Indian Journal of Fibre & Textile Research
Vol.35, September 2010, pp. 243-249
Prediction of tensile strength of polyester/cotton blended woven fabrics
a
Tanveer Hussain
Department of Textile Processing, National Textile University, Faisalabad 37610, Pakistan
Zulfiqar Ali Malik
Department of Yarn Manufacturing, National Textile University, Faisalabad 37610, Pakistan
and
Anwaruddin Tanwari
Department of Textile Engineering, Mehran University of Engineering & Technology, Jamshoro, Pakistan
Received 1 October 2009; revised received and accepted 11 December 2009
Statistical models have been developed for the prediction of tensile strength of polyester/cotton (52:48) blended woven
fabrics. The models have been developed based on the empirical data obtained from carefully developed 234 fabric samples
with different constructions using 15, 20 and 25 tex yarns in warp and weft. The prediction ability and accuracy of the
developed models are assessed by correlation analysis of the predicted and actual warp and weft fabric strip-strength values
of another set of 36 fabric samples. The results show a very strong ability and accuracy of the prediction models.
Keywords: Statistical model, Tensile strength, Fabric, Yarn, Polyester/cotton blend
1 Introduction
All finished fabrics must conform to certain
performance specifications depending upon their
intended end use. These performance specifications
include, although are not limited to, the type of fibre
or blend used, yarn linear density, fabric count, weave
design, fabric weight (g/m2 or oz/yd2), fabric breaking
strength, colour, and finish. Since fabric breaking
strength might change during wet processing,
depending upon the processing conditions, the
selection of greige cloth with suitable strength is
important in order to meet the strength requirement of
the finished fabric, taking into account any strength
loss during processing. Similarly, in order to produce
a woven fabric of a specified breaking strength, the
selection of yarn of suitable tensile strength is also
very critical.
Often the selection of yarn of suitable strength
along with other desirable characteristics is made
based on experience and/or hit and trial methods.
Sometimes the selected yarn would luckily result in
the production of fabric with specified strength, while
at times the desired results would not be obtained
resulting in huge loss of material, time and other
——————
a
To whom all the correspondence should be addressed.
E-mail: [email protected]
resources. A further complexity is that there is no
clearly defined exact relationship between the yarn
strength and the resulting fabric strength, as there are
many other factors which also play a vital role in
determining the final fabric strength, including fabric
density and weave design1-3.
Although some research has been done in the
past for the prediction of tensile behaviour of woven
fabric using geometric4-6, mechanical7,8, energy9 and
statistical models10, there is currently no simple
prediction model available based on the empirical
data which could be used for the prediction of fabric
strength of polyester/cotton blends, keeping into
account all necessary factors as given above.
The present study was therefore undertaken to
develop statistical models for the prediction of tensile
strength of 52:48 polyester/cotton blended woven
fabrics using empirical data based on a carefully
manufactured range of woven fabrics under controlled
conditions using a systematic selection of yarns.
2 Materials and Methods
Polyester/cotton (52:48) blended yarns of 15, 20
and 25 tex were spun by ring spinning method using
cotton fibres with 27.55 mm span length (2.5 %),
13.08 mm span length (50 %), 48.98% uniformity
index, 1.85 dtex fineness (4.70 µg/inch micronaire),
INDIAN J. FIBRE TEXT. RES., SEPTEMBER 2010
244
6.03 × 108 N/m2 (87500 lbs/in²) fibre bundle strength
and 7.2 % trash content; and polyester fibres
with 38mm staple length, 1.33 dtex (1.2 den) fineness,
6.8 g/tex tenacity and semi-dull lustre.
One hundred cones of yarn of each count were
selected randomly from the lot spun from the
polyester and cotton fibres of the specifications given
above and then tested for their characteristics after
conditioning under standard atmosphere for 48 h.
Linear density of yarns was determined according
to ISO 2060:1994 test method. Tensile properties
of yarns were measured by Uster Tensorapid-4
according to ISO 2062:1993 test method. Uster
Tester-4 was used to determine Um% and total
imperfections (thin places, thick places and neps).
Hairiness was determined at a speed of 400m/min
according to ISO 16549:2004 test method. Semiautomatic twist tester was used to measure the twist
per meter in the yarn according to ISO 17202:2002.
The specifications of yarns are given in Table 1.
One hundred and thirty five (135) fabric samples,
each in both plain weave (float length = 1) and twill
weave (float length = 3), were woven on projectile
weaving machine (P 7150) using the constructions
given in Table 2. All warp yarns were sized before
weaving with 12.5% size using a sizing recipe
containing mixture of thin boiling starch, poly vinyl
alcohol, acrylic size, and a softener.
All the woven fabric samples were desized by
enzymatic method using 2-4% (o.w.f.) Bactasol PHC
liquid desizing enzyme, 3-5 g/L Imerol PCJ liquid
(surfactant), and 0.5-1 g/L Sirrix 2UD liquid
(sequestering agent). All chemicals were provided
Table 1 — Specifications of polyester-cotton (PC) yarns
Property
15 tex PC
20 tex PC
25 tex PC
Breaking force, cN 272.47 (9.45) 391.82 (8.90) 537.93 (8.50)
Elongation, %
7.25 (9.85)
7.96 (9.90) 8.19 (10.10)
Linear density, tex
14.66 (1.23) 19.77 (1.54) 24.86 (1.25)
Unevenness, %
12.59
13.79
12.15
Total imperfections
956
785
731
Hairiness
5.79
6.16
6.72
Twists/m
1049.20 (3.22) 841.48 (3.92) 747.97 (3.95)
Values in parentheses are the coefficient of variation (%) for the
respective property.
Table 2 — Fabric constructions details
Sl No.
1
Set 1
a
Set 2
a
Set 3
a
Set 4a
Set 5a
Set 6a
15×15/
15×20/
15×25/
20×15/
20×20/
20×25/
40×40
40×40
40×40
40×40
40×40
40×40
2
15×15/
15×20/
15×25/
20×15/
20×20/
20×25/
50×40
50×40
50×40
50×40
50×40
50×40
3
15×15/
15×20/
15×25/
20×15/
20×20/
20×25/
50×50
50×50
50×50
50×50
50×50
50×50
4
15×15/
15×20/
15×25/
20×15/
20×20/
20×25/
60×40
60×40
60×40
60×40
60×40
60×40
5
15×15/
15×20/
15×25/
20×15/
20×20/
20×25/
60×50
60×50
60×50
60×50
60×50
60×50
6
15×15/
15×20/
15×25/
20×15/
20×20/
20×25/
60×60
60×60
60×60
60×60
60×60
60×60
7
15×15/
15×20/
15×25/
20×15/
20×20/
20×25/
70×40
70×40
70×40
70×40
70×40
70×40
8
15×15/
15×20/
15×25/
20×15/
20v20/
20×25/
70×50
70×50
70×50
70v50
70×50
70×50
9
15×15/
15×20/
15×25/
20×15/
20×20/
20×25/
70×60
70×60
70×60
70×60
70×60
70×60
10
15×15/
15×20/
15×25/
20×15/
20×20/
20×25/
70×70
70×70
70×70
70×70
70×70
70×70
11
15×15/
15×20/
15×25/
20×15/
20×20/
20×25/
80×40
80×40
80×40
80×40
80×40
80×40
12
15×15/
15×20/
15×25/
20×15/
20×20/
20×25/
80×50
80×50
80×50
80×50
80×50
80×50
13
15×15/
15×20/
15×25/
20×15/
20×20/
20×25/
80×60
80×60
80×60
80×60
80×60
80×60
14
15×15/
15×20/
15×25/
20×15/
20×20/
20×25/
80×70
80×70
80×70
80×70
80×70
80×70
15
15×15/
15×20/
15×25/
20×15/
20×20/
20×25/
80×80
80×80
80×80
80×80
80×80
80×80
a
Fabric constructions are given as: warp count × weft count/ends per 25mm × picks per 25mm.
Set 7a
Set 8a
Set 9a
25×15/
40×40
25×15/
50×40
25×15/
50×50
25×15/
60×40
25×15/
60×50
25×15/
60×60
25×15/
70×40
25×15/
70×50
25×15/
70×60
25×15/
70×70
25×15/
80×40
25×15/
80×50
25×15/
80×60
25×15/
80×70
25×15/
80×80
25×20/
40×40
25×20/
50×40
25×20/
50×50
25×20/
60×40
25×20/
60×50
25×20/
60×60
25×20/
70×40
25×20/
70×50
25×20/
70×60
25×20/
70×70
25×20/
80×40
25×20/
80×50
25×20/
80×60
25×20/
80×70
25×20/
80×80
25×25/
40×40
25×25/
50×40
25×25/
50×50
25×25/
60×40
25×25/
60×50
25×25/
60×60
25×25/
70×40
25×25/
70×50
25×25/
70×60
25×25/
70×70
25×25/
80×40
25×25/
80×50
25×25/
80×60
25×25/
80×70
25×25/
80×80
HUSSAIN et al.: TENSILE STRENGTH OF POLYESTER/COTTON FABRICS
by Clariant Pakistan Ltd. The desizing of all fabric
samples was done individually on laboratory winch
machine at liquor-to-goods ratio of 15:1, pH of 6
and temperature of 60-90°C. After desizing, fabric
samples were rinsed hot followed by cold and dried
at room temperature under shade in order to avoid
any possible effect of direct sunlight on the fabric
strength. The purpose of desizing was to remove the
warp size and its contribution to the fabric tensile
strength. The enzymatic method of desizing was used
because unlike oxidative or acidic desizing, it does
not cause any loss in fabric strength.
After desizing, all the fabric samples were first
preconditioned at 47°C and 10 - 25 % RH for 4 h in a
hot air oven and then conditioned for 24 h in standard
atmosphere. Then test specimens were prepared and
tensile strength was determined both in warp and weft
directions according to ISO standard test method
13934-1. Calibrated universal strength tester by
SDL Atlas UK was used for determining the fabric
245
tensile strength using a gauge length of 200 mm and
an extension speed of 100 mm/min.
Out of a total number of 270 samples, the data
of 234 samples were used for developing the
statistical prediction models while data of 36 samples
(18 plain weave + 18 twill weave) was used to check
the validity of the developed models. All statistical
analyses were done using MINITABTM statistical
software.
3 Results and Discussion
3.1 Warp-way Fabric Strength Prediction Model
Table 3 gives the best subsets of regression models
for fabric strength. The table shows 13 different
statistical models for warp-way strength, as given
by the MINITABTM, including different predictor
variables such as X (warp count), Y (weft count), warp
yarn strength (cN), weft yarn strength (cN),
E (ends/25mm), P (picks/25mm) and FL (float
length). Model numbers 9 and 10 are found to be the
Table 3 — Best subsets regression table for fabric strength models
Variable
R-Sq
R-Sq (adj)
C-p
1
1
2
2
3
3
4
4
5
5
6
6
7
49.8
49.6
94.5
94.3
95.2
95.1
95.9
95.7
96.2
96.2
96.2
96.2
96.2
49.5
49.3
94.5
94.3
95.2
95.1
95.8
95.6
96.1
96.1
96.1
96.1
96.1
2758.1
2769.9
99.0
110.9
56.6
62.7
20.3
31.7
4.0
4.0
6.0
6.0
8.0
S
X
Y
Wp. Str.
Warp-way fabric strength model
122.64
122.89
x
40.662
41.392
x
37.878
38.289
35.295
36.110
x
34.027
34.027
x
34.100
x
34.100
x
x
34.174
x
x
x
x
x
x
x
x
x
x
x
x
Wt. Str.
E
P
FL
x
x
x
x
x
x
x
x
x
x
x
x
x
x
-
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Weft-way fabric strength model
1
56.9
56.7
1985.2
97.891
x
1
37.1
36.8
3000.0
118.20
x
2
93.9
93.9
83.0
36.758
x
x
2
93.9
93.9
84.1
36.824
x
x
3
94.8
94.8
39.2
34.020
x
x
x
3
94.8
94.7
40.4
34.092
x
x
x
4
95.2
95.2
20.6
32.738
x
x
x
x
4
95.2
95.1
21.8
32.821
x
x
x
x
5
95.6
95.5
5.3
31.631
x
x
x
x
x
5
95.6
95.5
5.6
31.651
x
x
x
x
x
6
95.6
95.5
6.2
31.624
x
x
x
x
x
x
6
95.6
95.5
6.5
31.643
x
x
x
x
x
x
7
95.6
95.5
8
31.680
x
x
x
x
x
x
X
‘x’ sign indicates that the variables included in the model; and ‘-’ indicates that the variables are not included.
R-Sq —Percentage of response variable variation; R-Sq (adj) — Percentage of response variable variation, adjusted for the no. of predictors;
C-p — A statistic used as an aid in choosing between competing multiple regression models; S —Standard error of regression; X —Warp
count; Y — Weft count; Wp. Str — warp yarn strength (cN); Wt. Str. — weft yarn strength (cN); E —ends/25mm; P —picks/25mm;
and FL —Float length.
INDIAN J. FIBRE TEXT. RES., SEPTEMBER 2010
246
Table 4 — Analysis of variance for fabric strength models
Source
Regression
Linear
Interaction
Residual Error
Total
DF
6
5
1
227
233
Seq SS
6915909
6682408
233500
30483
6946392
Adj SS
Warp-way
6915909
5706480
233500
30483
6946392
Adj MS
F-value
P-value
1152651
1141296
233500
134
-
9E+03
8E+04
2E+03
-
0.000
0.000
0.000
-
Weft-way
Regression
6
5115380
5115380
852563
5E+03
0.000
Linear
5
4927089
4995255
999051
6E+04
0.000
Interaction
1
188291
188291
188291
1E+03
0.000
Residual Error
227
39834
39834
175
Total
233
5155214
DF —Degree of freedom; Seq SS —Sequential sum of squares; Adj SS —Adjusted sum of square; and Adj MS —Adjusted mean square.
best models with high R-Sq & adjusted R-Sq, and low
S & C-p values close to the number of predictors
contained in the model. Model 9 with warp strength,
weft strength, E, P and FL as predictor variables was
selected for further analysis using response surface
regression.
Analysis of variance for response surface
regression is given in Table 4. Values of P for
regression, linear and interaction indicate the
significant effects of the selected predictor variables
on the warp-way fabric strength.
The response surface regression coefficients are
given in Table 5. Values of P indicate the significant
linear effect of warp strength, weft strength, E, P, FL
and significant interactions of warp strength*E at
α-level (0.05). All analysis was done using coded
units of the predictor variables as recommended in
the MINITABTM help files. The regression equation
obtained form Table 5, which can be used to predict
the warp-way tensile strength of fabric, is given as
follows:
SSP = 434.93 + 132.32wp. str. + 11.66wt. str. + 170.13E
+ 24.46P - 14.90FL + 60.45 (wp. str.*E)
where SSP is the strip strength of fabric in warp
direction (N); wp. str., the coded value of single yarn
strength of warp; E, the coded value of ends/25mm;
P, the coded value of picks/25mm, and FL, the coded
value of float length.
This equation can be used to calculate the predicted
response by putting in the coded values of the
predictor variables. Because the coefficients were
estimated using coded units, putting uncoded factor
values into this equation would generate incorrect
predictions about warp strip strength. The following
alternative equation obtained from the response
Table 5 — Response surface regression coefficients for fabric
strength models
Predictor
Regression
coefficient
Standard error T-value P-value
coefficient
Constant
Wp. str.
Wt. str.
E
P
FL
Wp. str.*E
Warp-way strength
434.93
1.0604
410.153
132.32
1.0051
131.651
11.66
0.9262
12.589
170.13
1.3638
124.743
24.46
1.3415
18.233
-14.90
0.7575
-19.665
60.45
1.4496
41.699
R-Sq = 99.6% R-Sq(adj) = 99.5%
0.000
0.000
0.000
0.000
0.000
0.000
0.000
Constant
Wp. str.
Wt. str.
E
P
FL
Wt. str.*P
Weft-way strength
415.10
1.2122
342.430
9.42
1.0593
8.895
129.67
1.2097
107.185
16.94
1.5580
10.875
165.90
1.5344
108.117
-14.01
0.8660
-16.177
53.39
1.6299
32.757
R-Sq = 99.2% R-Sq(adj) = 99.2%
0.000
0.000
0.000
0.000
0.000
0.000
0.000
surface regression analysis using MINITABTM
contains the estimated regression coefficient using
data in uncoded units. This equation can be used to
calculate the predicted response by directly putting in
the uncoded values of warp yarn strength, weft yarn
strength, ends/25mm, picks/25mm and float length as
given below:
SSP = -5.00240 - 0.369284wp. str. + 0.0878511wt. str.
- 0.720099E + 1.22297P - 14.8974FL + 0.0227702 (wp. str.*E)
where SSP is the strip strength of fabric in warp
direction (N); wp. str., the single yarn strength of
warp (cN), E, the number of ends/25mm; P, the
number of picks/25mm; and FL, the actual float
length (e.g. 1 for plain weave, 3 for 3/1 twill fabric).
The SSP equation contains an interaction effect of
warp yarn strength and ends/25mm. Response surface
HUSSAIN et al.: TENSILE STRENGTH OF POLYESTER/COTTON FABRICS
247
Fig. 1— Response surface plots for (a) warp and (b) weft yarn strengths
plot for this interaction effect is given in Fig. 1a.
As can be seen from the figure, the increase in
warp strip strength with the increase in number of
ends/25mm is much sharper when the strength of
individual yarns is higher.
3.2 Weft-way Fabric Strength Prediction Model
Table 3 gives the best subsets regression table
for weft-way fabric strip strength. The table shows
13 different statistical models including different
predictor variables such as X (warp count), Y (weft
count), warp yarn strength (cN), weft yarn strength
(cN), E (ends/25mm), P (picks/25mm) and FL (float
length). Model numbers 9 seems to be the best model
with high R-Sq & adjusted R-Sq, and low S & C-p
values. Hence, model 9 with warp strength, weft
strength, E, P and FL as predictor variables was
selected for further analysis using response surface
regression.
Analysis of variance for response surface
regression is given in Table 4. Values of P for
regression, linear and interaction indicate the
significant effects of the selected predictor variables
on the weft-way fabric strength.
Response surface regression coefficients are given
in Table 5. Values of P indicate the significant linear
effect of warp strength, weft strength, E, P, FL and
significant interactions of weft strength*P at α-level
(0.05). The regression equation obtained form
Table 5, which can be used to predict the weft-way
tensile strength of fabric, is given below:
SST = 415.10 + 9.42wp. str. + 129.67wt. str. + 16.94E
+ 165.90P - 14.01FL + 53.39 (wt. str.*P)
strength of weft; E, the coded value of ends/25mm;
P, the coded value of picks/25mm; and FL, the coded
value of float length
This equation can be used to calculate the predicted
response by putting in the coded values of the
predictor variables. Because the coefficients were
estimated using coded units, putting uncoded values
into this equation would generate incorrect
predictions about weft strip strength. The following
alternative equation obtained from the response
surface regression analysis using MINITABTM
contains the estimated regression coefficient using
data in uncoded units. This equation can be used
to calculate the predicted response by directly putting
in the uncoded values of warp yarn strength, weft
yarn strength, ends/25mm, picks/25mm and float
length, as shown below:
SST = -41.0513 + 0.0709942wp. str. - 0.229831wt. str.
+ 0.847188E + 0.145404P - 14.0085 + 0.0201125 (wt. str.*P)
where SST is the strip strength of fabric in weft
direction (N); wt. str., the single yarn strength of
weft (cN); E, the number of ends/25mm; P, the
number of picks/25mm; and FL, the actual float
length (e.g. 1 for plain weave, 3 for 3/1 twill fabric).
The SST equation contains an interaction effect of
weft yarn strength and picks/25mm. Response surface
plot for this interaction effect is given in Figure 1b.
As can be seen from the figure, the increase in
weft strip strength with the increase in number of
picks/25mm is much sharper when the strength of
individual weft yarns is higher.
3.3 Validation of Prediction Models
where SST is the strip strength of fabric in weft
direction (N); wt. str., the coded value of single yarn
As mentioned above, out of a total number of
270 samples, the data of 234 samples were used for
248
INDIAN J. FIBRE TEXT. RES., SEPTEMBER 2010
Table 6 — Comparison of actual and predicted values
Plain weave (float length=1)
Warp strip strength, N
Weft strip strength, N
Predicted
Actual Diff. % Predicted
Actual Diff. %
348.45
358.00
2.67
242.24
230.00
-5.32
415.52
423.00
1.77
306.96
305.00
-0.64
371.17
384.00
3.34
415.09
423.00
1.87
413.78
416.00
0.53
343.30
339.00
-1.27
371.77
356.00
-4.43
448.18
429.00
-4.47
451.07
444.00
-1.59
675.94
680.00
0.60
506.84
514.00
1.39
306.97
288.00
-6.59
576.63
556.00
-3.71
259.18
247.00
-4.93
505.10
489.00
-3.29
343.30
343.00
-0.09
611.57
597.00
-2.44
512.29
552.00
7.19
530.16
544.00
2.54
566.30
580.00
2.36
612.18
628.00
2.52
574.77
582.00
1.24
673.54
675.00
0.22
261.08
250.00
-4.43
813.29
815.00
0.21
382.07
383.00
0.24
696.26
708.00
1.66
433.93
453.00
4.21
811.55
806.00
-0.69
442.41
454.00
2.55
696.86
704.00
1.01
467.03
466.00
-0.22
812.15
801.00
-1.39
475.50
479.00
0.73
Twill weave (float length=3)
Warp strip strength, N
Weft strip strength, N
Predicted
Actual Diff. % Predicted
Actual
Diff. %
318.66
320.00
0.42
214.22
219.00
2.18
385.73
373.00
-3.41
278.95
266.00
-4.87
341.37
335.00
-1.90
387.07
379.00
-2.13
383.98
383.00
-0.26
315.28
324.00
2.69
341.98
361.00
5.27
420.16
433.00
2.96
421.28
425.00
0.88
647.93
644.00
-0.61
477.05
484.00
1.44
278.95
272.00
-2.55
546.84
535.00
-2.21
231.17
219.00
-5.56
475.30
483.00
1.59
315.29
325.00
2.99
581.78
553.00
-5.20
484.27
455.00
-6.43
500.37
493.00
-1.49
538.28
527.00
-2.14
582.39
589.00
1.12
546.75
510.00
-7.21
643.75
637.00
-1.06
233.07
238.00
2.07
783.50
763.00
-2.69
354.05
364.00
2.73
666.46
671.00
0.68
405.92
418.00
2.89
781.75
775.00
-0.87
414.39
422.00
1.80
667.07
671.00
0.59
439.01
443.00
0.90
782.36
782.00
-0.05
447.48
447.00
-0.11
Fig. 2 —Fitted line plot for actual and predicted (a) warp and (b) weft strip strengths
developing the prediction models while data of 36
samples (18 plain weave + 18 twill weave) were used
to check the validity of the developed models.
A comparison of actual fabric strength values
and those predicted by the developed models
(SSP & SST equations) is given in Table 6.
Figure 2a gives the fitted line plot between
the actual fabric warp strip strength and the
warp strip strength predicted by the proposed model.
The Pearson correlation between the actual warp
strip strength and the predicted warp strip strength
is found to be 0.997 with a p-value of 0.000,
indicating a very strong ability and accuracy of
the prediction model.
Figure 2b gives the fitted line plot between the
actual fabric weft strip strength and the weft strip
strength predicted by the proposed model. The
Pearson correlation between the actual weft strip
strength and the predicted weft strip strength is found
to be 0.993 with a p-value of 0.000, indicating a very
strong ability and accuracy of the prediction model.
4 Conclusions
The Pearson correlations between the actual and
the predicted strength for warp and weft are found
to be 0.997 and 0.993 respectively with a p-value of
0.000, indicating a very strong ability and accuracy of
the prediction models.
Acknowledgement
The authors are thankful to the Higher Education
Commission of Pakistan for providing funding
for this research work. They are also grateful to
HUSSAIN et al.: TENSILE STRENGTH OF POLYESTER/COTTON FABRICS
Al-Karam Textile Mills Karachi, Al-Rehmat Textile
Mills Faisalabad as well as Clariant Pakistan Ltd
for providing support in warp preparation, fabric
tensile testing and provision of desizing chemicals
respectively during the study.
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