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Multivariate Studies of Mechanical Properties for Wool and Cotton Fabrics Abstract

In this study, the mechanical properties of fifty-eight light-weight wool/wool-blend fabrics and twenty medium to heavy-weight cotton denim fabrics were analyzed by multi-dimensional techniques of principal component analysis. The technique reduced the dataset of wool/wool-blend fabrics into seven components and explained 86% of the population variance. For the cotton denim fabrics, the dataset was reduced into five components and explained 95% of the population variance. Fabric surface properties and fabric bending and shear properties were the most important properties to explain the fabric stiffness hardness and tailorability for these two fabric classes. The results show how multivariate statistical analysis techniques of fabric mechanical and surface property data for two very different groups of fabrics can provide a basis for the specification and control of fabric quality along the textile and apparel supply chain. These reduced datasets with the most important component extracted first and the least important component extracted last, allow the supply chain members to focus directly on the key factors for product design and development.

Jimmy K. C. Lam1 Institute of Textiles & Clothing, The Hong Kong Polytechnic University, Hong Kong

Ron Postle School of Chemistry, University of New South Wales, Sydney 2052, Australia

Key words fabric objective measurement, fabric hand, fabric surface, tension, compression, bending, shear, wool/wool blend fabrics, cotton denim

The comparative studies on low-stress mechanical properties of wool and cotton fabrics using the fabric objective measurement (FOM) technology demonstrate that a large amount of fabric data is readily available to the textile and apparel supply chain [1]. However, the vast amount of FOM data makes the interpretation very difficult [2]. Therefore, the immediate application of FOM to the industry is very limited except for a few research institutions and very large companies. In addition, the techniques used by the comparative studies can only analyze a few data simultaneously. Such an analysis is normally based on fiber type, weave structure or the fabric end use. It is difficult to analyze all the variables simultaneously, not to mention the interaction between

variables and their effects on the fabric mechanical properties such as tensile, bending, shear and surface characteristics [3]. The mechanical variables discussed in the present paper1 include thirty parameters. If, for example, it is required to correlate each pair of fabric variables for lowstress mechanical properties, we would need to consider 435[(30 × 29)/2] combinations. Clearly, correlation tables of this order of magnitude are very tedious to analyze and this represents a major problem for the interpretation of fabric mechanical property data in the scientific literature.

Textile Research Journal Vol 76(5): 414–425 DOI: 10.1177/0040517506062768 Figures 1–3 appear in color online: http://trj.sagepub.com

www.trj.sagepub.com © 2006 SAGE Publications

1

Corresponding author: e-mail: [email protected]

Multivariate Studies of Mechanical Properties for Wool and Cotton Fabrics J. K. C. Lam and R. Postle In the present study, the statistical technique of multivariate factor analysis was employed. Factor analysis is a technique for analyzing the pattern of complex, multidimensional data set relationships. It can be utilized to examine the underlying patterns or relationships for a large number of variables and to determine whether the information can be condensed or summarized into a smaller set of factors. Factor analysis differs from the dependence techniques, in which one or more variables are explicitly considered

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dependent variables and all others are the independent variables. The advantage of factor analysis is that it is an independent technique in which all variables are simultaneously considered, each related to all others still employing the concept of the variate, the linear composite of variables. In factor analysis, the factors are formed to maximize their explanation of the entire variable set, not to predict dependent variables. In this study, factor analysis was used to analyze wool and wool-blend fabrics and cotton denim fabrics in terms

Table 1 Fabric characteristics for 58 wool/wool-blend fabrics.

Pure wool (31 samples) Range Average Wool/wool-blend (27 samples)* Range Average

Threads per cm

Yarn count (Tex)

Weight (g/m2)

Warp

Weft

Warp

Weft

140–273 185

22–59 31

19–38 26

18–41 31

18–44 30

125–242 172

21–55 28

16–33 24

22–45 30

22–45 30

* The wool-blend fabrics contain wool/polyester fibers with blend percentages of wool/polyester of 90/10; 80/20; 75/25; 60/40; 50/50.

Table 2 Fabric mechanical parameters measured on KES-F instruments for wool/wool-blend and cotton denim fabrics. Parameter symbol

Description

Unit

Tensile EMT LT WT RT

Fabric extension at 5 N/cm width Linearity of load extension curve Energy in extending to 5 N/cm width Tensile resilience

% – J/m2 %

Shear G 2HG 2HG5

Shear rigidity Hysteresis of shear at 8.7 mrad Hysteresis of shear at 87 mrad

N/m N/m N/m

Bending B 2HB

Bending rigidity Hysteresis of bending moment

µNm mN

Surface MIU MMD SMD

Coefficient of friction Mean deviation of MIU Geometrical roughness

– – µm

Compression LC WC RC T0 Tm

Linearity of compression-thickness curve Energy in compression fabric under 5 kPa Compression resilience Fabric thickness at 50 Pa pressure Fabric thickness at 5k Pa pressure

– J/m2 % mm mm

Fabric characteristics W Fiber Weave

Mass per unit area Pure wool /wool-blend Weave structure (plain or twill)

g/m2

For the tensile, bending and surface properties, each parameter has two values, representing the warp and weft directions of the fabric.

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of their low-stress mechanical properties of extension, compression, bending, shear and surface characteristics [4] (measured on the KES-F instruments). The characteristics of the wool/wool-blend fabrics considered in the present study are shown in Table 1 and the measured parameters from KES-F are shown in Table 2. The wool-blend fabrics contained wool and polyester fibers with blend percentages of 90/10, 80/20, 75/25, 60/40, and 50/50, with the major fiber content being wool.

Structured Approach to Multivariate Analysis To apply the multivariate factor analysis technique to the fabric mechanical parameters measured on the KES-F instruments, a five-stage structured approach model was used. This model-building approach focuses the analysis using a well-defined research plan, starting with a conceptual model detailing the relationships to be examined. Table 3 summarizes the five-stage structured model used in the present study. In this report, model interpretation based on rotated factor solutions is discussed for both wool/wool-blend fabrics and cotton denim fabrics. Further details for each stage of the model are presented elsewhere [1].

Rotated Factor Solution for Wool/ Wool-blend Fabrics The purpose of factor rotation is to redistribute the variables evenly among all the components extracted from principal component analysis. The initial solution obtained from principal component analysis (called the unrotated Table 3 Five-stage structured model approach. Stage

Purpose

1. Research objectives

To summarize 30 fabric mechanical parameters measured on the KES-F instruments into smaller data set for easy interpretation.

2. Analysis plan

Using R-type factor analysis on all the 30 fabric mechanical parameters.

3. Assumption test Testing on correlation coefficient, multi-collinearity of the data set 4. Extraction method

Using principal component analysis for data summarization for all wool/wool-blend and cotton fabrics

5. Model interpretation

Using rotated factor solutions for data interpretation.

factor solution) extracts the factors in the order of their importance. That is, the first component tends to have most variable loadings and accounts for the largest amount of variance. The second and subsequent components are then based on the residual variance and therefore account for successively smaller portions of variance. This principal component method, however, makes the data interpretation rather difficult as every variable seems to be concentrated in the first few components. We therefore used the Varimax rotation method of principal component analysis for the wool and wool-blend fabrics. The Varimax method has proved to be very useful on orthogonal rotation in the principal component analysis [5, 6]. The results of the Varimax rotation are shown in Table 4. To access the variables in each extracted component in Table 4, the highest loading factor for each fabric mechanical parameter is selected; the result is shown in bold type with an asterisk in Table 4. The percentage of the variance as explained by each of the seven components for wool/wool-blend fabrics for the rotated factor solution is shown at the top of Table 4.

(a) Component 1 Component 1 accounted for 19.9% of total explained variance for wool/wool-blend fabric mechanical properties. There are seven fabric mechanical parameters that have the highest loading with Component 1, six of which are tensile parameters namely EMT1, EMT2, LT1, LT2, WT1 and WT2. Both LT1 and LT2 are negatively correlated with Component 1. The last mechanical parameter in Component 1 is the compression energy WC, which again is negatively correlated with Component 1. The percentage contributions of these seven fabric parameters for Component 1 are shown in Figure 1. The strong correlation of tensile parameters of fabric extensibility, linearity and tensile energy and fabric compression energy (WC) with Component 1 means that fabric extensibility and firmness are important elements for the mechanical properties of these high-quality relatively lightweight wool and wool-blend fabrics. The average warp extensibility was 4.4% and weft extensibility was 7.2%, which fall within the acceptable region of the HESC (Hand Evaluation Standardisation Committee) Data Control Chart for both men’s winter and summer suits [4]. The tensile energy (WT) measures the energy under the load–extension curve for a fixed applied load and therefore, is directly related to fabric extension, EMT. Hence, both EMT and WT have strong positive correlations with Component 1. The fabric compression energy, WC is negatively correlated with Component 1 representing a direct relationship between Component 1 and fabric firmness. The tensile linearity (LT) measures the ratio of actual fabric tensile energy to the total energy for a hypothetical

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Table 4 Rotated principal component analysis on the wool and wool-blend fabrics (rotation method: Varimax with Kaiser normalization). Component Explained Variance%

1 19.9%

2 17.4%

3 15.6%

5 7.1%

6 5.7%

7 5.1%

–0.03 0.07 –0.21 –0.51 0.18

0.01 –0.05 0.11 0.37 0.39 –0.01

0.04 0.11 –0.16 0.10 –0.08 –0.03

–0.17 –0.15 –0.03 –0.05 –0.28 0.35

0.16 0.10 0.09 0.08 0.19 0.00

–0.12 0.25

0.05 –0.11 –0.05 –0.07

–0.10 0.20 –0.06 0.14

0.41 0.30 0.04

0.21 –0.07 0.19 0.00

0.06 –0.23 –0.07 –0.19

0.05 0.03 0.26 0.09

0.16 0.00 –0.45

–0.22 –0.23 0.08

MKSQG MKVMG MKUQG

–0.02 0.01 –0.08

0.57 0.06 –0.10

0.07 0.07 0.09

0.21 –0.09 –0.03

–0.03 –0.17 0.08 –0.01 –0.01 –0.17 0.11 0.07

0.20 –0.11 0.01 0.23 0.21 –0.13 –0.36 –0.14

0.04 0.06 –0.23 –0.20 –0.01 0.05

0.29 0.26

–0.21 –0.24 0.11 0.10 –0.23 –0.22 –0.06 –0.04

0.05 0.15 0.39 0.49 0.12 0.22 –0.08 –0.55

0.10 0.01 0.15 0.14 0.14 0.02 –0.11 0.15

–0.07 0.25 –0.28 –0.25 –0.35 –0.35

MKTMG MKSQG MKUVG MKUTG MKUVG MKUQG

0.35 0.48 –0.07 –0.06 –0.14 –0.13

0.04 0.07 –0.14 –0.20 –0.01 –0.10

–0.46 –0.42 0.03 –0.09 0.09 –0.01

–0.08 –0.02 0.01 0.04 0.10 0.17

–0.04 0.13 0.20 –0.12 –0.04 –0.09

0.03 0.16 –0.31

0.00 –0.03 0.09

0.01

–0.19 0.07

ÓMKUPG

0.12 0.06 0.07

Compression parameters To Tm EMC LC WC RC

ÓMKTOG

Bending parameters B-1 B-2 2HB-1 2HB-2 Shear parameters G 2HG 2HG5 Tensile parameters EMT-1 EMT-2 LT-1 LT-2 WT-1 WT-2 RT-1 RT-2

MKUUG MKUUG ÓMKSSG ÓMKTMG MKURG MKURG

Surface parameters MIU1 MIU2 MMD1 MMD2 SMD1 SMD2

0.24

MKTSG MKUMG MKVPG

Structural parameters W Fiber Weave

0.19 –0.25 0.52

–0.38 –0.16

ÓMKSOG

4 15.2%

MKVOG MKVNG

–0.22 –0.34 0.06

ÓMKUOG MKUNG

MKUQG

MKTUG MKRSG

–0.03

ÓMKVMG MKROG –0.23 0.08

1 and 2 refer to warp and weft directions respectively. *Highest loading factor for each fabric mechanical parameter.

linear load–extension curve. A negative correlation of LT with Component 1 can again be related to the strong positive correlation between fabric extensibility EMT and Component 1. The strong negative correlation between LT and EMT is a direct result of the fabric tensile test method adopted by the KES tensile tester [4] whereby the fabric is

extended to a fixed maximum load prior to recovery. Although it could be argued that the measurement of EMT may not add greatly to the information provided by measuring LT, the fact is that both parameters are obtained simultaneously from the one fabric tensile test and are thus included in the present analysis.

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Figure 1 Percentage distribution of fabric mechanical parameters in Component 1.

Component 1 which is strongly related to the tensile properties of the textile fabrics was named the “Fabric Extensibility” in this analysis.

(b) Component 2 Component 2 accounted for 17.4% of total explained variance for the mechanical properties of the light-weight wool and wool-blend fabrics. All the measured fabric surface characteristics of MIU1, MIU2, MMD1, MMD2, SMD1 and SMD2 which are all positively correlated with Component 2 are shown in Figure 2. The remaining property in Component 2 is the weave structure which has a negative correlation (with Component 2). Surface properties play an important role for the fiftyeight wool and wool-blend fabrics investigated in the present

study. Plain weave shows higher values of MIU, MMD and SMD than twill or satin weaves represented by the negative correlation between Component 2 and the weave structure. In the analysis, plain weave was arbitrarily regarded as positive and other weave structures such as twill were regarded as negative. The present results show that measurements in both warp and weft directions play an important role in explaining the surface properties of wool and wool-blend fabrics. These parameters explain the important attributes of the wool and wool-blend fabrics in terms of surface friction, smoothness or roughness, coarseness and hairiness. These attributes represent essential features of high-quality wool and wool-blend suiting materials. The main properties contributing to Component 2 were the fabric surface geometry and surface friction together

Figure 2 Percentage distribution of fabric mechanical parameters in Component 2.

Multivariate Studies of Mechanical Properties for Wool and Cotton Fabrics J. K. C. Lam and R. Postle with weave structure. Component 2 was therefore termed “Fabric Surface Geometry and Weave Structure” in the present study.

(c) Component 3 Component 3 accounted for 15.6% of total explained variance and it incorporates six fabric bending and shear mechanical parameters, all of which have strong positive correlation with Component 3. Three parameters represent fabric bending properties (B2, 2HB1, 2HB2) and the other three parameters represent fabric shear properties (G, 2HG, 2HG5). The positive correlation of fabric bending and shear parameters with Component 3 is to be expected for wool and wool-blend fabrics as both bending and shear stiffness and hysteresis are directly related to wool fabric stiffness, firmness and crispness. These fabric parameters are very important in terms of wool fabric quality and tailoring performance. It is interesting that warp bending rigidity (B1) is not included in Component 3 in the present study, but is included in Component 4. This may be a reflection of the fact that warp bending rigidity B1 for the fifty-eight wool and wool-blend fabrics is more significant in terms of fabric thickness (Component 4) than directly in terms of fabric bending and shear properties (Component 3). Component 3 was termed the “Fabric Bending and Shear Rigidity and Hysteresis” for the wool and woolblend fabrics.

(d) Component 4 Component 4 accounted for 15.2% of the total explained variance of the wool fabric mechanical properties and incorporates four fabric mechanical parameters and one structural parameter. They are To, Tm, RC, B1 and W. The first three parameters are fabric compression properties, the fourth is the warp fabric bending rigidity and the last is fabric weight (W). The high positive correlation of fabric thickness (To and Tm) with Component 4 can be explained in terms of the influence of wool fiber properties on fabric thickness and fullness. A bulky or high crimp wool fiber variety would yield more air space between fibers in the fabric, which is therefore thicker than fabric produced from less bulky wool fiber varieties. The positive correlation between fabric (warp) bending rigidity B1 and Component 4 is also related to the effect of fabric thickness. Fabric weight (W) is correlated with fabric thickness (both To and Tm) and is an important property to explain the fabric bulkiness and softness of these wool/wool-blend fabrics. The negative correlation of RC with Component 4 means that fabric compression resilience decreases when increasing fabric thickness. A heavy pressing would pro-

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duce a thinner finished fabric material which is relatively difficult to compress and will give a higher compression resilience. Component 4 was therefore termed the “Fabric Bulkiness and Weight”.

(e) Component 5 Component 5 accounted for 7.1% of total explained variance and incorporates two fabric mechanical parameters, namely RT1 and RT2. Tensile resilience (RT) is measured as the ratio of recovered energy per unit area to the energy of extending the fabric in the load–extension curve. A positive correlation of RT (both warp and weft) with Component 5 means that wool fabrics having high values of Component 5 are highly elastic during fabric extension. The spiral and helix shape of the crimped wool fiber structure can to some extent explain the elastic behavior of wool fabrics. Component 5 was termed the “Fabric Tensile Resilience Component”.

(f) Component 6 Component 6 accounted for 5.7% of the total explained variance and incorporates one fabric parameter, fiber composition. The fiber composition in the present study consists of two types, namely pure wool or wool-blend fabrics (wool/ polyester or wool/silk). This component plays a relatively small role in the explanation of the total variance of the fabric mechanical properties for the whole population. Component 6 in the present study was termed the “Fiber Component”.

(g) Component 7 Component 7 accounted for 5.1% of the total explained variance and consists of two fabric mechanical parameters, namely EMC and LC. The EMC is the fabric compressibility and is measured as the ratio of the difference between surface thickness at 4.9 kPa and 49 Pa, expressed as a ratio of the original fabric thickness at 49 Pa. This negative correlation of EMC with Component 7 can be explained in terms that some fabrics are highly pressed during finishing, the surface thickness is reduced and so the fabric density is increased, therefore giving a relatively low EMC value. The small positive correlation of LC with Component 7 is also a function of the inverse relationship between fabric compressibility EMC and linearity LC. Component 7 was therefore named “Fabric Compressibility”.

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Table 5 Summarized results of rotated factor solution for mechanical properties of 58 wool and wool-blend fabrics. Component

Name

Mechanical parameters

1 2

Extensibility Surface geometry and weave structure

3 4 5 6 7

Bending and shear rigidity and hysteresis Fabric bulkiness and weight Tensile resilience Fiber Compressibility

EMT1, EMT2, -LT1, -LT2, WT1, WT2, -WC MIU1, MIU2, MMD1, MMD2, SMD1, SMD2, -(Weave) B2, 2HB1, 2HB2, G, 2HG, 2HG5 To, Tm, -RC, B1, W RT1, RT2 -(Fiber) -EMC, LC

qçí~ä

(h) Summary Table 5 summarizes the results of the rotated factor solution for the fifty-eight lightweight wool and wool-blend fabrics analyzed in the present study. The seven component factors listed in Table 5 altogether explain 86% of the total variance for the mechanical properties of the fifty-eight wool/wool-blend fabrics analyzed in the present work. The first two components together with Component 5 in Table 4 account for 44.4% of the total variance of the mechanical properties of the light-weight wool and woolblend fabrics. These three components can be evaluated fully from the fabric tensile and shear tester (KES-FB1) and fabric surface tester (KES-FB-4). This means that only two KES-F mechanical testers are needed to account for

Explained variance 19.9% 17.4% 15.6% 15.2% 7.1% 5.7% 5.1%

USKMB

44.4% of the total variance of the wool and wool-blend fabrics. As the KES-FB1 also performs a fabric shear test, this test can therefore account for approximately half the variance of Component 3. Altogether, these two KESF testers (the fabric tensile/ shear tester and the fabric surface tester) together with some knowledge of fiber composition (Component 6) explain approximately 58%, which is over half of the total variance, of the mechanical properties for the 58 wool and wool-blend fabrics. Most of the remaining variance can be explained by obtaining the fabric weight W and by carrying out a fabric compression test (using the KES-F fabric compression tester) leaving only a small unexplained part of the variance attributable to the relatively difficult-to-measure fabric bending properties.

Table 6 Fabric characteristics for 20 medium/heavy-weight cotton denim fabrics. Fabric sett Fabric ID

Composition

Structure

W g/m2

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20

Cotton Cotton Cotton Cotton Cotton/Lycra Cotton Cotton Cotton Cotton/Lycra Cotton Cotton/Lycra Cotton/Lycra Cotton/Lycra Cotton Cotton/Lycra Cotton Cotton/Lycra Cotton/Lycra Cotton Cotton

Twill Twill Twill Twill Twill Twill Twill Twill Twill Twill Check Herringbone Twill Corduroy Twill Twill Twill Twill Twill Twill

252 311 199 265 260 362 430 421 409 303 243 251 281 303 343 453 409 290 414 499

(Threads per cm)

Yarn count (Tex)

Stretch

Ends

Picks

Warp

Weft

weft

50 50 43 47 50 31 24 24 31 28 31 31 59 25 35 27 25 43 29 24

24 19 23 20 24 18 16 19 18 18 24 24 20 50 18 18 22 24 20 17

30 30 28 30 30 59 84 84 84 49 37 37 30 49 62 69 84 37 61 107

37 84 28 59 29.5 + 70 Denier 59 98 84 60 + 70 Denier 84 37 + 70 Denier 37 + 70 Denier 37 + 70 Denier 37 37 + 70 Denier 107 59 + 40 Denier 59 + 150 Denier 84 98

No No No No Yes No No No Yes No Yes Yes Yes No Yes No Yes Yes No No

Multivariate Studies of Mechanical Properties for Wool and Cotton Fabrics J. K. C. Lam and R. Postle

Rotated Factor Solution for Cotton Denim Fabrics The multivariate technique of principal component analysis used for wool and wool-blend fabrics was also applied

to twenty medium to heavy-weight cotton denim fabrics manufactured in Hong Kong and China. Table 6 shows the fabric characteristics of these denim/trouser fabrics including eight fabrics containing Lycra in the weft. Table 7 shows the results after Varimax rotation by principal component analysis.

Table 7 Rotated principal component analysis on the cotton denim fabrics (Rotation Method: Varimax with Kaiser Normalization). Component Explained Variance

1 35.4%

2 19.6%

3 17.1%

4 12.2%

5 11.1%

–0.68* 0.04 0.08 –0.69* –0.67* –0.14 0.74* –0.24

0.51 –0.95* –0.03 0.54 0.50 –0.95* –0.50 0.92*

0.20 –0.22 0.26 0.37 0.22 –0.16 –0.42 0.15

–0.06 –0.06 0.94* 0.05 0.06 –0.04 –0.03 –0.02

0.32 0.12 0.15 0.31 0.37 0.11 0.08 0.25

0.73* 0.18 0.59 0.04

0.06 0.25 –0.28 0.16

–0.01 0.93* 0.02 0.76*

0.64 0.06 0.73* 0.59

–0.03 0.14 –0.19 –0.12

–0.13 –0.40 –0.11

0.54 0.04 0.62

0.82* 0.85* 0.73*

0.09 0.17 –0.09

0.09 –0.22 –0.12

0.70* 0.90* –0.70*

–0.04 0.21 –0.14

–0.65 –0.07 –0.44

0.24 0.02 –0.24

–0.14 –0.37 –0.05

0.97* 0.93* –0.25 0.90* –0.15 0.94*

0.12 0.11 –0.02 –0.16 0.11 –0.01

–0.03 –0.04 0.21 0.20 –0.22 –0.14

–0.07 0.26 –0.02 0.10 0.17 0.22

0.07 –0.11 0.92* 0.08 0.94* –0.14

0.93* 0.83* –0.13 0.35 –0.31

0.07 –0.15 0.38 0.15 –0.92*

–0.06 –0.28 0.39 0.10 –0.13

0.13 0.39 –0.52 0.76* 0.16

–0.14 0.22 –0.62* 0.48 –0.01

Tensile parameters EMT1 EMT2 LT1 LT2 WT1 WT2 RT1 RT2 Bending parameters B1 B2 2HB1 2HB2 Shear parameters G 2HG 2HG5 Compression parameters LC WC RC Surface parameters MIU1 MIU2 MMD1 MMD2 SMD1 SMD2 Thickness/structural parameters To Tm EMC W FIBER

1 and 2 refer to warp and weft directions, respectively. * Highest loading factor for each fabric mechanical parameter.

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(a) Component 1 Component 1 accounted for 35.4% of the total explained variance for these 20 cotton denim fabrics and contains fourteen mechanical parameters. These parameters can be grouped into three areas, namely surface characteristics (MIU1, MIU2, MMD2 and SMD2), compression properties (LC, WC, RC, To and Tm) and tensile properties (EMT1, LT2, WT1 and RT1) and one parameter on bending (B1). The distribution of each mechanical property for Component 1 is shown in Figure 3. The first group of surface properties accounted for 36% of Component 1 to explain the fabric properties for the twenty medium to heavy-weight cotton fabrics which are used for trousers and denim. Some denim fabrics are inserted with Lycra in the weft direction to make the denim highly extensible in the weft direction. As such, the weft yarn plays a significant role in these fabrics. This can be explained in terms of the surface characteristics of MMD2 and SMD2 in Component 1. Both MMD2 and SMD2 show a significant effect on surface properties for these denim fabrics because of the insertion of Lycra yarn in the weft direction. Both MIU1 and MIU2 are included in the surface properties of the cotton fabrics which can be explained by the fact that equal values of these parameters are obtained in the warp and weft directions. The second group accounted for 33% of Component 1 to explain fabric compression properties. Fabric thickness (To and Tm both measured at different pressure) is correlated with fabric weight to explain the fabric fineness, coarseness and roughness (for the denim fabrics). The positive correlation of LC and WC and negative correlation with RC can be explained from the correlation matrix for these cotton fabrics. Both LC and WC are related to measures of the energy used to compress the fabric up to 4.9 kPa pressure (under the compression–thickness curve).

There is a negative correlation of RC with fabric thickness (Tm or To); that is, when the fabric thickness increases, the fabric compression resilience is reduced. The possible explanation may be that highly compressed fabric (decreased thickness) is accompanied by increased compression resilience because of the finishing treatment applied to some of these cotton fabrics. The third group accounted for 25% on Component 1 to explain fabric extensibility. The tensile parameters EMT1 and WT1 are highly correlated, with correlation coefficient of 0.91. The negative value of EMT1 and WT1 with respect to Component 1 means that Component 1 is preferred for a less extensible fabric in the warp direction. This is true for these twenty cotton fabrics as the average warp extensibility was 7.5% (1.5–11.3%) and the average weft extensibility was 15.1% (3.9–56%) greatly influenced by the Lycra inserted in the weft direction for some fabrics). The relationship of RT1 and EMT1 has a negative correlation coefficient of –0.78 for these twenty cotton fabrics. Therefore, a negative correlation of EMT1 to Component 1 would imply a positive correlation of RT1 to Component 1. The reason is that the tensile resilience RT1 is a measure of the recovery process in the force–extension curve. A higher fabric extension means that the recovery process will take a longer time and therefore less energy is recovered. The relationship between RT and EM is therefore negative. The last mechanical parameter in Component 1 is warp-bending rigidity (B1) which is positively correlated with Component 1. The explanation is that fabric bending rigidity is correlated with fabric weight and the fabric weight in turn is correlated with fabric thickness. The bending rigidity and thickness play an important role in fabric stiffness and softness and these two attributes are important elements when defining quality jean fabrics.

Figure 3 Distribution of mechanical properties for Component 1 on cotton denim fabrics.

Multivariate Studies of Mechanical Properties for Wool and Cotton Fabrics J. K. C. Lam and R. Postle In summary, Component 1 contains fabric mechanical parameters of tensile, compression, bending and surface properties in order to define medium to heavy-weight cotton trouser and denim fabrics. Component 1 was therefore termed the “Basic Tensile, Compression, Bending and Surface Requirements” for medium to heavy-weight cotton fabrics in the present work.

(b) Component 2 Component 2 accounted for 19.6% total explained variance and consists of four mechanical parameters. Three are tensile parameters, EMT2, WT2 and RT2, and the fourth parameter is fiber composition (Fiber). The three tensile parameters are all measured in the weft direction. EMT2 and WT2 are both negatively correlated to Component 2 and RT2 is positively correlated to Component 2. The negative correlation of EMT2 and WT2 to Component 2 means that Component 2 is preferred for cotton fabrics with moderate weft extension and tensile energy. The weft extension for these twenty cotton fabrics ranges from 3.9 to 56% with an average of 15.1%. This result may demonstrate that extremely high weft extension is not the key property in these cotton fabrics. The last parameter for Component 2 is fiber composition (Fiber). All fabrics for these twenty samples are pure cotton with some fabrics having the insertion of Lycra yarn in the weft direction. If the correlation with pure cotton in the fiber composition is positive, then the correlation with Lycra in these fabrics would be negative. This means that the Lycra yarn used in the weft direction for these twenty cotton fabrics has a significant effect on Component 2. Since all the mechanical parameters in Component 2 represent tensile properties of fabric in the weft direction, Component 2 in the present study was termed the “Weft Extension Properties”.

(c) Component 3 Component 3 accounted for 17.1% of the total explained variance and incorporates five mechanical parameters. Two parameters are for fabric bending (B2 and 2HB2) and three parameters are for shear (G, 2HG and 2HG5). All five parameters are positively correlated with Component 3. The positive correlation of shear parameters with Component 3 can explain the important fabric properties of fullness, firmness, hardness, crispness and stiffness for these twenty heavy-weight cotton fabrics for denim and trousers. The product of shear rigidity and fabric extensibility may be related to the fabric formability in the bias or diagonal direction of the fabric, which can be related to the tailorability of these twenty heavy-weight cotton fabrics in the making up process.

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The positive correlation of B2 and 2HB2 with Component 3 can explain the fabric properties of stiffness, hardness and firmness, which are important attributes of denim. Component 3 includes only the bending parameters in the weft direction which can be explained by the importance of Lycra yarn added in the weft direction for these twenty cotton fabrics. Components 3 contains mechanical parameters on bending (weft direction) and shear for these medium to heavy-weight cotton fabrics for denim and trousers and was named “Shear and weft bending” in the present study.

(d) Component 4 Component 4 accounted for 12.2% of total explained variance and contains two mechanical parameters and one fabric structural parameter. They are LT1, 2HB1 and W (fabric weight per unit area) and all are positively correlated with Component 4. The fabric weight (W) is one of the important structural parameters for the twenty medium to heavy-weight cotton fabrics and has a high correlation with fabric thickness (Tm). The correlation between W and Tm is 0.90 and fabric weight explains the fabric properties of aerial density and thickness. The mechanical parameters of LT1 and 2HB1 are both measured in the warp direction. The correlation of LT1 and 2HB1 with Component 4 means that the tensile linearity and bending hysteresis in the warp direction have a significant effect on Component 4. Component 4 has two constituent mechanical parameters in the warp direction and was named “Warp Tensile Linearity and Bending Hysteresis” in this study.

(e) Component 5 Component 5 accounted for 11.1% of total explained variance and it has three parameters, namely MMD1, SMD1 and EMC. The first two parameters, MMD1 and SMD1, explain the fabric surface characteristics in the warp direction. For these twenty medium to heavy-weight cotton fabrics for denim and trousers, the fabric surface characteristics are very important and the weft surface parameters of MIU2, MMD2 and SMD2 were already included in Component 1 in the present study. It can be seen that the weft direction plays a very significant role in explaining the fabric surface characteristics of these twenty cotton fabrics and therefore, they are placed in Component 1. The parameters of MMD1 and SMD1 in Component 5 are used to supplement the explanation of fabric surface characteristics in Component 1. Component 5 explains the surface roughness and deviation of coefficient of friction of these twenty cotton fabrics in the warp direction.

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Table 8 Summary of mechanical parameters for cotton denim fabrics. Component

Name

Mechanical parameters

1

Basic tensile, compression, bending and surface requirements Weft extension properties Shear and warp bending Warp tensile linearity and bending hysteresis Supplementary warp surface parameters

MIU1, MIU2, MMD2, SMD2, LC, WC, -RC, To, Tm, -EMT1, -LT2, WT1, RT1, B1 -EMT2,-WT2, RT2, -(Fiber) B2, 2HB2, G, 2HG, 2HG5 LT1, 2HB1, W MMD1, SMD1, -EMC

2 3 4 5

qçí~ä The last parameter in Component 5 is EMC, which is negatively correlated with Component 5. The parameter EMC measures the change in fabric thickness under different pressures. A negatively correlated value of EMC can imply that the fabric is highly pressed in finishing, the space between each fiber is reduced and the fabric density is increased. As a result, fabric thickness decreases giving a negatively correlated value of EMC. The parameter EMC in Component 5 is used to supplement the parameters of To and Tm in Component 1. Component 5 in the present study was named “Supplementary Warp Surface Properties”

(f) Summary The mechanical parameters included in each component to explain these twenty medium to heavy-weight cotton denim and trouser fabrics are shown in Table 8. It should be noted that the Component 1 for these denim fabrics included surface characteristics, extensibility and compression parameters. As denim is normally a strong stiff fabric, tensile and compression tests are important for denim. As most denim will have special finishing treatments (e.g. washing and indigo dyeing), the surface characteristics are important for high-quality denim or trouser fabrics. Components 1 and 2 together can account for 55% of the total variance implying that fabric objective measurements such as tensile, compression and surface testing are essential for medium to heavy-weight cotton fabrics. The use of Lycra in the weft yarn for some of these denim fabrics is reflected in Components 1 and 2 in the present study. This elastic yarn has a significant effect on fabric surface and mechanical properties as demonstrated in this study. Since similar materials and production methods were used for the 20 cotton denim fabrics, the principal component analysis can successfully reduce the data set into five components explaining over 95% of the total population variance.

Explained variance 35.4% 19.6% 17.1% 12.2% 11.1%

VRKQB

Conclusions The principal component analysis was found to be very useful to analyse the complex, multi-dimensional relationships of the fabric objective measurement (FOM) datasets for both wool/wool-blend fabrics and cotton denim fabrics used for the present study. As the principal component analysis is an independent technique and does not explicitly require the variable to be divided into dependent and/or independent variables (as is normally required in multiple stepwise regression analysis), this technique has potentially much greater applicability to the specification of fabric quality along the textile and apparel supply chain. Although the end use for the lightweight wool/woolblend fabrics is for suiting material and the cotton fabrics are used for denim casual wear, these two very different fabric groups showed certain similarities in terms of fabric mechanical properties examined by the principal component analysis technique. Firstly, fabric surface properties (MIU, MMD, SMD) represent an important component for both wool and cotton fabrics. This surface component accounted for 17.4% (Component 2) of total population variance for wool/woolblend fabrics and a significant part of the 35% (Component 1) of total population variance for cotton fabrics. These fabric surface properties for wool fabrics can explain the fabric smoothness and softness which are directly related to the fabric handle. For the cotton fabrics, Component 1 included fabric surface properties, compression properties and fabric thickness which are essential properties for the medium to heavy-weight cotton fabrics used for denim and trousers for casual wear. Secondly, the bending and shear properties (B2, 2HB2, G, 2HG, 2HG5) represent another important component to explain the fabric quality and performance for both wool and cotton fabrics. These properties accounted for 17.1% (Component 3) of total population variance for wool/woolblend fabrics and 15.6% (Component 3) of total population variance for cotton fabrics. These bending and shear properties are important parameters to explain fabric hardness, stiffness and tailorabity for these fabrics.

Multivariate Studies of Mechanical Properties for Wool and Cotton Fabrics J. K. C. Lam and R. Postle On the other hand, there are some unique features of these two kinds of fabrics. The medium to heavy-weight cotton denim fabrics show strong fabric elasticity because of the insertion of Lycra yarn in the weft direction. This elastic yarn has a significant effect on fabric mechanical properties and is shown in Component 2 (EMT2, WT2, RT2) in the present study explaining 19.6% of population variance. Another unique feature of these medium to heavy-weight cotton denim fabrics is the fabric weight (W) in Component 4 which explained 12.2% of total population variance. As denim fabrics are commercially expressed in terms of fabric weight, this feature is reflected in the present study. The results show how multivariate statistical analysis techniques of fabric mechanical and surface property data for two very different groups of fabrics can provide a basis for the specification and control of fabric quality along the textile and apparel supply chain. These reduced datasets with the most important component extracted first and the least important component extracted last, greatly facilitate the data interpretation in the textile and apparel supply chain.

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Acknowledgements The authors wish to acknowledge the sponsorship from the Institute of Textiles and Clothing (ITC) at the Hong Kong Polytechnic University for providing partial financial support for this research work.

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