Tear resistance of woven textiles – Criterion and mechanisms

Composites: Part B 42 (2011) 1851–1859

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Tear resistance of woven textiles – Criterion and mechanisms Ennouri Triki, Patricia Dolez ⇑, Toan Vu-Khanh École de technologie supérieure, 1100 rue Notre-Dame Ouest, Montréal, QC, Canada H3C 1K3

a r t i c l e

i n f o

Article history: Received 22 October 2010 Received in revised form 30 April 2011 Accepted 15 June 2011 Available online 28 June 2011 Keywords: A. Fabrics/textiles B. Mechanical properties

a b s t r a c t The resistance to tearing of textiles is an important characteristic of materials, especially for fabrics used in personal protective equipment. In this project, work has been done to develop a criterion for textile structures based on the tearing energy. Tongue tear and tensile central crack tear tests were performed on plain and twill woven fabrics made of cotton, polyester/cotton blend and polyester. The tearing energy was computed from the variation of the work as a function of the tear crack surface area. Results show that for the two types of studied weaves, the tearing energy G is independent of the sample configuration. This tearing energy criterion was used to study the effect of fabrics linear density, yarn density and weave on their tearing performance. It also provided evidence of the occurrence of an additional phenomenon in the tongue tear mechanism, i.e. the sliding of transverse yarns in addition to the already reported sliding of longitudinal yarns. This tearing energy criterion appears as a valuable tool for the in-depth study of the tearing resistance of woven textiles. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction The tearing behavior of materials is a major component of their mechanical performance. In particular, in the case of protective materials, the tearing resistance is generally among the requirements, for example with protective gloves [1] and firefighter protective suits [2,3]. In the research community, large efforts have also been devoted to the understanding of the tearing behavior of materials. In the case of textiles, most of the work has dealt with the tongue tear (trouser) configuration [4]. Some authors also studied trapezoid [5,6] and wing tear [7] geometries. The evaluation of the tearing resistance was performed through maximum force or work determination. When a static load is applied to a pre-cracked sample, a tearing area called the Del zone [8] is formed as shown in Fig. 1 in the tongue tear configuration. The Del zone arises from the stretching and slippage of longitudinal yarns (yarns parallel to the tear) along the transverse yarns as well as the stretching and alignment/jamming of these transverse yarns [9]. As illustrated in Fig. 1, there is no longitudinal yarn in the Del zone. Due to contact friction between longitudinal and transverse yarns at the edge of the Del zone, the load is transferred to the transverse yarns. Rupture occurs when they reach their maximum tensile strength. More precisely, tearing proceeds step by step as each successive transverse yarn fails, which corresponds to local peaks in the force–displacement curve [9]. Then, the Del zone moves forward in the tearing direction with further sliding of the longitudinal ⇑ Corresponding author. Tel.: +1 514 396 8800x7820; fax: +1 514 396 8530. E-mail address: [email protected] (P. Dolez). 1359-8368/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesb.2011.06.015

yarns and stretching of the transverse yarns. With the saw-tooth shape of its force–displacement curve, the process has been qualified as discontinuous but in quasi-steady state since the number of transverse yarns in the Del zone remains generally constant [10]. In addition, the inner longitudinal yarns stay in a quasi stationary lateral slip motion. Various authors have looked at the effects of the fabric parameters on its tearing behavior. It was found that the tearing of woven fabrics is controlled mainly by the type of weave as well as by the density and characteristics of the yarns. More specifically, Teixeira et al. [9] indicated in their work that fabric weaves with fewer cross-over points like twill are more resistant to tearing than others like plain weave. Moreover, they showed that a lower density of yarns leads to an increased tear strength due to a larger yarn mobility. Scelzo et al. [10] confirmed these results and explained the higher tear strength of low yarn density fabrics by the presence of a larger number of transverse yarns in the Del zone. Regarding the effect of the characteristics of the yarns, while Lord and Stuckey [11] reported that the tear strength of fabrics increases with the yarn twist, Teixeira showed that this result is not always true [9]. Also on the subject of yarn characteristics, Teixeira reported that the fabrics made of continuous-filament yarns are more resistant to tearing than staple fiber ones. It must be noted that no result on the influence of the linear density on fabrics tearing behavior has been found. Several authors have attempted to develop models describing the tearing process in woven textiles. Teixeira proposed a rheological representation of the tongue tear specimen using springs as well as a geometrical description of the Del zone [9]. Taylor linked the tongue tear strength to fabric construction parameters as well as

E. Triki et al. / Composites: Part B 42 (2011) 1851–1859

50mm

1852

100mm Fig. 2. Schematic representation of the tongue tear sample.

Del zone

Fig. 1. Tongue tear sample configuration.

yarn strength and friction coefficient [12]. The model proposed by Seo is similar to that of Taylor but includes also the yarn elongation at break [13]. At last, Scelzo used the same rheological approach as Teixeira but with restricting it to the Del zone under that assumption that it sustains the entire applied load [14]. He distinguishes three individual contributions of the Del zone to the tearing process: yarn pull-out, yarn pull-ahead (jamming) and yarn tenacity [10]. Individual test procedures were also developed to provide the modulus corresponding to each of these three contributions. In their work, researchers have generally used one of two parameters to characterize the tearing resistance of fabrics. The first one is the force, either through its maximum value or through the average of its maxima [7–10,15,16]. However, this method only considers the yarn rupture phase and does not take into account the formation of the Del zone which corresponds to the intervals between force minima and maxima in the force–displacement curve. Others have computed the work corresponding to the tearing of the sample [8,16]. Teixeira et al. also reported some results in terms of energy [9]. However, these were obtained by multiplying the mean of the upper load and the lower load limits by the corresponding jaw displacement. These calculations involve only the tearing force and the jaw displacement, not intrinsic material parameters that characterize crack propagation. It is thus proposed in this study to investigate the tearing behavior of fabrics by the way of the tearing energy based on fracture mechanics approaches [17]. In this approach, the energy G is related to the work @W expanded to increase the surface of a crack by a quantity @A according to the relationship:

G¼

  @W @A

ð1Þ

It was shown that G is an intrinsic characteristic of the material. This new approach was applied to two geometries of tear samples, tongue and tensile central crack tear. Different types of fabrics with various weaves, yarn material, linear density as well as yarn density were used to evaluate to the robustness of the approach. This new tearing energy criterion for fabrics was used to study the effect of these various parameters on fabric tearing behavior. 2. Experimental 2.1. Test methods Tongue tear tests have been performed according to the EN388 standard method for protective gloves [1]. Trouser-shaped samples

Tearing force (N)

75

50

25

0 0

25

50

75

Displacement (mm) Fig. 3. Typical loading/unloading force–displacement curve in the tongue tear configuration.

with dimensions of 100  50 mm include a longitudinal 50 mm long pre-crack as illustrated in Fig. 2. They were cut along the warp direction of the fabrics. Sample tails were secured in the jaws of a universal testing machine (see Fig. 1) and pulled apart at a rate of 100 mm/min. Tests consisted in a loading/unloading cycle carried out at various values of the maximum jaw displacement. Fig. 3 provides an example of typical loading/unloading force–displacement curve measured in a tongue tear test. The loading curve shows two distinct parts. The first one (Region I in Fig. 3) corresponds the force necessary to bring the material to the first point of tearing. It includes the uniaxial deformation of the two tails as well as the formation of the first Del zone. From the first peak onwards, the crack starts propagating in the fabric. That second part of the loading curve (Region II in Fig. 3) presents a succession of minima and maxima which correspond to the building up of stress in the Del zone cyclically re-initiated by the failure of the outermost transverse (filling) yarn in the Del zone. Unloading is activated immediately after the set jaw displacement has been reached. The unloading curve is mostly due to the release of the elastic energy in the sample tails as well as in the Del zone. The length of the crack was measured for each specimen in the undeformed state. The second type of tear tests carried out corresponds to the tensile central crack geometry, as illustrated in Fig. 4. The same sample dimensions and orientation of the tear as the tongue tear test were used. A central 10 mm long pre-crack was performed in the warp direction of the samples. Also, test involved the same loading pattern, i.e. a loading/unloading cycle up to a set maximum displacement value, as well as the same loading rate as the tongue tear test. A typical force–displacement curve for a loading/unloading cycle carried out in the tensile central crack test configuration is displayed in Fig. 5. Contrary to the tongue tear, failure occurs much more rapidly and in a catastrophic way. In particular, except for the early failure of very few yarns to which can be attributed the

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higher than those obtained in the tongue tear geometry. Unloading at partial tearing also displays the characteristic initial rounded shape in the return force–displacement curve due to the release of elastic energy stored in the sample.

F

2.2. Materials Tests were carried out on cotton, polyester/cotton blend and polyester woven fabrics. Details about the tested fabrics are provided in Table 1. The first two materials are plain weave and correspond each to a single set of parameters. The third one includes plain and twill weave structures as well as various values of the linear and yarn density in the filling direction while characteristics in the warp direction are kept constant.

Central pre-crack

3. Formulation of the tearing energy criterion

F Fig. 4. Schematic representation of the tensile central crack sample geometry.

T¼

Tearing force (N)

300

  1 @W t @c l

ð2Þ

with t the thickness of the test piece (A = tc) and l the applied displacement. On the other hand, based on the principles of fracture mechanics, Felbeck and Atkins expressed the energy necessary to create a new facture surface Gs by [19]:

200

  @U DU  Gs ¼  @A DA

100

0

Following the initial work of Griffith on the phenomena of rupture in solids [17], Rivlin and Thomas proposed a criterion for tearing in rubbers that is independent of the sample geometry [18]. That tearing characteristic energy T corresponds to the work W spent irreversibly for a unit increase in the tear length c according to the following relationship:

0

5

10

15

20

Displacement (mm) Fig. 5. Typical loading/unloading force–displacement curve in the tensile central crack tear configuration.

little steps right before the peak, tearing involves the simultaneous breaking of most of the longitudinal (filling) yarns on each sides of the central pre-cut. This may explain why maximum force values measured in the tensile central crack test configuration are much

where DU is the change in strain energy corresponding to the change in facture surface DA. This approach was applied for the calculation of the fracture energy of rubber associated to needle puncture [20,21]. It involved computing the strain energy release rate from the area delimited by the puncture and return curves. The facture surface area in the undeformed state was measured by optical microscopy. The change in strain energy DUij corresponding to the change in fracture surface DAij is provided by:

DU ij ¼ U i  U j DAij ¼ Ai  Aj

Warp yarn linear density (Tex)

Cotton Plain 31.2 68% polyester and 32% cotton blend Plain 30.8 Polyester Plain 17.2

Twill

17.2

ð4Þ

with i and j corresponding to tests carried out at two different puncture depths.

Table 1 Characteristics of the tested fabrics. Weave

ð3Þ

Filling yarn linear density (Tex)

Yarn density: filling  warp (yarns/cm)

66

17  40

43.2

13  38

33 33 33 16.7 15 33 33 33 16.7 12

10  48 12  48 15  48 12  48 12  48 10  48 12  48 15  48 15  48 15  48

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Test 1: l = 30mm

75

Tearing force (N)

Test 2: l= 60mm

50

25

0 0

25

50

75

Displacement (mm)

The tearing energy criterion proposed for woven textiles in this work is based on elements of each of the preceding methods. The tearing energy G is obtained from the change in expanded work DW corresponding to a change in the tear surface area DA, that operation being carried out for a set value of the displacement l:

  DW G¼ DA l

ð5Þ

The validity of this criterion was tested with two geometries of samples, i.e. tongue tear and tensile central crack tear, and several types of woven fabrics.

Fig. 7. Computation of the expanded work DW from tongue tear force–displacement curves obtained with two values of the maximum applied displacement (l = 30 and 60 mm, plain weave cotton fabric).

Initial work (N.mm)

Fig. 6. Example of a force–displacement curve in the tongue tear for the plain weave cotton fabric with a set value of 60 mm for the maximum jaw displacement.

3.1. Tongue tear configuration

45

0 0

W ¼ W init þ W tear

ð6Þ

where Winit is the initial work necessary for the material to reach the tearing point and Wtear corresponds to the propagation of the crack in the material. It must be noted that the initial work Winit includes the formation of the first Del zone and thus needs to be taken into account into the determination of the tearing energy unlike what was done by Krook and Fox [8]. The computation of the change in expanded work DW in Eq. (5) can be performed by combining Eqs. (4) and (6):

DW ¼ W 1  W 2 ¼ ðW init þ W tear Þ1  ðW init þ W tear Þ2

ð7Þ

where the index 1 and 2 refer to tests performed at two different values of the applied jaw displacement, thus at two different values of the tear length c. Fig. 7 illustrates the principle of the computation of the change in expanded work DW according to Eq. (7). The initial work Winit includes the uniaxial deformation of the two tails as well as the formation of the first Del zone. In this case, the value of the tongue tear pre-crack, which affects the tail length, has been kept constant (c0 = 50 mm). Therefore, as shown in Fig. 8, the value of Winit is independent of the tear length c, thus of the displacement l. As a result, the change in expanded work DW can be simplified to:

DW ¼ W tear;1  W tear;2

ð8Þ

15

30

45

Tear length (mm) Fig. 8. Variation of initial work Winit as a function of the tear length c for a plain weave cotton fabric tested in tongue tear.

1200

Tearing work (Nmm)

Tearing experiments were carried out in the tongue tear configuration (see Fig. 1) using the plain weave cotton fabric. Fig. 6 illustrates the variation of the tearing force as a function of the jaw displacement for two different values of maximum applied displacement. As identified in Fig. 6, the crack starts propagating after a displacement Li. As a result, it is possible to decompose the work W corresponding to the tearing of the entire sample into two parts [8]:

y = 67.212x R² = 0.9581

800

400

0 0

4

8

12

16

Tear crack surface (mm2) Fig. 9. Variation of the tearing work Wtear as a function of the tear crack surface area A for a plain weave cotton fabric tested in tongue tear.

Fig. 9 displays the variation of Wtear as a function of the surface of tear crack A in the fabric for several values of the maximum applied displacement. The tearing work appears to be proportional to the tear crack surface measured in the undeformed state. This indicates that the proposed tearing energy criterion defined by Eq. (5) seems to be valid for that material and that sample configuration. The tearing energy is provided by the slope of the curve in Fig. 9 and is equal to 67 N/mm in that case.

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Test 1: l = 15mm Test 2: l = 12mm

300

2500

Work (N.mm)

Tearing force (N)

2000 200

100

1500

1000

500 0 0

5

10

15

20

Displacement (mm)

0

Fig. 10. Example of force–displacement curves in the tensile central crack tear for the plain weave cotton fabric for two values of the maximum applied displacement (l = 12 and 15 mm).

The same exercise as above was carried out in the tensile central crack configuration. Fig. 10 presents two examples of force– displacement curves obtained with the plain weave cotton for two different values of the maximum displacement l. In that case, since the process is very fast, any attempt to decompose the tearing work into the initial deformation steps and the tear propagation step would probably lead to a high level of uncertainty. As a result, the change in expanded work DW was directly computed from the entire curves provided by the loading /unloading cycle:

DW ¼ W 1  W 2

ð9Þ

with the index 1 and 2 referring to tests performed at two different values of the maximum applied displacement, thus at two different values of the tear crack surface area A. The results of tensile central crack tear tests performed at several values of the maximum applied displacement have been compiled in Fig. 11. Once again, the work is observed to be proportional to the tear crack surface area measured in the undeformed state. Therefore the proposed tearing energy criterion also seems to be valid in the tensile central crack configuration. The tearing energy thus obtained is equal to 68 N/mm. This value is very similar to what was measured in the tongue tear geometry. 3.3. Versatility of the criterion When establishing a criterion, the goal is to refer to an intrinsic material property, i.e. independent of the sample geometry. An-

Work (N.mm)

900

y = 68.199x R² = 0.9858

300

0 0

5

Tear crack surface

5

10

Tear crack surface

15

20

(mm2)

Fig. 12. Variation of the work as a function of the tear crack surface area A for a plain weave polyester/cotton blend fabric tested in the tongue tear (Wtear) and tensile central crack tear (W) configurations.

3.2. Tensile central crack configuration

600

0

10

15

(mm2)

Fig. 11. Variation of the work W as a function of the tear crack surface area A for a plain weave cotton fabric tested in the tensile central crack tear configuration.

other objective is also to have it apply to a wide range of materials and structures. As a first step, tests were performed with a plain weave polyester/cotton blend fabric both using the tongue tear and tensile central crack tear configurations. As shown in Fig. 12, the tearing work is proportional to the tear crack surface area. This indicates that the proposed tearing energy criterion applies also to polyester/cotton blend fabrics. In addition, the values obtained for the tearing energy in the tongue tear and tensile central crack configurations are very similar (respectively 122 N/mm for the tongue tear configuration and 116 N/mm in the tensile central crack configuration). This result confirms what had already been observed with the plain cotton fabric on the fact that these two sample configurations correspond to the same value of the tearing energy. This result is largely different from what has been reported in the case of bulk polymers for which the essential work of tearing in specimens tested in single and double edge notched specimens is much higher than that in the trouser configuration [22]. The observation is the same when the total tearing work is considered as observed in the data reported by Wong et al. for PETG films [23]. This might be attributed to a larger amount of plastic deformation around the crack zone in the Mode I configuration. On the other hand, in the case of tearing in woven fabrics, each yarn contributes individually to the fracture process which is controlled by the mobility and fracture behavior of the warp and filling yarns. Finally, the analysis using the tearing energy criterion was tested with fabrics of different weaves. For that purpose, tongue tear tests were performed with 33 Tex, 15 yarns/cm plain weave and twill polyester fabrics. As shown in Fig. 13, the tearing work is once again proportional to the tear crack surface area, which indicates that the tearing energy criterion applies independently of the weaving pattern. It may be also observed that, in that case, the tearing energy measured for the two tested weaves is similar (262 N/mm for the plain weave fabric and 272 N/mm for twill). More results on the effect of weave on the tearing energy will be provided and discussed in Section 4.3. As a result, the tearing energy criterion defined by Eq. (5) appears to apply independently of the sample configuration, yarn material and fabric weave. The corresponding tearing energy may thus be regarded as an intrinsic characteristic of the fabrics. In the next section, the effect of several fabric characteristics on that tearing energy is analyzed.

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7500

6000

Tearing work (N.mm)

Tearing work (N.mm)

7500

4500

3000

1500

10 yarns/cm 12 yarns/cm 15 yarns/cm

6000

4500

3000

1500

0 0

5

10

15

Tear crack surface

20

25

0 0

(mm2)

5

10

15

20

25

Tear crack surface (mm2) Fig. 13. Variation of the work as a function of the tear crack surface area A for plain weave and twill 33 Tex, 15 yarns/cm polyester fabrics tested in the tongue tear configuration.

4. Application of the tearing energy criterion to the study of the effect of fabric characteristics of its resistance to tearing This section looks at the effect of filling yarn density, filling yarn linear density and fabric weave on the tearing energy. These constitute the main manufacturing parameters of woven fabrics. Tests were performed in the tongue tear configuration on polyester fabric specimens cut along the warp direction (longitudinal tearing direction). 4.1. Effect of filling yarn density The influence of the filling yarn density on the fabric tearing energy is illustrated in Figs. 14 and 15 respectively for plain weave and twill. For both weaves, an increase in the yarn density results in an increase in the tearing energy. This tendency may be attributed to the interaction between warp and filling yarns. Indeed, an increase in the filling yarn density creates a decrease in the yarn mobility. This limits the possibility for filling yarns, which are oriented in the transverse direction in the Del-zone, to slip before eventually breaking. Since the force associated with slippage is much lower than that corresponding to yarn breaking [24], an increase in the tearing energy is thus produced. These results appear to contradict what has been reported in the literature, in particular in the works of Krook and Fox [8] and Teixeira et al. [9] where an increase of the fabric yarn density

300

10 yarns/cm 12 yarns/cm 15 yarns/cm

4500

1500

0

5

Twill 33Tex Plain 33Tex

3000

0

was associated with a decrease in tear strength. This was attributed to the decrease in longitudinal yarn mobility leading to a more rapid crowding of the yarns. The number of transverse yarns in the Del zone, which are supporting the applied load, is thus reduced. However, as raised by Scelzo [10] and as shown by his data, the trend is not that straightforward and discrepancies may arise due to differences in the failure mechanisms. In the case of the data reported in this paper, the filling yarn density of the tested fabrics is rather low compared to that of the samples used by Krook and Fox [8] and Teixeira et al. [9]. The level of yarn mobility is thus much higher and allows for transverse yarn slippage to occur, a phenomenon which had not been reported by these authors. Fig. 16 illustrates the influence of the filling yarn density on the fabric tearing energy. The increase in tearing energy is quite gradual for the plain weave fabrics. On the opposite, there is a major increase in the tearing energy between 10 and 12 yarns/cm for the twill specimens, which is followed by a more limited raise between 12 and 15 yarns/cm. This difference in behavior can be attributed to the evolution of the relative contributions of transverse yarn slippage and yarn breaking in the tearing process. In the plain weave fabric, the slippage contribution to tearing gradually decreased as the filling yarn density increased and reached a zeroslippage tearing at 15 yarns/cm. On the other hand, with the twill fabrics, the trend evolved from only slippage at 10 yarns/cm to a

Tearing energy (N/mm)

Tearing work (N.mm)

6000

Fig. 15. Variation of the tongue tear work as a function of the tear crack surface area A for twill 33 Tex polyester fabric specimens tested for three values of the filling yarn density (10, 12 and 15 yarns/cm).

10

15

20

Tear crack surface (mm2) Fig. 14. Variation of the tongue tear work as a function of the tear crack surface area A for plain weave 33 Tex polyester fabric specimens for three values of the filling yarn density (10, 12 and 15 yarns/cm).

225

150

75

0

5

10

15

20

Yarn density (yarns/cm) Fig. 16. Variation of the tearing energy in the tongue tear configuration as a function of the filling yarn density for 33 Tex plain weave and twill polyester fabrics.

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4.2. Effect of yarn linear density The effect of the filling yarn (transverse) linear density on the tearing energy was studied for the same plain weave and twill polyester fabrics as above. The results for three different values of the filling linear density are shown respectively in Figs. 17 and 18 for the plain weave and twill constructions. It can be seen that a larger yarn linear density in the transverse direction lead to a higher value of the tearing energy. This result may also be attributed to a reduction of the transverse yarn slippage effect, which corresponds to a lower level of resistance. Indeed, an increase in the yarn linear density leads to a larger yarn diameter. For a same yarn density, this reduces the yarn interspacing in the fabric, which limits yarn mobility, in particular in the transverse direction. As a result, if some level of transverse yarn slippage takes place at the lowest values of transverse yarn linear density, tearing only proceeds through yarn breaking at the highest ones, with the associated larger value of the tearing energy. Fig. 19 illustrates the variation of the tearing energy as a function of the filling yarn (transverse) linear density for the plain weave and twill fabrics. For both types of weaves, the increase in the tearing energy is steeper below 16.7 Tex and more limited above it. This behavior can be associated with the contribution of

6000 15 Tex

Tearing work (N.mm)

16.7 Tex 4500

33 Tex

3000

1500

0 0

5

10

15

20

Tear crack surface (mm2) Fig. 17. Variation of the tongue tear work as a function of the tear crack surface area A for plain weave, 12 yarns/cm polyester fabric specimens for three values of the filling yarn linear density (15, 16.7 and 33 Tex).

Tearing work (N.mm)

7500

12 Tex 16.7 Tex

6000

33 Tex 4500 3000 1500

300

Tearing energy (N/mm)

mix of slippage and yarn breaking at 12 yarns/cm to only yarn breaking at 15 yarns/cm. This demonstrates the importance of the transverse yarn slippage phenomenon in the tearing process.

Plain 12 yarns/cm Twill 15 yarns/cm

225

150

75

0

0

10

20

30

40

Linear density (Tex) Fig. 19. Variation of the tearing energy in the tongue tear configuration as a function of the filling yarn linear density for plain weave (12 yarns/cm) and twill (15 yarns/cm) polyester fabrics.

transverse yarn slippage to the tearing process. While, below 16.7 Tex, tearing occurs without any yarn breaking, i.e. only through transverse yarn slippage, it involves both yarn breaking and slippage at 16.7 Tex and only transverse yarn breaking at 33 Tex. This highlights the large influence of transverse yarn slippage in the tearing process and in the value of the tearing energy. 4.3. Effect of fabric weave The results displayed in Fig. 16 can be used to investigate the effect of the fabric weave, plain and twill, on the tearing energy. For the lowest value of the yarn density, the tearing energy of the twill fabric is much lower than that of the plain weave fabric. On the other hand, as the yarn density reaches 12 yarns/cm, the tearing energy values for the two types of weave close up. And the tearing energy of the twill fabric becomes slightly larger than that of the plain weave at 15 yarns/cm. This behavior seems to be in stark contrast to what has been reported by Teixeira et al. [9]. In their case, the twill fabric was more resistant than the plain weave. This effect was explained by an increase in yarn mobility with the reduction in yarn crossovers. However, their fabrics involved much higher values of yarn density than those used in this work. Their conclusions thus fit with the results obtained here at the highest value of yarn density, i.e. at 15 yarns/cm. The explanation for the crossing in the plain weave and twill fabric tearing energy observed in Fig. 16 may come from the fact that yarn mobility affects both transverse and longitudinal yarns with opposing effects. Indeed, an increase in longitudinal yarn mobility leads to a higher tearing energy as reported in the literature [8,9] while more mobile transverse yarns generate to a reduction in the tearing energy due to the occurrence of transverse yarn slippage. With its lower number of yarn crossovers, twill provides more mobility to the structure. At high yarn density, it thus allows for more longitudinal mobility with higher tearing energy value than plain weave. On the other hand, if yarn density and linear density are low enough for yarn slippage to occur, the larger transverse yarn mobility of the twill construction leads to a lower resistance to tearing. In addition, due to its larger yarn mobility, the twill construction also displays a lower onset value in terms of yarn density and linear density for transverse yarn slippage to occur.

0 0

10

20

30

Tear crack surface (mm2) Fig. 18. Variation of the tongue tear work as a function of the tear crack surface area A for twill, 15 yarns/cm polyester fabric specimens for three values of the filling yarn linear density (12, 16.7 and 33 Tex).

5. Discussion on the tearing mechanism The mechanisms of tearing in woven structures have been studied by several authors [7–10,12,25]. The general picture involves four main stages: first, the stretching and slippage of longitudinal

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Fig. 20. Pictures of partially torn samples displaying rupture by (a) yarn breaking with negligible transverse yarn slippage, (b) yarn breaking with large amount of transverse yarn slippage, and (c) full transverse yarn slippage.

yarns closest to the tip of the crack; then, the crowding of these longitudinal yarns on the edges of a Del zone and the transfer of the load to the transversal yarns held in tension in the so-formed Del zone; third, the stretching and alignment/jamming of these transverse yarns; and finally the rupture of the outer transverse yarn. These stages proceed cyclically until the whole sample has failed. However, in the experiments reported in this paper, an additional mechanism has been identified. It consists in the slippage of transversal yarns. This phenomenon has been seen to take place during the third stage of the tearing process. As displayed in Fig. 20, this transverse yarn slippage mechanism may contribute at various degrees to the tearing process. For example, in Fig. 20a, the contribution is minor, with only a few transversal yarns crimping the left tail along its width close to the extremity of the crack. The occurrence of this phenomenon with a similar minor contribution to the tearing process had already been reported by Hamkins and Backer [25]. On the other hand, as illustrated in Fig. 20b, transversal yarns may be subjected to a large amount of slippage before finally breaking. Finally, some samples may also fail solely through transverse yarn slippage as shown in Fig. 20c. This case represents the ultimate situation in the spectrum of transverse yarn slippage contributions to tearing. Another illustration of the contribution of the transverse yarn slippage can be observed in the shape of the force–displacement curves of the torn fabrics. As shown in Fig. 21, the curve corresponding to the 33 Tex fabric sample represents the standard tearing process described in the literature. It includes only two parts, the first one (part 1) due to the uniaxial deformation of the two

Tearing force (N)

90

15 Tex at 12 yarns/cm 16.7 Tex at 12 yarns/cm 33 Tex at 15 yarns/cm

60

30

0 0

40

80

tails as well as the formation of the first Del zone, and the second one (part 2) to the rupture of successive transversal yarns and the propagation of the Del zone. In the case of the 16.7 Tex sample, an additional regime can be seen between the previously identified part 1 and 2 (see Fig 21). It is due to the occurrence of partial transverse yarn sliding. This case corresponds to the picture in Fig. 20b. The lower level of force involved in the transverse yarn sliding compared to the yarn breaking explains the lower values of tearing energy measured for fabrics displaying a higher yarn mobility due to smaller values of yarn density and linear density. The curve corresponding to the 15 Tex sample illustrates the case where sample failure only occurs through transverse yarn sliding, with a largely lower value of the tearing energy. 6. Conclusion In this article, a simple criterion for the tearing energy of woven fabrics has been proposed. The tearing energy is computed from the variation of the work as a function of the tear crack surface area. The range of applicability of this tearing energy criterion was tested with two sample configurations, tongue tear and tensile central crack tear, as well as various fabric weaves, yarn material, density and linear density. This tearing energy criterion was used to study the effect of the linear density, yarn density and weave on the tearing performance of polyester fabrics. It was observed that the tearing energy increases with both the transverse yarn density and transverse yarn linear density. In the case of the effect of the weave, a lower value of the tearing energy was observed for the twill weave compared to plain wave fabrics at low yarn density while the trend was reversed at high yarn density. These results have been attributed to the occurrence of a new mechanism of transverse yarn slippage in addition to the stretching and slippage of longitudinal yarns as well as stretching, alignment/jamming and rupture of the transverse yarns already reported in the literature. This tearing energy criterion appears as a valuable tool for the in-depth study of the tearing resistance of woven textiles and the development of a model linking the tearing energy of a fabric to its characteristics. It will also be applied to the study of coated fabrics as well as of other types of textiles, in particular knits and nonwovens.

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Displacement (mm) Fig. 21. Examples of force–displacement curves in the tongue tear configuration for the plain polyester fabrics (15 Tex at 12 yarns/cm, 16.7 Tex at 12 yarns/cm and 33 Tex at 15 yarns/cm).

Acknowledgements The authors want to thank Prof. François Boussu at the Ecole Nationale Supérieure des Arts et Industries Textiles (Roubaix,

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