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 coefficient 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 onehour 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 coefficient value is lower
than 7^{[8]}.
A calculated inflation coefficient 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 coordinates corresponding to two centred and reduced
principal variables.
Contribution of the different factors
The statistical determination of the contribution coefficients 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 coefficients 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 coefficient of the normalised factor X_{i }
X_{i}: Centred and reduced variables
The contribution coefficient C_{i} of factor X_{i} is
calculated by the following formula:
Where: Y: Wrinkling output
R_{2} (adjusted): Correlation coefficient 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 coefficients 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:
Studied
parameters 
Wrinkle
degree in a warp direction 
Wrinkle degree in a weft direction 
Immediate evaluation of wrinkle index 
Wrinkle index
evaluated after 1 hour 
Material 
*** 
*** 
*** 
*** 
Warp
count 
*** 
** 
*** 
*** 
Weft
count 
** 
*** 
** 
** 
Twist
warp direction 
* 
* 
* 
* 
Twist
weft direction 
* 
* 
* 
* 
Twist
warp value 
* 
* 
** 
** 
Twist
weft value 
* 
* 
** 
** 
Weave 
* 
* 
*** 
*** 
Warp
rate 
*** 
** 
*** 
*** 
Weft
density 
** 
*** 
** 
** 
Contraction 
*** 
** 
*** 
*** 
Shrinkage 
** 
*** 
** 
** 
Thickness 
** 
** 
** 
** 
Weight 
*** 
*** 
*** 
*** 
Warp
bending rigidity 
** 
** 
** 
** 
Weft
bending rigidity 
** 
** 
** 
** 
Drape
coefficient 
*** 
*** 
*** 
*** 
Warp
initial modulus 
*** 
* 
** 
* 
Weft
initial modulus 
* 
*** 
** 
* 
Warp
break strength 
* 
* 
* 
* 
Weft
break strength 
* 
* 
* 
* 
Warp
extension at break 
* 
* 
* 
* 
Weft
extension at break 
* 
* 
* 
* 
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
coefficient, 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 coefficient 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

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

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), 4450 (2002).

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

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

Na Y, Pourdeyhimi B: Assessing Wrinkling Using
Analysis and Replicate standards, Textile Res J 65 (3), 149157 (1995).

Norme française NF G 07110 Mai 1972, essais des
étoffes  Détermination de l'autodéfroissabilité par mesurage de
l'angle rémanent après pliage.

Norme française NF G 07125, essais des étoffes
 Détermination de l'auto défroissabilité par mesure au cylindre
creux.

Sergent M, Mathieu D, PhanTanLuu R et Drava G:
Correct and Incorrect Use of Multilinear Regression, Chem and Intel
Laboratory Systems, 153162, 1995.

Shi F, Hu J, and Yu T: Modeling the Creasing
Properties of Woven Fabrics, Textile Res J 70 (3), 247255 (2000).
The authors are with the Textile Research Unit of
ISET Ksar Hellal, Tunisia. Email ID: slah_m@yahoo.com.
