Tensile and forming properties of auxetic warp-knitted spacer fabrics

Abstract

Poisson’s ratio (PR) is defined as the negative ratio between the lateral strain and the longitudinal strain of a material under tensile or compressive loading condition. Auxetic fabrics are those having a negative PR, which means that when their longitudinal strain is positive, their lateral strain is also positive, and vice versa. In this work, tensile and forming properties of auxetic warp-knitted spacer fabrics were investigated and compared with those of the conventional warp-knitted spacer fabrics. Both uniaxial tensile tests and hemispherical compression experiments were conducted, and the relationships of the tensile and forming properties with the auxetic effect were discussed in terms of different fabric structural parameters. The results show that the auxetic warp-knitted spacer fabrics have a prolonged low stress stage in the wale direction, indicating that they are more prone to undergo deformation along the wale direction, and fabric with a longer low stress stage has a better auxetic effect. The results also show that the formability of auxetic warp-knitted spacer fabrics is much better than that of conventional warp-knitted spacer fabrics, due to the much low forming energies required under hemispherical compression, which can be affected by many factors such as auxetic effect, fabric thickness and stiffness, yarn materials and the structure of the spacer layer. When all other parameters are similar, auxetic fabric with a better auxetic effect will have better formability. The study has provided useful information for the design and application of this type of nonconventional spacer fabrics.

Keywords

tensile behavior auxetic fabric knitting spacer fabric formability

Poisson’s ratio (PR) is defined as the negative ratio between the lateral strain and the longitudinal strain of a material under tensile or compressive condition. Auxetic fabrics are those having negative PR,¹ which means that when their longitudinal strain is positive, their lateral strain is also positive, and vice versa. Auxetic fabrics laterally expand when stretched or laterally shrink when compressed. Compared to conventional fabrics with positive PR, auxetic fabrics exhibit a number of unusual properties, including excellent formability, enhanced air permeability and reduced clothing pressure. Such properties are very useful in making functional garments for sportswear and medical care applications.¹

To date, a number of auxetic fabrics have been developed and manufactured by different technologies, such as weaving,² knitting,³ non-wovens⁴ and others.⁵ Weaving technology was first employed to produce auxetic fabrics from helical auxetic yarn by Miller et al.² However, due to the constraints imposed by woven structures, the auxetic effect of the woven fabrics is not as good as that of the auxetic yarn. In comparison with weaving, knitting is more suitable for producing auxetic fabrics due to its flexibility in structure design and fabrication process. Hu et al.³ and Liu et al.⁶ first used weft knitting technology to produce auxetic fabrics. Based on different auxetic geometries, including re-entrant hexagons, rotating units and folded structures, various weft-knitted auxetic fabrics were knitted with electronic flat knitting machines. Glazzard and Breedon⁷ also explored auxetic weft-knitted fabrics from a design perspective. Inspired by double arrowhead geometry, they produced a special type of auxetic fabrics made of purl rib structure to achieve a chevron shape, and suggested that auxetic fabrics would be more interesting and useful by collaborating knitting technology and design together. Compared with weft knitting, warp knitting is more suitable for making open structures, which are essential for many auxetics. Ugbolue et al.^8,9 developed a group of warp-knitted auxetic fabrics based on the re-entrant hexagonal structure. Highly elastic yarns were employed to realize the auxetic effect and the PR reached –0.86. Alderson et al.¹⁰ developed another type of warp-knitted fabrics based on double arrowhead geometry using three types of yarns. While two types of yarns were used to form the auxetic component, another type of yarn was used to form the stabilizing component in the warp-knitted structure. However, the developed fabrics only demonstrated auxeticity in the diagonal directions. Non-woven technology was also adopted for producing auxetic fabrics. Verma et al.⁴ developed a type of non-woven auxetic fabrics by the post-processing method and the non-woven fabrics obtained showed an auxetic effect in the thickness direction. Apart from single technology, Ge et al.^5,11,12 combined non-woven and stitching together to manufacture three-dimensional (3D) auxetic textile structures for composite reinforcement. In this type of structure, the auxetic effect was realized when compressed in the thickness direction.

Spacer fabrics are a type of 3D textile structure formed by connecting two fabric layers with a layer of spacer yarn, and have been applied in different areas, such as automotive,¹³ impact protection, ^14–16 sound absorption,¹⁷ medical care,^18,19 etc. In our previous studies,^20–22 auxetic fabrics with in-plane negative PRs up to –2.6²⁰ were successfully developed based on conventional warp-knitted spacer fabric structures by modifying their outer layer geometry through a compression and heat-setting process. The deformation behaviors²¹ of the developed fabrics were studied based on the experimental observations of the fabric unit cells and two semi-empirical models were built for predicting their PR values. A finite element model was also developed to simulate the deformation behaviors of these auxetic fabrics, and the simulated fabrics were very close to the real ones.²² However, the previous studies are still limited and they do not account for the auxetic behaviors of this type of auxetic fabric. In addition, up to now the studies on the mechanical behavior of auxetic fabrics have not been sufficient to deal with this type of auxetic fabric.^9,23 Therefore, it is of great significance to fill this gap in research.

Since the auxetic effect of these auxetic warp-knitted spacer fabrics is realized in the state of tension, the tensile property is very interesting and has a relationship with the auxetic behaviors. Formability is another interesting property of auxetic fabrics, which is very important for both garment and industrial uses. Fabrics with good formability are easier to fit the human body and exert less pressure on the wearer, bringing garments with a more comfortable feel and elegant appearance. It is well known that knitted fabrics have better formability than woven fabrics due to their extensible knitted loops.²⁴ Compared to conventional knitted fabrics, auxetic knitted fabrics fit even better on a curved surface because of the formation of synclastic curvature when bent,²⁰ which gives auxetic knitted fabrics much better formability. This paper presents a further study on the tensile behavior and formability of auxetic warp-knitted spacer fabrics.

Experimental details

Preparation of auxetic spacer fabrics

Auxetic spacer fabrics were made from existing conventional warp-knitted spacer fabrics as base fabrics by a compression and heat-setting process.²⁰ As shown in Figure 1, the base fabrics were made of polyester multifilament yarn as the outer layers and polyester monofilament yarn as the spacer layer. The base fabrics were first compressed along their wale direction (Figure 2) to transform their outer layer geometry from conventional hexagons (Figure 1(a)) to diagonal hexagons (Figure 1(k)). Then the compressed fabrics were subjected to a heat-setting process to keep this geometrical configuration to obtain the final auxetic fabrics (Figure 1(e)). The heat-setting process was carried out in an oven, and the condition was set at 200℃ for 25 minutes. Three types of base spacer fabrics (Base fabric A, Base fabric B and Base fabric C) were used. Their details are listed in Table 1. All the base fabrics have the same outer layer hexagonal geometry. They are different in the spacer yarn connecting method and hexagon size. Base fabrics A and B have the same size of hexagonal geometry, but the spacer yarns of Base fabric A cross through the hexagons (Figure 1(b)), and those of Base fabric B do not (Figure 1(c)). Base fabrics B and C have the same method for spacer yarn connecting, but Base fabric C has a smaller size of hexagons and less thickness (Figure 1(d)). All three base fabrics were compressed to a compression strain of 50% to produce auxetic fabrics. In order to make the comparison, another two compression strains (40% and 45%) were also used for Base fabric B as it was the fabric that was the easiest to transform to auxetic fabrics with better geometry regularity as compared to Base fabrics A and C, because the crossed yarns hindered the compression of Base fabric A, and the ribs of Base fabric C were the thinnest, which caused more irregular units after transformation. Therefore, five auxetic fabrics, namely Auxetic fabric A (Figure 1(f)), Auxetic fabric BS (Figure 1(g)), Auxetic fabric BM (Figure 1(h)), Auxetic fabric BL (Figure 1(i)) and Auxetic fabric C (Figure 1(j)), were produced. As shown in Figure 1(k), four geometrical parameters, long rib length L₀, short rib length l₀ and angles α₀ and β₀, are enough to determine the geometry of the auxetic spacer fabrics. The values of these geometrical parameters and the thickness for each auxetic spacer fabric are provided in Table 2.

Figure 1.

Photos of spacer fabrics: (a) three-dimensional (3D) view of a conventional spacer fabric; (b), (c), (d) amplified hexagon unit of Base fabrics A, B and C, respectively; (e) 3D view of an auxetic spacer fabric; (f), (g), (h), (i), (j) amplified outer layer of Auxetic fabrics A, BL, BM, BS and C, respectively; (k) amplified hexagon unit of auxetic fabric; (l) side view of a conventional spacer fabric.

Figure 2.

Schematic of the compression process.

Table 1.

Details of base spacer fabrics

	Base fabric A	Base fabric B	Base fabric C
Outer layer yarn	400D/96F Polyester DTY	400D/96F Polyester DTY	150D/48F Polyester DTY
Spacer layer yarn	0.15 mm Polyester monofilament	0.12 mm Polyester monofilament	0.10 mm Polyester monofilament
Chain notation of Base fabric A	GB1: (1-0-0-0/1-2-2-2)3/(2-3-3-3/2-1-1-1)3// GB2: (2-3-3-3/2-1-1-1)3/(1-0-0-0/1-2-2-2)3// GB3: 4-5-4-3/4-5-2-1/2-3-2-1/4-5-4-3/4-5-4-3/4-5-3-2/3-4-3-2/3-4-1-0/1-2-1-0/3-4-3-2/3-4-3-2/4-5-4-3// GB4: 1-0-1-2/1-0-3-4/3-2-3-4/1-0-1-2/1-0-1-2/1-0-2-3/2-1-2-3/2-1-4-5/4-3-4-5/2-1-2-3/2-1-2-3/1-0-1-2// GB5: (2-3-3-3/2-1-1-1)3/(1-0-0-0/1-2-2-2)3// GB6: (1-0-0-0/1-2-2-2)3/(2-3-3-3/2-1-1-1)3//
Chain notation of Base fabric B and Base fabric C	GB1, GB2,GB5 & GB6 are the same as Fabric A GB3: 4-5-4-3/4-5-4-3/4-5-4-3/4-5-4-3/4-5-4-3/4-5-3-2/3-4-3-2/3-4-3-2/3-4-3-2/3-4-3-2/3-4-3-2/4-5-4-3// GB4: 1-0-1-2/1-0-1-2/1-0-1-2/1-0-1-2/1-0-1-2/1-0-2-3/2-1-2-3/2-1-2-3/2-1-2-3/2-1-2-3/2-1-2-3/1-0-1-2//

Table 2.

Geometrical parameters of the auxetic spacer fabrics produced

Fabric name	Base fabric	Compression strain (%)	Thickness (mm)	L₀ (cm)	l₀ (cm)	α₀ (degree)	β₀ (degree)
Auxetic fabric A	A	50	7.4	0.44	0.221	32	24
Auxetic fabric BS	B	50	7.9	0.44	0.220	32	23
Auxetic fabric BM	B	45	7.8	0.44	0.222	36	30
Auxetic fabric BL	B	40	7.6	0.44	0.224	40	32
Auxetic fabric C	C	50	5.9	0.32	0.160	31	24

Tensile tests

The tensile tests of the produced auxetic warp-knitted spacer fabrics were conducted on an Instron 5566 tensile device equipped with a 10 kN load cell. The test followed ISO Standard 13934-1:2013 with modification of the gauge length from 200 to 150 mm. Due to the anisotropic behaviors of the warp-knitted spacer fabrics, each type of fabric was tested along the course direction and the wale direction, respectively (Figure 3). The sample size was 200 mm × 50 mm and the tensile speed was 50 mm/min. In order to get the information of fabric sample size changes during the test for calculating PR, nine dots were marked on each sample, as shown in Figure 4. A camera with a timer shot function was used to take a photo of the tested sample in every 6 seconds, which corresponded to a tensile strain of 3.33%. From the photos obtained, the values of the original length (X₀) and width (Y₀), as well as their variations X and Y during the test for each fabric sample, were obtained for calculating the tensile strain $ɛ_{a}$ and transverse strain $ɛ_{t}$ using equations (1) and (2), respectively

ɛ_{a} = \frac{X - X_{0}}{X_{0}}

(1)

ɛ_{t} = \frac{Y - Y_{0}}{Y_{0}}

(2)

Figure 3.

Fabric samples in different directions.

Figure 4.

Points marked on auxetic fabric: (a) initial state; (b) extended state.

After the tensile strain $ɛ_{a}$ and transverse strain $ɛ_{t}$ were found, PR υ was calculated from equation (3)

υ = - \frac{ɛ_{t}}{ɛ_{a}} (ɛ_{a} \neq 0)

(3)

Formability tests

The formability is the capacity of a fabric to shape into a specific geometry. A fabric with good formability will require lower forming energy, has fewer or no formation of wrinkles and does not break easily in the forming process. In this study, a self-made hemispherical compression device was used to evaluate the formability of the auxetic spacer fabrics. As shown in Figure 5(a), the hemispherical compression device consists of two separated parts, a hemispherical plunger (made of aluminum) and a fabric holder (made of stainless steel). The hemispherical plunger was attached to the load frame of an Instron 5566 machine by a connector. It was used for compressing the fabric along the vertical direction. The diameter of the plunger used was 100 mm. The fabric holder was used to tightly hold the fabric sample during test, as shown Figure 5(b).

Figure 5.

Hemispherical compression test: (a) testing device; (b) fabric under test.

The compression process was conducted with a compression speed of 50 mm/min. It stopped when the sample was broken or the plunger reached the maximum displacement, which was 50 mm when the plunger totally penetrated the fabric holder. The testing data, including the compression forces and the displacements of the hemispherical plunger, were recorded by the testing machine automatically every 0.1 seconds. From these recorded data, the total forming energy accumulated from the initial compression to the maximum displacement or breaking of the sample could be approximately calculated from equation (4)

W = \sum_{i = 1}^{max} F_{i} Δ x

(4)

where W is the total forming energy (unit: joule), i is the number of recording points, F_i is the force recorded at each recording point (unit: Newton) and

Δ x

is the increment of displacement of the plunger (unit: meter).

Results and discussion

Tensile properties

Comparison between conventional base fabric and auxetic fabric

Base fabric B and Auxetic fabric BS were selected as examples to compare the tensile properties of conventional and auxetic warp-knitted spacer fabrics, since Auxetic fabric BS was found to have the best auxetic effect among the auxetic fabrics produced. The stress–strain and PR–strain curves of both fabrics are shown in Figures 6(a) and (b), respectively. It can be found from Figure 6(a) that in the course direction, the strain range of the two fabrics is not very different, but the peak stress of Auxetic fabric BS is higher than that of Base fabric B. The peak stress of Auxetic fabric BS is 2.3 MPa, which is about twice the peak stress value of Base fabric B. This is because Auxetic fabric BS is made of Base fabric B by a 50% compression strain in the wale direction, which results in a double density of auxetic fabric in the course direction. For the wale direction, the difference of their peak stresses is relatively smaller, but the strain range of Auxetic fabric BS is much higher than that of Base fabric B. While Base fabric B could be only extended to 50% strain, Auxetic fabric BS could be extended to 225% strain. The same reason as mentioned above can be used to explain this phenomenon. As Auxetic fabric B is obtained by compressing Base fabric B in the wale direction during the fabrication process, a decompression process takes place in the beginning stage of the extension. In this stage, only a small tensile force can cause a large deformation of the auxetic fabric. Therefore, a prolonged low stress stage (defined as lower than 1% of the peak stress) appears in the wale direction of Auxetic fabric BS. The compression process of the base fabric to obtain the auxetic effect also causes a reduction in the peak stress of auxetic fabric due to a small damage of the regularity of the fabric geometry.

Figure 6.

Comparison between conventional base fabric and auxetic fabric: (a) tensile stress–strain curves; (b) Poisson’s ratio–strain curves.

Regarding the PR, it can be seen from Figure 6(b) that Auxetic fabric BS has a very obvious auxetic effect with the highest negative PR of –2.6 when stretched in the course direction. Since PR is defined as the negative ratio of the transverse strain to the tensile strain, the PR is affected by the values of these strains. When stretched in the course direction, the course direction contributes to the tensile strain and the wale direction contributes to the transverse strain. As mentioned above, the tensile stress of Auxetic fabric BS is very low in the wale direction in the initial stage. Therefore, the wale direction, as the transverse direction, is very easy to deform when stretched in the course direction and a high transverse strain is yielded. As a result, the high auxetic effect is obtained when stretched in the course direction. However, when stretched in the wale direction, the course direction as the transverse direction is not easy to open up, which yields low transverse strain. That is why the auxetic effect in the wale direction is not so evident.

Effects of compression strain and structural parameters

Effects of the compression strain or α₀ and β₀ on tensile properties and the auxetic effect of auxetic fabrics are shown in Figure 7. Auxetic fabrics BS, BM and BL were made of the same Base fabric B, but with different compression strains. Although rib lengths L₀ and l₀ in their outer layer unit geometry are maintained the same, angles α₀ and β₀ are different. The higher the compression strain, the smaller α₀ and β₀ are obtained, and vice versa. The smallest α₀ and β₀ could be obtained when the fabric was fully compressed. As shown in Table 2, Auxetic fabric BS has the smallest α₀ and β₀ and Auxetic fabric BL has the largest.

Figure 7.

Effects of α₀ and β₀ on tensile properties and the auxetic effect of auxetic fabrics: (a), (b) tensile stress–strain curves; (c), (d) Poisson’s ratio–strain curves.

From Figure 7(a), it can be found that the auxetic fabric with smaller α₀ and β₀ has higher peak stress in the course direction. The peak stress for Auxetic fabrics BS, BM and BL is 2.3, 1.9, and 1.7 MPa, respectively. This is because the auxetic fabric with smaller α₀ and β₀ has a higher density in the wale direction, resulting in higher peak stress in the course direction. From Figure 7(b), it can be found that all three fabrics have a prolonged low stress stage (defined as lower than 1% of the peak stress) in the wale direction, and the smaller α₀ and β₀ are, the longer low stress stage is obtained. The low stress stages could reach tensile strains of 140%, 130% and 110% for Auxetic fabrics BS, BM and BL, respectively, indicating that all these auxetic fabrics are very easy to deform in the wale direction.

Regarding the PR, it can be seen from Figures 7(c) and 6(d) that the effects of α₀ and β₀ are similar in both course and wale directions. When stretched in the course direction, the auxetic effect of the three fabrics increases with the decrease of α₀ and β₀. The same effect can be found when stretched in the wale direction: the auxetic effect of the three fabrics also increases with the decrease of α₀ and β₀. The results confirm again that the auxetic effect is much better when stretched in the course direction than when stretched in the wale direction. As previously mentioned, the wale direction is the transverse direction when stretched in the course direction. The auxetic fabric with smaller α₀ and β₀ has a longer low stress stage in the wale direction, which means that the auxetic fabric with smaller α₀ and β₀ is easier to deform in the transverse direction and yields more transverse strain. Therefore, Auxetic fabric BS with the smallest α₀ and β₀ has higher negative PR and keeps negative to a higher strain when stretched in the course direction.

Corresponding to the deformation of the auxetic fabric unit cell when stretched in the course direction, as shown in Figure 8(a), it can be found that the original state of the short ribs along the tensile direction are relaxed and curved. In the first 20% tensile strain, the ribs become tensioned and straight to the tensile direction, as shown in Figure 8(b). In this stage, the main deformation is the rotation and straightening of the ribs, so the required tension force is very low, which reflected on the stress–strain curves as the initial low stress stage, as shown in Figure 7(a). Another phenomenon that can be found from the unit cell is that the fabric opens up a lot in the transverse direction during the first 20% strain. This is why the fabrics have a very good auxetic effect in the first 20% tensile strain. When angles α₀ and β₀ become smaller, the fabric is more compact and opens up more, giving a better auxetic effect. After the ribs become straight, the extension of the fabric mainly comes from the extension of the ribs. Therefore, the required tension forces are higher, and a higher stress stage is reached.

Figure 8.

Deformations of an auxetic fabric unit at different strains when stretched in the course direction.

When stretched in the wale direction, as shown in Figure 9, there is an obvious decompression stage of the fabric at the beginning of the tension. The diagonal hexagonal units gradually are recovered to the conventional hexagonal units, and then the ribs continue to rotate to the tensile direction until they are totally aligned with it, as shown in Figure 9(d). During this process, only a low load is needed for the rotating and straightening of the ribs, and the extension of the fabric is very large. This is why a prolonged low stress stage appears on the stress–strain curves when stretched in the wale direction, as shown in Figure 7(b). In the first 20% strain, from Figures 9(a) and (b), there are few changes in the width of the fabric unit, but one of the short ribs (as indicated by arrow in the Figure 9(a)) in the unit is curved in the original state, and it becomes straighter during tension, as shown in Figure 9(b), which may be the reason that the fabric has a very small auxetic effect in the first 20% strain in this direction.

Figure 9.

Deformations of an auxetic fabric unit at different strains when stretched in the wale direction.

Effects of rib length and spacer layer structure on tensile properties and auxetic effect of auxetic fabrics are shown in Figure 10. Auxetic fabrics BS and C have the same knitted structure and the same geometry angles α₀ and β₀, but they have different rib lengths, as shown in Table 2. From Figures 10(a) and (b), it can be found that the peak stresses of Auxetic fabric C in the course direction and wale direction are about 3.1 and 2.5 MPa, respectively. Both are higher than those of Auxetic fabric BS. This could be because Auxetic fabric C has a smaller size of hexagon units, making it have more units in the same sample size, which gives the sample higher strength. Another phenomenon that can be found from Figure 10(b) is that Auxetic fabric BS has a longer low stress stage than that of Auxetic fabric C in the wale direction. Regarding the PR, it can be seen from Figures 10(c) and (d) that the auxetic effect of Auxetic fabric BS is better than that of Auxetic fabric C when stretched in the course direction, which obeys the same rule as that mentioned above, that is, when an auxetic fabric has a longer low stress stage and is easier to deform in the transverse direction, it will have a better auxetic effect in the tensile direction.

Figure 10.

Effects of rib length and spacer layer structure on tensile properties and the auxetic effect of auxetic fabrics: (a), (b) tensile stress–strain curves; (c), (d) Poisson’s ratio–strain curves.

The main difference between Auxetic fabrics A and BS is that they have the different spacer layer structures. Auxetic fabric A is made of spacer yarns that cross through the hexagons, as shown in Figure 1(b). From Figures 10(a) and (b), it can be found that their peak stresses are similar, but again, Auxetic fabric BS has a longer low stress stage in the wale direction. Again, the auxetic effect of Auxetic fabric A is not as good as that of Auxetic fabric BS. This could be because the crossing yarns in the spacer layer of Auxetic fabric A hinder the deformation of the fabric and lower the auxetic effect of Auxetic fabric A, especially at the initial stage of tension, the interaction of the crossing yarn hinders the opening up of the fabric, causing the lower PRs of Auxetic fabric A at the initial stage.

Comparison of stiffness among auxetic fabrics

From the tensile curves of the auxetic fabrics, it can be found that their stiffness is very different in the course and wale directions. Therefore, their stiffness was calculated and is listed in Table 3. Auxetic fabric A has the highest stiffness in both course and wale directions with values of 440.79 and 25.96 N/m, respectively. For Auxetic fabrics BS, BM and BL, their stiffness has a reverse order in course and wale directions. Auxetic fabric BS has the highest stiffness at 235.58 N/m in the course direction among the three fabrics, but has the lowest value at 8.15 N/m in the wale direction. Since the stiffness of all five auxetic fabrics is very different in the course and wale directions and the orders are irregular, the stiffness ratios of the course direction to the wale direction were calculated and are also listed in Table 3. From Table 3, it can be found that the descendent order of the stiffness ratios of the five auxetic fabrics is BS > A > BM > C > BL. Auxetic fabric BS has the highest stiffness ratio. Its auxetic effect is also the best among all the auxetic fabrics, as shown in Figure 11. Auxetic fabric BL has the lowest stiffness ratio, and its auxetic effect is also the lowest among the auxetic fabrics. Therefore, a higher stiffness ratio between the course and wale directions of fabric may be helpful for the design of auxetic fabric with a higher auxetic effect.

Figure 11.

Poisson’s ratio–strain curves of all auxetic fabrics.

Table 3.

Stiffness of the auxetic fabrics in the course and wale directions

Auxetic fabric Direction	A	BS	BM	BL	C
Course (N/m)	440.79	235.58	149.77	97.433	110.13
Wale (N/m)	25.96	8.15	9.43	12.36	10.55
Course/wale (–)	16.98	28.91	15.88	7.88	10.44

Formability

Comparison between conventional base fabrics and auxetic fabrics

The hemisphere compression load–displacement curves of the base and auxetic spacer fabrics are shown in Figure 12(a). It can be found that the trends of the curves for the base fabrics and the auxetic fabrics are similar, but the loads of the base fabrics are much higher than those of the auxetic fabrics. The compression peak loads of the base fabrics all exceed 2000 N, while the peak loads of the auxetic fabrics are between 100 and 450 N. This means that the auxetic fabrics are easier to deform. Base fabric A, which is the stiffest one, has the highest load at 2500 N, and it is the only one fabric that was broken during testing at a displacement of 44 mm. As shown in Figure 13, Base fabric A was broken in the central part of the sample during testing. This is because Base fabric A has spacer yarns passing through the hexagonal units, causing poor flexibility of the fabric. The other fabrics all reached the maximum displacement without rupture. During the test, wrinkles were found in none of the fabrics.

Figure 12.

Comparison between the base and auxetic fabrics: (a) load–displacement curves; (b) forming energies.

Figure 13.

Fabric samples after the forming test: (a) Base fabric A; (b) auxetic fabric.

The forming energies of the base fabrics and auxetic fabrics were calculated using equation (4) and the results are shown in Figure 12(b). It can be found that all the auxetic fabrics require less forming energies than those of the base fabrics. Since Base fabric A was broken, the forming energy of Base fabric A was calculated until 44 mm displacement, but its forming energy is still 10 times of that of Auxetic fabric A. Three of the Auxetic fabrics B (BS, BM and BL) and Auxetic fabric C require about one-30th of the forming energy of their base fabrics, that is, Base fabrics B and C, indicating that auxetic warp-knitted spacer fabrics have much better formability than those of the conventional warp-knitted spacer fabrics.

Comparison of different auxetic fabrics

Figure 14(a) shows the load–displacement curves of all the auxetic fabrics. It can be found that the trend of the load–displacement curves of the auxetic fabrics inherits the trend of the base fabrics. The peak load of Auxetic fabric A is about 420 N, which is the highest among the auxetic fabrics. The peak load of Auxetic fabrics BL, BM and BS is 150, 140, and 120 N, respectively. Auxetic fabric C has the lowest peak load of 100 N. Figure 14(b) compares the forming energies of the auxetic fabrics. The forming energy of Auxetic fabric A is the highest (about 4.1 J), while that of Auxetic fabric C is the lowest (about 0.7 J), and Auxetic fabrics BL, BM and BS require forming energies between those of Auxetic fabrics A and C. Auxetic fabric A has the highest stiffness (Table 3) in both course and wale directions, and its thickness is similar to Auxetic fabric B but higher than that of Auxetic fabric C, which is why Auxetic fabric A has the highest forming energy. From Figure 10(c), it can be found that Auxetic fabric BS has a better auxetic effect than that of Auxetic fabric C, but its forming energy is higher than that of Auxetic fabric C, as shown in Figure 14(b). This is because Auxetic fabric C is made of thinner yarns, and its thickness is less, which increases its formability. Auxetic fabrics BS, BM and BL are all made of Base fabric B. They have the same material, thickness and a similar structure, but have different stiffness and auxetic effect. As previously mentioned, Auxetic fabric BS has the highest stiffness in the course direction, but has the lowest stiffness in the wale direction, among Auxetic fabrics BS, BM and BL. Therefore, their forming energies could not be simply compared in term of stiffness in one direction, but could be compared in terms of auxetic effect. As shown in Figure 7(c), the descending order of the auxetic effect of these auxetic fabrics is Auxetic fabrics BS > BM > BL, which is opposite to the descending order of forming energies of these fabrics, as shown in Figure 14(b). Therefore, auxetic fabric with a better auxetic effect needs less forming energy and has better formability. The results show that the formability of auxetic warp-knitted spacer fabrics is affected by many factors, including the auxetic effect, fabric thickness, stiffness, yarn materials and the structure of the spacer layer. When other parameters are similar, auxetic fabric with a better auxetic effect will have better formability.

Figure 14.

Comparison among auxetic fabrics: (a) load–displacement curves; (b) forming energies.

Conclusions

From the results obtained, the following conclusions could be drawn.

The auxetic warp-knitted spacer fabrics have very different tensile behaviors compared to their base spacer fabrics. They have higher peak stress in the course direction and a prolonged low stress stage in the wale direction.

Auxetic fabric with a longer low stress stage in the wale direction has a better auxetic effect when stretched in the course direction.

Auxetic warp-knitted spacer fabrics have much lower forming energies than conventional warp-knitted spacer fabrics; therefore, they have much better formability than conventional warp-knitted spacer fabrics.

The fabric stiffness ratio between the course direction and the wale direction has a positive effect on the auxetic behavior of auxetic fabrics. A higher stiffness ratio between these directions can lead to a higher auxetic effect.

Structural parameters, including rib length, the angles between the ribs, the structure of the spacer layer and fabric thickness, have obvious effects on the tensile behavior and the auxetic effect, as well as on the formability of auxetic fabrics. When other parameters are similar, auxetic fabric with a better auxetic effect will have better formability.

Footnotes

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 Research Grants Council of Hong Kong Special Administrative Region Government (grant number 518109).

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