A novel approach for precise determination of in-plane shear behavior of woven fabrics

Abstract

The ability of a textile product to change shape under motion-based diagonal forces defines the shear behavior of a fabric and its suitability for a wearable garment design. The principal aim of this study is to introduce a new shear frame and investigate the effects of raw material and setting on in-plane shear behavior of woven fabrics. For this purpose, the mechanical properties of systematic and commercially available non-systematic fabrics were measured. A novel approach to determine the in-plane shear behavior of woven fabrics via two complementary shear frame measurements was presented. The results were also compared with a conventional method known as the bias extension method. It was established that the proposed method provides more accurate and precise results. In order to investigate the correlation between in-plane shear behavior and other mechanical properties, bending rigidity and extension ability of fabrics were measured as well. The analyses regarding the relations between selected fabric parameters showed that there are considerably high correlation coefficients. The effect of raw material and setting was likewise found out to be statistically significant.

Keywords

shear deformation in-plane shear behavior shear frame bias extension

The in-plane shear behavior of woven fabrics plays a crucial role in the apparel industry, where it is essential to determine how clothing materials will perform when subjected to a broad array of complex deformations during use. The movement of joints, limbs, and specific other sections of the human body causes various forces on the garments and the shear behavior of a fabric under such forces defines its suitability for a wearable garment design. At this point, to ensure that the desired properties will be achieved, it is necessary to have a full command of production parameters and their influence on the mechanical fabric properties.

Shear behavior of fabrics has been examined since the 1950s; thenceforth, various experimental methods and devices were proposed. In early works, Morner and Eeg Olofsson¹ developed the primal technique to measure the shear rigidity of woven fabrics by gripping an initially rectangular specimen with clamps on opposing edges and measuring the resistance to lateral movement of the clamps, which was later improved by Behre,² Cusick,³ Spivak and Treloar,⁴ and Treloar.⁵

Conventional methods used nowadays having commercial acceptance include the Kawabata Evaluation System for Fabrics (KES-F) and Fabric Assurance by Simple Testing (FAST). In the KES-F, a rectangular fabric sample is clamped along the two opposite long edges and sheared by moving one of the clamped edges at a constant speed.⁶ When the stress developed during a KES-F test was examined, it was concluded that both tensile and shear stresses are efficient, the specimen is not subjected to pure shear, and the KES-F test results may not directly determine fabric shear rigidity.⁷ The FAST system has been developed by the Commonwealth Scientific and Industrial Research Organisation (CSIRO) to predict the tailoring performance and the appearance of the tailored garments of wool and blended fabrics. The FAST system measures the fabric shear according to the bias extension principle. However, the shearing is reported to be non-uniform throughout the specimen due to the distortion of width uniformity.⁸

The bias extension method is a conventional method preferred by many researchers as it is a simple and easy way of measuring the shear rigidity. Buckenham⁹ compared the KES-F and bias extension test methods and concluded that the bias extension test is more appropriate for characterizing fabrics in the trellising deformation. Takatera et al.¹⁰ carried out the bias extension test using the rod-clamp method and concluded that deformation in a fabric sample tested with the bias extension method cannot correspond to the pure shear state when large loads are applied. Potluri et al.¹¹ proposed a wide strip bias extension test and investigated the meso-scale shear deformation of textile composites.

In order to comprise pure shear deformation and more accountable test results, researchers suggested more effective devices and new methods, such as the shear frame method. In the shear frame method, a fabric sample is placed to a square-shaped frame and stretched by a tensile testing machine along the diagonal direction and, consequently, the fabric sample deforms into a rhomboid. Zheng et al.¹² presented a shear frame apparatus based on the trellis shear model and concluded that there is a good agreement between the test results of different methods and the shear frame method is more effective in measuring shear behavior in the natural state. Cavallaro et al.¹³ developed a combined multi-axial tension and shear test fixture, capable of applying biaxial tension or compression loads optionally combined with in-plane shear loads. Zhu et al.¹⁴ investigated the large shear deformation of composite fabrics and its contribution to wrinkling. Cao et al.¹⁵ studied the shear rigidity of identical fabrics, tested with the bias extension method and six different shear frames used in various laboratories and concluded that the results show consistency and picture frame tests are able to produce valuable experimental data for characterizing the shear behavior of textiles. Launay et al.¹⁶ studied the in-plane shear behavior of textile preforms and its dependence on the tension in the yarns by using a shear frame equipped with numerical cameras and load sensors. Abed et al.¹⁷ suggested a shear frame with a modified gripping mechanism where the fabric was rolled upon a steel stick and fixed by screws. Harrison et al.¹⁸ investigated the wrinkling behavior of plain weave glass fabrics under large shear deformations using the shear frame method, conventional bias extension method, and wide strip bias extension test in which the sample was clamped with extra orthogonal grippers.

Bilisik and Yolacan¹⁹ presented the yarn pull-out method and a new fixture for shear measurements in which the fabric sample is clamped from both opposing edges to the fabric holding fixture and the free yarn ends extruding from the center of the fabric sample are clamped by the upper jaw of the tensile testing machine. Several studies reported by Bilisik^20–22 showed that the yarn pull-out method is applicable for technical woven fabrics. Majumdar and Laha²³ investigated the effects of weave and setting on yarn pull-out force for untreated and shear thickening fluid (STF) treated p-aramid fabrics.

Mohammed et al.²⁴ reported a micro-structural analysis to investigate the shear locking angle by using the shear frame method. Lo and Hu²⁵ derived a model to predict fabric shear rigidity in different directions and presented the results as polar diagrams. Harrison et al.²⁶ presented a method of normalizing shear frame and bias extension data. Sun and Pan²⁷ proposed a mechanical model to evaluate the shearing properties of fabrics during the initial slip region. Liu et al.²⁸ developed a picture frame model to calculate the stress and stiffness of the fabrics in the case of large deformations. Lomov and Verpoest²⁹ presented a model to predict the shear behavior of fabrics using various fabric parameters, such as bending, friction, and compression. Boisse et al.³⁰ proposed a finite element analyses and investigated the importance of in-plane shear rigidity. Dolatabadi et al.³¹ studied the geometrical deformation of fabrics under shear stress by detecting the exterior position of yarns in sheared fabrics. In further studies, Dolatabadi and Kovar^32,33 simulated the shear behavior of fabrics and compared the simulation with the previous findings. Kim and Takatera³⁴ investigated the shear stiffness of laminated fabrics using the KES-F and proposed a shear model for laminated fabrics bonded with dot-type adhesive interlining.

The related literature showed that the results obtained by commercially available test devices may not account for pure shear behavior and the yarn pull-out method is verified only for technical fabrics. Hence, shear frame tests appear to be the most convenient method for researchers working on various textile structures. In this study, shear behavior of fabrics was investigated by a new shear frame device and a conventional method as well. Properties of the designed shear frame apparatus, sample dimensions, and test parameters were optimized for a precise shear measurement. A novel approach for the determination of in-plane shear behavior, on the basis of two complementary shear frame experiments carried out in reciprocal diagonal directions, was proposed. The accuracy and precision of the proposed apparatus and test method were investigated and statistically verified.

Materials and methods

In the present study, the shear behavior of 12 different shirting fabrics was investigated. In order to examine the effects of setting and raw material on shear behavior, custom-made systematic fabrics were produced. The fabrics that were examined in this study were classified into three groups. In the first group (S1) and second group (S2), there are six satin weave systematic fabrics with two different weft raw materials and three levels of weft settings. In the third group (N) there are six non-systematic fabrics, having various raw materials and weave patterns. The physical and structural properties of the yarns and fabrics are presented in Tables 1 and 2, respectively.

Table 1.

Physical and structural properties of the yarns used in the study

Fabric group	Fabric code	Material		Yarn count
Fabric group	Fabric code	Warp	Weft	Warp	Weft
S1	S1.1	Cotton^bc	PA 66^e	9.8 tex	44/33 dtex/f
	S1.2	Cotton^bc	PA 66^e	9.8 tex	44/33 dtex/f
	S1.3	Cotton^bc	PA 66^e	9.8 tex	44/33 dtex/f
S2	S2.1	Cotton^bc	Tencel^b	9.8 tex	9.8 tex
	S2.2	Cotton^bc	Tencel^b	9.8 tex	9.8 tex
	S2.3	Cotton^bc	Tencel^b	9.8 tex	9.8 tex
N	N1	Cotton^a	Cotton^a	30 tex	30 tex
	N2	60/40 Cotton/Tencel^ac	60/40 Cotton/Tencel^ac	30 tex	30 tex
	N3	Cotton^ac	Cotton^ac	30 tex	30 tex
	N4	Cotton^ac	82/18 Cotton/Polyester^d	30 tex	30 tex
	N5	Cotton^bc	Cotton^bc	20 tex	20 tex
	N6	Cotton^a	96.3/3.7 Cotton/Elastane^ac	42 tex	33 tex

Ring carded.

Ring combed.

Compact.

Compact combed.

Core spun combed.

Fully drawn multifilament yarn.

Table 2.

Physical and structural properties of the fabrics used in the study

Fabric group	Fabric code	Weave pattern	Setting (cm⁻¹) (warp × weft)	Mass per unit area (g/m²)	Thickness (mm)
S1	S1.1	Satin	85 × 46	108.2 (1.0)	0.24 (0.01)
	S1.2	Satin	85 × 50	111.4 (0.3)	0.24 (0.01)
	S1.3	Satin	85 × 55	114.1 (0.5)	0.24 (0.00)
S2	S2.1	Satin	82 × 40	122.5 (0.5)	0.25 (0.01)
	S2.2	Satin	82 × 45	129.1 (0.9)	0.26 (0.01)
	S2.3	Satin	82 × 50	135.1 (0.4)	0.26 (0.01)
N	N1	Plain	28 × 21	179.4 (0.4)	0.44 (0.01)
	N2	2/1 Twill	40 × 23	207.0 (0.5)	0.45 (0.00)
	N3	2/1 Twill	39 × 22	202.0 (1.0)	0.42 (0.01)
	N4	3/1 Twill	36 × 24	196.4 (0.8)	0.45 (0.02)
	N5	3/1 Twill	50 × 34	190.1 (0.9)	0.40 (0.01)
	N6	3/1 Twill	37 × 25	274.0 (1.7)	0.57 (0.02)

Note: The mass per unit area and thickness values are reported as means (standard deviations) of five measurements.

Fabrics were conditioned for 24 hours at standard atmospheric conditions (20 ± 2℃, 65 ± 2% relative humidity (RH)) before the tests in accordance with ASTM D1776/D1776M-15. The mass per unit area and setting were measured in accordance with ASTM D3776/D3776M-09a and ASTM D3775-12, respectively. The fabric thickness was measured using James Heal R&B Cloth Thickness Tester, having a circular presser foot of 100 mm² size, and the applied pressure was 5 gf/cm². For each fabric type, five trials were done.

Bending measurements

Bending rigidity measurements were carried out in warp, weft, and two diagonal directions, using the Shirley Stiffness Tester – a cantilever stiffness measurement equipment – according to ASTMD1388-14e1. The bias bending samples were cut into a rectangular shape, oriented initially +45° and −45° to the production direction – as seen in Figure 1 – and tested according to the related standard. Orientation of the diagonal samples was determined according to the face side of the fabric. For each fabric type, four trials were done in the warp, weft, and two diagonal directions. Bending length and bending rigidity for each test direction were calculated.

Figure 1.

Orientation of the diagonal samples.

Tensile tests

The tensile test refers to the uniaxial fabric extensibility measurements carried out by stretching the fabric sample in the warp or weft direction under a fixed low load. In the present study, the tensile tests were carried out using Instron 4411 Universal Tensile Tester, working with the constant rate of extension principle. Five samples were prepared in the warp and weft directions and the sample size was set to 250 mm × 50 mm. The measuring length between two clamps was 150 mm, the applied tensile stress was 100 N/m, and the test speed was 25 mm/min. The tensile properties of fabrics were calculated from the test results.^35,36

Shear measurements

When a fabric sample is subjected to pure shear, shear angle and shear rigidity can be calculated based on the test results. As presented in Figure 2, the x and y directions indicate the initial weft and warp directions and the square OABC represents the pure shear zone of the fabric sample, where each side of it is equal to L. This dimension is assumed to remain constant during shear deformation. When the shear force is applied to the specified area in its selected diagonal direction, the initial angle (90°) between the warp and weft yarns changes and the square-shaped object deforms into a rhomboid.

Figure 2.

Pure shear kinematics.

The amount of change in the angle between warp and weft yarns is called shear angle (γ) and the difference between |OB| and |OB'| is the shear displacement (d). Both values are terms of shear deformation and shear angle can be calculated by using equation 1. Shear rigidity (G) can be calculated by stress strain relations using the following equation where F is the shear force and w is the fabric width perpendicular to the load applied.

γ = \frac{π}{2} - 2 \cos - 1 (\frac{1}{\sqrt{2}} + \frac{d}{2 \times L})

(1)

G = (\frac{F / w}{\tan γ})

(2)

Bias extension method

The bias extension method is a widely used conventional method, which can be achieved using a tensile testing machine where no special instrument or apparatus is required. Considering the fact that bias extension tests are simple to perform and the method requires no additional apparatus, it is preferred by many researchers.

In the bias extension method, yarns inside the fabric structure are assumed to exhibit different reactions under shear forces and, after deformation, three different zones are created. These zones are shown in Figure 3. In zone I, the warp and weft yarns do not change their initial positions and no shear deformation occurs. In zone II, one set of yarns (warp or weft yarns) rotates so there is half-shear deformation. In zone III both warp and weft yarns rotate and pure shear deformation occurs.^17,31 In many studies, zone I and II are neglected and the height of section III ( $l - w$ ) is equal to the diagonal length of the pure shear zone.¹⁶ In this case, the shear angle for bias extension measurements (γ _b ) is calculated by using equation (3), where d is the shear displacement, l is the distance between two clamps and w is the sample width.

γ_{b} = \frac{π}{2} - 2 \cos - 1 (\frac{1}{\sqrt{2}} + \frac{d}{\sqrt{2} \times (l - w)})

(3)

Figure 3.

The shear deformation in the bias extension method: (a) initial position; (b) after deformation.

In this study bias extension samples were prepared in two diagonal directions, as shown in Figure 1. These samples were cut into a rectangular shape with a length of 250 mm and a width of 50 mm. The measuring length between the two clamps was 150 mm. For each fabric type, five trials were done in two diagonal directions. The average shear rigidity result for each fabric type was reported as the means of 10 measurements.

Shear frame method

In this study a shear frame apparatus – designed by Uren as a part of an ongoing PhD thesis work – and a novel shear measurement method were presented. In order to achieve pure shear deformation during shear frame tests and obtain precise results, relevant key factors were investigated. Properties of the designed shear frame apparatus, sample dimensions, and test parameters were optimized. Shear angle verification, tension estimation, and relaxation analysis were carried out. The information regarding the indicated processes, calibration of the designed shear frame device, and method validation are presented below in detail.

The frame dimensions were set to 130 mm × 130 mm. Screws and metal plates were used to apply the required pressure to the edges of the fabric sample and the fabric slippage from the clamped sections was effectively prevented by this gripping mechanism. The disposition of the test sample was set parallel to the warp and weft directions and the sample size was 190 mm × 190 mm. The corners of the sample were cut out to obtain a cruciform shape with a pure shear zone of 80 mm × 80 mm dimensions, which corresponds to the square ABCD in Figure 4.

Figure 4.

Shear frame sample and two diagonal test directions.

In the present study, each shear frame sample was tested in +45° and −45° directions and the average shear rigidity result of the sample was calculated as the mean of two complementary experiments. For the measurement in the +45° direction, the sample was rotated counter-clockwise from its initial position and fixed to the frame, as shown in Figure 5. Two diagonally opposite corners of the frame were pulled apart by the tensile testing machine and the pure shear zone of the sample was deformed into a rhomboid. When the maximum displacement value was achieved, the results were recorded. After the measurement in the +45° direction, the upper jaw on the tensile machine was returned to the zero displacement position and the fabric sample was deformed back to its initial cruciform shape. The sample was then relaxed for at least 48 hours in standard atmospheric conditions. For the measurement in the −45° direction, the relaxed sample was rotated clockwise from its initial position and the previously mentioned test steps were repeated. For each fabric type, five trials were done in two test directions. The average shear rigidity results were reported as the means of five measurements of two complementary experiments.

Figure 5.

Placing the sample on the shear frame.

Launay et al.¹⁶ stated that for shear angles smaller than the shear locking angle, the strain in the yarns was found to be negligible. When the shear angle observed is larger than the shear locking angle, the yarns contact with the adjacent yarns and the geometry of the fabric weave does not allow the yarn rotation anymore.^17,30 At a small angle of shearing, the acting tensile force component will have negligible magnitude and hence can be ignored.²⁷ In order to have pure shear results, the maximum displacement limits were set in accordance with the maximum shear angle desired (approximately 12°) for both shear test methods.

The effect of cross-head speed on the shear behavior of plain weave fabrics is reported to be considerably small. However, for twill and satin weave fabrics, as the cross-head speed increases, the shear curve moves to the right, leading to lower shear rigidity results.²⁴ Zhu et al.¹⁴ adopted different loading speeds and concluded that the overall deformation stiffness increases with the loading speed. In order to select the optimum test speed for this study, different cross-head speeds were attempted and the influence of test speed on the shear rigidity results obtained by the shear frame and bias extension methods was examined. The investigations showed that the test speed has a significant effect on the bias extension results (p < 0.05). The shear rigidity results obtained by this method with 100 mm/min test speed are approximately 30% lower than the results with 25 mm/min test speed. The effect of test speed on shear frame results was considerably small and statistically not significant (p > 0.05). Based on previous literature and current findings, the test speed was set to 25 mm/min for all shear measurements.

To determine the relation between measured and calculated shear angles, a marked sample was fixed to the shear frame and stretched by the tensile testing machine, as shown in Figure 6. When the maximum displacement value was achieved, the shear angle was measured by defining the difference between initial and final angles on each corner of the effective sample area. Statistical examinations proved that there is no significant difference between calculated and visually measured shear angle values (p > 0.05).

Figure 6.

The shear frame device on the tensile testing instrument: (a) before deformation; (b) after deformation.

Different approaches used for formulating shear behavior come with the assumption that the tension does not play a role in shear results. In order to realize this assumption, it is important to set the initial tension to zero. To confirm that the proposed shear frame fulfils the indicated condition, the edges of the effective sample area were marked on the free fabric sample. The length of the marks was measured before and after fixing the fabric sample on the shear frame, and the initial tension on the fabric sample was determined. Statistical analyses showed that there is no significant change in the length of marks before and after fixing (p > 0.05). Consequently, the initial tension in the shear frame method was assumed to be approximately zero.

The efficiency of the relaxation process between two complementary shear frame measurements was validated by relaxation analysis. Five fresh shear frame samples with no previous deformation were prepared for each fabric type. The fresh samples were tested by single experiments carried out only in the –45° test direction. The results of single experiments were compared with the results of complementary experiments. For the fabrics used in the present study, the difference between the shear rigidity results of fresh and previously deformed samples in the –45° test direction was not significant (p > 0.05). Accordingly, the relaxation process carried out in the present study was found out to be sufficient.

Calibration

In order to ensure that the load value recorded by the tensile testing machine during shear deformation is solely caused by the shear rigidity of the fabric sample, it is essential to maintain the minimum amount of forces resulting from frame movement. The shear frame device used in the present study was designed with special junction mechanisms to provide the frictional stability and minimize the undesired frictional forces. To calculate net stress, the empty shear frame was adjusted to the tensile machine and the load–displacement diagrams of empty frame tests were recorded. The maximum load recorded by the empty frame test is 0.0268 N. The repeated tests showed that this is a constant value with zero deviation. Two empty frame test trials were done before each fabric sample. The load–displacement diagrams of the empty shear frame tests in comparison with a sample loaded shear frame test are presented in Figure 7.

Figure 7.

The load–displacement diagrams of two sequential empty shear frame tests (specimen 1 and specimen 2) and a sample loaded shear frame test (specimen 3).

Validation

The shear results measured by the shear frame apparatus are expected to be consistent and reproducible. In order to confirm that, validation tests were carried out. A plain weave, 100% cotton fabric with 158 g/m² mass per unit area was used as the validation fabric. The validation fabric was chosen in accordance with the parameters of shirting fabrics. Validation tests were carried out as two sets having six shear tests, each with five trials. Sixty validation samples were prepared, as 30 of these samples were tested in the first set and the remaining 30 samples were tested later in the second set. For every sample, each trial was done in the +45° and −45° test directions. The means of five subsequent trials – of two complementary experiments – were calculated as one shear test result. The two sets were analyzed by the one-way analysis of variance (ANOVA) statistical method and no significant difference was found (p > 0.05).

According to the experimental plan, the results regarding the shear rigidity, bending rigidity, and extension ability measurements were evaluated at the 95% confidence level, using SPSS 22.0 statistical software by applying independent t-tests, paired t-tests, variance, and correlation analyses.

Results and discussion

Among the various fabric properties, evaluation of the shear behavior of a textile product is essential when it comes to fabric hand and formability. In many cases, yarns inside the woven fabric structure are forced to change their initial positions, forming a new geometry, and the resistance to this displacement is known as shear rigidity. Fabric parameters, such as setting, raw material, mass per unit area, and yarn count, can have various effects on the shear behavior of fabrics. The results regarding the influence of the test method, test parameters, and fabric parameters on the in-plane shear behavior of the studied fabrics are stated below. Relations between shear behavior, bending rigidity, and extension ability were also established.

The shear results given by the shear frame and bias extension methods are presented in Table 3. When the average shear rigidity results from two methods were examined, it was seen that the shear frame results have lower standard deviation values. In this context, the shear rigidity results obtained by shear the frame method that was carried out with two complementary experiments were found out to be more precise compared to the conventional method.

Table 3.

Shear rigidity results obtained by the shear frame and bias extension methods

Fabric code	Shear rigidity (N/m)
	Shear frame			Bias extension
	Average	+45°	−45°	Average	+45°	−45°
S1.1	34.8 (5.5)	29.1	40.4	42.1 (7.3)	37.8	46.4
S1.2	40.4 (5.8)	36.3	44.4	56.9 (11.1)	47.6^b	66.1^b
S1.3	52.1 (2.6)	53.6	50.5	78.1 (12.8)	82.2	74.0
S2.1	74.7 (6.9)	72.1	77.2	82.5 (12.9)	73.3^b	91.8^b
S2.2	99.3 (7.8)	93.8	104.8	114.4 (16.2)	127.9^b	100.9^b
S2.3	118.9 (14.5)	126.2	111.6	139.4 (21.3)	158.5^b	120.4^b
N1	275.4 (17.7)	281.0	269.7	302.3 (22.3)	292.3	312.2
N2	91.4 (9.3)	103.5^a	79.3^a	116.7 (30.2)	104.0	129.4
N3	168.6 (13.0)	202.9^a	134.4^a	207.4 (60.4)	264.1^b	150.6^b
N4	57.1 (1.8)	62.4^a	51.8^a	56.5 (10.7)	66.5^b	46.6^b
N5	124.0 (8.1)	155.3^a	92.8^a	141.3 (47.2)	185.2^b	97.4^b
N6	135.1 (3.8)	148.5^a	121.8^a	125.7 (21.5)	145.9^b	105.4^b

The difference between the shear frame results in two diagonal directions is significant (p < 0.05).

The difference between the bias extension results in two diagonal directions is significant (p < 0.05).

Notes: The average shear rigidity results for the shear frame method are reported as means (standard deviations) of five measurements of two complementary experiments.

The average shear rigidity results for the bias extension method are reported as means (standard deviations) of 10 measurements.

The shear rigidity results in the +45° and −45° test directions are reported as means of five measurements.

The shear frame results are expected to be consistent with the results of alternative methods. In order to verify that, the results obtained by the shear frame and bias extension methods were compared. Correlation coefficients between the results of the two methods were found to be considerably high and statistically significant, as presented in Table 4. In the present study, there is no systematic change in the warp direction. Therefore, correlations between shear rigidity and other parameters of systematic fabrics in the warp direction were neglected.

Table 4.

Correlation coefficients between mechanical properties

			Shear rigidity (N/m)
			Shear frame			Bias extension
			Average	+45°	–45°	Average	+45°	–45°
Shear rigidity	Average	r	1	0.987**	0.982**	0.986**	0.948**	0.944**
(Shear frame)	Average	r^s	1	0.994**	0.991**	0.981**	0.963**	0.971**
(N/m)	+45°	r	0.987**	1	0.938**	0.979**	0.975**	0.898**
	+45°	r^s	0.994**	1	0.969**	0.989**	0.972**	0.976**
	−45°	r	0.982**	0.938**	1	0.960**	0.884**	0.966**
	−45°	r^s	0.991**	0.969**	1	0.955**	0.935**	0.950**
Extension	Warp	r	0.319	0.406	0.204	0.255	0.337	0.137
(%)	Warp	r^s	−0.563	−0.539	−0.582	−0.582	−0.502	−0.698
	Weft	r	−0.462	−0.465	−0.443	−0.555	−0.540	−0.524
	Weft	r^s	−0.949**	−0.933**	−0.951**	−0.932**	−0.889*	−0.969**
Bending rigidity	Warp	r	0.797**	0.736**	0.842**	0.764**	0.609*	0.876**
(µJ/m)	Warp	r^s	−0.781	−0.741	−0.817*	−0.647	−0.592	−0.716
	Weft	r	0.829**	0.821**	0.810**	0.752**	0.703*	0.743**
	Weft	r^s	0.951**	0.969**	0.914*	0.937**	0.922**	0.924**
	+45°	r	0.872**	0.830**	0.892**	0.818**	0.703*	0.881**
	+45°	r^s	0.968**	0.956**	0.965**	0.949**	0.911*	0.976**
	−45°	r	0.850**	0.791**	0.891**	0.799**	0.659*	0.892**
	−45°	r^s	0.972**	0.951**	0.982**	0.921**	0.878*	0.957**

r: Pearson correlations of all fabrics (sample size N = 12); r^s: Pearson correlations of systematic fabrics (sample size N = 6).

Correlation is significant at the 0.01 level (two-tailed).

Correlation is significant at the 0.05 level (two-tailed).

Even though the shear results of the two test methods follow a similar track, the difference between the pairs is quite obvious, as shown in Figure 8. This difference is also visible on the shear stress–shear angle curves of systematic fabrics, obtained by the two test methods, as presented in Figure 9.

Figure 8.

Shear rigidity of fabrics: (a) systematic; (b) non-systematic.

Figure 9.

Shear stress–shear angle curves of systematic fabrics.

When the results of the shear frame and bias extension methods were examined by paired sample t-test, the difference between the pairs was found to be statistically significant (p = 0.001). This result is in accordance with the related literature, which states that the bias extension method gives higher shear rigidity results when compared to the shear frame method.^12,17 Zheng et al.¹² asserted that the difference between the results of the shear frame and bias extension methods corresponds with the effect of tensile rigidity. On the other hand, in the shear frame method all the recorded force is assumed to be equal to the shear force. Certifying the current claims, the fabrics that have high extension ability – as presented in Table 5 – have similar shear rigidity results for the two test methods.

Table 5.

Extension results of fabrics

Fabric code	Extension (%)		Tensile rigidity (kN/m)
Fabric code	Warp	Weft	Warp	Weft
S1.1	1.00 (0.07)	7.16 (0.48)	10.0 (0.73)	1.40 (0.10)
S1.2	0.95 (0.06)	6.26 (0.31)	10.5 (0.60)	1.60 (0.08)
S1.3	0.95 (0.04)	5.34 (0.33)	10.6 (0.48)	1.88 (0.11)
S2.1	0.93 (0.10)	3.87 (0.27)	10.8 (1.04)	2.59 (0.18)
S2.2	0.93 (0.09)	3.19 (0.42)	10.8 (0.97)	3.18 (0.43)
S2.3	0.95 (0.08)	3.05 (0.07)	10.6 (0.89)	3.28 (0.08)
N1	2.26 (0.25)	2.94 (0.30)	4.47 (0.50)	3.43 (0.50)
N2	2.86 (0.23)	3.78 (0.19)	3.51 (0.27)	2.65 (0.27)
N3	2.88 (0.11)	3.18 (0.19)	3.48 (0.14)	3.15 (0.14)
N4	3.94 (0.05)	11.6 (0.28)	2.54 (0.04)	0.86 (0.04)
N5	3.08 (0.08)	3.00 (0.21)	3.25 (0.09)	3.35 (0.09)
N6	3.54 (0.23)	8.40 (0.29)	2.83 (0.19)	1.19 (0.19)

Note: All data are reported as means (standard deviations) of five measurements.

The extension ability of fabrics N4 and N6 in the weft direction is higher than the rest of the fabric samples, as shown in Figure 10. Fabric type N4 has core spun polyester/cotton blend weft yarns and fabric type N6 has cotton/elastane blend weft yarns; hence, it is expected that those fabric samples will exhibit higher extension abilities.

Figure 10.

Extension of the fabrics under 100 N/m load: (a) systematic; (b) non-systematic.

Considering the fact that in the bias extension method the recorded force is a combination of resistance to shear and resistance to extension, the difference between shear frame and bias extension results is expected to be smaller for fabrics that have a higher extension ability. In fact, the difference between the shear rigidity results obtained by the shear frame (G) and bias extension (G_b) test methods is found to be significantly correlated and reversely proportional to the extension ability in the weft direction (ɛ_x) (r = −0.721 and p = 0.008). The linear regression equation regarding the stated relation is presented as equation (4)

G_{b} - G = 33.8 - 3.47 \times ɛ_{x}

(4)

In consideration of the anisotropic nature of textiles, the shear tests were carried out in two diagonal directions; thus, fabrics exhibited different shear rigidity behaviors in the +45° and −45° test directions. When the shear rigidity results obtained by the shear frame method were investigated, it was seen that the samples of plain weave fabric have almost similar shear rigidity values in the +45° and –45 ° test directions and the difference between the shear results of the two diagonal test directions for this fabric type is statistically not significant (p > 0.05). For the systematic fabrics used in the present study, the difference between the shear results of the two diagonal test directions is statistically not significant (p > 0.05). However, all twill weave fabrics have higher shear rigidity values in the+45° test direction and the differences are statistically significant (p < 0.05). The shear rigidity results obtained by the bias extension method demonstrated that the difference between the shear results of the two diagonal test directions is statistically not significant (p > 0.05) for fabric types S1.1, S1.3, N1, and N2. However, for the remaining fabric types, the differences between the +45° and −45° bias samples are significant (p < 0.05).

The bending length and bending rigidity of fabrics in the warp, weft, and diagonal directions are presented in Table 6. The shear rigidity values are significantly correlated and directly proportional to the bending rigidity results in the warp, weft, +45°, and −45° directions. The correlation coefficients are introduced in Table 4.

Table 6.

Bending results of fabrics

Fabric code	Bending length (mm)				Bending rigidity (µJ/m)
Fabric code	Warp	Weft	+45°	−45°	Warp	Weft	+45°	−45°
S1.1	22.1 (0.5)	8.63 (0.7)	13.7 (0.1)	14.9 (0.4)	16.6 (1.0)	1.00 (0.2)	3.94 (0.1)	5.07 (0.4)
S1.2	22.4 (0.8)	8.97 (0.3)	14.2 (0.4)	15.1 (0.6)	17.9 (2.0)	1.15 (0.1)	4.50 (0.4)	5.43 (0.6)
S1.3	22.9 (0.5)	9.13 (0.5)	15.0 (0.2)	15.1 (0.3)	19.5 (1.4)	1.24 (0.2)	5.44 (0.2)	5.58 (0.4)
S2.1	19.7 (0.3)	10.4 (1.0)	15.7 (0.2)	16.3 (0.2)	13.3 (0.6)	2.00 (0.5)	6.76 (0.2)	7.47 (0.3)
S2.2	19.7 (0.3)	11.0 (0.5)	15.9 (0.1)	16.3 (0.5)	14.1 (0.6)	2.43 (0.3)	7.38 (0.1)	7.98 (0.8)
S2.3	19.0 (0.3)	12.9 (0.9)	15.9 (0.3)	16.4 (0.2)	13.1 (0.7)	4.17 (0.9)	7.78 (0.3)	8.43 (0.4)
N1	32.1 (1.4)	20.0 (0.2)	27.1 (1.3)	27.2 (1.1)	84.3 (11)	20.5 (0.7)	51.0 (7.2)	51.7 (6.1)
N2	23.1 (1.2)	13.8 (0.4)	18.6 (0.4)	18.4 (0.5)	36.3 (5.7)	7.75 (0.7)	18.8 (1.2)	18.4 (1.5)
N3	20.2 (0.3)	14.6 (0.4)	17.1 (0.2)	15.6 (0.3)	23.7 (1.0)	8.95 (0.7)	14.3 (0.4)	10.9 (0.7)
N4	17.1 (0.2)	12.3 (0.3)	15.9 (0.4)	12.8 (0.1)	13.9 (0.5)	5.20 (0.3)	11.2 (0.8)	5.79 (0.2)
N5	16.8 (0.5)	13.2 (0.2)	16.1 (0.3)	14.2 (0.3)	12.8 (1.1)	6.25 (0.3)	11.3 (0.6)	7.70 (0.5)
N6	22.1 (0.8)	17.0 (0.4)	19.3 (0.3)	19.2 (0.2)	42.2 (4.5)	19.0 (1.4)	27.8 (1.3)	27.4 (1.0)

Note: All data are reported as means (standard deviations) of four measurements.

When the results in the diagonal directions were examined, the −45° samples of satin weave fabrics seem to have slightly higher bending length values compared to the +45° samples, as shown in Figure 11. On the other hand, the +45° samples of twill weave fabrics have higher bending length values compared to the –45° samples and the plain weave fabric has similar bending length values in the +45° and –45° test directions. The satin fabric surface has a left oblique view, as shown in Figure 12, and the warp dominant twill weave pattern produces the right oblique diagonal ribbings. It is possible to assert that those slopes contribute to the resistance of samples prepared in corresponding diagonal directions. As the weft setting of systematic fabrics increases, the difference between bending results in the two diagonal directions decreases. Hereunder this finding, it is possible to say that when the difference between warp and weft settings decreases, the bending rigidity values in different diagonal directions will be closer. In this case, the difference between bending results of the two diagonal test directions can be related to the weave pattern and the setting.

Figure 11.

Bending length of fabrics: (a) systematic; (b) non-systematic.

Figure 12.

Surface view of satin fabric: (a) face; (b) back.

During shear deformation, yarns rotate on each other and surface friction of the yarns plays a significant role in the shear rigidity. Staple spun yarns tend to have higher surface friction values compared to filaments because of the yarn hairiness and the essential amount of twist in the yarn structure. In this study, the shear rigidity of the first fabric group, made of polyamide 66 and multifilament weft yarns, is lower than the second group, made of Tencel staple spun weft yarns. This difference is statistically significant (p = 0.000) and fairly consistent with the previously stated facts. For systematic fabric samples, the influence of the change in weft setting on the shear results is statistically significant (p = 0.000). Shear rigidity values of systematic fabrics are directly proportional to the fabric unit weight (r = 0.998) and fabric thickness (r = 0.969) as well (p < 0.01). In Figure 13 the relations between the weft setting (0–60 cm⁻¹), the mass per unit area (0–150 g/m²), shear rigidity (0–150 N/m), bending rigidity (0–10 µJ/m), and tensile rigidity (0–4 kN/m) of systematic fabrics are presented as spider diagrams.

Figure 13.

Relations between various fabric parameters of (a) the first systematic fabric group and (b) the second systematic fabric group.

Conclusion

This study mainly focuses on introducing a new shear frame device, determining the in-plane shear behavior of woven shirting fabrics, investigating its relations with various mechanical fabric parameters, and examining the effects of raw material and setting. The calibration and validation data proved that the shear frame results obtained by the new shear frame device were viable and reproducible. The correlation between the results of the shear frame and bias extension methods was significant and the relations between shear stress–shear angle curves obtained by two test methods were consistent with the previous literature. The difference between shear results in the +45 and –45 test directions and its relations with weave pattern and yarn setting were established. A novel approach to determine the in-plane shear behavior of woven fabrics via two complementary shear frame measurements was presented and proved to be precise and reliable.

In the current study, the in-plane shear behavior of 12 different shirting fabrics was examined. Statistical analyses proved that shear rigidity is strongly related to bending rigidity and tensile rigidity, as high correlation coefficients were established between these parameters. The effect of the selected production parameters was investigated by custom-made systematic fabrics and was found out to be significant.

The designed shear frame apparatus suggested that the test parameters and presented test method can be a helpful guide for researchers, while the experimental results provide useful information for future studies.

Footnotes

Acknowledgment

The authors would like to thank the R&D Department of SOKTAS for production of the fabrics used in the present study.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Council of Higher Education, Faculty Development Programme (OYP).

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