.57 rad (Phase IX), representing a 241% increase. This directly raises the friction force because the warp and weft yarns are forced into tighter sinusoidal contact. The highest absolute friction force (5.8 cN at Phase IX) occurs for modal–modal pairs, which explains why 100% modal fabrics feel stiffer and resist yarn slippage better. Conversely, cotton–Lavsan pairs (f=0.21) produce only 3.3 cN at Phase IX, indicating that polyester-blend shirting fabrics are more prone to seam slippage but offer better drape.

For summer shirting (hot, dry climate), a blend of 60–80% modal with cotton warp is recommended: high air permeability (190–195 dm³/m²·s), moderate friction (3–4 cN), and excellent moisture absorption (34–37% at 95% RH). For autumn-winter shirting (cool, humid), a 40–60% modal blend with Lavsan accents (every 10th weft pick as Lavsan) provides durability and shape retention, as shown in the patented structure [8].

The nine-phase geometric model allows precise tuning of fabric tightness. Phase V (h_warp = h_weft = 2r) represents balanced construction with equal bending in both systems, yielding isotropic friction behavior. Phases I–IV are weft-dominated (weft more bent), suitable for warp-faced fabrics; Phases VI–IX are warp-dominated, suitable for weft-faced fabrics.

Conclusion

A validated linear regression model Y = 144 + 0.55X predicts air permeability of plain weave shirting fabrics from weft modal content (R² not calculated but Fisher test confirms adequacy). Friction angle between warp and weft increases from 0.46 to 1.57 rad across phases I–IX, causing a 68% increase in friction force. Modal–modal pairs exhibit the highest friction coefficient (0.37) and friction force (5.8 cN at Phase IX); cotton–Lavsan pairs the lowest (0.21 and 3.3 cN). For summer fabrics: 60–80% modal in weft, Phase III–V structure. For winter fabrics: 40–60% modal + periodic Lavsan picks, Phase VI–VIII structure. The proposed methodology (active experiment + phase analysis) enables scientific control of fabric performance without trial-and-error weaving.

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