Objective Evaluation of Fabric Wrinkles and Using Fractal Geometry TAE JIN KANG

AND

Department of Fiber and Polymer Science,

Seam Puckers

JAE YEOL LEE

Seoul National

University, Seoul, Korea

ABSTRACT Fractal geometry is used to objectively evaluate the surface ruggedness of fabric wrinkles and seam puckers. To measure the fractal dimension (FD) of wrinkles and puckers, both the spatial cubical box-counting method and the cross-sectional method are employed. The results of the fractal dimensions of wrinkles and puckers are compared with subjective evaluations of the AATCC rating method, and they show that the new objective fractal dimension gives a quantitative practical value for evaluating fabric wrinkles and seam puckers with more accuracy and reproducibility. Thus, the fractal dimension can be used to evaluate the surface ruggedness of wrinkles and puckers. Reliable objective five-rating and ten-rating methods using the fractal dimension are suggested as substitutes for the conventional subjective AATCC five-rating test method to establish a new industrial standard.

The fractal dimension is a quantitative value describing a crinkled, random structure, which Mandelbrot [6] proposed for objects that had not been defined with the classical Euclidean integer dimension because of their abstruseness. In earlier work (Kang et al. [4]), we reported that the fractal dimension could be used to evaluate the complexity of fiber crimp. The surface smoothness of a garment is very important to its aesthetic appearance and wrinkles and seam puckers are often the most important factors affecting fabric smoothness. Therefore, fabric and garment manufacturers have made considerable efforts to improve the surface smoothness of fabrics, and there have been many attempts to objectively evaluate the surface ruggedness with more accuracy and speed. No-iron shirts or shaperetention shirts are widely sold on the market at a premium price. In developing these products, it is often necessary to establish methods for evaluating fabric surface smoothness after washing with different chemical treatments. Since fabrics go through different post-cure resin treatments after liquid ammonium treatments, the effects of resin application and liquid ammonium treatment on the retention properties of shape and surface smoothness after washing are often inaccessible or undifferentiable. Accurate measurements of fabric surface ruggedness would help to establish optimum processing conditions for these products, and there have been many evaluations of fabric wrinkles and seam puckers.

The method of simply comparing the standard with the specimen is widespread [1, 21, but it is tedious and inherently subjective. Recently, Na et al. [7] and Xu et al. [13J used the image of a fabric’s surface to quantify wrinkles, treating the gray value intensity as altitude. However, the gray-value intensity cannot reveal the altitude of every position on the fabric surface because it is bound to change with the intensity and location of the light source, and even with the camera settings of lens, contrast, and brightness. Thus, some wrinkles are emphasized while others are hidden. Amirbayat et al. [3] and Park et al. [8] proposed using a laser probe to measure the real altitude of a fabric surface wrinkle or seam pucker. Stylios et al. [ 11 ] attempted to establish a model of the cognitive process involved in seam pucker assessment.

In this study, using a laser scanning system, we obtain the surface contours of wrinkled fabrics and puckered seams, and we evaluate the degree of the fabric surface’ss ruggedness using the fractal dimension.

Experimental We prepared 25 specimens of wrinkled fabrics and 25 specimens of seam puckers at different levels of wrinkle and pucker grades. Table I lists the wrinkle and seam pucker specimens and their AATCC grades, obtained by subjective human eye evaluation through comparison

469

470 TABLE I. Wrinkle and seam pucker fabric specimens and their AATCC grades by human eye evaluation.

(b) Reconstructed surface after scanning

with the AATCC standard replicas. The contour of the specimen surface was revealed with the laser scanning system, and the box-counting method [9]~ was used to measure the fractal dimension of the surface. A 3D cube was adopted as a unit cell to cover the wrinkle or the pucker. It is well known that a self-similar structure has the following relationship between the unit cell length (l) and the number of occupied unit cells (N), where D is the fractal dimension [4, 12]:

ln N = -D In I + constant .

(1)

The fractal surface has a dimension 2 when the surface is

perfectly smooth plane and a dimension 3 when the extremely rugged surface fills most of the 3D space. Its cross section, cut from the fractal surface, produces a

(c) Cube-counting method

(d) Iteduced cross-sectional method in X-direction

. FIGURE 1. Processes of the cube-counting method and reduced crosssectional method of a rugged fabric surface for measuring fractal dimensions.

a

fractal

with

reduced fractal dimension of D - 1 reduced fractal dimension, the contoured images obtained with the laser scanning system are cut through the cross section in the X-, Y-, and Z-directions using automated image and fractal processing programs. These programs are designed to employ the cube-counting method and the reduced cross-sectional method without any mechanical setting or cutting of the specimen as attempted in other work [5]. The processes of fractal dimension measurements are illustrated schematically in Figure 1, which demonstrates curve

[5, 10]. To

use a

a

the cube-counting and reduced cross-sectional methods. The surface of the fabric (Figure 1 a) is scanned with a laser probe and reconstructed virtually in computer memory, as shown in Figure 1 b. After repeating the procedure used to cover the reconstructed surface with cubes of various sizes, as shown in Figure lc, the fractal dimension of the surface can be obtained with Equation 1, as shown in Figure 3. Figure ld shows a cross section of the reconstructed surface in ~the x-direction; the fractal dimension of the cross section decreases by unity from that of the surface, providing an ideal fractal structure. The size of the cube in the cube-counting method and the size of the grid in the reduced cross-sectional method

471

(a) Perfectly smooth fabric surface

FIGURE 3. Double logarithmic plot of the number of occupied unit (N) and unit cell length (l ) of specimen S5 with a fractal dimension of 2.012. cells

(b) Extremely rugged fabric surface

sections. The FIGURE 2.

Examples of imaginary fabric surface measuring fractal dimensions.

models for

vary from 2 to 10 pixels. A system has been designed to repeatedly perform the automatic evaluation procedure when the contour information has been dumped from the laser scanning system. Figure 2 shows examples of imaginary fabric surface models that were virtually produced in the system. The perfectly smooth surface has a fractal dimension of 2, which belongs to a Euclidean integer dimension, and the extremely rugged surface has a fractal dimension closer to 3 due to its space-filling property. Table II summarizes the fractal dimensions of the imaginary fabric surfaces generated by our system. In the cross-sectional method, six cross sections were cut in the X-, Y-, and Z-directions, and the fractal dimensions of the six cross sections were averaged and added to 1 because they are reduced fractal dimensions. But with a perfectly smooth surface, only one cut of the cross section was made in the Z-direction, because it had no higher altitude. We found that the standard deviation of fractal dimensions of six cross sections remains at about 0.001, which means good reproducibility of the cross

perfectly smooth fabric surface showed fractal dimensions of about 2 in all three cross-sectional directions as well as the cube-counting method. However, the extremely rugged fabric surface had fractal dimensions of about 2.6 to 2.9. The different fractal dimensions are due to the fact that fabric wrinkles or puckered surfaces are not ideal fractal surfaces with eternal complexity and self-similarity, no matter what the magnification. Next we discuss the in-depth explanations for the differences in the X-, Y-, and Z-directions along with the results of a wide range of fabric tests.

Results and Discussion 3 shows the double logarithmic plot between the unit cell length (t) and the number of occupied unit cells (N) with a high correlation coefficient of 0.999, which means that the surface ruggedness of the fabric can be evaluated with high accuracy using fractal geometry. The constant value of 11.379 in the equation implies the factored side length of the whole object, which is derived from the following equation [ 12]:

TABLE II. Fractal dimensions of the

Figure

sample fabric

surface models.

472

Compared constant in

with

Equation 1, the term of D In L is the Equation 1. Therefore, the value of L is

285.878 because D In L 11.379 in this case. Accordto Tsonis [ 12), the value of L is the side length of the ing whole object, and in this work we have also found that the value of L is equivalent to the geometric mean of both side lengths when the object is not a regular square. The size of the specimen was 508 x 160 pixels, and the geometric mean was 508 x 160 285.096, with a difference of only 0.782 from 285.878. Figures 4-6 show the results of the fractal dimension measurements, in which the reduced cross-sectional dimensions have been added with unity. In Figure 4, the fractal dimensions of wrinkled fabric specimens range from 2.010 to 2.050, except for the cross-sectional method in the Z-direction. The fabric specimens with severe wrinkles show higher fractal dimensions compared to the smooth surfaced fabric with all methods. Note that the cross-sec=

=

tional method in the Z-direction shows higher values than other methods. This difference originates from the anisotropy of the fabric. An object that has an isotropic structure has similar shapes in each cross section in any direction, but for the fabric with a transversely isotropic structure, the transverse cross section in the Z-direction shows a different trend from those in X- and Y-directions. Figure 5 shows the cross-sectional shapes in all three directions for a wrinkled fabric specimen. The transverse cross section in the Z-direction shows more complex profiles than cross sections in the X- and Ydirections because many peaks of wrinkles protrude in the Z-direction, resulting. in a higher cross-sectional fractal dimension in that direction. The surface of Figure 2b shows the same tendency as the results in Table II. In addition, the low altitude of the fabric surface close to the plane doesn’t allow many cross-sectional layers in the Z-direction, and thus the standard deviation of crosssectional fractal dimensions in the Z-direction has a

FIGURE 4. Fractal dimensions of wrinkled specimens: (a) reduced cross-sectional method in ~-direction. (b) reduced cross-sectional method in Y-direction, (c) reduced cross-sectional method in Z-direction, (d) cubecounting method.

473 value of about 0.04. This value is considered to be very large compared to 0.002 in the X- or Y-directions, in which a large number of cross-sectional layers can be taken. Therefore, we have found that the cross-sectional method in the X- and Y-directions is more reliable than in the Z-direction with wrinkled fabric samples. The decimal numbers of the fractal dimensions indicate the out-of-plane degree of the fabric surface. The fractal dimensions of the fabric are very close to 2, because the fabric surface is still Hat and close to the plane even with severely wrinkled or puckered specimens.

Figure 6 shows the fractal dimensions of seam pucker specimens that have values of 2.000 to 2.030, except for the

Ficutte 5.

of cross sections of wrinkled in the X-, Y-, and Z-directions.

Shapes

specimens

Ficutte 6. Fractal dimensions of seam reduced cross-sectional method in cube-counting method.

(b)

cross-sectional method in the Z-direction. The fractal dimensions of the puckered specimens show same trend as the wrinkled specimens; more severely puckered fabrics have higher fractal dimensions proportionally, and the Zdirection cross-sectional dimension shows higher values than those of other directions. But they differ from wrinkled

pucker specimens: (a)

reduced cross-sectional method in X-direction.

Y-direction, (c) reduced cross-sectional method in Z-direction. (d)

474

Objective AATCC seam

FIGURE 7.

Shapes of cross

sections of seam pucker in the X-, Y-, and Z-directions.

specimens

where FD is the fractal dimension by the cube-counting method. Also, it is possible to establish a new ten-scale grade to objectively evaluate the surface ruggedness of fabric wrinkles or seam puckers as follows:

specimens in that the fractal dimension in the Y-direction is relatively small. This results from the fact that the cross section in the Y-direction is perpendicular to the seam line, so it has a simpler profile with the seamed point at the center, as shown in Figure 7b. The seam line in the equator is also shown in Figure 7c. With repeated experiments, we found that the subjective AATCC grades don’t have equal intervals; this is unavoidable, since the AATCC evaluation method is based on the five-standard replica system, which has been constructed subjectively with no quantitative basis. However, the fractal dimension is a quantitative geometric value, which is not a discretional indicator or parameter, but a topological dimension that defines a plane cube, or intermediate structure precisely. We propose to substitute the objective methods described in this study for the subjective AATCC wrinkle and seam pucker grades to achieve more precise and linear scale evaluations and equal grade intervals. Both fabric wrinkle and seam pucker grades can be rectified with five ranks as with the conventional AATCC grades:

Objective AATCC

where FD

the fractal dimension

=

by the cube-counting

method, Gw the new ten scale fabric wrinkle grade by the fractal dimension, and GSP the new ten scale seam =

=

the fractal dimension. The fractal dimension grade is sensitive to subtle differences in the surface smoothness of fabrics, and each step in the grade has equal proportionality with the ruggedness of the fabric surface, which is not possible with the conventional, subjective AATCC grading.

pucker grade by

Conclusions We have used fractal geometry to objectively evaluate the surface ruggedness of fabric wrinkles and seam puckers. Fractal dimensions by the cross-sectional method in the Xand Y..directions and the cube-counting method have

proved

useful for

puckers. Also,

quantitative evaluations of wrinkles and objective five-rating and ten-rating

our new

475 methods for fabric wrinkles and seam puckers can rectify the problems with the subjective AATCC test method.

Literature Cited 1. AATCC Test Method 88B, Smoothness of Seams in Fabrics after Repeated Home Laundering, AATCC Technical Manual, pp. 115-118, 1994. 2. AATCC Test Method 124, Appearance of Fabrics after Repeated Home Laundering, AATCC Technical Manual, pp. 210-213, 1994. 3. Amirbayat, J., and Alagha, M. J., Objective Assessment of Wrinkle Recovery by Means of Laser Triangulation, J. Textile Inst. 87, 349-355 (1996). 4. Kang, T. J., Lee, J. Y., Chung, K., and Lee, S. G., Evaluating Yarn Crimp with Fractal Geometry, Textile Res. J. (7), 527-534 (1999). 69 5. Mandelbrot, B. B., and Passoja, D. E., Fractal Character of Fracture Surfaces of Metals, Nature 308 ( 19), 721-722 (1984). 6. Mandelbrot, B. B., "The Fractal Geometry of Nature," Freeman, NY, 1983, pp. 14-43.

7. Na, Y. J., and Pourdeyhimi, B., Assessing Wrinkling Using Image Analysis and Replicate Standards, Textile Res. J. (3), 149-157 (1995). 65 8. Park, C. K., and Kang, T. J., Objective Evaluation of Seam Pucker Using Artificial Intelligence: Parts I, II, III, Textile Res. J. 69 ( 10) 735, (11) 835, (12) 919 (1999). 9. Peitgen, Jurgens, and Saupe, "Fractals for the Classroom, Part 1," Springer-Verlag, NY, 1992, pp. 199-250. 10. Russ, J. C., "Practical Stereology," Plenum Press, NY, 1991, pp. 124-136. 11. Stylios, G., Sotomi, J. O., Investigation of Seam Pucker in Lightweight Synthetic Fabrics as an Aesthetic Property: Parts I, II, J. Textile Inst. 84, 593-610 (1993). 12. Tsonis, A. A., "Chaos: from Theory to Applications," Plenum Press, NY, 1992, pp. 49-54. 13. Xu, B., and Reed, J. A., Instrumental Evaluation of Fabric Wrinkle Recovery, J. Textile Inst. 86, 129-135

( 1995). Manuscript

received November 23. 1998;

accepted May 4. 1999.

Evaluating Peracetic

Acid Bleaching of Cotton as an Environmentally Safe Alternative to Hypochlorite Bleaching NEVIN

ÇIĞDEM

GÜRSOY

AND

HABIP DAYIOĞLU

Istanbul Technical University, Mechanical Faculty, Textile Engineering

Department,

80191 Istanbul,

Turkey

ABSTRACT

Peracetic acid is

produced directly in the bleaching liquor from acetic anhydride and The acid can be catalyzed to bleach knitted cotton fabric at temperatures as low as 30°C in the presence of 2.2’ bipyridine, sodium lauryl sulfate, and sodium tetraborate. We evaluate the effects of the concentrations of hydrogen peroxide and acetic anhydride as well as treatment temperature, time, and pH on whiteness, bursting strength, and water absorbency of the fabric. The results of our investigation show that peracetic acid can be acceptable as a bleaching agent for the textile industry as an alternative to hypochlorite bleaching.

hydrogen peroxide.

The content of halogenated organic compounds (Aox) is the most important criteria for determining the quality of industrial effluents. This factor has become even more critical since legal regulations have stipulated very low limiting values for such pollutants (4]. Hypochlorite is one of the oldest industrially used bleaching chemicals. Due to its bleaching power at low temperatures and its relatively low cost, hypochlorite is used in the textile and laundry industries [ 1 ]. Alone of

though hypochlorite offers some advantages--it is a very cheap oxidizer, it has considerably more brilliant white effects than one or several peroxide bieaches, and it has a high bleaching rate even at room temperature [7~ formation of highly toxic chlorinated organic by-products (Aox) during the bleaching process has limited its use. Peracetic acid is environmentally safe, since it decomposes to acetic acid and oxygen. The decomposition prod-