Energy absorption and Poisson's ratio of warp-knitted spacer fabrics under uniaxial tension

Abstract

This paper presents five different auxetic warp-knitted spacer fabrics and discusses their energy absorption under uniaxial tension through integrals of stress on strain. Structures of auxetic fabrics are designed based on rotating hexagonal models and knitted for experimental tests, including Poisson's ratio tests and tensile tests. Results show that energy absorption of auxetic warp-knitted spacer fabric is mainly determined by its structural deformation capacity and yarn loading capacity, between which the yarn loading capacity of fabrics plays the dominant part in energy absorption, while the structural deformation capacity, which is affected by Poisson's ratio, has relatively little influence. With equivalent yarn loading capacity, the energy absorption of fabrics with negative Poisson's ratios are relatively better.

Keywords

auxetic warp-knitted spacer fabric energy absorption tensile property

A typical warp-knitted spacer fabric usually consists of two face layers that are composed of many vertical interlocking loop chains, and spacer yarns that connect the two face layers. It is knitted on a double needle bar machine with the distance between the two surfaces retained after compression by the resilience of the pile yarn (usually mono-filament) that passes between them. Due to its unique knitting process, mechanical properties of a warp-knitted fabric along the loop forming direction and along the guide bar moving direction are usually different, making it anisotropic intrinsically. Auxetic warp-knitted spacer fabrics are a kind of novel fabric structure combining auxetic structures with warp-knitted spacer fabrics, endowing fabrics with excellent properties such as tunable permeability, cushioning performance and resilience, as well as shock resistance¹ and abnormal deformation characteristics under uniaxial tension or pressure, which means that they could expand or contract in the direction perpendicular to the uniaxial tension or stress. These properties make auxetic warp knits perfect for protective clothing and equipment, such as knee pads, elbow pads and bullet proof vests. They are also a better option for composite reinforcement with curved surfaces mostly used in high-speed trains and aircraft. Therefore, the application potentials call for more thorough researches on the energy absorption of auxetic spacer warp knits.

The tensile property is one of the key indexes for evaluating the mechanical property of fabric materials. The failure mode and the load capability of materials under stress can be determined through tensile tests. Excess elastic deformation, plastic deformation and fracture are three typical failure modes.² Two indicators used for characterizing tensile performance are breaking strength and breaking elongation. There are three steps when conducting tensile tests: cut the sample into a desired size first, and then stretch it at a constant speed until it breaks, after which measure the maximum bearing capacity and its corresponding elongation, namely breaking strength and its breaking elongation. The method of fabric tensile fracture tests is similar to that of fibers or yarns, except that the tensile direction of fabrics should be determined in the fabric plane. Fabrics could be stretched along the walewise direction, coursewise direction, diagonal direction or be stretched along both walewise and coursewise directions spontaneously. For now, fabric tensile tests are usually conducted under uniaxial stretch, the fracture mechanism of which is shown in Figure 1.

Figure 1.

Fracture mechanism of fabrics under uniaxial stretch.

In previous researches, Liaqat et al.³ provided a modified four-layer through-the-thickness woven structure with auxetic fabric and researched its impact resistance and energy absorption compared to standard non-auxetic fabric. Imbalzano et al.⁴ developed an effective numerical model to simulate auxetic composite sandwich panels and studied their impact resistance performance. Zeng et al.⁵ studied the negative Poisson's ratio behavior of a three-dimensional (3D) auxetic orthogonal textile composite under compression by theoretical analysis and two-dimensional (2D) finite element method (FEM) simulation. Jiang and Hu⁶ focused on the study of energy absorption and impact resistance of a novel multilayer orthogonal structural composite with auxetic effect. Zhang et al.⁷ investigated the dynamic thermo-mechanical and impact properties of helical auxetic yarns using a high-rate tensile impact test. Liu et al.^8,9 studied the impact behavior of a typical spacer fabric impacted at different levels of energy and investigated the effects of fabric structural parameters and lamination on the protective properties of spacer fabrics under impact. Ugbolue et al.^10,11 developed several warp-knitted structures based on helical yarn models and re-entrant polygons, and investigated their lapping movement, respectively providing wider thoughts on auxetic knitted structures. None of these researches have investigated the energy absorption of warp-knitted spacer fabrics with negative Poisson's ratio under uniaxial tension.

In this paper, uniaxial tensile tests are conducted on four kinds of warp-knitted spacer fabrics along the walewise direction and the coursewise direction, respectively. The structure of these fabrics is designed based on rotating hexagons.¹² Values of tensile loading and elongation during stretch are recorded and saved so that they can be transformed into values of stress and strain. The energy absorption of fabrics can be characterized by integrals of stress on strain and the Poisson's ratio of fabrics can also be calculated from stresses and strains, after which the energy absorption and Poisson's ratio of the spacer fabric samples are analyzed synthetically to evaluate their influential relations. The fracture process and fracture morphology of the fabric samples under stretch are also discussed in the paper. Research on energy absorption of warp-knitted spacer fabrics with negative Poisson's ratio under quasi-static tension is intended to lay a basis for their further applications in composite reinforcements with higher requirements, and also help with the structural design or technical parameter design of warp-knitted spacer fabrics with Negative Poisson's Ratio (NPR) in the future.

Experimental details

Sample preparation

The samples used for testing are spacer fabrics knitted by a Raschel warp knitting machine (Karl Mayer RD7/2-12EN, Germany) with two needle bars. Draw texturing polyesters of 22.22 tex are used for the first, the second, the sixth and the seventh guide bars. Draw texturing polyesters of 11.11 tex are used for the third and the fifth guide bars. Draw texturing polyester is a kind of textured filament yarn using polyester as the raw material, and produced by drafting after false twisting the polyester pre-oriented yarn. Polyester mono-filaments with diameter of 0.09 mm are used for the fourth guide bar as the spacer yarn. Fabric structures are designed and constructed based on the rotational hexagon model,¹³ as shown in Figure 2(a). The hexagon structures are rotated and arranged as a zigzag under the original state, while these rotational hexagons could expand both horizontally and longitudinally under tension, as shown in Figure 2(b), thus presenting an auxetic effect. Fabric samples with four different structures are manufactured, and chain notations and threading of all guide bars except GB4 are as follows

GB1: (2-3-2-2/2-1-2-2)×3/(1-0-1-1/1-2-1-1)×3//, 1 in 1 empty

Figure 2.

Rotational hexagon model: (a) under the original state; (b) under tension.

GB2: (1-0-1-1/1-2-1-1)×3/(2-3-2-2/2-1-2-2)×3//, 1 in 1 empty

GB3: 1-0-0-0/0-1-0-0/0-0-0-0/0-0-0-0/0-1-1-1/1-0-0-0/ 0-1-1-1/1-0-1-1/1-1-1-1/1-1-1-1/1-0-0-0/0-1-1-1//, full

GB5: 1-1-1-0/0-0-0-1/1-1-0-0/0-0-0-0/0-0-0-1/1-1-1-0/ 0-0-0-1/1-1-1-0/0-0-1-1/1-1-1-1/1-1-1-0/0-0-0-1//, full

GB6: (1-1-1-0/1-1-1-2)×3/(2-2-2-3/2-2-2-1)×3//, 1 in 1 empty

GB7: (2-2-2-3/2-2-2-1)×3/(1-1-1-0/1-1-1-2)×3//, 1 in 1 empty

The chain notations of GB4 with full threading are listed in Table 1 and the parameters of let-off values are listed in Table 2. The unit of rack means millimeters of yarn needed for 480 courses of the fabric. The sectional multivelocity letting-off of GB3 and GB5 in Table 2 is namely a segmentation of a 12-course unit into two courses with 860 racks, two courses with 290 racks, four courses with 860 racks, two courses with 290 racks and the last two courses with 860 racks. The pulling density is set as 11 cpc, which means 11 courses per centimeter, and the interval between the front needle bar and the back needle bar is 4 mm. Photographs of fabric samples with different structures are shown in Figure 3.

Table 1.

Changes of GB4 chain notations

Samples	Chain notations of GB4
1#	0-1-0-1/1-0-1-0//
2#	1-0-1-0/0-1-0-1//
3#	(0-1-0-1)×6/(1-0-1-0) × 6//
4#	(1-0-1-0)×6/(0-1-0-1) × 6//

Table 2.

Let-off parameters of all guide bars

Guide bar	Course number	Letting-off values/rack
GB1, GB2, GB6, GB7	12	970
GB3, GB5	2	860
	2	290
	4	860
	2	290
	2	860

Figure 3.

Photographs of fabrics with different structures: (a) Sample 1#; (b) Sample 2#; (c) Sample 3#; (d) Sample 4#.

Poisson's ratio tests

Samples with four different structures are cut into the size of 50 mm × 180 mm along the walewise direction and the coursewise direction, respectively. The testing equipment includes a HD026N + fabric strength tester (Nantong Hongda Experiment Instruments Co., Ltd, Jiangsu, China), a computer processor and a high-speed camera. Tensile tests with fixed elongation are conducted using the strength tester, during which the dimensional changes along and vertical to the stretch direction are monitored and recorded. As shown in Figure 4, the middle widths of the testing sample before and after stretch are labeled as AB and A′B′, respectively, and the middle lengths of the testing sample before and after stretch are labeled as CD and C′D′, respectively. Then the values of Poisson's ratios of all fabric samples are calculated according to the following definition

μ = - \frac{ɛ_{y}}{ɛ_{x}} = - \frac{l_{A' B'} - l_{AB}}{l_{C' D'} - l_{CD}} \cdot \frac{l_{CD}}{l_{AB}}

(1)

where μ is the Poisson's ratio, ε_y is the strain perpendicular to the stretch direction, ε_x is the strain along the stretch direction, l_AB and l_CD are the middle width and the middle length of the testing sample before stretch, respectively, and l_A′B′ and l_C′D′ are the middle width and the middle length of testing sample after stretch, respectively.

Figure 4.

Testing method of the Poisson's ratio.

The fixed elongation is set as 10 mm, the stretching velocity is set as 200 mm/min and the spacing distance between the two clamps is 100 mm. The high-speed camera starts to take pictures of fabric samples when the stretch starts and three pictures are taken per second to record the fabric appearance during the process. Nine pictures in total are taken for each sample, after which these pictures are processed, and the middle lengths of the fabric as well as the middle widths of fabric samples are measured to calculate its Poisson's ratios under stretch.

Tensile tests

According to the international standard ISO 13934.1-1999, a multi-functional electronic fabric strength testing machine (YG026D, Ningbo Textile Instrument Factory, Zhejiang, China) is used for tensile tests along with control programs and data collection by computers. Samples are also cut into the size of 50 mm × 180 mm along the walewise direction and the coursewise direction, respectively, and tensile tests are conducted with a pretension of 2 N to acquire breaking strengths, breaking elongations and pull–elongation curves during the stretch of all samples.

The approximate calculation formula of the strain rate¹⁴ is

\overset{\cdot}{ɛ} = \frac{ν}{L}

(2)

where

\overset{\cdot}{ɛ}

is the approximate strain rate, ν is the stretching velocity and L is the sample length. The spacing distance of two clamps is set as 100 mm, the stretching velocity is set as 10 mm/min and, therefore, the strain rate approximates 0.001/s. The test equipment used for the uniaxial tensile tests is shown in Figure 5.

Figure 5.

Quasi-static tensile test equipment.

Pull values and elongation lengths of the fabric samples under stretch are recorded in the tensile tests, and stress values and strain values of the fabrics under stretch are acquired according to the following formulas

σ = \frac{F}{A}

(3)

ɛ = \frac{Δ L}{L}

(4)

where σ is the stress (MPa), F is the pull force under stretch (N), A is the cross-sectional area of the fabric perpendicular to the stretch (m²), namely thickness multiplied by width of fabric sample, ε is the strain; ΔL is the elongation along the stretch direction (mm) and L is the original length, namely the spacing distance between two clamps before stretch (mm).

Results and analysis

Poisson's ratio analysis

The Poisson's ratio of fabric samples with four different structures is tested and calculated respectively along the walewise direction and along the coursewise direction. OriginPro9.1 software is used for data statistics and analysis. Relations between Poisson's ratio and uniaxial strain of all fabric samples are shown in Figure 6, in which curves with square points represent walewise tension while curves with round points represent coursewise tension.

Figure 6.

Diagrams of Poisson's ratio and uniaxial strain: (a) Structure 1#; (b) Structure 2#; (c) Structure 3#; (d) Structure 4#.

It can be seen from Figure 6 that neither Samples 1# nor 2# have negative Poisson's ratio along the walewise direction. Samples 3# and 4# are non-auxetic in the walewise direction but appear to be auxetic in the coursewise direction. In addition, the absolute value of the negative Poisson's ratio decreases with the increase in uniaxial strains. When coursewise strain starts to increase, the absolute value of the negative Poisson's ratio recedes quickly; when the strain increases to a certain value, the Poisson's ratio tends to be stable; and when the strain exceeds a critical value, the Poisson's ratio remains positive constantly.

From Figures 3 and 6, it is evident that the Poisson's ratio of a fabric sample is significantly influenced by its original structure and deformation degree after relaxation. Apparently, coursewise contractions of four samples are all remarkable, while walewise contractions vary. Walewise contractions of Samples 1# and 2# before tension are not obvious, while walewise contractions of Samples 3# and 4# are relatively more remarkable and appear to be zigzag-shaped; however, the contractions are inconspicuous and unstable. It can be seen that only when the fabrics contract both walewise and coursewise under natural state can a negative Poisson's ratio be achieved; any monodirectional deformation alone cannot bring a negative Poisson's ratio to the fabric. It can be predicted from Samples 3# and 4# that the successive homodromous yarn laying movement of the guide bar knitting miss-lapping chain stitches could lead to rotational deformation of the hexagon structure. In this experiment, the Poisson's ratio of fabrics is mainly determined by the rotating degree of the hexagon structure. As demonstrated in Figure 7, fabric (b) that apparently has a higher rotating degree predictably possesses a higher absolute value of negative Poisson's ratio comparing with fabric (a).

Figure 7.

Fabric comparison in rotating degrees of a hexagon.

Tensile property and energy absorption analysis

According to data collected from pull–elongation curves in tensile tests, stress–strain curves are obtained using OriginPro9.1 software. The integral of stress on the strain is used to characterize the energy absorption property of the fabrics. The integral formula is as follows

C = \int_{0}^{ɛ} σ d ɛ

(5)

where ε represents strain, σ represents stress and C is the value of absorbed energy (10⁵ J·m⁻³).

A representative stress–strain curve of fabric samples under walewise and coursewise tension is shown in Figure 8. Shaded areas in the figures formed by stress–strain curves and coordinate axes represent the absorbed energy of fabrics under tension. Comparative results are shown in Figure 9.

Figure 8.

A representative stress–strain curve: (a) under walewise tension; (b) under coursewise tension.

Figure 9.

Energy absorption of all samples in walewise and coursewise directions.

The following can be seen from the histogram in Figure 9.

under coursewise tension fabric 1# has the lowest energy absorption while fabric 4# has the highest, and the energy absorption of the sample increases progressively from fabric 1# to fabric 4#;

under walewise tension fabric 2# has the lowest energy absorption while fabric 4# has the highest, and there is no simple linear trend in energy absorption of the four fabrics;

the energy absorption of all fabrics under walewise tension is much higher than that under coursewise tension.

It is clearly shown in the stress–strain curves that under coursewise tension stress increases slowly at first. Stress increases drastically with increase in strain until fabrics break. Under walewise tension stress increases at a much faster speed compared to that under coursewise tension until fabrics break. The fracture strain of fabrics under coursewise tension is almost three times that under walewise tension, while the fracture stress of fabrics under walewise tension is nearly six times that under coursewise tension. The integral value, which represents the capacity of fabrics under walewise tension, is much higher than that under coursewise tension, indicating that energy absorption of fabrics under walewise tension is much higher than that under coursewise tension.

Comparison analysis of Poisson's ratio and energy absorption

Combining the Poisson's ratio and energy absorption of all fabrics, fabrics with structures 3# and 4# both have a negative Poisson's ratio under coursewise tension, with the latter having a better auxetic performance; fabrics with structures 3# and 4# have a better energy absorption ability, with the latter best of the four fabric samples under coursewise tension. It is predicted that fabrics with a negative Poisson's ratio under uniaxial tension have better energy absorption abilities along the tensile direction. Besides, higher energy absorption comes with better auxetic performance under uniaxial tension.

Due to the blurry changing tendency of energy absorption under walewise tension, we can hardly draw any conclusion about the energy absorbing abilities of fabrics with a positive Poisson's ratio from the comparison analysis. However, it is obvious that the energy absorption and fracture stress of all fabrics under walewise tension are much higher than that under coursewise tension, while walewise fracture strain is much lower than that in the coursewise direction. This phenomenal result is closely related to the original structure of fabrics before tension. Due to the remarkable contraction in the coursewise direction before tension, the structure of the rotational hexagon turns regularly under tension, and stress increases slowly with increase in strain during this process, showing an auxetic performance. The energy absorption during this process is defined as structural deformation capacity. Stress increases faster with increase in strain after the regular hexagon structure is fully recovered. In this process, the intrinsic property of yarns plays the main part in the energy absorption of fabrics, which is defined as the yarn loading capacity. It is obvious that the yarn loading capacity takes a dominant position in the overall energy absorption of fabrics under tension, which means that the structural deformation capacity does not matter as much as the yarn loading capacity in the energy absorption of fabrics. If yarns or fibers are highly oriented in a certain direction of the fabric, the fabric could absorb more energy when pulled in this direction.

Tensile damage and fracture mechanism analysis

It can be seen from the tensile fracture pictures in Figures 10 –13 that fracture sections of the fabrics under walewise and coursewise tension are all irregularly zigzag-shaped. When walewise tension is applied to the fabric, breakage starts with weak point damage and spreads across the whole range of fabric under tension, mostly along the tensile direction, until it breaks completely. When coursewise tension is applied to the fabric, breakage also starts with weak point damage and spreads across a small range near the first breakage point, mostly vertical to the tensile direction, until it completely breaks. The deformations of fabric structures under walewise and coursewise tension are shown in Figure 14 and the parts that are easily fractured are marked with red color. It can be seen from the sketches that fabric fractures tend to spread along the tensile direction, forming a fracture section with high slope under warp tension, while fabric fractures tend to spread vertical to the tensile direction, forming a fracture section with a low slope. As shown in Figure 15, the parts easily fractured are corresponding to the warp sateen structures (Part 1) in the fabric, which means that when tricot stitches (Part 2) turn into warp sateen (Part 1) in the hexagonal structure, the fabric is more easily fractured under tension.

Figure 10.

Fracture profile pictures of Sample 1#: (a) under walewise tension; (b) under coursewise tension.

Figure 11.

Fracture profile pictures of Sample 2#: (a) under walewise tension; (b) under coursewise tension.

Figure 12.

Fracture profile pictures of Sample 3#: (a) under walewise tension; (b) under coursewise tension.

Figure 13.

Fracture profile pictures of Sample 4#: (a) under walewise tension; (b) under coursewise tension.

Figure 14.

Fabric structure deformation: (a) under walewise tension; (b) under coursewise tension. (Color online only.)

Figure 15.

Diagram of warp tricot and sateen structures.

Conclusion

Poisson's ratio tests and uniaxial tensile tests are conducted on the warp-knitted spacer fabrics with four different structures designed from the rotating hexagonal model, based on which comparison analysis of the Poisson's ratio and energy absorption under uniaxial tension is carried out. Tensile damage propagation and fracture mechanism of the fabric are also analyzed, combining the fracture profiles.

Only when fabric contracts in both walewise and coursewise directions before tension can a negative Poisson's ratio be obtained, and uniaxial contraction cannot bring a negative Poisson's ratio; if the fabric is auxetic in a certain direction, its Poisson's ratio is not necessarily negative in other directions; the more obvious the walewise and coursewise contraction are originally, the better auxetic performance could be achieved.

Energy absorption of the fabric under tension is higher if it has a negative Poisson's ratio in the tensile loading direction. The overall energy absorption of the fabric under uniaxial tension is determined by the structural deformation capacity and the yarn loading capacity, with the latter playing a dominant role and the former minimal; the effect of its auxetic performance contributes to the structural deformation capacity of the fabric.

Deformed hexagonal warp-knitted spacer fabrics fracture more easily in the warp sateen structures. When the fabric is pulled in the walewise direction fracture propagates mainly along the tensile direction, while when the fabric is pulled in the coursewise direction fracture propagates mainly vertical to the tensile direction. The fracture profiles are both irregularly zigzag-shaped or slant under walewise tension and coursewise tension.

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: The authors acknowledge the financial support from the China Postdoctoral Science Foundation (2017T100325, 2016M591767), the Fundamental Research Funds for the Central Universities (JUSRP51625B), and the Applied Foundation Research Funds of China Textile Industry Association (J201604), and the Natural Science Foundation of China (11502163).

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