1. Introduction

A specific property of fabrics made of differently coloured threads is that the colour values of surface are not influenced only by the colour values of individual components – threads and their number but also by a fabric constructional parameters such as the warp and weft threads fineness, density and weave. With analytical estimation of the influence of the threads fineness and density, coupled with equations for determining colour differences in the CIE L*a*b* colour space (Mc Donald, 1997), the fractions of individual colour components in a colour repeat can be determined relatively precisely and on that basis also its colour values. But the fact is that in such calculations, except in the number of the warp and weft interlacing points, a weave with its specifies never appears. In other words, with the same number of the warp and weft interlacing points in a colour repeat, the same colour values are always obtained by calculation, despite different weaves and visible colour differences. In practise the surface effect of different weaves has always been evaluated visually, without further objective measurement. Such estimations were made on the basis of subjective preference and in consequence there were frequent misunderstandings about colour effect. The contribution of the paper is the verification of theoretical calculations of colour values on different weaves and the estimation of deviations between calculated and spectrophotometrically determined colour values. The researches will try to find out how can different disposition and agglomeration of interlacing points on woven structure influence on sectrophotometrically determined colour values. Moreover the connection between constructional parameters (threads density and fineness) and the weave will be detailed analysed with a purpose to put light on the possibilities of colour control of woven fabrics with a help of constructional parameters and thread colours.

  1. Theoretical part

2.1 Colour Deviation

The CIE L*a*b* colour space defines the value of a colour deviation between a pattern and a selected standard through the E*ab values. Their relation with L*, a* and b* colour values is presented in Equations 1 and 2 (Nassau, 1998).

(1)

(2)

Where:

  • a* is the difference in the a* (red – green) value between the pattern and the standard and b* is the difference in the b* (yellow – blue) value between the pattern and the standard;
  • L* is the difference in the L* (lightness) value between the pattern and the standard;
  • C*ab is the difference in the C*ab (chroma) value between the pattern and the standard and C*ab = ((a*)2 + (b*)2)1/2;
  • H*ab is the difference in the H*ab (hue) value between the pattern and the standard, where H*ab = C*abhab( /180) and hab=arc tg*(b*/a*);
  • E*ab is the colour difference between the pattern and the standard.

Colour deviation in the mentioned system means the shortest distance in the CIE L*a*b* co-ordinate space from the position of a certain colour to the position of the standard colour which it is compared to. Most common comparisons in practice are made between the obtained colour and the colour required and evaluated through colour values by customer.

Fig. 1. CIE L*a*b* colour space and colour difference between colour P and standard colour S.

The first question that arises in the case of fabrics made of differently coloured threads which differ in weave only is which colour value is to be taken as a reference for determination of colour deviations.

The colour deviation between the woven fabric made of differently coloured threads and the woven fabric with standard colour values can be calculated as:

(3)

Where:

  • Ui - the fraction of i colour component in the entire colour repeat (Dimitrovski & Gabrijelčič, 2001);
  • a*i, b*i and L*i - the colour values of i component of woven fabric;
  • a*s, b*s and L*s - the colour values of standard woven fabric;
  • E*ab - the colour difference between two woven fabrics;
  • n number of colour components;
  • i - colour component.

2.2Basic Weaves and Geometrical Arrangement of Their Interlacing Points

Plain weave is the simplest and the most common weave with the smallest repeat unit. It is characterised by the tightest and maximally possible interlacing of the warp and weft threads. All other weaves have reduced interlacing of the warp and weft threads and larger repeat units. In these weaves the agglomeration of warp and weft interlacing points increases the size of colour surfaces.

Different configuration of the warp and weft interlacing points in plain weave and similar weaves as well as the increase of the weave repeat and the colour repeat are presented in Fig.2.

In plain weave (a) four warp interlacing points surround one weft interlacing point, in rep 2/4 weave (b) three warp and one weft interlacing point surround a single weft points, while in basket 4/4 a weft point is surrounded by two weft and two warp interlacing points.

It is evident that the specificity of a weave leads to agglomeration of the same type interlacing points and, consequently, to increase of the size of individual colour surfaces and their relocation – grouping into a narrow areas with prevailing surfaces of one colour (Božič, 2002).

Fig. 2. Schematic presentation of weaves with different size of repeat and agglomeration: a – plain, b – rep 2/4 and c – basket 4/4.

The warp and weft interlacing point is made up of three different colour components: warp thread, weft thread and the space between threads, which all contribute to the colour values of a final fabric (Gabrijelčič & Dimitrovski, 2002).

Colour values of colour repeat in the weave can be calculated if taking in consideration colour values of its colour components (warp, weft and space between threads) and constructional parameters of woven structure (threads diameter and warp and weft density). Every single component in one repeat has its surface, which size and shape depend on threads diameter and density. The characteristics of components surface change with a change of constructional parameters. As a consequence the influence of single colour component on colour values of surface of woven fabrics is more or less perceivable.

  1. Experimental part

Computer simulations of seven different weaves are prepared by using the Arahne CAD system (Arahne, 2002). All weaves were chosen with the same ratio between the number of warp and weft interlacing points on the face side and identical constructional parameters: plain, rep 2/4, rep 2/8, twill 4/4, basket 4/4, twill 8/8 and basket 8/8. Weave patterns are shown on the Fig. 3.

1 / 2 / 3 / 4 / 5 / 6 / 7
plain / rep 2/4 / rep 2/8 / twill 4/4 / basket 4/4 / twill 8/8 / basket 8/8

Fig. 3. Patterns of plain, rep 2/4, rep 2/8, twill 4/4, basket 4/4, twill 8/8 and basket 8/8 weaves.

The warp threads are red, weft threads are yellow and the foundation is white with L*, a*, b*, C*ab and hab colour values given in Table 1.

Colour value
/ Warp-red / Weft-yellow / Foundation-white
L* / 47,18 / 84,71 / 94,16
a* / 57,65 / -7,29 / 4,14
b* / 17,49 / 69,69 / -11,20
C*ab / 60,24 / 70,07 / 11,94
hab () / 16,87 / 95,97 / 290,29

Table 1. Measured L*, a*, b* and calculated C*ab, hab colour values of red warp thread, yellow weft thread and white foundation.

The simulations had constant warp and weft thread fineness 30 tex. Density was variable, from initial 30 threads/cm with the reduction of 10 % to 27, 24 and 21 threads/cm.

The fractions of individual threads and of foundation reflectance were determined by calculation on the basis of constructional parameters (Gabrijelčič & Dimitrovski, 2002), which are presented in Table 2 and schematically on Fig. 4. Where go and gw is the density of warp and weft threads (threads/cm), do and dw is the diameter of warp and weft threads (mm) and Uo, Uw, Uf are the fractions of warp and weft threads and of the space between threads.

With the help of colour values of warp and weft threads and fractions of colour component (Uo, Uw, Uf) the theoretical colour values L*, a*, b*, C*ab and hab of different weaves were calculated(Gabrijelčič & Dimitrovski, 2001), (Bregar, 2002), (Kožuh, 2002), (Kysselef, 2002).

Colour values of the obtained surfaces were measured with the Spectrolino SpectroScan spectrophotometer of GretagMacbeth. Light source was D65.

Constructional parameters
Patterns / Warp / Weft / Fund.
go / do / Uo / gw / dw / Uw / Uf
1-7 / 30 / 0,304 / 0,496 / 30 / 0,304 / 0,496 / 0,007
1-7 / 27 / 0,304 / 0,484 / 27 / 0,304 / 0,484 / 0,032
1-7 / 24 / 0,304 / 0,463 / 24 / 0,304 / 0,463 / 0,073
1-7 / 21 / 0,304 / 0,435 / 21 / 0,304 / 0,435 / 0,131

Table 2. Constructional parameters of fabric and calculated fractions of the warp and weft threads and the space between the threads (foundation) for pattern 1 to 7.

Fig. 4. Schematically presentation of the density of warp and weft threads (go, gw) and warp and weft diameter (do, dw).

Finally, colour differences E*ab were defined by means of Equations (1), (2) and (3):

-between plain weave taken as standard and other weaves;

-between theoretically calculated and measured colour values of the patterns in different weaves.

  1. Measurements and results

Calculated and measured colour values L*, a*, b*, hab and C*ab of patterns are presented in Table 3 and Fig. 5, 6, 7 and 8 at varying densities 30, 27, 24 and 21 warp and weft threads/cm, where index m means the measured (capital characters) and index t theoretically calculated values (small characters).

Theoeretical calculated colour values are the same for all weaves, because there is the same ratio between the number of warp and weft interlacing points in colour repeat.

Plain is pattern 1, rep 2/4 is pattern 2, rep 2/8 pattern 3, twill pattern 4/4 pattern 4, basket 4/4 pattern 5, twill 8/8 pattern 6 and basket 8/8 pattern 7.

Density / Col. value / Calculated /
Measured
Plain / Rep 2/2 / Rep 2/8 / Twill 4/4 / Basket 4/4 / Twill 8/8 / Basket 8/8
1-7 / 1 /

2

/

3

/ 4 / 5 / 6 / 7
30 / L* / 66,15 / 61,97 / 62,00 / 62,15 / 63,04 / 63,69 / 64,79 / 65,93
a* / 25,01 / 30,31 / 29,14 / 27,43 / 26,27 / 26,19 / 25,03 / 22,37
b* / 43,15 / 36,69 / 37,71 / 38,50 / 40,09 / 40,16 / 42,05 / 43,88
hab () / 59,90 / 50,44 / 52,30 / 54,53 / 56,77 / 56,89 / 59,24 / 62,99
C*ab / 49,87 / 47,59 / 47,66 / 47,27 / 47,93 / 47,95 / 48,94 / 49,26
27 / L* / 67,86 / 63,36 / 63,26 / 63,06 / 64,80 / 63,73 / 65,35 / 63,92
a* / 24,41 / 28,16 / 29,08 / 28,26 / 25,68 / 27,36 / 24,82 / 26,19
b* / 42,67 / 37,02 / 37,69 / 37,42 / 39,45 / 38,27 / 40,48 / 38,51
hab () / 60,23 / 52,74 / 52,34 / 52,94 / 56,93 / 54,44 / 58,49 / 55,78
C*ab / 49,16 / 46,51 / 47,60 / 46,90 / 47,07 / 47,04 / 47,48 / 46,57
24 / L* / 67,93 / 64,70 / 64,27 / 63,81 / 64,79 / 65,04 / 64,89 / 65,08
a* / 23,61 / 26,09 / 26,80 / 25,63 / 23,93 / 25,73 / 24,21 / 24,38
b* / 39,55 / 36,90 / 35,87 / 36,14 / 38,36 / 36,91 / 37,86 / 37,66
hab () / 59,16 / 54,74 / 53,24 / 54,66 / 58,05 / 55,12 / 57,41 / 57,08
C*ab / 46,06 / 45,19 / 44,78 / 44,31 / 45,21 / 44,99 / 44,94 / 44,87
21 / L* / 69,70 / 66,47 / 66,55 / 66,43 / 66,25 / 66,39 / 66,09 / 67,29
a* / 22,44 / 23,63 / 24,33 / 23,03 / 23,45 / 24,08 / 23,95 / 21,87
b* / 36,45 / 32,89 / 33,62 / 33,11 / 34,23 / 33,54 / 33,85 / 34,86
hab () / 58,17 / 54,31 / 54,11 / 55,19 / 55,58 / 54,33 / 54,72 / 57,90
C*ab / 42,80 / 40,50 / 41,50 / 40,33 / 41,49 / 41,29 / 41,46 / 41,15

Table 3. Measured and calculated colour values L*, a*, b*, hab () and C*ab of the patterns in different weaves 1-7 and warp and weft densities 30, 27, 24 and 21 threads/cm.


Fig. 5. Curves of measured and theoretically determined colour values L*, a*, b*, hab and C*ab for the weaves 1 to 7 at the warp and weft threads density 30 threads per cm.


Fig. 6. Curves of measured and theoretically determined colour values L*, a*, b*, hab and C*ab for the weaves 1 to 7 at the warp and weft threads density 27 threads per cm.


Fig. 7. Curves of measured and theoretically determined colour values L*, a*, b*, hab and C*ab for the weaves 1 to 7 at the warp and weft threads density 24 threads per cm.


Fig. 8. Curves of measured and theoretically determined colour values L*, a*, b*, hab and C*ab for the weaves 1 to 7 at the warp and weft threads density 21 threads per cm.

The results of colour differences E*ab between different weaves given in Table 4 and Fig. 9. Plain weave is taken as standard woven structure and its colour differences are 0,00, other differences are calculated with Equations (1) and (2).

E*ab /
Patterns
Weave / Plain / Rep
2/4 / Rep
2/8 / Twill
4/4 / Basket
4/4 / Twill
8/8 / Basket
8/8
Density / 1 / 2 / 3 / 4 / 5 / 6 / 7
30/30 / 0,00 / 1,55 / 3,41 / 5,39 / 5,65 / 8,03 / 11,42
27/27 / 0,00 / 1,14 / 0,51 / 3,76 / 1,53 / 5,20 / 2,53
24/24 / 0,00 / 1,32 / 1,26 / 2,61 / 0,49 / 2,12 / 1,91
21/21 / 0,00 / 1,01 / 0,64 / 1,37 / 0,79 / 1,08 / 2,77

Table 4. Colour differences of weaves 2, 3, 4, 5, 6 and 7 in comparison with a standard fabric in plain weave-1 at densities 30, 27, 24 and 21 threads per cm.


Fig. 9. Curves of colour differences E*ab of weaves 2, 3, 4, 5, 6 and 7 in comparison with a standard fabric in plain weave-1 at densities 30, 27, 24 and 21 threads per cm.

The results of colour differences E*ab between theoretically calculated and spectrophotometrically determined colour values for all weaves 1-7 at densities 30, 27, 24 and 21 threads per cm are given in the Table 5.

E*ab / Density (go/gw)
Weave
/ 30/30 / 27/27 / 24/24 / 21/21 / Average E*ab
Plain / 9,34 / 8,14 / 4,86 / 4,95 / 6,82
Rep 2/4 / 7,99 / 8,23 / 6,09 / 4,64 / 6,74
Rep 2/8 / 6,59 / 8,09 / 5,72 / 4,71 / 6,28
Twill 4/4 / 4,54 / 8,14 / 3,37 / 4,23 / 5,07
Basket 4/4 / 4,05 / 4,62 / 4,45 / 4,70 / 4,46
Twill 8/8 / 1,75 / 6,72 / 3,53 / 4,70 / 4,17
Basket 8/8 / 2,75 / 3,36 / 3,51 / 2,94 / 3,14
Average E*ab / 5,29 / 6,76 / 4,50 / 4,41

Table 5. Colour differences E*ab between calculated and measured colour values of weaves 1, 2, 3, 4, 5, 6 and 7 at densities 30, 27, 24 and 21 threads per cm.


On Fig. 10 the graphic presentation of differences between theoretically calculated and spectrophotometrically determined colour values of different weaves by threads density 30, 27, 24 and 21 threads/cm are presented.

Fig. 10. Curves of colour differences E*ab between calculated and measured colour values of weaves 1, 2, 3, 4, 5, 6 and 7 at densities 30, 27, 24 and 21 threads per cm.

  1. Disscusion

5.1 Influence of weave on colour values at different densities

In Fig. 5, 6, 7 and 8 presenting the curves of the calculated and measured colour values of simulations in different weaves at density 30, 27, 24 and 21 threads per cm, it is evident that the colour values L*, a*, b*, hab and C*ab change differently with the change of the weave from plain (pattern 1) through rep 2/4 and 2/8 (patterns 2 and 3) to twill 4/4, basket 4/4 (patterns 4 and 5) and twill 8/8, basket 8/8 (patterns 6 and 7). It can be observed, that influence of weave depends on warp and weft thread density. The biggest change of colour values is at thread density go=gw=30 /cm (Fig. 5), where curves of L*, a*, b* and hab indicate different but considerable changes in colour values.

  • Density 30/30

Lightness L* of the patterns at density 30 threads per cm increases from the pattern 1 (plain) to the pattern 7 (basket 8/8). The simulations in basket 4/4 weave are substantially lighter in view of twill 4/4 and rep 2/4 weave, even if on the surface of the same size, there are the same number of warp and weft interlacing points. Similar is with weaves basket 8/8, twill 8/8 and rep 2/8. Different arrangement and agglomeration of interlacing points influence in different way on colour values of surfaces. Lightness L* increases due to increase of the colour repeat surface (threads agglomeration on the simulation surface), the result of which are outstanding yellow weft threads which have higher lightness (L*yell =84,71, L*red = 47,18). Gradation of the colour value b* and decrease of the parameter a* from plain weave to basket 8/8 weave can be explained accordingly. Namely, the colour values b* of yellow weft threads (b* yell = 69,69) are higher than the colour values a* of red warp threads which contain a small portion of yellow colour (a* red = 57,65, b* red = 17,49). The consequence is a considerable change of the colour hue hab, which is 50,44 in plain weave and even 62,99 in basket 8/8 weave (Table 3). On the contrary, the chroma of all simulations in all weaves remains practically unchanged due to equal ratio of the values b* and a* in all weaves (Equation 2). In weaves twill 8/8 and basket 8/8 chroma is increased, what is the consequence of points grouping on the surface.

  • Densities 27/27, 24/24, 21/21

Similar results are obtained in simulations of the warp and weft density 27 threads per cm, however, in simulations of the warp and weft density 24 and 21 threads per cm the situation is completely different. Colour differences between simulations of different weaves are small at low densities (Table 2). The fractions pertaining to the surfaces of the warp and weft threads and to the space between the threads in an individual colour repeat are presented in Table 1. When the densities are low, the effect of the foundation reflectance on colour values is small. At density 30 threads per cm the space between the threads occupies 0,78 % of the entire surface (Uf) and at density 27 threads per cm 3,2 %, which has minimum effect on the colour values of the fabric surface. On the other hand, the surfaces of the warp and weft threads by occupying 49,6% at density 30 and 48,4% at density 27 (Uo and Uw) have considerable effect on colour values of the fabric surface. At lower densities the influence of the reflectance of the foundation and of the threads in bottom layers of the fabric on the colour values of simulations considerably increases due to the 7.31 % fraction of foundation at density 24 threads per cm and 13,1 % fraction of foundation at density 21 threads per cm. These fractions are high and white colour of space between threads affects the colour effect of warp and weft threads on the surface. Grouping and agglomeration of interlacing points at low densities don’t have such a role in determination of colour values of woven structure.

5.2 Colour deviations E*ab between different weaves

Colour differences between the weave, which was taken as standard – plain and other weaves, are given in Table 4 and on Fig. 9. The curves on Fig. 9 show the important difference between higher densities 30 and 27 threads/cm and lower densities 24 and 21 threads/cm. The curve of density 30 increases from initial E*ab value of 1,55 by rep 2/4 weave to final 11,42 by basket 8/8 weave. In the case of density 27 the curve is variable. It seems that twill weaves play different role in colour changing in comparison with plain weave. Pattern 4-twill 4/4 and pattern 6-twill 8/8 have higher colour deviation as other weaves. Twill 4/4 has E*ab value 3,76 and twill 8/8 value 5,20. The reason for this phenomenon can be found out in typical disposition of interlacing points on the surface. By twill weave warp and weft interlacing points are not grouped in square groups as by other weaves and the disposition of points is graduated (Fig. 3). Likewise, the colour deviations of twill weave are higher at density 24 threads/cm (2,61 by twill 4/4 and 2,12 by weave 8/8) but not so obviously as at density 27. At thread density 21, E*ab values between colour values of standard plain weave and other weaves are low around value 1, except weave basket 8/8, where value of colour difference is 2,77. At this low density the influence of white foundation reflectance and threads in lower layer is high and the agglomeration and different disposition of points don’t affect the colour of surface. Colour deviations between different weaves are minimal.

5.3 Deviations between theoretically calculated and measured colour values

The calculated colour values of individual colour at all weaves are constant at the same density and presented in diagrams (Fig. 5, 6, 7 and 8) as straight hatched lines. With their help the deviations between the calculated and the measured values at different densities can be analysed (Table 5). Equal calculated colour values of all weaves are the result of the same ratio between the number of warp and weft interlacing points.

At higher densities (30 and 27 threads per cm) the deviations between the calculated and the measured values are bigger than at lower densities (24 and 21 threads per cm). The curves of measured L*, hab, a* and b* values in Fig. 5 considerable differ from calculated values in weaves plain-1, rep 2/4-2, and rep 2/8-3. But in weaves twill 4/4-4, basket 4/4-5, twill 8/8-6 and basket 8/8-7 the curves of measured values approach the lines of calculated and at density 30 threads/cm in weaves 6 and 7 they cross them. At densities 27, 24 and 21 the measured values are more constant in different weaves and closer to the lines of calculated values. At lower densities the colour values of woven structure can be better predicted.