Poisson’s ratio of 3D printed auxetic re-entrant pattern and its two-types of composite fabrics by tilting angles
Poisson's ratio is the ratio of lateral strain and axial strain that shrinks or expands when a load is applied in the tensile direction of the material, and the auxetic structure has a negative Poisson's ratio (Kolken & Zadpoor, 2017; Lakes, 2017). In this study, to apply the re-entrant structure to the shoe uppers according to the previous study (Kim et al., 2020), we measured the Poisson's ratio by two tilting angles of the 3D printed auxetic re-entrant pattern and the 3D printed auxetic re-entrant pattern/aramid knit composite fabric to confirm that they are auxetic structures. The Poisson's ratio values for each tilting angle when tensioned to increase the strain from 0 to 30% are shown in Fig. 2.
The 3DP-RE-n in Fig. 2a showed negative values at all tilting angles and was identified as an auxetic structure. The Poisson's ratio by tilting angles was measured as − 0.18 ~ 0.00, − 0.65–− 0.09, − 0.47–− 0.14, − 1.06–− 0.28, and − 0.17–0.00; were in the order of 3DP-RE-90 > 3DP-RE-0 > 3DP-RE-30 > 3DP-RE-45 > 3DP-RE-60. 3DP-RE-0 and 3DP-RE-90 values were close to 0 because the units of the re-entrant structure were oriented parallel or vertically in the tensile direction, resulting in greater strain in the tensile direction. In addition, 3DP-RE-60 is considered to have appeared a lot of shear deformation because the units of the re-entrant structure were most inclined in the tensile direction.
3DP-RE-n/ARNT-0 in Fig. 2b also showed a negative values at all tilting angles. The Poisson's ratio by tilting angles is measured as − 0.12–0.00, − 0.89–0.00, − 0.96–0.00, − 2.09− 0.00; appeared larger in the order of 3DP-RE-0/ARNT-0 > 3DP-RE-90/ARNT-0 > 3DP-RE-30/ARNT-0 > 3DP-RE-45/ARNT-0 > 3DP-RE-60/ARNT-0. Similar to the 3DP-RE-n, it was measured closer to 0 at 0° and 90° rather than the bias directions of 30°, 45° and 60°, and the strain of 3DP-RE-60/ARNT-0 was the greatest under the influence of the 3D printed auxetic re-entrant pattern.
The Poisson's ratio by tilting angles of 3DP-RE-n/ARNT-n in Fig. 2c was measured as − 0.03–0.05, − 0.37–0.00, − 0.86–− 0.36, − 1.03–0.00, and 0.00–0.19; appeared larger in the order of 3DP-RE-90/ARNT-90 > 3DP-RE-0/ARNT-0 > 3DP-RE-30/ARNT-30 > 3DP-RE-45/ARNT-45 > 3DP-RE-60/ARNT-60. The 3DP-RE-30/ARNT-30, 3DP-RE-45/ARNT-45, and 3DP-RE-60/ARNT-60 in the bias direction were all identified as having negative Poisson's ratios, and were confirmed to be auxetic structures, however, 3DP-RE-0/ARNT-0 showed a positive Poisson's ratio from a strain of 25.5%.
In addition, the Poisson's ratio of 3DP-RE-n/ARNT-n is more stable than that of 3DP-RE-n/ARNT-0. It is considered to have been easier to tensile because the tilting angle of the 3D printed auxetic re-entrant pattern and aramid fabric were applied equally, and the 3D printed re-entrant pattern had a greater effect than the aramid fabric.
Bending property of aramid knit, 3D printed auxetic re-entrant pattern and its two-types of composite fabrics by tilting angles
The bending test has recently been used to analyze mechanical properties when 3D printed materials are given a constant load (Li & Wang et al., 2017). This present study investigated the bending properties by pattern tilting angle of the aramid knit, the 3D printed auxetic re-entrant pattern by tilting angle developed in the previous study, and the two types of composite fabrics laminated with the aramid knit. Figure 3 shows a graph of bending strength and strain.
Figure 3a shows a graph of bending strength by sample, and compares by dividing the thickness by sample. First of all, the bending strength values by sample were 0.19–0.21 MPa for ARNT-n, 0.05–0.11 MPa for 3DP-RE-n, 0.09–0.18 MPa for 3DP-RE-n/ARNT-0, and 0.04–0.11 MPa for 3DP-RE-n/ARNT-n; appeared larger in the order of ARNT-n > 3DP-RE-n > 3DP-RE-n/ARNT-n > 3DP-RE-n/ARNT-0 as a result. It was also confirmed that the ARNT-n was about three times higher than the values of 3DP-RE-n/ARNT-0 and 3DP-RE-n/ARNT-n.
For the tilting angle of each sample, ARNT-n, which appeared similar to about 0.20 MPa, was found to have no difference in bending properties by tilting angle, while 3DP-RE-n and 3DP-RE-n/ARNT-n showed a tendency for increase bending strength to increase as tilting angle increases. This is confirmed that the molten filament stacking direction according to the nozzle movement direction and the aramid knit fabric influenced the bending strength of each sample tilting angle when printing a 3D printed auxetic re-entrant pattern. And for the sample with an tilting angle of 0°, the strength was found to be significant in the experiment because the direction applied to the load and the direction in which the filaments were stacked during the experiment were positioned perpendicular to each other, causing the most impact on the load (Somiredy & Czekanski, 2020; Yao et al, 2020). In addition, as in the previous study, 3DP-RE-n/ARNT-n appeared similarly to the 3D printed auxetic re-entrant pattern; it was more affected by the 3D printed auxetic re-entrant pattern rather than the aramid knit fabric. On the other hand, it was found that the bending strength of 3DP-RE-n/ARNT-0 decreases as the tilting angle increases. In the case of 3DP-RE-90/ARNT-0, the direction in which the load is applied is the same as the stacking direction of the 3D printed auxetic re-entrant pattern and the MD direction of the knit, so that the strength seems to decrease because it is less affected by the load.
Figure 3b is a graph of strain at the maximum bending strength for each sample. ARNT-n was measured to be 1.21–1.74%, 3DP-RE-n was 3.55–5.09%, 3DP-RE-n/ARNT-0 was 4.86–7.26%, and 3DP-RE-n/ARNT-n was 7.26–9.04%; appeared larger in the order of 3DP-RE-n/ARNT-n > 3DP-RE-n/ARNT-0 > 3DP-RE-n > ARNT-n as a result. When manufactured as a 3D printed auxetic re-entrant/aramid knit composite fabric, it was found to be more than four times larger than the existing aramid knit, and it was found that bending properties during the manufacture of the composite fabric.
For each tilting angle, ARNT-n had the greatest strain at 45°; it is considered to be the largest because the fabric direction was the bias direction. On the other hand, 3DP-RE-n and 3DP-RE-n/ARNT-n showed the smallest strain at 45°. This composite fabric, similar to the tendency of bending strength, was found to be more affected by the 3D printed auxetic re-entrant pattern than the effect of aramid knit. On the other hand, 3DP-RE-n/ARNT-0 showed the smallest strain at 90°. In the same way as the bending strength, it is confirmed that the elongation appeared to be small because the stacking direction of the 3D printed auxetic re-entrant pattern, the MD direction of the aramid knit and the applied loading direction are the same. Therefore, when manufacturing composite fabrics, the bending strength and bending strain of 3DP-RE-n/ARNT-n, which are bonded with the same tilting angle of the aramid knit and the 3D printed auxetic re-entrant pattern, were improved.
Compression property of aramid knit, 3D printed auxetic re-entrant pattern and its two-types of composite fabrics by tilting angles
The compressive properties by tilting angle of aramid knit, 3D printed auxetic re-entrant pattern, and 2 types of 3D printed auxetic re-entrant/aramid knit composite fabric are shown in Figs. 4 and 5. Figure 4 is the compressive strength-strain curve graph, and Fig. 5 is a graph summarizing the compressive properties.
For the compressive strength-strain curve, the compression behavior appeared similar regardless of the pattern tilting angle. ARNT-n showed almost no change in compressive strength up to 50% of the compressive strain, and at 50%, compressive strength showed about 0.02 MPa, then gradually increased at 80%. However, at 100%, the compressive strain was found to be about 0.13 MPa, and it can be seen as not significantly affected by compression due to the thin fabric thickness. On the other hand, the compression strength of the 3D printed auxetic re-entrant pattern and the composite fabric increased gradually to about 20% and then rapidly increased to about 0.33 MPa after 20%, and the compressive strains at 50% were about 0.33, 0.33, and 0.40 MPa, respectively, indicating that the compressive strength was improved by more than 17 times compared to ARNT-n.
Toughness when compressed is about 1.54 J for ARNT-n, about 1.55 J for 3DP-RE-n, about 2.05 J for 3DP-RE-n/ARNT-0, and about 2.06 J for 3DP-RE-n/ARNT-n; appeared larger in the order of 3DP-RE-n/ARNT-n > 3DP-RE-n/ARNT-0 > 3DP-RE-n > ARNT-n as a result. Accordingly, as the compressive strength and toughness were improved in the manufacture of the composite fabric, it was confirmed that the compression performance was improved because it was able to withstand the load more during compression as the 3D printed auxetic re-entrant pattern printed as the elastomer and the swelling properties that can be represented by the structural features of the aramid knit were laminated. Therefore, it is considered that the energy absorption properties of the 3D printed auxetic re-entrant pattern/aramid knit composite fabric representing excellent compressive properties will be improved than that of the substrate fabric.
Tensile property of aramid knit, 3D printed auxetic re-entrant pattern and its two-types of composite fabrics by tilting angles
This study have identified the tensile properties of the aramid knit, the 3D printed auxetic re-entrant pattern, and the 2 types of 3D printed auxetic re-entrant/aramid knit composite fabric by tilting angles. Figure 6 shows the stress–strain curve for each sample, Fig. 7 shows the initial modulus and toughness, and Table 4 compares and analyzes the max stress, breaking stress, strain at max and breaking stress in the table.
The stress–strain curve for each sample shown in Fig. 6 shows that the aramid knit was fractured at high stress and low strain in the case of ARNT-n, whereas the 3DP-RE-n was fractured at low stress and high strain. The tilting angles of the initial modulus region of ARNT-n appeared steeper, and 3DP-RE-n was confirmed to be a more flexible material showing elastic behavior in the initial stage. 3DP-RE-n showed better tensile properties than aramid knit when printed as TPU materials with excellent elasticity. In addition, the composite fabrics 3DP-RE-n/ARNT-0 and 3DP-RE-n/ARNT-n were fractured at a high elongation similar to 3DP-RE-n, and the tilting angles of the initial modulus region was gradual. On the other hand, in the case of the tensile behavior, it can be seen that the aramid knit was first fractured, and then the 3D printed auxetic re-entrant pattern was fractured during applied loading. In addition, since 3DP-RE-n/ARNT-0 has the same tilting angles of aramid knit, it was found that until the aramid knit fracture, it had a similar tendency to ARNT-0, ARNT-30 and ARNT-45, however, after it was fractured, it was found to be affected by the 3D printed auxetic re-entrant pattern. On the other hand, 3DP-RE-n/ARNT-n show the similar tendency at 0° and 30° as ARNT-0 and ARNT-30 same as 3DP-RE-n/ARNT-0 until the aramid knit was fractured, however, 3DP-RE-45/ARNT-45, 3DP-RE-60/ARNT-60 and 3DP-RE-90/ARNT-90 were found to be more affected by 3D printed auxetic re-entrant pattern. It is considered that this is because the tilting angles of the aramid knit and the 3D printed auxetic re-entrant pattern increases in the same way.
Based on the S–S curve analyzed earlier, the stress and strain are shown in Table 4. First, the max stress appeared in the order of ARNT-n > 3DP-RE-n/ARNT-0 > 3DP-RE-n/ARNT-n > 3DP-RE-n, and the aramid knit was found to be the strongest material as a result. In addition, as confirmed in the stress–strain curve, the max stress of 3DP-RE-n/ARNT-0 is considered to be large under the influence of aramid knit, and 3DP-RE-n/ARNT-n is considered small under the influence of the 3D printed auxetic re-entrant pattern. In the case of ARNT, as the thread fell out after the fabric was partially fractured, the breaking stress appeared to be more than 50% smaller than the max stress, and 3DP-RE-n appeared similar to the max stress, after the specimen was completely fractured at the end during tensioning under the influence of TPU. In the case of 3DP-RE-n/ARNT-0 and 3DP-RE-n/ARNT-n, only the 3D printing auxetic re-entrant pattern was fractured during tensioning after the aramid knit was broken first, and the fracture strength was found to be 33% less than the max stress at the tilting angles excluding the tilt of 90°.
Next, the strain at the max stress was small in the order of 3DP-RE-n > ARNT-n > 3DP-RE-n/ARNT-n > 3DP-RE-n/ARNT-0. And the strain at breaking stress was small in the order of 3DP-RE-n/ARNT-0 > 3DP-RE-n/ARNT-n > 3DP-RE-n > ARNT-n. ARNT-n and 3DP-RE-n were similar to the strain at max and breaking stress with the same tendency as the stress. The elongation at the max stress and the strain at breaking stress of the composite fabrics 3DP-RE-n/ARNT-0 and 3DP-RE-n/ARNT-n were found to be affected by the aramid knit fabric that was fractured first, after then it was shown that affected by the 3D printed auxetic re-entrant pattern.
When comparing stress and strain by tilting angle, the strength of ARNT-0 and ARNT-90 at ARNT-n was first measured greater than ARNT-30, ARNT-45 and ARNT-60. 3DP-RE-n, 3DP-RE-n/ARNT-0, and 3DP-RE-n/ARNT-n were all measured highest at 90°. This tends to be the same as in the previous study (Kim et al., 2020) because the stacking and tensile directions of the 3D printed auxetic re-entrant pattern are greatly affected by the load in the opposite direction. Next, the strain of ARNT-n was measured the highest at ARNT-90. 3DP-RE-n increased in the order of 3DP-RE-45 < 3DP-RE-30 < 3DP-RE-60 < 3DP-RE-0 < 3DP-RE-90. It was confirmed that the samples in the tilting angles of 0º and 90º with the same tendency as the stress have the superior stress and strain that the samples in the bias direction. The stress and strain of the composite fabrics 3DP-RE-n/ARNT-0 and 3DP-RE-n/ARNT-n were also confirmed to be excellent in the direction of tilting angles of 0˚ and 90˚.
As the initial modulus can be seen in the stress–strain curve of Fig. 7a, 3DP-RE-n, 3DP-RE-n/ARNT-0, 3DP-RE-n/ARNT-n have been found to be more flexible than ARNT-n due to the influence of the 3D printed auxetic re-entrant pattern, and the initial modulus tended to increase as the tilting angle increased. All samples also showed the best at an tilting angle of 90°. The toughness shown in Fig. 7b was greater in the order of 3DP-RE-n/ARNT-0 > 3DP-RE-n/ARNT-n > 3DP-RE-n > ARNT-n. The toughness by tilting angle of ARNT-n showed no significant difference. On the other hand, 3DP-RE-n, 3DP-RE-n/ARNT-0, and 3DP-RE-n/ARNT-n were the best at an tilting angle of 90°. Therefore, when manufactured as a composite fabric, the durability of these fabrics was confirmed to have been improved because their toughness was increased as compared with the existing aramid knit and the 3D printed auxetic re-entrant pattern.