chapter 4 the effect of weave structures on the...
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CHAPTER 4
THE EFFECT OF WEAVE STRUCTURES ON THE LOW
STRESS MECHANICAL PROPERTIES OF WOVEN
COTTON FABRICS
4.1 INTRODUCTION
The structural design of a textile fabric is largely dictated by its
end-use application. In the case of apparel and house hold fabrics, subjective
factors such as drape, handle, wrinkle recovery, crease resistance, pilling,
texture and softness are important. Consequently rational design of apparel
and house hold fabrics involves an understanding of the mechanical properties
that control these subjective characteristics and their correlation with end-use
performance.
Goswami (1978) studied the shear behavior of cotton polyester
blended fabrics, which had plain, basket and satin structures. He found that
the yarn float length and the yarn twist had a significant effect on the shear
behavior. It is a well known fact that weave structure affects the most of the
mechanical properties of woven fabric. Although some isolated studies were
made in the past to correlate weave structure to the mechanical properties of
woven fabrics, they were incomplete and did not provide any useful
information. With the introduction of parameters such as Crossing over
Firmness Factor (CFF) and Floating Yarn Factor (FYF) which have been
suggested by Morino et al (2005), our understanding about fabric structure
has improved. Milasius (2000) suggested a parameter called Fabric Firmness
Factor (FFF) which takes into account both weave and sett. Matsudaira’s
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parameters do not consider fabric sett. Although work on this aspect was
carried out by Hitomi Morino and Mitsuo Matsudaira (2005) this was found
to have limitations, which were pointed out by Milasius. Matsudaira (2007),
admitted the drawbacks in his paper and mentioned that further work in this
area was desirable.
There are seven major parameters of a fabric structure, which affect
the properties. These are the type of fibre, warp and weft sett, the warp and
weft linear density of the yarn and the fabric weave. Milasius has taken into
account all these factors, while suggesting integrated fabric structure factors.
This weave factor has been found to affect fabric weaveability (Kumpikaite
2003), beat up force (Kumpikaite et al 2003), fabric breaking force and
elongation (Kumpikaite 2007) at break, fabric breakage and the relation
(2008) between raw materials (Adomaitiene et al 2009) used and fabric
structure factor. Padaki et al (2010) have proposed interlacement index and
float index to quantify the structural influence of multilayer interlocked
woven fabrics. Chen and Liu (2011) have recently used fabric firmness factor
for relating fabric structural properties to surface structure of silk fabrics. This
paper is concerned with the effect of weave structures on the mechanical
properties of fabrics using the parameters suggested by Milasius and Morino
et al (2005) and Matsudaira et al (2000, 2005). Recent work by Fatahi and
Alamdar Yazdi (2012) has highlighted the importance of weave parameters in
their contribution to air permeability of fabrics.
4.2 MATERIALS AND METHODS
Three groups of fabrics were considered. In the first group 2/20 Ne
yarns were used in warp and weft and woven on an automatic loom. The five
fabric samples with different weave structures include a plain weave, 3/1 twill
weave, Honey comb weave, Huck a back weave and Mock leno weave. All
the fabrics have the same yarn and weave densities. The same finishing
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conditions were used. Weave structures for the samples included in group 1
are shown in Figure 4.1.
a. Plain b. 3/1 Drill [Twill] d. Mock Leno
c. Honey comb e. Huck-a-back
Figure 4.1 Weave structures of group 1
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Fabric structural parameters are given in Table 4.1.
Table 4.1 Details of fabrics of group 1
Count Per Decimeter
# Weave Cotton Warp
Tex
Weft
Tex Ends Picks
Yarn
Struc
ture
a Plain 59.05 59.05 157.5 157.5 2 fold
b 3/1 Twill [Drill] 59.05 59.05 157.5 157.5 2 fold
c Honey Comb 59.05 59.05 157.5 157.5 2 fold
d Mock Leno 59.05 59.05 157.5 157.5 2 fold
e Huck-a-back 59.05 59.05 157.5 157.5 2 fold
The second group consisted of eleven samples with different weave
structures, woven on the same automatic loom. These are Plain, 2/2 Twill, 4/4
Twill, 2/2 Pointed Twill, 8 thread Hopsack, 8 thread Weft Sateen, 8 thread
Honey Comb, 8 thread Brighton Honey Comb, 8 thread Huck-A-Back, 8
thread Crepe Cord & 8 thread Pin Head Crepe.
2/40 Ne cotton yarns were used in warp and weft. The same
finishing treatment was provided to all the fabric samples, so that comparison
with weave structures was made possible. Thus, two counts, one coarser and
the other fine counts were used.
Weave structures for the samples included in group 2 are shown in
Figure 4.2.
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a] Plain b] 2/2 twill c] 4/4 Twill
d] 2/2 Pointed twill e] 8 THD. twilled f] 8 THD weft sateen HOPSACK
g] 8 THD. honey comb h] 8 THD brighton i] 8 THD huck-a-back Honey comb
j] 8 THD crepe cord k] 8 THD pin head crepe
Figure 4.2 Weave structures of group 2
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Fabric structural parameters are given in the following Table 4.2.
Table 4.2 Details of fabics of group 2
Count Tex Per Decimeter # Weave Cotton
Warp Weft Ends S1 Picks S2
Yarn
Structure
a Plain 30 30 210 220 Two Fold
b 2/2 Twill 30 30 220 240 Two Fold
c 4/4 Twill 30 30 210 220 Two Fold
d 2/2 Pointed Twill 30 30 220 220 Two Fold
e 8 Thread Twilled Hopsack 30 30 210 230 Two Fold
f 8 Thread Weft Sateen 30 30 210 210 Two Fold
g 8 Thread Honey Comb 30 30 210 190 Two Fold
h 8 Thread Brighton Honey
Comb 30 30 210 220
Two Fold
i 8 Thread Huck-a-back 30 30 210 200 Two Fold
j 8 Thread Crepe Cord 30 30 210 210 Two Fold
k 8 Thread Pin Head Crepe 30 30 220 210 Two Fold
Table 4.3 Details of Group 3 fabrics
Bleached samples details Calculated weave
factors values # Weave
EPI PPI GSM Thickness
(mm)
Ends/
dm
Picks/
dm CFF FYF (FFF)
1 Dice 135 71 129.82 0.36 531.5 279.5 0.88 1.12 0.4451
2 Sponge 138 72 129.61 0.37 543.3 283.5 1.25 0.75 0.5813
3 Special Honey
Comb 140 69 129.53 0.38 551.2 271.6 0.84 1.16 0.4837
4 Granite 136 70 130.39 0.27 535.4 275.6 1.00 1.00 0.5076
5 2/2 Twill 146 70 129.55 0.28 574.8 275.6 1.00 1.00 0.5576
6 Plain 134 70 127.92 0.24 527.6 275.6 2.00 0.00 0.6815
7 4/1 Satin 133 70 131.45 0.32 523.6 275.6 0.80 1.20 0.4605
8 Crape 142 70 129.73 0.31 559.1 275.6 1.38 0.62 0.6027
9 3/1 Twill 146 70 134.33 0.29 574.8 275.6 1.00 1.00 0.5290
10 9/1 Satin 134 70 119.12 0.33 527.6 275.6 0.40 1.60 0.3407
11 Huck-a-back 140 70 131.36 0.43 551.2 275.6 1.44 0.56 0.6155
Table 4.3 contains details of Group 3 samples.
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1. Determination of the Parameters for Weave Structures.
a) Crossing Over Firmness Factor (CFF)
This, as defined by Morino et al (2005), is given by the following
formula:
Number of crossing-over lines in the complete repeat
CFF = (4.1)
Number of interlacing points in the complete repeat
Figure 4.3 gives details of a plain weave and its CFF.
Interlacing Point
Crossing-over line
Inter-space of weave
Figure 4.3 Complete repeat of one pain weave.
b) Floating Yarn Factor (FYF)
This is defined as follows:
(Type1-1x-1) x (existing number of type1-1x in the complete repeat)
FYF = (4.2)
Number of interlacing points in the complete repeat
c) Fabric Firmness Factor (FFF)
This is calculated using the following formula given by Milasius
(2000):
1 2
1 2 1 2
2/3 T /T1
1 2/3 T /T 1 2/3 T /Taverage
2 1
T12 1S S
P' (4.3)
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Where T1, T2 and Tavg are respectively warp count, weft count and average
count in Tex. P’ is the Milasius weave factor and is the fibre density. S1 and
S2 are ends and picks per decimeter. The third group comprised of eleven
fabrics and their details are shown in Figure 4.4.
(a) Dice Weave (b) Sponge weave (c) Special honey comb
(d) Granite weave (e) 2/2 Twill (f) Plain (g) 4/1 Satin
(h) Crape weave (i) 3/1 Twill (j) 9/1 Satin (k) Huck-a-back
Figure 4.4 Weave structures of Group 3
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d) Low Stress Mechanical Properties
The low stress mechanical properties such as tensile, bending,
shearing, compression, and surface properties were measured by the KES-FB
system maintaining standard atmospheric conditions namely 250 ± 2
0 C and
relative humidity 65 ± 2%. For the first group of samples bending rigidity by
cantilever, air permeability, drape, bursting strength and crease recovery
properties were also measured. In addition to measuring shear properties by
Kawabata’s shear tester, they were also measured by using bias extension
method as suggested by Buckenham (1997).
4.3 RESULTS AND DISCUSSION
Table 4.6 furnishes correlation coefficient between mechanical
properties and the weave parameters of group 1 samples and Table 4.5 shows
correlation coefficient between mechanical properties and the weave
parameters of group 2 samples.
In the case of group 1 fabric samples, CFF gives an indication of
the frequency of interlacing yarn. It is apparent that plain weave shows a
higher value of CFF and honey comb shows the lower value. Milasius [3]
Fabric Firmness Factor also shows the same trend although the methods of
calculation are quite different.
In the case of group 2 fabrics, the same trend has been noticed.
Fabric Firmness Factor is likely to be different since it takes into account
fabric sett. It is interesting to note that the addition of CFF and FYF is 2.
It is noticed that correlation between CFF (Crossing Over Firmness
Factor) and crease recovery shear is high and significant in group 1 samples.
The correlation between air permeability and the weave parameters is also
high and significant. Since CFF & FYF are interrelated in the sense that the
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sum of these two parameters is 2, the correlation between floating yarn factor
(FYF) and mechanical properties is negative. Thus the correlation between
FYF and the mechanical properties is a mirror image of CFF and other
properties. Since shear parameters are relevant to technical textiles
particularly in designing them for end uses such as conveyor belts and sail
cloth, this correlation between the various weave parameters and the
properties will assist a great deal. Also, since shear parameters are well
correlated the CFF & FFF in both the groups, it is considered to be a very
critical parameter for the woven fabric. This also means that it will suffice if
shear and bending parameters are measured for correlating weave structures
to mechanical properties. This also shows that the models which have been
developed for predicting shear properties of fabrics by Leaf and Sheta (1984),
Grosberg, Leaf and Park (1968) have to be modified in view of good relation
between weave structure and shear. As regards group II samples, again it is
noticed that the correlation between tensile energy (WT) and the weave
parameters is significant. Also bending and shearing properties are well
correlated with the weave parameters. This again shows that it is possible to
predict these properties precisely. The presence of floats in fabrics is
responsible for the decrease in shear parameters.
Table 4.4 gives the CFF and FYF values of group 1 fabric samples
and Table 4.5 gives the CFF and FYF values of group 2 fabric samples.
Table 4.4 Calculated results of CFF and FYF and FFF for Group 1 fabrics
# Weave CFF FYF FFF
a Plain weave 2.00 0.00 0.60
b 3/1 twill 1.00 1.00 0.45
c Honey comb 0.875 1.125 0.42
d Huck a back 1.44 0.56 0.53
e Mock leno 1.36 0.64 0.52
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Table 4.5 Calculated results of CFF and FYF and FFF for Group 2 fabrics
# Weave CFF FYF FFF
a Plain weave 2.00 0.00 0.59
b 2/2 Twill 1.00 1.00 0.50
c 4/4 Twill 0.50 1.50 0.33
d 2/2 Pointed Twill 0.969 1.031 0.46
e 8 Thread Twilled Hopsack 1.00 1.00 0.60
f 8 Thread Weft Sateen 0.50 1.50 0.32
g 8 Thread Honey Comb 1.188 0.812 0.43
h 8 Thread Brighton honey comb 1.50 0.50 0.53
i 8 Thread Huck-a-back 1.25 0.75 0.47
j 8 Thread Cord Crepe 1.50 0.50 0.52
k 8 Thread Pin Head Crepe 1.125 0.875 0.47
Table 4.6 Correlation Coefficient of Group 1 Samples
Property CFF FYF FFF
GSM -0.50155 0.44863 -0.76209
Flexural Rigidity 0.321913 -0.36598 -0.02493
Bending rigidity -0.28281 0.244039 -0.5112
2HB 0.146788 -0.16292 0.037228
2HB/B 0.124828 -0.09092 0.361459
Air Permeability -0.5404* 0.503927* -0.70321*
Drape Co Efficient 0.441818 -0.50001* 0.00817
Bursting Strength -0.39151 0.372745 -0.40298
Crease Recovery -0.95129* 0.923385* -0.96841*
Shear By Bias Extension Method 0.822168* -0.82908* 0.650427*
Kawabata Shear Tester 0.974827* -0.97705* 0.811077*
* Significant at 1% level.
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Table 4.7 Correlation Coefficient of group 2 Samples
Property CFF FYF FFF
Tensile
LT 0.512 -0.497 0.528
WT 0.674* -0.642* 0.661*
RT -0.507 0.485 -0.563
EMT 0.407 -0.378 0.374
Bending
B 0.659* -0.678* 0.514*
2HB 0.763* -0.779* 0.614*
Shearing
G 0.644* -0.654* 0.581*
2HG 0.673* -0.682* 0.612*
2HG5 0.659* -0.669* 0.608*
Compression
LC 0.142 -0.19 0.042
WC -0.127 -0.094 0.306
RC 0.011 -0.09 -0.09
Surface Properties
T -0.117 -0.118 -0.354
MIU 0.9 0.12 -0.058
MMD 0.505 -0.499 0.153
SMD 0.37 -0.321 -0.118
Weight 0.134 0.145 -0.02
THV 0.074 -0.11 0.357
* Significant at 1% level
Since the correlation between CFF and FFF in both the groups is
very high, it can be concluded that this relationship is independent of the
counts and sett used. The influence of fabric sett on the fabric integrated
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factor shows that the variations in this parameter are significant as Table 4.8
will demonstrate:
Table 4.8 Variations in FFF
Count tex PICKs #
Warp Weft Per dm Weave FFF
1 30 30 126.0 Plain 0.53
2 30 30 141.7 Plain 0.57
3 30 30 149.6 Plain 0.59
4 30 30 157.5 Plain 0.60
5 30 30 173.2 Plain 0.64
An examination of the data given in Table 4.8 shows that there is a
20% increase in FFF at a pick density of 173.2 in comparison with 126. In
view of the above, it is felt that Milasius’ method of representing fabric
structure is desirable and can be used for quantifying the fabric properties.
The correlation between CFF & FFF is excellent, as noticed in the
Figures 4.4a.
Figure 4.4a Correlation between CFF & FFF for Group 1
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Table 4.9 gives CFF, FYF and FFF for group 3 samples.
Table 4.9 Calculated results of CFF and FYF and FFF for Group 3 fabrics
# Weave CFF FYF FFF (B) FFF (G)
a Dice Weave 0.88 1.12 0.4451
b Sponge Weave 1.25 0.75 0.5813
c Special Honey Comb 0.84 1.16 0.4837
d Granite 1.00 1.00 0.5076
e 2/2 Twill 1.00 1.00 0.5576
f Plain 2.00 0.00 0.6815
g 4/1 Satin 0.80 1.20 0.4605
h Crepe 1.38 0.62 0.6027
i 3/1 Twill 1.00 1.00 0.5290
j 9/1 Satin 0.40 1.60 0.3407
k Huck-a-back 1.44 0.56 0.6155
Table 4.9 shows the calculated results of CFF, FYF and FFF. CFF
becomes bigger if the frequency of interlacing yarns is larger. The plain
weave shows a larger CFF and weave has the smallest CFF for the same warp
and weft yarn densities. FYF becomes larger with a longer floating length.
Satin weave has the largest FYF while the plain weave has the smallest value.
Relationship between parameters of weave structure and mechanical
properties is shown in Table 4.10.
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Table 4.10 Correlation coefficients between mechanical properties and
weave structure parameters (Group 3)
Mechanical properties CFF FYF FFF
LT 0.401 -0.401 0.451
WT -0.142 0.142 0.051
RT 0.141 0.141 0.205 Tensile
EMT -0.216 0.216 0.0046
B 0.413 -0.413 0.639* Bending
2HB 0.533 -0.533 0.729*
G 0.830* -0.830* 0.671*
2HG 0.874* -0.873* 0.775* Shearing
2HG(5) 0.871* -0.871* 0.726*
LC 0.075 -0.075 0.176
WC -0.104 0.104 -0.192 Compression
RC 0.269 -0.369 0.325
T -0.476 +0.476 -0.356
TM -0.599 +0.599 -0.241
MIU -0.626 0.626 -0.437
MMD -0.172 0.172 0.088
Surface
SMD 0.054 -0.054 0.295
Weight W 0.461 -0.461 0.504
* r (9,0.05) = 0.602 **r = (9, 0.01)
= 0.735
A single asterisk indicates 5% significance level and a double
asterisk means a 1% significance level. The correlation between CFF and
shear parameters is highly significant. However, FFF introduced by Milasius
is highly correlated with bending and shear parameters. This means that
bending and shear parameters can be predicted from FFF.
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Hand values and parameters of weave structures
Table 4.11 gives the correlation coefficients between hand values
and weave structure parameter. That Koshi is well correlated with all the
weave parameters can be noticed.
Table 4.11 Correlation coefficients between hand values and weave
structure parameters for group 3 samples
Hand value CFF FYF FFF
Koshi +902** -0.902** +842**
Numeri -0.07 0.07 -0.341
Fukurami +0.017 -0.017 -0.221
THV -0.414 0.414 -0.597
** r = (9, 0.05) = 0.605;
* r = (9, 0.01) = 0.764
The charts obtained from the KES-F system for fabrics have been
analysed for bending, shear, compression and surface properties. The various
deformations of the eleven fabrics included in Group 3 are discussed below in
seriatim.
4.4 BENDING DEFORMATION
Figures 4.5 to 4.15 show the bending curves for the samples.
It is clear that sponge weave shows higher area which means higher
hysteresis. By and large there is not much variation in the shapes of the
hysteresis curves.
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Figure 4.5 Bending hysteresis curve (Dice)
Figure 4.6 Bending hysteresis curves (sponge)
Figure 4.7 Bending hysteresis curve (Special honey comb)
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Figure 4.8 Bending hysteresis curve (Granite)
Figure 4.9 Bending hysteresis curve (Twill)
Figure 4.10 Bending hysteresis curve (Plain weave)
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Figure 4.11 Bending hysteresis curve (Satin)
Figure 4.12 Bending hysteresis curve (Crape)
Figure 4.13 Bending hysteresis curve (Drill)
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Figure 4.14 Bending hysteresis curve (Satin 9/1)
Figure 4.15 Bending hysteresis curve for Huckaback
Shear stress strain curves
From the Figures 4.16 to 4.26, it is apparent that plain weave shows
the highest shear value and the 9/1 satin shows the least value. Shear
hystereses (2HG, 2HG5) values follow the same trend.
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Figure 4.16 Shear stress strain curves for dice
Figure 4.17 Shear stress strain curves for sponge
Figure 4.18 Shear stress strain curves for special honey comb
125
Figure 4.19 Shear stress strain curves (Granite)
Figure 4.20 Shear stress strain curves (2/2 Twill)
Figure 4.21 Shear stress strain curves (Plain)
126
Figure 4.22 Shear stress strain curves (4/1 Satin)
Figure 4.23 Shear stress strain curves (Crape)
Figure 4.24 Shear stress strain curves (3/1 Twill)
127
Figure 4.25 Shear stress strain curves (9/1 satin)
Figure 4.26 Shear stress strain curves (Hackaback)
Tensile properties
Figures 4.27 to 4.37 show the tensile curves of the samples. It is
apparent that 3/1 twill, sponge and 2/2 twill exhibit higher extension in weft
way in comparison with warp way. Thus fabric anisotropy is evident in these
weaves. Plain weave, among all the weaves, shows the least difference. Thus
the tensile curves also can be used for mapping the structures.
128
Figure 4.27 Tensile curves (Dice)
Figure 4.28 Tensile curves (Sponge)
Figure 4.29 Tensile curves (Special honey comb)
129
Figure 4.30 Tensile curves (Granite)
Figure 4.31 Tensile curves (2/2 Twill)
Figure 4.32 Tensile curves (Plain)
130
Figure 4.33 Tensile curves (Satin)
Figure 4.34 Tensile curves (Crape)
Figure 4.35 Tensile curves (3/1 Drill)
131
Figure 4.36 Tensile curves (9/1 Satin)
Figure 4.37 Tensile curves (Huckaback)
Compression curves
Figures 4.38 to 4.48 show the lateral compression curves. Plain
weave shows the highest compression as evidenced, from the curves. Among
the two satin weaves, 4/1 and 9/1, the former exhibits higher compression
than that of the latter.
132
Figure 4.38 Compression curves (Dice)
Figure 4.39 Compression curves (Sponge)
Figure 4.40 Compression curves (Special honey comb)
133
Figure 4.41 Compression curves (Granite)
Figure 4.42 Compression curves (Twill)
Figure 4.43 Compression curves (Plain)
134
Figure 4.44 Compression curves (Satin)
Figure 4.45 Compression curves (Crape)
Figure 4.46 Compression curves (3/1 Drill)
135
Figure 4.47 Compression curves (9/1 Satin)
Figure 4.48 Compression curves (Huckaback)
Surface properties
Figures 4.49 to 4.59 show typical records from the surface tester in
respect of eleven weaves. It is clear that all the fabrics show higher
coefficients of friction in weft way, the highest being dice. Plain weave shows
no difference at all between the two directions.
As regards SMD values, huckaback displays highest peak
amplitude compared to 4/1 satin weave. That peak amplitude and resistance to
motion can be related to smoothness is well known. It is interesting to see that
136
the peak amplitudes show an increase in weft way. Between the two satin
weaves, 4/1 satin has lower value of surface smoothness. This could serve as
a pointer for fabric selection.
Figure 4.49 Typical records from surface tester (Dice)
137
Figure 4.50 Typical records from surface tester (Sponge)
138
Figure 4.51 Typical records from surface tester (Special honey comb)
139
Figure 4.52 Typical records from surface tester (Granite)
140
Figure 4.53 Typical records from surface tester (2/2 Twill)
141
Figure 4.54 Typical records from surface tester (Plain)
142
Figure 4.55 Typical records from surface tester (4/1 Satin)
143
Figure 4.56 Typical records from surface tester (Crape)
144
Figure 4.57 Typical records from surface tester (3/1 Twill)
145
Figure 4.58 Typical records from surface tester (9/1 Satin)
146
Figure 4.59 Typical records from surface tester (Huckaback)
Table 4.12 presents correlation coefficients. Prediction equation are
given in Table 4.13.
147
Table 4.12 Correlation table for Kawabata results (Group 3)
Parameters CFF FYF FFF
Air Permeability Bleached 0.827 0.881 0.881
Water vapour Permeability -0.295 0.295 -0.302
Sinking Time 0.497 -0.497 0.496
Thermal Resistance -0.508 0.508 -0.602
Koshi 0.893** -0.893** 0.846**
Numeri -0.384 0.384 -0.337
Fukurami -0.276 0.276 -0.217
THV (Total hand value) -0.684* 0.684* -0.599 *
Bending Recovery % -0.291 0.291 -0.210
Shear Recovery % 0.313 -0.313 0.281
LC 0.172 -0.172 0.166
WC -0.226 0.226 -0.189
RC 0.371 -0.371 0.317
% Compression 0.170 -0.170 0.157
To -0.398 0.398 -0.357
Tm -0.269 0.269 -0.243
W 0.313 -0.313 0.497
LT 0.497 -0.497 0.456
WT -0.205 0.205 0.041
RT 0.199 -0.199 0.208
EMT -0.250 0.250 -0.005
G 0.796** -0.796** 0.677*
2HG 0.868** -0.868** 0.782**
2HG5 0.814** -0.814** 0.733*
2HG/G -0.129 0.129 0.016
2HG5/G 0.275 -0.275 0.476
B 0.572 -0.572 0.641*
2HB 0.659* -0.659* 0.733*
2HB/B 0.690* -0.690* 0.765**
M1U -0.430 0.430 -0.438
MMD 0.134 -0.134 0.081
SMD 0.304 -0.304 0.291
Note: ** - Significant at 1% level;
* - Significant at 5% level;
r = (9, 0.05) = 0.605
r = (9, 0.01) = 0.764
148
Table 4.13 Multiple Regression Analysis
1. Air Permeability = 85.693 + 17.979 FYF - 66.422 FFF
2. Water Wapour Permeability = 4012.63+ 64.278 FYF - 824.44 FFF
3. Sinking Time = 1.382 - 0.506 FYF + 1.929 FFF
4. Thermal Resistance = 29.941 - 4.110 FYF - 33.005 FFF
5. Koshi = 7.530 - 0.903 FYF - 0.205 FFF
6. Numeri = 2.035 + 1.935 FYF + 3.890 FFF
7. Fukurami = 3.009 + 1.472 FYF + 4.298 FFF
8. THV = -0.010 + 1.759 FYF + 3.602 FFF
9. Bending Recovery % = 65.821 + 3.762 FYF + 12.289 FFF
10. Shear Recovery % = 81.239-5.151 FYF-8.536 FFF
11. LC = 0.570 - 0.014 FYF + 0.010 FFF
12. WC = 0.051+ 0.004 FYF + 0.011 FFF
13. RC = 49.973 - 4.719 FYF - 10.984 FFF
14. % Compression = 39.346 - 2.998 FYF - 3.062 FFF
15. To = 0.456 + 0.094 FYF + 0.158 FFF
16. Tm = 0.280 + 0.074 FYF + 0.118 FFF
17. W = 9.139 + 1.044 FYF + 5.727 FFF
18. LT = 0.877 - 0.043 FYF - 0.052 FFF
19. WT = -1.770 + 0.691 FYF + 2.962 FFF
20. RT = 40.094 - 0.093 FYF + 7.833 FFF
21. EMT = -7.414 + 3.006 FYF + 12.646 FFF
22. G = ->(5.449-2.152 FYF-5.122 FFF v
23. 2HG = 6.723 - 2.829 FYF - 4.563 FFF
24. 2HG5 = 13.911 - 6.067 FYF - 9.898 FFF
25. 2HG / G = -1.333+ 1.162 FYF+ 4.951 FFF
26. 2HG5/G = -5.020 + 2.435 FYF + 12.931 FFF .
27. B = 0.005 + 0.009 FYF + 0.097 FFF
28. 2HB = -0.026 + 0.012 FYF + 0.144 FFF
149
29. 2HB/B = 0.408 + 0.072 FYF + 0.891 FFF
30. MIU = 0.189 + 0.004 FYF - 0.037 FFF
31. MMD = 0.059 - 0.014 FYF - 0.052 FFF
32. SMD = 9.078 - 2.807 FYF + 0.600 FFF
MULTIPLE CORRELATIONS (r)
TABLE 4.13.1
CFF FYF FFF Air Permeability
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952 1.000
Air Permeability 0.881** 0.827** 0.881** 1.000
Note : ** - Significant at 1% level; * - Significant at 5% level
TABLE 4.13.2
CFF FYF FFF Water Wapour
Permeability
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
Water Vapour
Permeability -0.295 0.295 -0.302 1.000
Note : ** - Significant at 1% level; * - Significant at 5% level
TABLE 4.13.3
CFF FYF FFF Sinking Time
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
Sinking Time 0.497 -0.497 0.496 1.000
Note : ** - Significant at 1% level; * - Significant at 5% level
150
TABLE 4.13.4
CFF FYF FFF Thermal
Resistance
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
Thermal Resistance -0.508 0.508 -0.602 1.000
Note : ** - Significant at 1% level; * - Significant at 5% level
TABLE 4.13.5
CFF FYF FFF Koshi
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
Koshi 0.893** -0.893** 0.846 1.000
TABLE 4.13.6
CFF FYF FFF Numeri
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
Numeri -0.384 0.384 -0.337 1.000
TABLE 4.13.7
CFF FYF FFF Fukurami
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
Fukurami -0.276 0.276 -0.217 1.000
151
TABLE 4.13.8
CFF FYF FFF THV
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
THV -0.684* 0.684* -0.599 1.000
TABLE 4.13.9
CFF FYF FFF Bending
Recovery %
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
Bending
Recovery % -0.291 0.291 -0.210 1.000
TABLE 4.13.10
CFF FYF FFF Shear
Recovery %
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
Shear
Recovery % 0.313 -0.313 0.281 1.000
TABLE 4.13.11
CFF FYF FFF LC
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
LC 0.172 -0.172 0.166 1.000
152
TABLE 4.13.12
CFF FYF FFF WC
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
WC -0.226 0.226 -0.189 1.000
TABLE 4.13.13
CFF FYF FFF RC
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
RC 0.371 -0.371 0.317 1.000
TABLE 4.13.14
CFF FYF FFF % Compression
CFF 1.000
FYF -1.000** 1.000-
FFF 0.952** -0.952** 1.000
% Compression 0.170 -0.170 0.157 1.000
TABLE 4.13.15
CFF FYF FFF TO
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
FT_TO -0.398 0.398 -0.357 1.000
153
TABLE 4.13.16
CFF FYF FFF FT_TM
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
FT_TM -0.269 0.269 -0.243 1.000
TABLE 4.13.17
CFF FYF FFF W (Weight)
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
W 0.313 -0.313 0.497 1.000
TABLE 4.13.18
CFF FYF FFF LT
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
LT 0.497 -0.497 0.456 1.000
TABLE 4.13.19
CFF FYF FFF FT_TM
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
WT -0.205 0.205 0.041 1.000
154
TABLE 4.13.20
CFF FYF FFF EMT
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
EMT -0.250 0.250 -0.005 1.000
TABLE 4.13.21
CFF FYF FFF G
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
G 0.796** -0.796** 0.677 1.000
TABLE 4.13.22
CFF FYF FFF 2HG
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
2HG 0.868** -0.868** 0.782 1.000
TABLE 4.13.23
CFF FYF FFF 2HG5
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
2HG5 0.814** -0.814** 0.733 1.000
155
TABLE 4.13.24
CFF FYF FFF 2HG/G
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
2HG/G -0.129 0.129 0.016 1.000
TABLE 4.13.25
CFF FYF FFF 2HG5/G
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
2HG5/G 0.275 -0.275 0.476 1.000
TABLE 4.13.26
CFF FYF FFF B
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
B 0.572 -0.572 0.641 1.000
TABLE 4.13.27
CFF FYF FFF 2HB
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
2HB 0.659* -0.659* 0.733 1.000
156
TABLE 4.13.28
CFF FYF FFF 2HB/B
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
2HB/B 0.690* -0.690* 0.765 1.000
TABLE 4.13.29
CFF FYF FFF MIU
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
MIU -0.430 0.430 -0.438 1.000
TABLE 4.13.30
CFF FYF FFF MMD
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
MMD 0.134 -0.134 0.081 1.000
TABLE 4.13.31
CFF FYF FFF SMD
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
SMD 0.304 -0.304 0.291 1.000
157
TABLE 4.13.32
CFF FYF FFF SMD
CFF 1.000
FYF -1.000** 1.000
FFF 0.952** -0.952** 1.000
SMD 0.304 -0.304 0.291 1.000
4.4 CONCLUSIONS
There exists a positive correlation between CFF and bending and
shear properties. The same comments hold good for FYF and mechanical
properties also. Most of the correlation coefficients are in line with FYF and
CFF. As the float length increases, the shear rigidity decreases and the
converse is true for CFF. These are in agreement with the findings of Morino
and Matsudaira (2005). It is interesting to note that the correlation between
the weave parameters and compression and surface properties is very poor.
THV and surface parameters have very poor correlation with weave
parameters. Tensile properties, save in one or two cases, also bear very little
relation with the weave parameters. The above findings show that bending
and shearing parameters can only be predicted with the weave structures.
With an increase in float length, the bending and shear rigidities show a
decrease. Milasius’s parameter merits consideration, as it includes fabric sett.
Matsudaira’s parameter can be used as it is quite simple to compute for
fabrics. Shear parameters are found to be independent of yarn count used in
the current study and are highly dependent on CFF & FFF. It will suffice, if
only shear and bending parameters of fabrics are determined. Fabrics become
soft with larger value of FYF. It is possible to predict the mechanical
properties namely bending and shear from weave parameters using the
prediction equations.