Yarn count, density, tensile rigidity, weight and drape co-efficient have a greater influence on the wrinkling of a woven structure, infer Raja Zaouali, Slah Msahli and Faouzi Sakli.

Whether discussing aesthetic or comfort performance properties of fabrics, wrinkle resistance^[9] is one of the most important properties that is regularly evaluated with reference to objective and subjective analysis. Indeed, fabric wrinkle recovery is a major concern for consumers over their visual judgement of textiles.

Wrinkle recovery can be defined as the capacity to recover and make the wrinkles disappear after stress releasing. The wrinkling is influenced by several physical and mechanical parameters, which are related to the fibres, yarns and fabrics^[2,5]. The number of parameters influencing wrinkling is important, and this article is the result of a study aimed at identifying most important of the parameters.

Experimental

Elaboration of an experimental database

In order to determine the parameters influencing the wrinkled fabrics, the authors constructed experimentally a database of fifty kinds of different fabrics, describing for each one the input and output parameters.

The input parameters were represented by fibres characteristics such as the fibres chemical nature, yarn characteristics like count, twist direction and value, and fabric characteristics among which the authors selected physical parameters like weave, density, thickness and weight, and mechanical parameters such as the bending rigidity, drape co-efficient as well as the tensile strength and the elongation at break.

The output parameters evaluating the fabrics wrinkling were determined objectively and subjectively. Indeed, on the one hand, the authors determined the wrinkle degree in warp and weft directions by the remnant angle measure method^[6] that consists of maintaining a fabric sample folded during a given time under a predetermined load. On the other hand, we visually determined the wrinkle index measured by the French method "cylindre creux"^[7] which consists of introducing a fabric sample in a hollow cylinder, then submitting it during a fixed time to the static action of the mass. The assessment is immediately done after removing the sample and after one-hour time in order to consider the relaxation.

It is important to note that all data base parameters were measured according to the international norms in the normal atmosphere of textiles conditions.

Analysis of the database

 In order to determine the correlations between the different parameters, three quantitative methods were used.

Inflation factor

Once the database are established, the authors tried to evaluate the intensity links between the different variables by the inflation's theories^[1] invented essentially in order to study the quality of data distribution and the base homogeneity. A parameter is considered

significant in the database when its inflation co-efficient value is lower than 7^[8].

A calculated inflation co-efficient is given by:

Where:

X: Information matrix of the database

Cjj: Diagonal element of the matrix [Xtr . X]^-1

X_moy: Average of the matrix column

N: Number of experiments

Principal component analysis

The principal component analysis (PCA) is a method of extraction of the main factors based on a quantitative analysis of the correlations^[3]. Its goal is to study and reduce the survey space of variables in order to simplify the raw data, to find out (graphically) some links and to identify some macro features (principal components). This method consists on subjective grouping of the correlated variables, which were represented graphically by the co-ordinates corresponding to two centred and reduced principal variables.

Contribution of the different factors

The statistical determination of the contribution co-efficients of the different factors allows us to study the internal dispersion of each group determined by the principal component analysis. Besides, the aim of this method is to reduce the number of factors and to eliminate the low influence parameters^[4].

In order to determine the contribution of each factor on the studied properties, the analysed data had to be centred and reduced. Then, the standardised regression co-efficients have been calculated in accordance with the Path analysis^[8], which is the multiple regression application. The contribution of the variables (X_i) according to the wrinkle variation (Y) is based on a contribution law obtained under the following shape:

Where:

ai: Regression co-efficient of the normalised factor X_i

X_i: Centred and reduced variables

The contribution co-efficient C_i of factor X_i is calculated by the following formula:

Where: Y: Wrinkling output

R₂ (adjusted): Correlation co-efficient of the normalised regression Y vs X_i



Results and discussion

After an experimental achievement of 50 tests on different woven structures and determination of the wrinkling influencing parameters for each fabric, the authors got an important database including 27 parameters (twenty three input and four output ones). This database was analysed by the means of different statistical methods in order to reduce the important number of parameters and to identify those, which are the most influential on the wrinkling of fabrics.

Here one can notice that the inflation factor of each parameters is lower than 7. So, one can assure that the database is significant and it does not present any important imprecision in the evaluations. Besides, most inflation factors are close to 1, which means that the parameters are very bound.

After "ensuring" the significance of the database and according to the application of the principal component analysis method, the authors obtained the graph shown in Figure 2.

The Figure 1 represents the distribution of the inflation factors of each database variable. Figure 2 shows that the two principal factors have an important weight with a ratio of 45%. The correlated parameters are grouped in small groups like for example: the twist direction and value as well as the yarn count in the warp and the weft directions.

Furthermore, one can note the oddness of the parameter "weave" which is independent and cannot present any correlation with the other parameters.

One can also note according to the graph of Figure 2, that the two groups ("warp and weft count" and "warp rate and weft density") are nearly opposed. In fact, they are negatively correlated. In addition, many parameters like the drape, the thickness and the weight are correlated with bending rigidity.

However, this method does not allow one to judge the internal dispersion of each group. Thus, it is necessary to analyse the database by the method of contribution of the different factors.

The authors worked out the graph of the Figure 3 after representing the distribution of the contribution co-efficients of the different parameters, which are calculated for the wrinkling degree in the warp direction.

One can deduce from Figure 3 that the drape is the most influencing parameter on the wrinkling in warp direction. One can also note that the most influencing parameters on the warp wrinkle degree are: nature of fibres, warp count, warp rate, weight, warp bending rigidity, drape and warp initial modulus of traction.

Consequently, these results showed that wrinkling in the warp direction was influenced by the whole warp parameters. With the same contribution method applied to the different other outputs concerning the fabrics wrinkling, the authors identified the most influencing parameters on the wrinkle degree in the weft direction and in the same way for the wrinkle index measured by the subjective French method, "cylindre creux" immediately after removing the sample, then after an hour time of relaxation.

Since the groups determined by the method are correlated, the authors have selected from every group one parameter only having the most important contribution factor in order to reduce the space of the study.

Table 1: Influence of the different parameters on fabrics wrinkling:

For every PCA group, the influence of the parameter having the most important contribution factor was noted in the Table 1 by (* * *), the one having a weak influence was designated by (* *) and the one which do not have an influence on fabrics wrinkling was noted by (*).

As shown in Table 1 recapitulating the results of the data base analysis of the four wrinkling outputs, one can note that the nature of fibres, the weight and the drape have an important effect on the woven wrinkling whatever the evaluation method used is, objective or subjective.

One can also deduce from Table 1 that the wrinkling of a woven structure evaluated in one direction (warp or weft), is more influenced by the yarn and fabric parameters analysed in the same direction.

Besides, the parameter "weave" does not have any important influence on the wrinkle degree measured by the remnant angle method; nevertheless, it has an important effect on the wrinkle index measured by subjective method of "cylindre creux" which is based on the visual assessment of the fabric's aspect.

Finally, the parameters of strength and elongation to break as well as the twist direction and value do not have a considerable influence on the fabric wrinkling whatever the control method is.

Conclusion

In this study, several parameters that are related to fibres, yarns and fabrics, occur in the wrinkling assessment. One can note that the yarn and the fabric parameters analysed in one direction (warp or weft) such as the yarn count, the density, the tensile rigidity, the weight and the drape co-efficient, have a greater influence on the wrinkling of a woven structure, which is estimated by measure of the remnant angle in the same direction. Besides, the material, the weight and the drape co-efficient have an important influence on the wrinkling of fabrics whatever the method of evaluation is used.

The principal components analysis and the path analysis were used in order to reduce the number of influential factors on the fabrics wrinkling. This reduction can be used thereafter for the modeling of fabrics wrinkling.

References

1. Jambu M: Méthode de base de l'analyse des données, Edition 1999, page 431.

2. Kang T J, Cho D H and Kim S M: Geometric Modeling of a Cyber Replica System for Fabric Surface Property Grading, Textile Res J 72 (1), 44-50 (2002).

3. Lagarde J: Initiation à l'analyse des données, Dunod, 1995.

4. Legendre P: l'Analyse Statistique Multivariée des Cartes et Données, décembre 1999.

5. Na Y, Pourdeyhimi B: Assessing Wrinkling Using Analysis and Replicate standards, Textile Res J 65 (3), 149-157 (1995).

6. Norme française NF G 07-110 Mai 1972, essais des étoffes - Détermination de l'auto-défroissabilité par mesurage de l'angle rémanent après pliage.

7. Norme française NF G 07-125, essais des étoffes - Détermination de l'auto- défroissabilité par mesure au cylindre creux.

8. Sergent M, Mathieu D, Phan-Tan-Luu R et Drava G: Correct and Incorrect Use of Multilinear Regression, Chem and Intel Laboratory Systems, 153-162, 1995.

9. Shi F, Hu J, and Yu T: Modeling the Creasing Properties of Woven Fabrics, Textile Res J 70 (3), 247-255 (2000).

The authors are with the Textile Research Unit of ISET Ksar Hellal, Tunisia. Email ID: slah_m@yahoo.com.