Influence of re-entrant hexagonal structure and helical auxetic yarn on the tensile and auxetic behavior of parametric fabrics

Abstract

This paper focuses on systematically analyzing the influence of macro fabric structure and yarn architecture on the mechanical and auxetic performance of parametric auxetic fabrics. Re-entrant hexagonal (REH) and helical auxetic yarn (HAY) were adopted as a macro fabric structure and weft yarn to produce three kinds of auxetic fabrics: REH fabric with HAY as weft yarn (REH-HAY); REH fabric with elastic yarn as weft yarn (REH-1, REH-2, REH-3); and plain fabric with HAY as weft yarn (NREH-HAY). By controlling the existence of the HAY and REH structure, the influence of the REH structure and HAY on the mechanical and auxetic properties was thoroughly analyzed. It is demonstrated that both the REH macrostructure and HAY micro configuration can contribute to the performance of the auxetic fabric. Specifically, in the presence of the REH structure and HAY, the auxeticity was found to a 77% increase compared with NREH-HAY and the breaking strain and load rises by about 37.50% and 90.42%, respectively. Notably, the variation of the polyurethane (PU) weft yarn per unit length influenced the tensile and auxetic performance to a lesser extent, while by changing PU to HAY, a significant increase of negative Poisson’s ratio value from –1.155 to –1.492 was noticed without greatly jeopardizing the stretchability. Furthermore, the cyclic tensile results demonstrate the stability and elasticity of the fabric. The comparative analysis can give guidance to optimize fabric design and inspire the innovative design of the auxetic textiles, all of which will pave the way for a quantitative and optimizing design for auxetic textiles.

Keywords

Re-entrant hexagonal helical auxetic yarn auxetic fabric negative Poisson's ratio

Many practical applications require an anisotropic structure that can bear considerable load in tension and that shows flexibility and stability when subjected to a bend or cyclic load. At this time, materials with a negative Poisson’s ratio (NPR), auxetic materials, constitute another class of system, which is becoming increasingly popular due to its unusual deformation behavior of expanding laterally when subjected to tensile load. It is known that auxetic textiles present many advantages over their conventional counterparts, such as increased fracture toughness, shear and compress stiffness, whilst a dome shape (synclastic curvature) will naturally appear when bent, which endows auxetic fabric with a superior indentation resistance and shape adaptability.¹ All of these benefits make them became an ideal candidate for applying in protective equipment (seat belts, cushions, helmets, wristbands), filter products, medical devices (artificial vessels, drug release) and aerospace technologies (wing panels).

Up to now, a number of NPR materials have been found in nature or synthetic materials, which range from single metal crystals²,³ to foam⁴,⁵ and from nanomaterials⁶^–9 to models and macrostructures.¹⁰^–14 Apart from these auxetic materials, other auxetic textiles have also attracted a tremendous amount of attention considering the rising requirements of flexibility and comfort; these mainly include helical auxetic yarn (HAY),¹⁵^–18 auxetic fabric¹⁹^–24 and auxetic composites.²⁵^–29 Meanwhile, with the advancement of textile manufacturing technology and the deepening of research, a variety of geometric structures³⁰,³¹ have been utilized to realize auxeticity. In fact, prior art on the subject has dealt mainly with auxeticity in the component types of HAY^32–34 or, in the scale of fabric, potential auxeticity in different foldable geometric structures.³⁵^–38 These studies are mainly focused on separately comparing and optimizing the auxetic behavior from the perspective of yarn (the diameter and modulus of the components, the wrap density) or fabric (the type of component yarn, ends and pick of the fabric) scale, while it is rare to simultaneously explore the optimization method of auxetic properties from multiple-level within a specific geometric architecture and yarn configuration. Thus, a systematic parametric comparison to clarify how a specific geometric architecture and yarn structure can influence the auxetic behavior of fabric is still to be identified, which is a path to determine what parameters can be selected collaboratively to design fabrics with superior tensile and auxetic performance.

To simultaneously elucidate the contribution of the macro fabric geometric structure and micro yarn composition to the tensile and auxetic behavior of re-entrant hexagonal (REH) auxetic fabric, this work focuses on comparative studies about REH auxetic fabric from the scale of yarn and fabric at the same time. The REH geometric structure and HAY have been adopted and assigned as the macro geometric structure and weft component to produce a series of auxetic fabrics with different design parameters, including REH fabric with HAY as weft yarn (REH-HAY), REH fabric with conventional yarn as weft yarn (REH-1, REH-2, REH-3) and plain fabric with HAY as weft yarn (NREH-HAY), as comparisons to explain how the weft yarn auxeticity, weaving density and REH geometric structure influence the NPR value of the REH fabric so as to make it amenable to exhibit a satisfying NPR effect without impairing its performance. In addition, the stability of these auxetic fabrics was also verified via cyclic stretching, desirable stability and auxetic retention ability, demonstrating a pathway for daily applications. It is expected that this work can provide a guide and optimal design ideas for auxetic textiles, which can further create considerable potential for more practical applications.

Material and methods

Auxetic fabric manufacturing

In our previous work, a multi-scale auxetic fabric (REH-HAY) was designed by utilizing HAY as weft yarn and the REH geometry structure as the macroscale to achieve the auxetic behavior both on the scale of yarn and fabric.²² As shown in Figure 1(a), the REH geometric structure was realized by the combination of the twill weave (1/3, Part A), plain weave (Part B) and high float weave (Part C), whose weave structure is shown in Figure 1(a).

Figure 1.

(a) The re-entrant hexagonal (REH) geometric structure and weave structure of auxetic fabric. (b) Real photographs of different auxetic fabrics. (c) Mechanism of the auxetic behavior. HAY: helical auxetic yarn.

For further clarifying the contribution of the macroscopic geometric structure and the microscopic yarn to the final performance of the auxetic fabric, a series of comparative samples have been fabricated. Primarily, three types of REH fabrics with micro geometry of conventional yarn were developed, namely REH-1 and REH-3 with different numbers of polyurethane (PU) filaments in the weft and REH-2 with PU and polyethylene terephthalate (PET) filaments alternating in the weft. Besides, in order to quantitatively investigate whether the REH can contribute substantially to the macroscopic mechanical and auxetic performance, plain weave fabric with HAY in the weft direction (NREH-HAY) was fabricated to evaluate the effect of the REH structure. The components and specifications of all auxetic fabrics are summarized in Table 1; it is noted that all the fabrics in this work were fabricated by a semi-automatic loom (SGA598) at room temperature unless otherwise specified, and the HAYs used in this work were all composed of PET filaments (wrap component, 150D/36f) and PU filaments (core component, 1680D) with an initial wrap density of 150 m⁻¹. After fabrics were off-loom, fabrics with different fabrication parameters were immediately put into a separate sealed bag and placed in the same environments until measurement. The corresponding photographs of these auxetic fabrics are shown in Figure 1(b), and the principle of auxetic behavior is explained in Figure 1(c). It can be found that the auxetic behavior of the fabric can follow from two aspects: one is the REH macro geometric structure, as when stretched in one direction, the diagonal ribs tend to straighten and an expansion can be seen in the vertical direction. Secondly, the auxetic performance can be obtained via the helical-like yarn, as shown in the bottom of Figure 1(c), and the two components of the HAY will exchange their position; thus, the thick core would be helically around the thin wrap yarn when suffering a tensile load, which leads to auxetic effects. In addition, the HAYs were inserted out of the register to maximize the auxetic effect, as shown in Figure 1(c).

Table 1.

The structural parameters of auxetic fabrics

Fabric code	Warp yarn		Weft yarn		Fabric density		Fabric structure
Fabric code	Material	Linear density	Material	Linear density	Ends (cm^–1)	Picks (cm^–1)	Fabric structure
REH-1	Aramid F-12	207D	PU	1680D	20	15	REH
REH-2			PU/PET = 1/1	1680D/150D	20	10	REH
REH-3			PU	1680D	20	10	REH
REH-HAY²²			HAY	/	20	10	REH
NREH-HAY			HAY	/	20	10	Plain

REH: re-entrant hexagonal; HAY: helical auxetic yarn; PU: polyurethane; PET: polyethylene terephthalate.

Uniaxial tensile behavior testing

Consider that fabrics are inevitably required to bear load during practical application, either in a static manner (simple tensile) or in a dynamic one (fatigue). Herein, all the fabrics were mechanically characterized in tension by using a universal testing machine (INSTRON 5967). Moreover, since the elastic component or HAYs were incorporated in the weft direction of the samples, the assessment for tensile properties was conducted in the weft direction with reference to standard ASTM D3107-1975. All the auxetic fabrics were stretched at a rate of 50 mm/min until breaking with the original dimension of (50 × 150) mm².

In addition, taking into account the auxetic effect that occurs simultaneously during the fabric tensile process, every specimen was marked with a (10 × 10) mm² square before stretching, then continuous images of the test specimens were captured by using a high-resolution camera (SONY A7R3) at 2-s intervals (which corresponded to a 1.1% interval of the tensile strain). Then the lateral dimension under different axial strain can be measured through ImageJ software and thus the lateral strain and Poisson’s ratios of the auxetic fabric can be derived via the ratio of the lateral strain to axial tensile strain; the calculation expression is as follows

ν = - ε_{y} / ε_{x}

(1)

Cyclic tensile and elastic behavior testing

In addition to the ultimate load, cyclic mechanical behavior is also important for the long-term use of textiles. Thus, to evaluate the deformation stability and durability, measurements for 10 cycles of tension based on Chinese standard FZ/T 01034-2008 were performed, including the following three processes: firstly, fabric of 150 mm length and 50 mm width was stretched cyclically to 15 mm (10% tensile strain) maximum deformation related to its initial state at a speed of 50 mm/min. Afterward, this stretched state was retained for 60 s, after which the fabric was released to its initial dimension. Finally, another 180 s passed before the next tension cycle.

Simultaneously, the cycle auxetic behavior has been characterized too; photos of every cycle with the fabric at maximum tensile strains were taken and the lateral deformation can be measured. Similarly, the Poisson’s ratio value after every stretching cycle can be obtained according to the formula (1).

Results and discussion

Mechanical behavior of auxetic fabric

In our daily life, textiles always endure various deformation, stretching being one of the most common mechanical actions, and it is necessary to measure and evaluate this. Figures 2(a) and (b) show the force–tensile strain curves of REH fabrics with different weft components and different structures, respectively. It can be seen that by completely adopting PU filaments in the weft direction, the fabric exhibits a good stretchability (REH-1, REH-3) but poor load resistance; when alternately using PET and PU as the weft yarn (REH-2), the strength of the fabric is enhanced while the stretchable shows a sharp drop. Moreover, if the weft yarn is neither rigid PET filaments nor super-elastic PU filaments, but composite yarn (HAY) with a helical configuration composed of the above two filaments, the mechanical behavior of the fabric can be enhanced without greatly jeopardizing the tensile performance, as shown in Figures 2(b) and (c); the REH-HAY fabric has a breaking strain of about ∼110% and a breaking load of about ∼212.7 N, which is better than that of REH-1 with the strength of about 56.2 N. Apart from the type of weft yarn, the fabric pattern also has a significant effect on mechanical properties; this can be found from the comparison of samples REH-HAY and NREH-HAY in which the REH geometric structure is beneficial to improve both the stretchability and load-bearing capacity (Figures 2(b) and (c)).

Figure 2.

The mechanical performance of auxetic fabrics: (a)-(b) force–tensile strain curves; (c) breaking strain and load histogram; (d) the differential modulus curves. HAY: helical auxetic yarn; REH: re-entrant hexagonal.

In the comparison of the main tensile parameters of the fabrics mentioned above, major differences can be observed in Figures 2(c) and (d). It can be seen from Figure 2(c) that while increasing the number of the elastic PU filaments per unit length, an increase can be found in both the breaking load and breaking strain by about 32.86% and 17.65%, respectively. On the other hand, by changing the fabric structure from NREH-HAY to REH-HAY, the breaking strain and the breaking load can be increased by about 37.50% and 90.42%, respectively. Moreover, it can be seen that the REH-1 with PU filaments in the weft direction and REH-2 with PET and PU arranged in the weft direction exhibit mechanical behavior with an ultimate load and strain of 56.2 N, 196.8% and 113.1 N, 33.1%, respectively, while by combining the HAY (a composite yarn with PET filament helical around the PU filament) and REH geometry structure, the load resistance value of the REH-HAY fabric can reach 212.7 N with the maximum tensile strain about is 107.9%, that is, the final load can be increased by about 278.5% and 87.6% compared to REH-1 and REH-2, respectively, which indicated the superiority of the combination design of the REH structure and HAY.

As for textiles, flexibility is also an important factor affecting their comfortable, which can be characterized by the modulus. Figure 2(d) shows the differential moduli of REH-1, REH-HAY and NREH-HAY. It can be seen that the fabrics with HAY in weft direction follow the same tendency as a function of the tensile strain, including a low modulus region at the beginning of the stretching resulting from the elongation properties of the PU core component, followed by a gradually rising modulus region and another dropping modulus region coming from the PET component, which is caused by the position exchange of the components of the HAY, as can be seen in Figure 1(c). However, the modulus of REH-1 fabric with PU in the weft direction only experienced a minor fluctuation during the entire stretching process, which indicated the desired elasticity. This difference can be derived from the different deformation principle of the HAY and pure PU filament. Overall, it can be concluded that the ultimate tensile force and tensile strain, as well as modulus of the auxetic fabric, can be tailored via the constitute and type of the weft yarn as well as fabric pattern.

Auxetic behavior of auxetic fabric

Auxetic performance plays a vital role in protective textiles and functional textiles. Figure 3 summarizes the lateral deformation and Poisson’s ratio of all auxetic fabrics under stretching. The results show that all the curves have similar trends but with different characteristic values, such as maximum NPR value, corresponding tensile strain and strain value at which the phenomenon of NPR disappears.

Figure 3.

Auxetic behavior of auxetic fabrics: (a)-(b) typical lateral deformation versus tensile strain and corresponding Poisson’s ratio versus tensile strain curves; (c) Poisson’s ratio curves of different structure auxetic fabrics; (d) maximum negative Poisson’s ratio of all auxetic fabrics. HAY: helical auxetic yarn; REH: re-entrant hexagonal.

As shown in Figures 3(a), (b) and (d), the fabrics with the REH geometric structure exhibit NPR effects once the strain is applied, and similar low strain behavior in the sharp increase to a minimum NPR value of –1.198 (REH-1 at the strain of 2.2%), –0.755 (REH-2 at the strain of 3.3%) and –1.155 (REH-3 at the strain of 1.1%), and a subsequent decrease in ν can be founded. It is worth noting that the maximum transverse dimension and NPR value of the REH fabric do not occur synchronously. In addition, with the increase of the PU filament number (which means the stretchability of weft direction increases), both the maximum NPR value and the duration of the NPR behavior can be boosted. Significantly, it is clear that the final auxetic behavior of the fabric can be mainly attributed to the REH structure by comparing the maximum NPR value of the NREH-HAY and REH-HAY fabric.

Furthermore, the HAY has been used as weft yarn to explore whether the helical auxetic structure also can contribute to the macroscopic auxetic performance of the fabric; prominent differences can be observed in Figures 3(c) and (d), where the variation of the Poisson’s ratio of the REH-HAY and NREH-HAY is almost the same as that of REH-1 and REH-3. Nonetheless, by replacing the PU weft yarn with HAY, the maximum NPR value can be increased from –1.198 to –1.492, which indicates that the addition of HAY can contribute about 20% to the final auxetic performance. This phenomenon can be explained by the following mechanism: when subjected to a tensile load, the REH-HAY fabric will undergo two stages: the expansion of the REH geometry structure and the position exchange of the component yarns in HAYs, as depicted in Figure 1(c); in brief, the final auxetic behavior of the REH-HAY fabric can be ascribed to the HAY and REH structure. In order to further confirm our conclusion, we use NREH-HAY fabric as the comparison; as can be seen in Figure 3(d), the ultimate NPR is –0.348, which is decreased about 71% and 77% compared to the REH-1 and REH-HAY, respectively. All these differences demonstrate that both HAY and REH structures can promote the enhancement and optimization of auxetic behavior, and the REH geometric structure, that is the macrostructure, has a relatively major contribution.

Stretchable stability of the auxetic fabric

The stretchable stability is especially critical for its durability and long-term use. On the basis of the mechanical behavior of various auxetic fabric, the cyclic mechanical behavior of REH-1, REH-2, REH-3 and REH-HAY fabrics under the strain of 10% have been selected and investigated, as shown in Figure 4. The cyclic testing procedure was described in the Material and methods section. Figures 4(a)–(d) show the force–tensile strain and corresponding force–time curves of the aforementioned auxetic fabrics in 10 tension cycles, respectively. The tensile performance of all fabrics can reach a stable state after the second stretching cycle with the maximum force achieved at consecutive cycles drifting downward marginally, which reveals the structural stability of the auxetic fabric samples. In particular, the largest hysteresis loop was realized by the REH-2 fabric, since it underwent the largest irreversible deformation when compared with REH-1 and REH-3, which used PU as weft yarn. For REH-HAY, there is a relatively large hysteresis phenomenon that occurs in the first tensile cycle, which is mainly caused by the existence of the PET component in the weft direction, and this phenomenon can be quickly eliminated after the second cyclic stretching.

Figure 4.

Cyclic tensile behavior of (a) REH-1 fabric, (b) REH-2 fabric, (c) REH-3 fabric and (d) REH-HAY fabric at the strain of 10%. REH: re-entrant hexagonal; HAY: helical auxetic yarn.

Generally speaking, the ultimate deformation properties of as-prepared auxetic fabrics with the warp and weft yarns arrangement in a REH geometry structure show that they can meet the daily requirements of flexibility and strength, which demonstrate its superior potential for application in the field of protective textiles.

Auxetic stability of the auxetic fabric

To analyze the auxetic stability of the different fabrics, the NPR values after different tensile cycles were plotted to evaluate the auxetic stability for their long-term effectiveness. Figure 5 gives the lateral deformation and Poisson’s ratio–tensile cycle curves at 10% tensile strain of REH fabrics with and without HAY in the weft direction.

Figure 5.

Lateral deformation and corresponding Poisson’s ratio versus tensile cycles of auxetic fabric samples with 10% strain. REH: re-entrant hexagonal; HAY: helical auxetic yarn.

As shown in Figures 5(a) and (c), the lateral deformation and NPR value of REH-1 fabric remain stable from the third cycle with a 68% reduction, and the fabric REH-2 keeps stability from the fourth cycle with the lateral deformation and NPR value decrease of about 33%. For REH-3, there is almost no obvious variation observed, besides a fluctuation at a low lateral deformation and NPR level. In addition, by comparing the auxetic stability of REH-1 and REH-HAY, as plotted in Figures 5(b) and (d), it can be deduced that the stability can be greatly improved via inserting the HAY as the weft yarn.

The parametric comparison results implied that the cyclic auxetic behavior, that is, the lateral deformation and NPR value of auxetic fabrics, can be enhanced by using appropriate weft yarn to meet the durability requirements with good auxetic retention. Simultaneously, it can be seen that a stable auxetic fabric not only needs good elasticity but also a certain load resistance to ensure its shape retention ability.

Elastic stability of the auxetic fabric

Elastic stability is an effective performance for evaluating the ability of textiles to resist external load and keep their original shape; it is vital in clarifying the dimensional stability and its response to instant body movement. For evaluating the elastic stability, the total elastic deformation (TD) including instantaneous elastic deformation (IED), slow elastic deformation (SED) and plastic deformation (PD) under 10% strain, were extracted from the 10 cycle stretching curves and are plotted in Figure 6(a). In addition, the elastic recovery work ( $W_{e}$ ) and total work ( $W$ ) in every tensile cycle is also calculated and summarized in Figure 6(b). The characteristic indexes elastic recovery ratio (R) and work recovery coefficient ( $e_{W}$ ) are given in Figures 6(c)–(f) via

R (%) = (IED + SED) / T D \times 100

(2)

e_{W} (%) = W_{e} / W \times 100 %

(3)

Figure 6.

Cyclic elastic behavior of re-entrant hexagonal (REH) fabrics at 10% strain: (a) elastic deformation; (b) elastic recovery work; (c)-(d) elastic recovery ratio; (e)-(f) work recovery coefficient. HAY: helical auxetic yarn.

As can be seen in Figure 6(a), REH-1, REH-2 and REH-3 all showed small SED and PD, which can be explained by the higher elasticity of PU filament in the weft direction of the fabric. Meanwhile, as shown in Figure 6(c), the PD for all samples almost decreases to 0 after initial stretching cycle, with the R changing from 93% (REH-1), 91% (REH-2) and 97% (REH-3) to nearly 100%. That is, the deformation of the REH auxetic fabric caused by stretching can be almost completely recovered after the second tensile cycle. Similarly, comparing the R of REH-1 and REH-HAY in Figure 6(d), it can be found that the initial elastic recovery ratio R of REH-HAY is lower than that REH-1, but it tends to be the same after the first stretching cycle, which demonstrates that it will not impair the elastic recovery of the fabric when improving the auxetic properties by choosing HAY as weft yarn, it also further proves the superiority elasticity of the REH-HAY multiple-scale auxetic fabric.

In short, all the results indicate desirable elastic performance and shape retention of the auxetic fabrics. Meanwhile, it also can be concluded that the improvement of retention ability can be achieved easily without conflict with the auxetic performance.

In addition, through plotting the elastic recovery work ( $W_{e}$ ) and the total work (W) of the auxetic fabrics separately in a stacked histogram in Figure 6(b), we can observe that the W of REH-2 is significantly higher than those of REH-1 and REH-3, which is mainly due to the existence of PET filaments within the weft yarn of the fabric. Simultaneously, the same conclusion can be obtained in Figure 6(e), which shows that the lowest $e_{W}$ , and the $e_{W}$ of all samples have an upward trend after the first stretching process and realize a stable $e_{W}$ , but there is still a gap between REH-2 and the other fabrics, the reason for which can also be attributed to the low elastic component (PET). Similarly, the $e_{W}$ values of REH-1 and REH-HAY are also listed here to clarify the effects of HAY in elastic recovery behavior. As diagramed in Figure 6(f), both REH-1 and REH-HAY can reach a stable $e_{W}$ value of over 70% after the first tensile cycle, which can meet the elastic stability requirement of textiles.

Conclusion

To conclude, three types of auxetic fabric have been developed via controlling the presence of HAY and the REH geometry structure; the parametric comparative research of these fabrics shows that both the REH macro geometric structure and the HAY micro configuration can contribute to the tensile and auxetic performance of the final products. Specifically, by replacing the PU weft yarn with HAY, the maximum NPR value and ultimate load of REH fabric can increase by about 20% and 278.5%, respectively. Furthermore, by tuning the fabric pattern to the REH structure, a 77% increase is demonstrated in NPR behavior compared with that of plain fabric (NREH-HAY). Furthermore, the stability of as-prepared auxetic fabric is successfully demonstrated through cyclic stretching, the results implying that the optimized REH-HAY fabric has desirable stability and auxetic retention ability. It is hoped that our results will give guidance to the design of auxetic fabric with superior auxetic behavior, stretchability and mechanical stability and stimulate further research in the innovative design of the auxetic textiles, especially work of an experimental and theoretical nature, which better provides the quantitative design strategy for auxetic fabric with the required mechanical performance and NPR value. It is also exciting that this study will start to pave the way for a new generation of auxetic production. We believe the optimized ideas in our work and the REH structure are important steps toward moving from auxetic materials to industrial applications, especially for applications in functional textiles (such as cushions, wristbands, seat belts, filter textiles, etc.) and textile composites (artificial vessels).

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 Natural Science Foundation Project of Shanghai “Science and Technology Innovation Action Plan” (No. 20ZR1400200), by the Open Project Program of the Fujian Key Laboratory of Novel Functional Textile Fibers and Materials, Minjiang University, China (FKLTFM2002) and by the Fundamental Research Funds for the Central Universities (2232021G-06) and Graduate Student Innovation Fund of Donghua University (CUSF-DH-D-2019056).

ORCID iDs

Junli Chen

Zhaoqun Du

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