Study on the structure formation and heat treatment of helical auxetic complex yarn

Abstract

Currently, auxetic yarns consisting of a core filament and a wrap filament are generally utilized as complex materials, which are attributed to residual torque. Thus, the main content dealt with in this paper was to analyze the structure formation and effect of heat treatment of helical auxetic complex yarn spun by a modified ring-spinning system. Firstly, an orthogonal experiment with three factors and three levels was carried out to study the effects of diameter ratio, yarn twists and initial helical angle on the structure and Poisson’s ratio of complex yarn. Secondly, a heat treatment process with polyamide filament with low melting point (80℃) was conducted to improve the structural stability of auxetic complex yarn. It was found that the heat treatment process can not only improve the structural stability of complex yarn, but also promote the expansion effect. By comparing experimental and theoretical results, it was found that the variation of Poisson’s ratio with axial strain had good consistency. Therefore, the heat treatment method can effectively solve the slippage problem of helical auxetic complex yarn.

Keywords

auxetic effect complex yarn structure formation heat treatment

Auxetic yarns with negative Poisson’s ratio are different from conventional yarns with positive Poisson’s ratio. When stretched longitudinally, the apparent contour of auxetic complex yarn expands radially. Auxetic material has special properties, such as shear stiffness, fracture toughness, indentation resistance, energy absorption and synclastic curvature.^1–7 Auxetic yarn with a double helix structure was firstly proposed by Miller et al.⁸ and manufactured as a modified wrap/core yarn, in which a wrap filament was helically wound around a core filament, and was woven into a woven textile structure. In addition, Wright et al.⁹ reported the development of low-stiffness auxetic yarns whose stiffness was highly dependent upon yarn geometry. Bhattacharya et al.¹⁰ analyzed the effect of the interaction and relative moduli between the core filament and the wrap filament on the auxetic behavior. A semi-auxetic yarn was explored by means of sewing an inextensible thin cord through an elastic fat cord in a triangular pattern.¹¹ In addition, the ring-spinning system was used to effectively produce auxetic yarn,¹² and a novel type of plied yarn structure with negative Poisson’s ratio was conducted by two stiff yarns and two soft yarns.¹³ The four fed yarns were twisted together by rotating a circular disc. There have also been investigations showing that a larger negative Poisson’s ratio in a dual helix yarn can be realized by simply downsizing the diameter of the carbon-based wrap yarn from micron to nano scale.¹⁴ Furthermore, a systematic study of the helical auxetic yarn was acquired and the effect of the core/wrap diameter ratio and the initial wrap angle on the yarn auxetic behavior have also been discussed.^15,16

Auxetic yarns are potentially useful in a wide range of engineering applications.^17–19 However, some intrinsic structural drawbacks are that the wrap yarn can easily slip along the surface of the core yarn, and the phenomenon of kinking and loose structure will occur in the free tension state of complex yarn. To improve the possibility of practical applications of auxetic yarn, some researchers have tried methods to solve the problem or new structures to avoid it. A three-component auxetic yarn based on a stiff wrap fiber (the first component) helically wound around an elastomeric core fiber (the second component) coated by a sheath (the third component) to avoid slippage of the wrap.²⁰ Nevertheless, larger coating thickness could cause the three-component auxetic structure to lose its partial auxetic effect. The latest study showed a tubular braided structure with negative Poisson′s ratio and the wrap yarn was fixed with braiding yarns to form a uniformed and stable state.²¹

Based on the existing research, this paper primarily aims to study a post-processing system to prepare complex yarn with a negative Poisson′s ratio and stable structure. A filament with a lower melting point was used to manufacture auxetic complex yarn, and a heat treatment process was conducted with an oven at two temperatures (100℃ and 120℃). The effects of the structure parameters and heat treatment process on the Poisson’s ratio of helical auxetic complex yarn were analyzed. In addition, according to the theoretical modeling of helical auxetic yarn,²² the relation between the Poisson′s ratio and structure parameters was established to predict the theoretical value of the auxetic effect and was compared with the experimental results. It is expected that this study could promote the applications of auxetic yarns.

Experimental details

Materials, fabrication and tests

The helical auxetic complex yarn is composed of two filaments, namely one core filament and one wrap multifilament, as shown in Figure 1. Several kinds of yarns with different materials, twists and initial helical angles were spun. White spandex filament with three different finenesses (560D, 840D, 1120D) and black polyester multifilament (Finess150D/36f) were utilized as the core and wrap, respectively. To solve the slippage problem of the wrap from the core in the free state, a polyamide filament (70D) a with melting point of 80℃ was used as the third component to bind the other two components together.

Figure 1.

Schematic illustration of the helical auxetic yarn: (a) initial state with wrap angle θ and diameter D₀; (b) stretching state with diameter D.

The complex yarns were spun based on the modified ring-spinning machine shown in Figures 2(a) and (b), including adding a positive feeding roller of spandex, double tension discs and a multiple thread guide so as to respectively control the feeding state. The two components were twisted together in the jaw of the front roller and the helical wrapping structure was formed by controlling the tension of the structures during spinning. The helical angle and yarn tension could be adjusted by the tension disc and the speed ratio of the positive feeding roller to the front roller. When spun with three components, the core was helically wrapped by the polyamide filament and polyester together. The positions of the yarn components were limited by the multiple thread guide. Then heat treatment process was conducted with an oven to improve the contact state between the core and the wrap. The type of oven used was an electric blower (GZX-9076MBE from Bo Xun Industrial Co., Ltd, Shanghai, China). Firstly, the sample was fixed on a glass rod in a straight state. Then the samples were put in the oven and the temperature was set to 100℃ (or 120℃). Finally, the sample was taken out of the oven after 30 minutes treatment at 100℃ (or 120℃) and kept for several hours at room temperature.

Figure 2.

(a) Photograph of the ring-spinning system. (b) Schematic of the ring-spinning system.

Axial tensile test was carried out using an XL-1A extension tester (Xinxian Instrument Co., Ltd, Shanghai, China). The gauge length was 250 mm and the tensile speed was set as 250 mm/min. A high-definition digital microscope (DIGITAL MICROSCOPE (x200), China), which was connected with a PC through a USB port, was utilized to capture images in the entire test process, and the apparent diameter D of the complex yarn in the tensile state could be obtained using the software by pixel conversion. Then the diameter variety rate ɛ_r and Poisson’s ratio could be calculated by equations (1) and (2), respectively, where D₀ represents the outer contour diameter of yarn in the initial state and ɛ_t represents the axial strain of the complex yarn under tension:

ɛ_{r} = (D - D_{0}) / D_{0}

(1)

σ = - ɛ_{r} / ɛ_{t}

(2)

In accordance with standard ISO 3343-2010 (Reinforcement yarns-determination of twist balance index),²³ the curl length and number of knots were tested and recorded to characterize the structural stability of the complex yarn. After removing tension to keep the sample yarn straight, the length and number of curling parts in the length of 25 cm were separately identified as curl length and knots number.

Design of the orthogonal experiment

To confirm the optimal structure parameters, an orthogonal experiment was carried out to better evaluate the effect of the heat treatment process.²⁴ Then considering the effects on the structure and the Poisson’s ratio of complex yarn, three parameters, namely the diameter ratio of core yarn to wrap yarn, yarn twists and the initial helical angle, were chosen as factors to study. Details of the experimental design are listed in Table 1. Thus, nine yarn samples were tested to obtain curves of the Poisson’s ratio with axial strain. Moreover, the apparent diameter was calculated from averaging the testing values of 10 repeated measurements on different segments of yarn samples to reduce errors as much as possible.

Table 1.

Details of the orthogonal experiment

No.	Materials	Diameter ratio	Yarn twist (turns/m)	Helical angle (degree)
1	Core: spandex, 560D	3.7	40	27
2	Wrap: polyester, 150D;	3.7	50	29
3	Tensile Modulus: 48.8 CN/tex	3.7	60	31
4	Core: spandex, 840D	5.6	40	29
5	Wrap: polyester, 150D;	5.6	50	31
6	Tensile Modulus: 48.8 CN/tex	5.6	60	27
7	Core: spandex, 1120D	7.5	40	31
8	Wrap: polyester, 150D;	7.5	50	27
9	Tensile Modulus: 48.8 CN/tex	7.5	60	29

Results and discussion

The variety of radial strain and Poisson’s ratio

Orthogonal experiments with three factors and three levels were conducted according to Table 1. The radial strain of complex yarn was recorded during tensile tests. Curves of diameter variety rate and Poisson’s ratio of complex yarn with axial strain are shown in Figures 3(a) and (b).

Figure 3.

(a) Diameter variety rate with axial strain curves of samples 1–9. (b) Poisson’s ratio with axial strain curves of samples 1–9.

It can be seen from Figures 3(a) and (b) that the diameter variety process of complex yarn can be analyzed from three periods corresponding to the variation tendency of the Poisson’s ratio. For the first stage, the diameter decreased because of cross-sectional contraction resulting from compression force of the core filament and wrap multifilament; thus, the complex yarn had increasing positive Poisson′s ratio in this stage. For the second stage, the diameter of complex yarn was expanded to be the same size as the original yarn, and it continued to increase rapidly. This could be because the wrap multifilament replaced the position of the core filament gradually and extruded the core filament to be completely straight from the helical state. Correspondingly, the Poisson’s ratio of complex yarn changed from a positive value to zero and gradually to be negative. Besides, the value of negative Poisson’s ratio was increasing to the maximum with the extension of the complex yarn in the radius direction. For the third stage, the growth rate of the diameter of complex yarn decreased under the larger longitudinal strain, which corresponded to the negative Poisson’s ratio of complex yarn from maximum to zero. This indicated that the yarn diameter was expanded slightly, which was larger than the initial value. Therefore, the complex yarn still had an auxetic effect in the third stage.

Determination of the optimal system parameters

The results of orthogonal experiments were analyzed by the extremum analysis method, as listed in Table 2. The orthogonal experiment was carried out with three factors and three levels and each level with one factor corresponds to three results. Then the average value of every level was calculated, and the largest difference between them was named as the extreme value. Moreover, the extreme value was related to the effect of different factors on the samples, while the effect of each factor with different levels on the Poisson′s ratio could be discussed according to the average value.

Table 2.

Results of the extremum analysis method

No.	Maximum negative Poisson’s ratio	Diameter ratio		Yarn twist		Helical angle
No.	Maximum negative Poisson’s ratio	Average value	Extreme value	Average value	Extreme value	Average value	Extreme value
1	–0.69	–0.75	0.1	–0.74	0.11	–0.84	0.04
2	–0.76
3	–0.81
4	–0.78	–0.83		–0.85		–0.8
5	–0.83
6	–0.87
7	–0.75	–0.85		–0.84		–0.8
8	–0.96
9	–0.85

The average value of the Poisson’s ratio about the three factors and three levels in Table 2 shows that the negative Poisson’s ratio effect increased with the increase of the diameter ratio and the decrease of the helical angle of the core filament to the wrap filament. This was due to the fact that when the diameter ratio was larger or the helical angle was smaller, the larger deformation of the core filament was caused by lower extrusion from the wrap multifilament in the initial strain stage. In addition, below a certain twist, it played a positive role on the auxetic effect of complex yarn and then was negative. This was because the increasing twist could shorten the process of balance interaction between the core filament and the wrap multifilament. Then the apparent contour of the elastic core filament expanded in smaller axial strain. On the contrary, excessive twist limited its deformation and the auxetic effect would be lower. Therefore, a larger diameter ratio and smaller initial helical angle can lead to a more visible auxetic effect and the conclusion was the same with the results.^12,16 The structural parameters of sample 9 were selected to be processed by heat treatment.

Effect of the heat treatment process

Effect on structure stability

When complex auxetic yarn was spun by the core filament and the wrap filament, it showed residual torque and kinking performance. In order to solve the problem, a polyamide filament with low melting point (80℃) was selected to manufacture auxetic complex yarn. A heat treatment process with different oven temperatures was conducted to improve the structural stability of auxetic complex yarn. As shown in Figure 4(a), sample T1 was a three-component complex yarn with 1120D spandex, 150D polyester and 70D polyamide filament with a melting point of 80℃ and sample T2 was a two-component yarn without polyamide. When spinning with the three components, the 1120D spandex as the core was wrapped by polyester and polyamide together. Yarn samples T1 and T2 after heat treatment of 100℃ and 120℃ were separately named T1-100, T1-120, T2-100 and T2-120. After the heat treatment process under two different oven temperatures (100℃ and 120℃), the state of yarn samples without tension were as shown in Figures 4(b) and (c).

Figure 4.

Photographs of samples T1 and T2 in the free state: (a) without the heat treatment process; (b) with 30 minutes heat treatment under 100℃; (c) with 30 minutes heat treatment under 120℃.

Compared with the initial state of complex yarn before the heat setting process in Figure 4(a), the stability and integrity of the helical wrap structure of complex yarn were obviously improved after 30 minutes of heat treatment process. In Figures 4(b) and (c), the structure of samples with the polyamide filament with a low melting point was better than that of samples without it. This could be attributed to the existence of low melting point polyamide filament that leads to more contact points between yarn components. When the temperature of the heat treatment process was higher than the melting point, the surface of the polyamide filament would become sticky and it made the components tightly wrap together. Thus, complex yarn could keep the initial helical structure in the free state.

In addition, yarn with a large residual torque will shrink quickly in the natural free state, which results in a number of kinks and poor applicability. Therefore, curl length and number of knots of auxetic complex yarns before and after heat treatment process were tested and are shown in Table 3.

Table 3.

Comparison of auxetic complex yarns before and after the heat treatment process

No.	Curl length (cm)	Number of knots	Beginning of strain being auxetic (%)	Maximum of negative Poisson’s ratio
T1	9	2	10	–0.8692
T2	4.5	3	10	–0.8762
T1-100	4.5	3	2.5	–0.7805
T2-100	4.2	2	5	–0.8086
T1-120	4	2	7.5	–1.1238
T2-120	3.5	3	10	–1.0639

In Table 3, the maximum curl length of complex yarn with the low melting point polyamide filament decreased from 9 to 4.5 cm and 4 cm after 100℃ and 120℃ heat treatment process, respectively. This means that the residual torque of complex yarns are greatly reduced after 30 minutes of heat setting process. Therefore, considering the apparent structure and maximum curl length of auxetic complex yarns, both the structural stability and the residual torque of the complex yarns were better after the heat treatment process. Moreover, in order to analyze the effect of heat treatment on Poisson’s ratio, the beginning of strain becoming auxetic and the maximum negative Poisson’s ratio before and after the heat treatment process are also presented in Table 3. It can be seen from Table 3 that complex yarns began to be auxetic in the least axial strain with treatment temperature of 100℃ and exhibited the maximum negative Poisson’s ratio with treatment temperature of 120℃. Therefore, the heat treatment process can not only improve the structural stability of complex yarn, but also slightly promote the expansion effect.

Effect on Poisson’s ratio

In order to analyze the effect of heat treatment on the Poisson’s ratio, the diameter variety rate and Poisson’s ratio with axial strain of the complex yarns before and after the heat treatment process were tested and analyzed, and their corresponding curves are shown in Figures 5(a) and (b).

Figure 5.

(a) Diameter variety rate and axial strain curves of auxetic complex yarns before and after the heat treatment process. (b) Poisson′s ratio–axial strain curves of auxetic complex yarns before and after the heat treatment process.

The diameter variety process of complex yarn in Figure 5(a) can also be divided into three stages corresponding to the variation tendency of the Poisson’s ratio in Figure 5(b). The first stage range of samples T1 and T2 after the heat treatment process was shortened. This indicated that more contact points and lower residual torque made the equilibrium state easier between the wrap multifilament and the core filament with extrusion and friction. Even if the axial strain was relatively small, the diameter of complex yarn increased and showed a negative Poisson’s ratio. In the second stage, the value of the negative Poisson’s ratio was increasing to the maximum with the extension of the complex yarn in the radius direction. In addition, complex yarns with a polyamide filament with low melting point and heat treatment of 120℃ exhibited the maximum value of negative Poisson’s ratio. Therefore, the heat treatment is effective to improve structural stability of complex yarn and is helpful for the auxetic effect.

Comparison of Poisson′s ratio between experimental and theoretical results

According to the theoretical modeling of helical auxetic yarn,²² the entire tension process of auxetic yarn was divided into two stages. The first stage is that the helical radius of the wrap filament decreases with the increase of longitudinal extension, and the core filament has corresponding deformation according to the helical path of the wrap filament. The second stage is that the wrap filament is stretched in the center position with the extension of yarn. The outer contour diameter D of auxetic yarn is the larger value of D₁ or D₂ in the first stage; in the second stage, it is calculated by D₁, which are all given as follows. The involved structure parameters are listed in Table 4

D_{1} = 2 \times (R + r)

(3)

D_{2} = 2 \times (d_{0} / 2 + l_{0} \times sin (θ') / 2 π)

(4)

Table 4.

Definition of auxetic yarn structural parameters

Name	Meaning
R ₀	Core filament initial radius
d ₀	Wrap filament initial diameter
R	Radius of the core filament after deformation
r	Helical radius of the core filament axis
θ′	Wrap angle of the wrap filament after deformation
l ₀	The initial length of the core filament axis

For equations (2)–(4), the theoretical model²² was utilized to analyze the complex yarn consisting of a wrap filament and a core filament, where the filament is a single filament with circular shape. However, the wrap component used in the complex yarn is a kind of multifilament. The cross-section shape of the wrap is flat ribbon and the packing density was changing along with the axial strain ɛ_t. By fitting the variation curve of the wrap yarn during the axial tensile test, the diameters modified by ɛ_t were as shown in equations (5) and (6), d₁ for the first stage and d₂ for the second stage

d_{1} = 0.0078 - 0.0014 \times ɛ_{t} + 8.2857 \times ɛ_{t}^{2}

(5)

d_{2} = d_{0} - 0.152 \times ɛ_{t}

(6)

The experimental Poisson’s ratio was compared with the theoretical results of sample T2-120, as shown in Figure 6. It is obvious that there exists deviation between the theoretical and experimental results in the second stage. This is attributed to the cross-section shape of the wrap multifilament being a flat ribbon in the complex yarn, and the shape contour nonlinearly changes with axial elongation. Along with the neglect of the extrusion force between components of complex yarns,²² some assumptions of the model in experiments lead to deviations between the experiments and theoretical results. When the diameter of the wrap multifilament is modified by equations (5) and (6), and the heat treatment process endowed the complex yarn with smaller deformation and more stable structures, the Poisson′s ratio–axial strain curves had good accordance between the experimental and modified theoretical results, especially for the second stage from the maximum point to the end. This is because the thickness of the warp multifilament with a flat ribbon nonlinearly increased with the increase of the axial tension and extrusion between the wrap multifilament and the core filament until it became a bundle during the first stage. Conversely, the wrap multifilament became thinner slowly with the axial strain in the second stage. The corresponding theoretical modeling will be considered in a further theoretical analysis of helical auxetic complex yarns.

Figure 6.

Comparison of theoretical and experimental Poisson’s ratio of sample T2-120.

Conclusions

Several kinds of helical auxetic complex yarns with different materials and parameters were spun by a modified ring-spinning system. Orthogonal experiments with three factors and three levels were designed. The results, based on the extremum analysis method, showed that all three factors, diameter ratio, yarn twist and helical angle, played an important role on the Poisson’s ratio of complex yarn. This indicated that a larger diameter ratio and twist and smaller initial helical angle can lead to a more visible auxetic effect. Based on the experimental results, three-component complex yarn with a filament with lower melting point and the heat treatment method with an oven were utilized to solve the slippage problem of the helical auxetic structure. The curl length and number of knots were tested according to the related ISO standard to assess the structural stability of the yarn samples. Through comparing the results before and after the heat treatment process, it was shown that the method with the oven temperature of 120℃ can not only improve the structure stability of auxetic complex yarn, but also increase the expansion effect. Moreover, according to the modified theoretical model, the experimental and theoretical results of the Poisson’s ratio with axial strain were in good consistency in the whole region. Thus, the heat treatment process is a feasible method to effectively improve the auxetic effect and structure stability of helical wrapping structure complex yarn.

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 National Key Research and Development Program of China (Grant No. 2016YFC0802802), the Fundamental Research Funds for the Central Universities, the Fok Ying Tung (huoyingdong) Education Foundation (151071), the Fujian Provincial Key Laboratory of Textiles Inspection Technology (Fujian Fiber Inspection Bureau) of China (2016-MXJ-02), and a Project (Grants 11272086, 51203022, 51403078) supported by the National Natural Science Foundation of China.

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