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A finite element analysis of auxetic behavior of complexyarns with negative Poissons ratio

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Citation for published version (APA):Liu, S., Chen, X., & Du, Z. (2018). A finite element analysis of auxetic behavior of complex yarns with negativePoissons ratio.

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Download date:13. Jul. 2021

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A finite element analysis of auxetic behavior of complex yarns with

negative Poisson′s ratio

Sai Liu 1,2, Zhaoqun Du 1 and Xiaogang Chen 2 1 Key Laboratory of Textile Science & Technology, Ministry of Education, College of Textiles, Donghua

University, Shanghai 201620, China 2 School of Materials, The University of Manchester, Manchester M13 9PL, UK

Abstract. Textile materials with negative Poisson′s ratio possessed auxetic behavior and excellent properties which resulted in all kinds of potential applications in various fields. This paper aims to study the deformation behavior and auxetic mechanism of complex yarns with negative Poisson′s ratio by the finite element software Abaqus. The analysis results showed as Poisson′s ratio under certain axial strain were corresponding to the experimental results that have been reported. Then the deformation process and reason were discussed according to the Mises Stress distributions. The differences between auxetic yarns with elastic and hyperelastic core were also compared and analysed from Poisson’s ratio, load and normal contact pressure. The finite element modal and analysis was expected to be a positive guidance to prepare auxetic yarns with obvious auxetic effect.

Keywords: auxetic behavior, finite element analysis, complex yarns, Poisson′s ratio.

1. Introduction Auxetic materials have been paid more and more attention as a result of special characters such as

indentation resistance [1] and energy absorption [2]. More importantly, the studying of auxetic behaviors and mechanism could play positive role on predicting and improving the expanding effect practically. Some researchers provided the theoretical method [3-4] to calculate the deformation, while others concentrated on the numerical study by finite element analysis as a result of efficient and direct simulation of the expanding behavior and mechanical properties. Ge et al. [5] reported the finite element analysis of an innovative 3D auxetic textile structure consisting of three yarn systems (weft, warp and stitch yarns). The finite element model was validated and finally used to simulate the auxetic behaviour of the structure under compression with different structural parameters and yarn properties. Wang et al. [6] produced a finite element model to predict the deformation behaviors of the auxetic warp-knitted spacer fabric stretched in different fabric plane directions.

In recent years, more and more auxetic materials have been reported and yarns, as the foundation of formating a fabric to be used, have been also studied the structure, preparation and characterization [7-9]. Ge et al. [4] produced a kind of auxetic yarn structure formed with two stiff yarns and two soft yarns with experimental and geometrical study. The Poisson’s ratio of yarn samples were tested and calculated with the gauge distance and tensile speed set as 250 mm and 50 mm/min respectively. Bhattacharya et al. [10] studied the effect of the interaction between the core and the wrap fibre on the auxetic behaviour of the helical auxetic yarn. It showed that the core–wrap moduli ratio should be high enough to yield an auxetic effect and low enough to prevent the core-indentation effect to make yarn with largest negative Poisson’s ratio. Tensile measurements were taken with a 70 mm gauge length and a speed of 5 mm/min. One of the yarn sample with the core-wrap young’s modulus ratio about 500 showed the maximum negative Poisson’s ratio of -13.52 at axial strain of 0.02, while using the polyurethane core to replace elastomeric polyester and with the same wrap, the max value was -1.65.

Most auxetic yarns having been reported was with the polyurethane core which greatly limited the applicability, while, yarns with high performance were necessary when applied such as ballistic protective equipment material. Thus the paper was taken to study the difference of the polyurethane core with hyperelasticity and other general elastic core when forming helical auxetic yarns in the mechanical property, Poisson’s ratio and auxetic mechanism.

Proceedings of the 8th World Conference on 3D Fabrics and Their Applications Manchester, UK, 28-29 March 2018

2. Modelling Finite element analysis was carried out with the software of Abaqus/CAE 6.14-4 and the units of

SI/mm. Figure 1 (a) and (b) showed the basic modal of the core and the wrap. The dilameter of the core and the wrap were 1 mm and 0.2 mm, respectively. For the helical auxetic yarn, the core was helically wrapped the wrap filament like showed in Figure 1 (c). The core was presented with a thicker cylinder, while, the wrap was showed as a thinner spiral. Then the helical auxetic yarn was formed by assembling them together. The wrap angle was 13 degree and the length of the yarn was 24 mm. Regarding the property, the elastic core was defined with young’s modulus 1 Mpa and Poisson’s ratio 0.45, while, the hyperelastic core was defined with Mooney-rivlin coefficients as C10 = 3.2 and C01 = 0.8, which coressponding to a Poisson’s ratio of 0.475. Besides, the young’s modulus and Poisson’s ratio of the wrap were set as 1000 Mpa and 0.3, respectively.

Figure. 1: The basic modals: (a) core; (b) wrap; (c) helical structural yarn.

Under the axial tension, the yarn would produce deformation behavior of slidding and friction. The

contact property between the surface of the core and the wrap was defined as hard contact without separation after deformation as showed in Figure 2. The surface of the wrap was as the master, while the other as the slave to avoid the nesting between each other. To carry out the axial tensile test, all freedom of one end of six directions were set as zero in the initial step shown in Figure 3 (a). The velocity load of 1 mm/s was conducted to the other end in the analytical step shown in Figure 3 (b). The seed of the two parts, the core and the wrap, for meshing was 0.1 and 0.3, respectively. A three dimentional element type of C3D8H was used to mesh the core part shown in Figure 4 (a), which means 8-node linear brick, hybrid, constant pressure, to simulate the large deformation behavior. The meshing of hyperelastic core with hybrid formulation was to ensure the accuracy and effectiveness in the case of avoiding hourglass proplem. And the wrap part was meshed by C3D8 elements shown in Figure 4 (b). Then the rationality of mesh equality was checked through the verify founfation. Finally, the job could be created and submitted after deta check.

Figure. 2: The contact property between the surface of the core and the wrap.

(a) (b) (c)

Figure. 3: Boundary condition.

Figure. 4: The mash for (a) the core and (b) the wrap.

3. Finite element analysis

3.1. Auxetic mechanism

All the deformation behaviors of the helical auxetic yarn under axial tension could be presented through finite element analysis. After varify the rationality of the mesh size by almost the same result with bigger seeding desity, the deformable forms of the yarn at different tensile strains were showed in Figure 5. When the axial strain was from 0 to 0.48%, the outer outline of the yarn was the wrap which was the same as the initial state as showed in Figure 5 (a). Besides, at the whole stage, the wrapping angle of the wrap to the core and the diameter of the yarn was always kept decreasing which brought out positive Poisson’s ratio. However, continuing to stretch, the wrap gradually straightened from helical wrapping state and the core was being arched as a result of the mutual extrusion and friction. Thus the yarn presented negative Poisson’s ratio and the outer outline changed to the core. As showed in Figure 5 (b) and (c), the yarn showed the maximum negative Poisson’s ratio and deformation degree at axial strain of 3.65% and 7.29%, respectively. It illustrated that the growth rate of the apparent diameter of the yarn began to reduce when the aixal strain was more than 3.65% as Poisson’s ratio defined with the nagative value of the ratio of the radial strain to the axial strain.

(a) (b)

(b) (a)

0.48%

3.65%

7.29%

Figure. 5: Mises Stress distributions at different tensile strains.

As shown in Figure 5, the Mises stress was mainly distributed in the wrap filament at different tensile strains. It was mostly because of the higher Young’s modulus of the wrap. When the yarn was stretched in the axial direction, the core could be extened as the elastic property, while, the wrap with litle elongation had to be the tight state. In order to achieve dynamic balance, the wrap was wrapped by the elongated core which led to the position exchange and larger contour as the diameter of the core was bigger than the wrap. During the deformation process, the poisson’s ratio of the yarn changed from positive to negative.

3.2 Poisson’s ratio

(a)

(c)

(b)

Through the extration of the coordinates, the radial strain could be got and Poisson’s ratio of the yarn

could be calculated. The variation of Poisson’s ratio with the increasing of axial strain was showed in Figure 6. Two curves presented the same trend, but the maxmium of Poisson’s ratio had greatly difference. The yarn with elastic core got the higher positive and negative value of Poisson’s ratio which was accordance with the experimental results that have been reported by some researchers [10]. However, the simulation results have a little higher than the maxmium value of Poisson’s ratio that from experimental tests. On the one hand, the surface of the core and the wrap was defined as hard contact, while, the effect of core-indentation to Poisson’s ratio has been reported. On the other hand, the cross section of the core and the wrap were defined as circular, even more without change during the whole deformation process.

Figure. 6: Comparison of Poisson’s ratio-axial strain curves of auxetic yarns with elastic and hyperelastic core.

As shown in Figure 7, compared with the yarn with hyperelastic core, the yarn with elastic core presented larger deformation and better auxetic effect with smaller tension. Polyurethane, as a kind of hyperelastic material, was widely used in auxetic complex yarn. It was defined with Mooney-rivlin coefficients which was corresponding to the Poisson’s ratio of 0.475. However, general elastic material was defined as low modulus. Thus the auxetic yarn with elastic core could extend easier with the axial tension. Besides, the normal contact pressure during the whole tensile process was showed in Figure 8 to be analysed due to the necessity of mutual extrusion to the expand behavior. The normal contact pressure between the hyperelastic core with the wrap was much bigger than the elastic one, which was coincindent with the load as it led to the larger friction. Thus, considering the surface friction coefficient of the filament may also be meaningful when preparing auxetic complex yarns.

Figure. 7: Comparison of load-axial strain curves of auxetic yarns with elastic and hyperelastic core.

Figure. 8: Comparison of normal contact pressure-axial strain curves of auxetic yarns with elastic and hyperelastic core.

4. Conclusion

Two parts of the helical auxetic yarn, the core and the wrap, were created as the initial modal and finite element analysis was carried out after a seris of parameters and properties being defined. Auxetic mechanism was tried to interpreted according to the Mises Stress distributions. Through the coordinates extration of element modal in radial direction, Poisson’s ratio was calculated and the curves over axial strain were got. The two curves of helical auxetic yarns with elastic and hyperelastic core showed the same trend, while, the former presented much higher value of negative Poisson’s ratio and better expand effect. Besides, the load and normal contact pressure during the whole deformation process were also analysed. It was believed that the general elastic filament was also suitable to prepare auxetic complex yarns with greatly expand property.

5. References [1] R, Lakes, and K, Elms. Indentability of Conventional and Negative Poisson's Ratio Foams, J. Compos. Mater. 1992, 27 (12): 1193-1202. [2] F, Scarpa, L, Ciffo and J, Yates. Dynamic properties of high structural integrity auxetic open cell foam, Smart. Mater. Struct. 2004, 13 (1): 49-56. [3] Z, Du, M, Zhou, H, Liu, and L, He. Study on negative Poisson's ratio of auxetic yarn under tension: Part 1 - Theoretical analysis, Text. Res. J. 2014, 85 (5): 487-498. [4] Z, Ge, H, Hu, and S, Liu. A novel plied yarn structure with negative Poisson's ratio, J. Text. Inst. 2015, 107 (5): 578-588. [5] Z, Ge, H, Hu, and Y, Liu. A finite element analysis of a 3D auxetic textile structure for composite reinforcement, Smart Mater. Struct. 2013, 22 (8): 084005. [6] Z, Wang, and H, Hu. A finite element analysis of an auxetic warp-knitted spacer fabric structure, Text. Res. J. 2015, 85 (4): 404-415. [7] Z, Du, M, Zhou, L, He, and H, Liu. Study on negative Poisson's ratio of auxetic yarn under tension: Part 2 – Experimental verification, Text. Res. J. 2015, 85(7): 768-774. [8] J, Wright, M, Burns, E, James, et al. On the design and characterisation of low-stiffness auxetic yarns and fabrics, Text. Res. J. 2012, 82 (7): 645-654. [9] N, Jiang, H, Hu. A study of tubular braided structure with negative Poisson's ratio behavior, Text. Res. J 2017, https://doi.org/10.1177/0040517517732086 . [10] S, Bhattacharya, G, Zhang, and O, Ghita, et al. The variation in Poisson's ratio caused by interactions between core and wrap in helical composite auxetic yarns, Compos. Sci. Technol. 2014, 102: 87-93.