Development of uni-stretch woven fabrics with zero and negative Poisson’s ratio

Abstract

Fabrics with zero or negative Poisson’s ratio are referred as auxetic fabrics, which have the unusual property of lateral expansion or zero expansion upon stretch. The use of conventional materials and machinery to produce auxetic fabrics has gained the interest of researchers in recent years. However, this approach is limited to knitted fabrics only. The development of auxetic fabric using conventional yarns and weaving technology is a research area that is still unaddressed. This paper reports a study on the development of a novel class of stretchable auxetic woven fabrics by using conventional yarns and weaving machinery. The phenomenon of differential shrinkage was successfully employed to realize auxetic geometries capable of inducing auxetic behavior in woven fabrics, and a series of auxetic woven fabrics were fabricated with elastic and non-elastic yarns and a dobby machine. The uni-axial tensile tests showed that auxetic woven fabrics developed exhibited zero or negative Poisson’s ratio over a wide range of longitudinal strain.

Keywords

auxetic fabric interlacement pattern negative Poisson’s ratio weaving

Auxetic materials are those materials that possess zero or negative Poisson's ratio (NPR). Such materials possess the unusual property of either preserving their dimensions or expanding in the lateral direction.^1,2 In contrast to most conventional materials, auxetic materials become fatter when stretched or narrower when compressed, as shown in Figure 1.The term auxetic was derived from the Greek word (auxetos), which means “that which tends to increase” by Evans et al.³ of the University of Liverpool. Poisson’s ratio is an elastic constant and is independent of the material scale. Therefore, auxetic materials can be single molecules or a particular structure of macroscopic to micro level.^4–10 It is claimed that auxetic materials have enhanced mechanical properties, such as shear modulus, energy absorbance, vibration damping,^11–15 sound absorption,¹⁶ indentation resistance¹⁷and synclastic behavior for better formability.¹⁸ As a special type of auxetic materials, auxetic textiles have become a point of focus for many researchers during the past 10 years. The auxetic textiles that have been developed and investigated include fibers, moisture sensitive yarn and helical auxetic yarns,^19–22 monofilaments,²³ woven fabrics,^24,25 weft knitted^26–31 and warp knitted fabrics,^18,32–35 three-dimensional (3D) textile structures,^36,37 fiber-reinforced laminated composites^8,38,39 and non-woven fabrics.⁴⁰

Figure 1.

Deformation behavior of materials when stretched: (a) auxetic; (b) conventional; deformation behavior of materials when compressed: (c) auxetic; (d) conventional

Since the inception of auxetic textiles up until today, woven and knitted auxetic fabrics have been produced based mainly on two approaches. The first one is using auxetic fibers or yarns to fabricate auxetic fabrics and the second one is to fabricate auxetic fabrics from conventional yarns, as the auxetic behavior is purely linked with the geometrical arrangements of structural units.^41–43

Various types of auxetic woven fabrics have been produced by using helix auxetic yarns (HAYs).^24,25,44 The first one was produced by using the HAY in the weft direction and non-auxetic yarn in the warp direction.²⁵ This type of fabric produced an out-of-plane NPR and an in-plane positive Poisson’s ratio. However, when the fabric was tested with thickness constrained between two glass plates, an in-plane NPR of −0.1 was observed. The second one was also produced by using the HAY in the weft direction and non-auxetic yarns in the warp direction with three weave patterns, which are plain, 2/2 twill and 3/5(3) satin.²⁴ It was found that while both the plain and twill fabrics exhibited most auxeticity, the satin woven fabric was significantly less auxetic. The third one was the 2-ply plain woven narrow auxetic fabric produced with HAY in the warp direction and non-auxetic yarn in the weft direction.⁴⁴ The fabric exhibited an in-plane NPR in the strain range of 15–40%, reaching a maximum NPR value of −0.1 at approximately 32% strain. It should be pointed out that the Poisson’s ratio value is significantly important for the clothing materials and applications where lateral contraction, due to stretch, might be problematic. Such applications may include clothing for periods of growth, such as maternity clothing and child development, possibilities for promoting clothing permanency due to adaptability in sizing, under garments, shape wear, under wear, leggings and sportswear. In the case of fashion clothing, smocking and pleating are two recognized techniques used to overcome the problem of lateral contraction. Smocking is used to gather the fabric so that it can stretch when required and pleating is used to add fullness from the waist or hips. Smocking is also suggested as a solution to the longevity problem of maternity wear.^45–47 These two techniques are labor intensive and require specialized machinery; auxetic fabrics can also be used as alternatives for these two techniques.

Up until today, auxetic woven fabrics were only produced by using auxetic yarns. The disadvantages of this approach are the availability of very few auxetic fibers and yarns. The development of auxetic woven fabrics by using conventional yarns is still unaddressed. Furthermore, due to limitations like low structural stability, low elastic recovery, higher thickness and difficulty in the fabrication because of their complicated geometrical structures, mostly auxetic knitted structures have not yet been produced on a larger scale. The fabrication of auxetic woven fabrics from conventional yarns with reduced thickness and better formability that can easily be shaped into garments is still a great challenge for weaving specialists. This paper reports a study on the development of a novel class of stretchable auxetic woven fabrics for clothing material by using readily and inexpensively available conventional elastic and non-elastic yarns and weaving machinery. The phenomenon of differential shrinkage is created to realize specially designed auxetic geometries into woven architecture to produce auxetic woven fabrics with zero or NPR.

Materials and methods

Design concept, fabrication and post weaving treatment of auxetic fabrics

Auxetic fabrics for clothing applications must have two key properties, elasticity and the auxetic effect. The elasticity in the fabric structure facilitates the deformation at different parts of the garment during movement or exercise, while the auxetic effect helps the garment to take the continuously changing body shape during movement or exercise. Woven fabrics with these two features are possible to fabricate. Since the auxetic effect is purely linked to the geometrical shape of the fabric structural units, realizing auxetic geometries capable of inducing auxetic behavior into a woven fabric is important. Such geometries can be realized by creating the phenomenon of differential shrinkage into the fabric structure in order to enable different sections of a fabric unit cell to endure different levels of shrinkage upon relaxation.

The differential shrinkage effects can be created in both warp and weft directions or in one direction only, by using elastic and non-elastic yarns with different stretch properties, and by employing interlacements patterns with combinations of loose and tight weave having different contraction properties. In this study, the elastic yarns are only used in the weft direction. As the fabrics have extensibility only in one direction, they are named uni-stretch fabrics. In such fabrics, the elastic yarns induce elasticity into the fabric structure and act as a return spring. The non-elastic yarns are used as a stabilizing component, and the interlacement pattern with combinations of loose and tight weave is capable of inducing auxeticity into the fabric structure and helps to retain the transverse dimensions of the fabric upon stretching. Therefore, the auxetic effect is resulted due to the interplay between the interlacement pattern of warp and weft, different stretch properties of elastic and non-elastic yarn and the mechanism of deformation of the fabric.

The specially designed interlacement patterns based on auxetic geometries for this kind of uni-stretch auxetic fabrics are a combination of different weaves and are not regular. Such patterns can only be weaved by using a weaving machine equipped with dobby shedding or a Jacquard shedding mechanism. Further, in order to create differential shrinkage along the weft direction, elastic and non-elastic yarns have to be used alternately or in different combinations, depending upon the geometry that needs to be realized in the fabric structure. Therefore, only a weaving machine capable of inserting more than one kind of weft yarn or with more than one weft supply can be used to produce these fabrics.

The computerized rapier weaving machine manufactured by CCI Intech Taiwan with the option of eight weft supplies and a dobby shedding mechanism with 22 heald frames can meet these requirements and was used to weave uni-stretch auxetic fabrics based on the three different kinds of geometrical structures, namely, the foldable structure, rotating rectangles and re-entrant hexagons. The woven fabrics obtained were then subjected to hot washing for about 45 min at 60℃ followed by tumble drying for 60 min at 70℃. After washing and drying, the fabrics were allowed to relax for 24 h in order to facilitate the creation of the differential shrinkage effects of elastic and non-elastic yarn into the woven fabric structure and to realize the shapes of auxetic geometries. These geometries are capable of inducing auxetic behavior in the fabric. The testing samples were then cut and prepared for the measurement of Poisson’s ratio.

Measurement of Poisson’s ratio

The developed fabrics are uni-stretch fabrics, which means that they have extensibility only in one direction, that is, the weft direction; therefore, tests were carried out along this direction only. However, the fabrics can also be tested along the warp direction but, due to the limited extensibility in this direction, the fabrics may break at smaller strains and cannot be tested over a wider strain range. Furthermore, the folded structures cannot fully open at smaller strains and do not exhibit the auxetic effect.

The tensile tests were conducted on an Instron 5566 tensile machine. The capacity of the load cell used was 500 N. The gauge length and tensile speed were set as 150 mm and 50 mm/min, respectively. The schematic of the testing setup is shown in Figure 2(a). Three fabric strips of dimension (50 mm × 200 mm) were cut for each sample, as shown in Figure 2(b). The central point of the fabric strip was first located and then four points were marked with the central point at a distance of 20 mm in order to facilitate recording of the information of fabric deformation during the tensile test.

Figure 2.

Tensile test for the auxetic fabric: (a) schematic of testing setup; (b) fabric with oblique foldable stripes in the stretched state.

The distances of two marks in the tensile and transversal direction were first photographed by a camera with a time interval of 3 s or after each 3 mm extension for each sample, until the sample broke. Then, the distances of the marks in the photos were measured via a screen ruler to calculate the engineering strains of the fabric structure in both tensile direction and transversal directions. Finally, the Poisson’s ratio was calculated using Equation (1)⁴⁸

v = - \frac{ɛ_{y}}{ɛ_{x}}

(1)

where

ɛ_{x}

is the longitudinal strain and

ɛ_{y}

is the transverse strain. Poisson’s ratio versus longitudinal strain curves were then generated and presented.

Auxetic fabrics developed and their auxetic behavior

Auxetic fabrics developed based on foldable geometries

The principle of using foldable structures to create an auxetic effect is that a folded structure can be unfolded when stretched in one direction, increasing the dimensions in the lateral direction. Foldable structures can be produced by exploiting the phenomenon of differential shrinkages. The characteristics of the interlacement pattern together with different stretch and shrinkage properties of elastic and non-elastic weft yarns enable the sections of fabric with different tightness of weave to undergo different levels of shrinkage for the creation of folds. Based on this approach, three different kinds of fabrics with foldable geometries were designed and fabricated. The first one was with foldable stripes created in parallel in-phase zig-zag fashion. The architecture of this fabric consists of alternate folded stripes and flat stripes placed in parallel in-phase zig-zag manner runing along the weft direction or warp direction, as shown in Figures 3(a) and (a₀). The second one was foldable stripes created in an oblique fashion. This fabric has a geometry formed by placing folded stripes in an oblique fashion, which means that the stripes intersect each other in a diagonal fashion. The spaces formed between these stripes are flat and may form a parallelogram shape, as shown in Figure 3(c). The third one was foldable stripes in the form of convexities running along the warp direction. This fabric has an architecture comprising of folded abrupt convexities or protuberances along the warp with a flat portion of fabric between two consecutive convexities, as shown in Figure 3(e). The minimal repeating unit or unit cell of each geometry is highlighted by a red color box in each of the corresponding figures. In the case of folded stripes arranged in parallel in-phase zig-zag fashion along the warp or weft direction and folded stripes in the oblique fashion, when these folded structures are subjected to an extension in one direction, the structures also expand in the lateral or transversal direction due to the flattening of folded sections, resulting in the NPR ratio effect, as shown in Figures 3(b), (b₀) and (d). In the case of folded stripes in the form of convexities, upon extension the transposition of convexities in the tensile direction tend to retain their lateral dimensions, resulting in the zero Poisson’s ratio effect, as shown in Figure 3(f).

Figure 3.

Foldable geometries: (a) and (b) folded stripes in parallel in-phase zig-zag fashion along the weft in the free state and stretched state; (a0) and (b0) folded stripes in parallel in-phase zig-zag fashion along the warp in the free state and stretched state; (c) and (d) folded stripes in the oblique fashion in the free state and stretched state; (e) and (f) folded convexities along the warp in the free state and stretched state. (Color online only.)

It is important to mention that the geometries illustrated in Figure 3 can be realized either into single layer fabric or double layer fabric. In the case of single layer fabric, the face and back of the fabric will not be truly flat due to the formation of folded sections, whereas in the case of double layer fabric, the back of the fabric can be made flat and the folded section can be created on the face of the fabric. In this study, single layer fabrics were produced with the geometries including folded stripes in parallel in-phase zig-zag and oblique fashion. In order to produce double layer fabrics with these geometries, more heald frames are required as the size of the unit cell of the interlacement pattern becomes larger. Therefore, the weaving machine shedding mechanism is a limitation in the fabrication of double layer fabrics with these geometries. For this reason, the double layer fabric was only produced with folded stripes in the form of convexities on the face of the fabric, due to the fact that the size of the unit cell of the interlacement pattern is smaller and more simple, which makes it easy to realize this geometry in the double layer fabric.

Transformation of foldable geometries into interlacement patterns and fabrication of auxetic fabrics

The schematics of the foldable geometries formation for folded stripes in parallel in-phase zig-zag fashion along the weft, folded stripes in parallel in-phase zig-zag fashion along the warp and folded stripes in oblique fashion are shown in Figures 4(a), 5(a) and 6(a), respectively. In these figures, the dashed lines represent loosely woven area with long floats of weft yarns, while the solid lines represent the tightly woven area. The black lines represent non-elastic weft yarns and the red lines represent elastic weft yarn. In order to create the differential shrinkage effect, the loose weave and tight weave are arranged in parallel in-phase zig-zag pattern running along the warp direction or weft direction and in oblique fashion. The yarn sections of the warp and weft within the structure of stripes are loosely woven with long floats, while the yarn sections of the warp and weft that are not in the structure of stripes are woven by employing a firm and tight weave.

Figure 4.

Fabric with parallel in-phase zig-zag folded stripes along the warp: (a) schematic of fabric showing loosely and tightly woven parallel in-phase zig-zag stripes; (b) interlacement pattern; (c) real fabric; (d) Poisson’s ratio as a function of longitudinal strain when stretched along the weft direction. (Color online only.)

Figure 5.

Fabric with parallel in-phase zig-zag folded stripes along the weft: (a) schematic of fabric showing loosely and tightly woven parallel in-phase zig-zag stripes; (b) interlacement pattern; (c) real fabric; (d) Poisson’s ratio as a function of longitudinal strain when stretched along the weft direction. (Color online only.)

Figure 6.

Fabric with oblique folded stripes: (a) schematic of fabric showing loosely woven oblique stripes; (b) interlacement pattern; (c) real fabric; (d) Poisson’s ratio as a function of longitudinal strain when stretched along the weft direction. (Color online only.)

Two single layered fabrics based on parallel in-phase zig-zag folded stripes in alternate fashion running along the warp and weft direction were developed. The unit cells of interlacement patterns are shown in Figures 4(b) and 5(b). The real fabrics are shown in Figures 4(c) and 5(c). In these fabrics, alternate elastic yarn (core spun spandex Ne 16/s) and non-elastic yarn (cotton Ne 30/s) were used in the weft direction in order to exploit the differential shrinkage effect. The non-elastic yarn (cotton Ne 20/2) was used in the warp direction. The warp and weft densities were set at 40/inch. One single layered fabric based on folded stripes in oblique fashion was also developed. The interlacement pattern is shown in Figure 6(b) and the real fabric is shown in Figure 6(c). In this fabric, a bi-component rubber elastic yarn was used. The wrapping component was of 86D polyester multifilament yarn with 46 filaments and the core was of polyurethane monofilament with a diameter of 0.5 mm and stretch of 300%. The non-elastic yarn used was (cotton Ne10/s). The elastic and non-elastic yarns were used in alternate fashion in the weft, and non-elastic yarn (cotton Ne20/2) was used in the warp direction. The warp and weft densities were set at 48/inch and 40/inch, respectively.

The face and back of all the fabrics differs greatly in appearance. On the face of the fabric, at the loose weave stripe sections, the long floats of the warp yarns are prominent and the elastic weft yarn undergoes high shrinkage due to the loose weave structure or longer float than non-elastic weft yarn. Meanwhile, at the tight weave sections, both the elastic and non-elastic weft yarns are firmly woven and undergo less shrinkage. On the back of the fabric, at the loose weave stripes sections, the long floats of the weft yarns are prominent and, as a result of high shrinkage of elastic weft yarns due to the loose weave structure, the warp yarns tend to come closer to each other. Moreover, at the tight weave stripes section in the case of fabrics with parallel in-phase zig-zag folded stripes, and at the tight weave tetragonal section held between oblique folded stripes in the case of fabric with folded oblique stripes, the texture of the fabric is not truly flat. Due to the high shrinkage of elastic weft yarns at the loose weave stripes section, the tightly woven section is slightly rucked up and a bulge is formed. This rucking up and bulge formation is even greater in fabric with parallel in-phase zig-zag folded stripes along the weft than in the other two fabrics. This might be due to the fact that the loose weave stripes in this fabric run along the weft direction, which is also the direction of elastic yarn. In addition to this, if the interlacement patterns of all three fabrics are compared, it is clear that although the size of the repeating unit of the interlacement patterns is almost the same, in the case of the interlacement pattern of fabric with parallel in-phase zig-zag folded stripes along the weft, the longer floats along the elastic weft are more and it endured more shrinkage and larger bulge formation than the other two fabrics.

The geometry with folded convexities is transformed into an interlacement pattern for a double layered fabric. The schematic for the formation of folded convexities along the warp is shown in Figure 7(a). This geometry comprises of two layers and yielded a texture with a flat portion (where the two layers are self-stitched) and a portion with an abrupt convexity or protuberance (where the two layers are not self-stitched) in an alternate fashion. In the structure of fabric, two sets of warp yarn are interlaced with two sets of weft yarns. In order to produce differential shrinkage among the two layers, one set of warp yarns is interlaced with elastic yarn in the lower layer of the fabric and the second set of warp yarns is interlaced with non-elastic yarn in the face layer of the fabric. The core spun spandex Ne 20/s elastic yarn is used as the weft for the lower layer, cotton Ne 20/s non-elastic yarn is used as the weft for the face layer and cotton Ne 20/s non-elastic yarn is used as the warp. The warp and weft densities were set at 60/inch.

Figure 7.

Fabric with folded abrupt convexities: (a) schematic of fabric showing self-stitched portion and unstitched portion with convexities or protuberances on the face of the fabric and flat back of the fabric; (b) weave of face of non-elastic wefts; (c) weave of lower elastic wefts; (d) stitching weave of the face and lower layer; (e) mechanism of convexity or protuberance formation on the face of the fabric; (f) real fabric; (g) Poisson’s ratio as a function of longitudinal strain when stretched along the weft direction. (Color online only.)

The interlacement pattern of non-elastic weft in the face layer is shown in Figure 7(b). The shaded cells in the red color shown in Figure 7(c) depict the loose weave with longer floats for the elastic weft in the lower layer. The shaded cells in the black color shown in Figure 7(d) represent the points where the two layers are self-stitched. Figure 7(e) shows the mechanism of convexity formation. The blue solid line represents the non-elastic weft yarn and the dashed black line represents the elastic weft yarn. Due to the characteristics of the interlacement pattern together with different stretch and shrinkage properties of the two sets of weft yarns (elastic and non-elastic), the two layers of fabric with different kinds of weft yarns endured different levels of shrinkage. The real fabric is shown in Figure 7(f).

The face and back of the fabric realize different appearances. In the face layer of the fabric, forced by the higher shrinkage of the lower elastic filling due to the loose weave structure or longer float, the upper non-elastic yarns tend to form a convexity with protuberance appearing on the face of the fabric, as shown in Figure 7(e). Meanwhile, the back of the fabric, which consists of elastic filling, appears truly flat and shows normal behavior of elastic fillings. In short, the face layer of the fabric with non-elastic yarns has regular convexities formed in alternate fashion, while the back layer with elastic yarn appears smoother and tidier. The fabrics with parallel in-phase zig-zag folded stripes yielded NPR up to 20% of longitudinal strain and the fabric with folded oblique stripes exhibited NPR up to 38% of longitudinal strain, as shown in Figures 4(d), 5(d) and 6(d), respectively. The double layer fabric with folded convexities produced zero Poisson’s ratio up to 29% of the longitudinal strain when stretched along the weft direction, as shown in Figure 7(g).

Deformation behavior of developed auxetic fabrics with foldable geometries

The foldable structures are formed by the creation of the differential shrinkage effect, which enables different sections of fabric with different tightness of weave to endure different levels of shrinkage upon relaxation. The fabric sections with tighter weaves undergo less shrinkage, while the sections with loose weave experience more shrinkage and the folds in predesigned patterns are created. In addition, it was also observed that the warp yarns and weft yarns do not occupy the same path at tightly woven sections and loosely woven sections, in reality as a result of more shrinkage at the loosely woven section; they deviate from the position held by both yarns at the tightly woven sections and tend to come closer. Therefore, in the relaxed state the warp and weft yarns are not truly straight.

In the case of fabric with parallel in-phase zig-zag folded stripes along weft or warp and fabric with folded stripes in the oblique fashion, upon stretching in the weft direction that is also the direction in which there are alternate elastic yarns, and the bulged or folded sections tend to open up, expanding in the transversal direction and the yarns in tensile direction tend to get straight. Furthermore, due to frictional binding forces between the yarns at the cross-over points, the yarns in the transversal direction also experience a persuasive force and tend to get straight to the position that they held at the tightly woven section until there is yarn slippage at the cross-over point. Thus, the stretching force is consumed in flattening of the bulge or folds formed due to the differential levels of shrinkage, followed by straightening of warp and weft yarns until the slippage point is reached. Consequently, the yarn systems get more in order to achieve a more consolidated form, that is, the straight form, and the width of the fabric increases due to the opening of the bulge or folds in the transversal direction giving rise to the NPR effect.

In the fabric with folded convexities or protuberances, convexities are created along the warp direction with elastic yarn along the weft direction. It is also observed that both of the yarns (warp and weft) deviate from their original right-angled position, and some kind of undulation is occupied by both of the yarns in the fabric structure, as shown in Figure 7(f). When the fabric is stretched along the weft direction, the convexities run along the transversal direction and are opened up in the tensile direction; some of the stretching force is also consumed by yarns in the tensile direction in order to adopt the consolidated form. Therefore, no expansion in the transversal direction arises and the width of the fabric remains unchanged, which results in zero Poisson’s ratio. After the yarn slippage is reached at the cross-over point, the yarns in the tensile direction come closer and the fabric undergoes contraction in the transversal direction, giving rise to positive Poisson’s ratio or conventional behavior.

Auxetic fabrics developed based on rotating rectangle geometry

The architecture of this geometry is a rotating quadrilateral, illustrated in Figure 8(a). Its unit cell is highlighted in black color. In the unit cell, four rigid rectangles are connected together at their vertices by hinges, in such a way that the empty spaces between the rectangles form rhombi. It is assumed that these rectangle units are rigid and do not change their shape, and are allowed to rotate freely under loading and collapse in the relaxed state. When the structure is subjected to an extension in one direction, due to the free rotation of the rectangle units, the structure ascents from the collapsed state and expands in the transverse direction, as shown in Figure 8(b), resulting in a NPR effect, which depends on the strain and dimensions of the rectangles.

Figure 8.

Development of fabric with rotating rectangle geometry:(a) free state of geometry; (b) extended state of geometry; (c) schematic of interlacement pattern; (d) real fabric; (e) Poisson’s ratio as a function of longitudinal strain when stretched along the weft direction. (Color online only.)

In order to produce a single layer fabric with this rotating rectangle geometry, an interlacement pattern was designed. The schematic of this interlacement pattern is shown in Figure 8(c). The individual rectangle units were woven continuously by employing tight plain weave and connected them together at their vertices (area shaded with gray color). The sections between two tightly woven rectangular units were woven with a loose weave (non-shaded area), while the central rhombi section (formed by joining corners of four plain woven rectangle units) is kept free of interlacements of the warp and weft (area shaded with the red color). The elastic yarn (core spun cotton spandex Ne 16/s) and non-elastic yarn (cotton Ne 20/1) were used in the weft. The non-elastic yarn (cotton Ne 20/2) was used in the warp direction. The non-elastic yarn was used to impart stability to the structure, especially to the tightly woven rectangular sections. The warp and weft densities used were 40/inch and 50/inch, respectively. The real fabric is shown in Figure 8(d).

During fabrication, only the elastic weft yarn was inserted at central part of the rhombi, while at other sections elastic and non-elastic weft yarns were inserted alternately. It was assumed that the use of elastic yarn can increase the axial deformation and recovery capacity of the structure after release from extension. In addition, the elastic yarn facilitates the rectangular units to collapse upon relaxation. The three sections of the fabric unit cell with different tightness of weave undergo different levels of shrinkage. The higher shrinkage of elastic weft yarns together with the absence of interlacements at the central rhombi section compels the plain woven rectangular units to collapse. Although the individual rectangular units are weaved by employing tight plain weave, they are not stable enough to withstand the shrinking force of elastic weft yarns and hence lose their shape. The rectangular units are gathered in the direction of the elastic yarn and shrinking and slight bumps are formed on the face of the fabric at tightly woven rectangle sections. On the face of the fabric, the elastic weft yarns are prominent at sections, with the absence of interlacements. On the back of the fabric the warp yarns are prominent at sections, with the absence of interlacements and slight depressions are formed at plain woven rectangle sections. This fabric produced smaller values of NPR over a smaller range of longitudinal strain. The NPR effect is achieved up to 11% of longitudinal strain when stretched in the weft direction, as shown in Figure 8(e).

Upon stretching, the bumps resulting from the higher shrinkage of elastic weft yarn at tightly woven rectangle units are transposed in the transversal direction and then the rectangle units ascend from their collapsed state. The yarns in the tensile direction tend to become straight. Therefore, the stretching force is mainly consumed in transposition of the bumps, in ascending of rectangular units from the collapsed state due to the free rotation of rectangular units to some extent and straightening of yarns in the tensile direction until the slippage point is reached. However, the true rotating rectangles effect could not be achieved in this development. In order to achieve a true rotating rectangles effect, the rectangular units should collapse or rotate freely in both directions. Conversely, due to the absence of elastic yarn in the warp direction, the tightly woven rectangular units collapsed only in the weft direction. The rectangular units were also not stable enough to resist change of shape and, due to higher shrinkage caused by elastic yarns in the weft direction, they lose their rectangular shape. The free rotation is also restricted due to the warp and weft yarns passing from one rectangle to the other. All these factors resulted in smaller transversal expansion and smaller NPR effect.

Auxetic fabrics developed based on re-entrant hexagonal geometry

This fabric is based on a re-entrant hexagone geometry, as illustrated in Figure 9(a).The unit cell of this geometry is highlighted in the red color. When this structure is subjected to an extension in a direction, the structure will expand in the transverse direction due to the translation of the walls or the ribs of the hexagons, resulting in the NPR effect, as shown in Figure 9(b). In order to realize this geometry into woven fabric, the geometry was transformed into the interlacement pattern. The schematic of this interlacement pattern is shown in Figure 9(c). The unit cell of the interlacement pattern has two vertical grids woven tightly, using plain weave and higher denting of the reed. The single layered tightly woven sections, single layered loosely woven sections, double layered self-stitched woven sections and double layered unstitched woven sections are arranged between the two tightly woven vertical grids. The double layered self-stitched woven sections and double layered unstitched woven section are arranged in alternate fashion between each two loosely woven sections.

Figure 9.

Development of fabric with re-entrant hexagon geometry:(a) free state of geometry; (b) extended state of geometry; (c) schematic of interlacement pattern; (d) real fabric; (e) Poisson’s ratio as a function of longitudinal strain when stretched along the weft direction. (Color online only.)

This arrangement creates a rectangular unit with double layered self-stitched woven sections at the edges of the rectangle, double layered unstitched woven section at the center of the rectangle and loosely woven sections between the edges and center of the rectangle, as highlighted with solid black lines in Figure 9(c). The double layered sections have a face layer with loose weave and a back layer with tight weave. The single layered section also has loose weave. The aim of employing an unstitched double layer structure at the center of the unit cell is to facilitate more shrinkage due to the loosely woven face layer and at the same time avoiding the creation of bumps and folds in the thickness direction, which might be created if a single layer structure is used. Moreover, the two layers at the edges of the unit cell are self-stitched to impart rigidity and reduce shrinkage at the edges of the unit cell.

During fabrication, only elastic weft yarns were inserted at the double layered section, and alternate elastic and non-elastic yarns at the single layered loosely woven sections. The aim of inserting only elastic yarn at the double layered section was to make fabric shrink more at this section so that the shape of the re-entrant hexagon can be realized. The use of elastic yarn can increase the recovery capacity of the structure after release from extension and can also increase the axial deformation. It was assumed that upon relaxation different sections undergo different levels of shrinkage and the unit cell realizes the shape of re-entrant hexagonal geometry.

The elastic yarn (core spun cotton spandex Ne 16/s) and non-elastic yarn (cotton Ne 20/1) were used in the weft. The non-elastic yarn (cotton Ne 20/2) was used in the warp direction. The warp and weft densities used were 36/inch and 30/inch, respectively, and a uni-stretch fabric was produced by using this interlacement pattern, as shown in Figure 9(d).

Upon relaxation, the four different sections of the fabric unit cell with different tightness of weave undergo different levels of shrinkage. The face and back of the fabric is almost same in appearance after relaxation. The plain woven vertical grids appeared stiffer due to the use of tight plain weave and higher denting of the reed. The unstitched double layered section at the center of the rectangular unit undergo higher shrinkage due to loose weave in the face layer, while the double layered self-stitched section undergoes lower shrinkage, due to the fact that the two layers are self-stitched together and the tightly woven back layer restricts shrinkage of the loosely woven face layer. The loosely woven sections near the edges of the rectangular unit endure less shrinkage in comparison with the central double layered unstitched section, but are forced by the higher shrinkage of the central double layered unstitched section, so these sections were rucked up, forming very prominent bumps. The tightly woven vertical grids will also bend at the center due to the higher shrinkage of the central double layer section and the rectangular unit takes the shape of a dumbbell-like hexagon geometry, as highlighted with dashed line in black color in Figures 9(c) and (d). The fabric produced NPR up to 52% of longitudinal strain, as shown in Figure 9(e).

When the fabric is stretched, the bumps formed near the edges of the unit cells at loosely woven single layered sections due to the higher shrinkage of double layered unstitched sections at the center are transposed in the transversal direction. In addition, the vertical grids adapting bend form due to the higher shrinkage of the central unstitched double layer section are translated to the straight form and the width of the fabric increases in the transversal direction, giving rise to the NPR effect. Thus, the stretching force is consumed in transposition of the bumps near the edges of the unit cell and the translation of bent vertical grids followed by straightening of yarns in the tensile direction until slippage point is reached. When the slippage point is reached at the cross-over points, the yarns in the stretch direction tend to come closer and the width of the fabric decreases, which leads to a positive value of Poisson’s ratio and the fabric behaves conventionally.

Comparison among auxetic fabrics developed

Table 1 show the Poisson’s ratio values and corresponding longitudinal strains for all the auxetic fabrics developed. A comparison of their auxetic behavior is illustrated in Figure 10. Among all six fabrics developed, five fabrics yielded NPR and one fabric exhibited zero Poisson’s ratio. The fabrics with parallel in-phase zig-zag folded stripes along the warp and weft produced the auxetic effect over a smaller strain range, from 2% up to 20% of longitudinal strain. The fabric with folded stripes in the oblique fashion showed NPR up to 38% of longitudinal strain. The double layer fabric with folded convexities generated zero Poisson’s ratio up to 29% of longitudinal strain. The fabric with rotating rectangle geometry produced NPR over a smaller longitudinal strain up to 11% only and the fabric with re-entrant hexagonal geometry exhibited NPR over a larger strain range, starting from 3% up to 52% of longitudinal strain.

Table 1.

Poisson’s ratio values and corresponding longitudinal strains of developed fabrics

Sr. No.	Fabric name	Maximum negative Poisson's ratio exhibited	Corresponding longitudinal strain (%)	Poisson's ratio is negative up to longitudinal strain (%)	Poisson's ratio is zero up to longitudinal strain (%)
1	Fabric with parallel in-phase zig-zag folded stripes along warp	–0.1	2	21	–
2	Fabric with parallel in-phase zig-zag folded stripes along weft	–0.17	2	20	–
3	Fabric with oblique folded stripes	–0.045	20	38	5
4	Fabric with abrupt convexities	0.0	–	–	29
5	Fabric with rotating rectangles geometry	–0.05	7	11	6
6	Fabric with re-entrant hexagon geometry	–0.1	9	52	–

Figure 10.

Comparison of auxetic behavior of the fabrics developed.

Potential applications of woven fabrics with auxetic behavior

The developed woven fabrics with auxetic behavior may find their potential applications in the area of fashion garments, including girls’ tops, stoles, long tops for girls, smocking stoles, round neck and V-neck tops cushion covers, smart maternity wear, sportswear, etc. For fashion garments, two types of techniques are common: smocking and pleating. Smocking can be used for dresses and a variety of outfits. Smocking is the process of putting a design of creases into fabric by using an embroidery technique. Most importantly, it is used to gather the fabric so that it can stretch when required. Smocking reduces the dimensions of a piece of fabric to one-third of its original width and enhances the properties of form fitting and flexibility in the garment. Smocking is a complicated process. It cannot be easily used in mass produced clothing. The cost and complication have thus made smocking a relatively rare decorative device in fashion clothing but smocking has not entirely disappeared in our modern world.^45,46,49

Pleating is realized by machine. Pleating also involves a steam heating process to achieve permanency of the pleat. Pleats of many types are extensively used in fashion garments, including skirts, dresses and kilts, to add fullness from the waist or hips, or at the hem, to achieve design effects and to allow freedom of movement. For example, pleats near the hem of a straight skirt allow the wearer to walk comfortably while preserving the narrow style line. The disadvantage of some pleating techniques is added bulk to the seam.⁴⁷

The developed auxetic woven fabrics with folded geometries and double layer fabrics with abrupt convexities or protuberance can be employed as more economical seamless alternative for smocking and pleating techniques. The fabric with folded stripes and woven convexities can be used to gather a large amount of fabric into a small waistband without a seam and the problem of adding bulk to the seam, as in case of traditional pleating, can be resolved. Another advantage of using this fabric is that it allows the garment to drape straight down when standing and to expand its shape during movement without any lateral shrinkage.

Auxetic fabrics with NPR can also be used for sportswear and as a solution to the longevity problem of maternity wear, as the defamation of the fabric will be consistent with body movement, and therefore comfort and shape fitting of sportswear and maternity wear will be enhanced. Undoubtedly, auxetic woven fabrics have great potential to be classified as smart and intelligent textiles and to be incorporated into real life applications.

Conclusions

In this study a number of single layered and double layered uni-stretch auxetic woven fabrics were developed using conventional weaving machinery and conventional elastic and non-elastic yarns. The developed auxetic woven fabrics were based on foldable geometrical structures, a rotating rectangle geometrical structure and a re-entrant hexagonal structure. The basic principle used to realize these geometries into woven fabrics was the differential shrinkage effect. The auxetic behavior of these fabrics was discussed in terms of tensile deformation, longitudinal strain, response of fabric geometrical structure and transverse strain. From this study, the following conclusions can be drawn.

It is possible to produce auxetic woven fabrics by using conventional yarns and machinery. Differential shrinkage effects can induce auxetic behavior in woven fabrics and can be created by combinations of loose and tight weaves together with the use of elastic and non-elastic yarns, having different stretch properties.

Foldable structures can be produced by exploiting the phenomenon of differential shrinkage. The characteristics of the interlacement pattern together with different stretch and shrinkage properties of elastic and non-elastic weft yarns enable the sections of fabric with different tightness of weave to undergo different levels of shrinkage for the creation of folds. The foldable structures can be unfolded when stretched in one direction, preserving or increasing the dimensions in the transversal direction and giving rise to zero Poisson’s ratio or the NPR effect.

The rotating rectangular geometry can be realized in uni-stretch woven fabrics. However, the true rotating rectangle effect could not be achieved due to the three major limitations. Firstly, the absence of elastic yarn in the warp direction, which makes rectangular units collapse only in the weft direction. Secondly, unstable rectangular units cannot resist change of shape and, due to higher shrinkage caused by elastic yarns in the weft direction, they lose their rectangular shape. Thirdly, the free rotation of rectangular units is restricted due to the warp and weft yarns passing from one rectangle to the other. All these factors resulted in smaller transversal expansion and smaller NPR effect.

With precise placement of loose and tight weave within the unit cell of the fabric structure, it is possible to realize the re-entrant hexagonal geometry in woven fabrics. The longer ribs of the unit cell of hexagonal geometry can be made to bend upon relaxation due to the differential shrinkage effect and to translate into straight form upon stretching, which will increase the transversal dimension, and a large NPR effect can be achieved over a larger longitudinal strain range.

Footnotes

Declaration of conflicting interests

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

Funding

The author(s) 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 15205514).

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