# Impact Testing of 3D Re-Entrant Honeycomb Polyamide Structure Using Split Hopkinson Pressure Bar

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{3}at the impact velocity of 22 m/s and was 5.1 times that in the quasi-static test. Specimen C5 had the longest horizontal length of the diagonal bar ${L}_{0}$, and its energy absorption was 1.222 J/cm

^{3}at the impact velocity of 22 m/s and was 15.7 times that in the quasi-static test, reflecting the superiority of a structurally stable specimen in energy absorption under impact loading. The test results can provide a reference for the optimization of the design of the same or similar structures.

## 1. Introduction

## 2. Related Theories on the SHPB Test

## 3. Materials and Methods

#### 3.1. Specimen and Material

_{0}. C3 was designed to investigate the effects of both t

_{2}and θ.

#### 3.2. SHPB Setup

#### 3.3. SHPB Tests

## 4. Results and Discussion

#### 4.1. Waveform Analysis

_{1,}X

_{2}and X

_{3}on the incident bar. Three transmitted waveforms can be measured from the strain gauges X

_{4,}X

_{5}and X

_{6}on the transmission bar. It can be found that the trend, the pulse width and the amplitude of these waveforms all follow similar rules and have good consistency, which can reflect the wave propagation process in the viscoelastic PMMA bar and the energy absorption characteristics of specimens.

_{1,}X

_{2}and X

_{3}in turn. It can be seen from Figure 4 that the incident wave gradually attenuates in the PMMA bar, i.e., the wave amplitude tends to decrease along the direction of wave propagation. It also can be seen that the wave attenuation is not proportional to the propagation distance. In addition, at the end of the incident pulse, the compression wave does not immediately unload to 0, but presents a “creep” characteristic with time growth, that is, so-called compression strain delay, as shown from ellipse A in Figure 4. It can be interpreted that the viscosity of the PMMA bar is the reason for the “creep” phenomenon without the influence of other external factors. Subsequently, the specimen deforms at high speed under the action of the incident wave, and propagates the reflected stretch wave to the incident bar and the transmitted compression wave to the transmission bar simultaneously.

_{3,}X

_{2}and X

_{1}in turn. As can be seen from the partial enlarged subgraph, namely rectangle box C, when the reflected wave reaches the strain gauge for the first time, the compression “creep” caused by the incident wave is still incomplete, resulting in the superposition of the head of the reflected wave and the tail of the incident wave. From the time period between the arrival of the incident wave and the arrival of reflected wave, it can be found that it spends the longest time when the reflected wave reaches the position of strain gauge X

_{1}. At this time, the compression deformation caused by the incident wave has basically completed; that is, the “creep” effect is minimal. However, the “creep” at the position of strain gauge X

_{3}is maximal, and the deformation hysteresis is not completed before it enters the stretch wave. After one pulse width, the tail of the reflected wave passes through the strain gauge. It can be observed from the B ellipse in Figure 4 that the reflected wave does not immediately unload to 0, but directly changes from the stretch wave to the compression wave. This phenomenon indicates that the incident bar is under pressure after the tail of the first reflected wave. It can be interpreted that the high-speed deformation of the specimen causes it to compress and absorb a lot of impact energy, including elastic and plastic potential energy. Then, the elastic potential energy is released and acts on the incident bar to place it in a compression state.

_{4,}X

_{5}and X

_{6}in turn. As these three strain gauges are spaced 20 cm apart, it was shown in Figure 4 that the transmitted wave spacing was about twice that of the incident wave or the reflected wave. In order to more clearly express the transmitted wave, the transmitted waveforms are taken out for analysis separately, as shown in Figure 5. It can be seen the three transmitted waveforms all have the super-long pulse width which is much longer than the loading pulse width, that is, the so-called extended pulse width. The extended part is shown in the rectangle box D in Figure 5, with a total pulse width of about 1.4 ms. The reasons for the occurrence of the super-long pulse width are as follows: on the one hand, the compression delay phenomenon appears in the rising process of the transmitted pulse, because after the incident wave is transmitted to the specimen interface, it passes through the specimen with relatively small impedance, and its propagation velocity slows down, leading to the increase in the pulse width of transmitted wave when it is transmitted to the transmission bar. On the other hand, when the specimen conducts the transmitted wave, it releases the absorbed elastic potential energy to the transmission bar, which causes the secondary compression of the transmission bar, resulting in the extension of the pulse width and compression “creep”. After that, the transmitted wave reaches the end of the transmission bar and the sparse wave is reflected back, which passes through the strain gauges X

_{6,}X

_{5}and X

_{4}in turn. As shown from the partial enlarged subgraph, namely rectangle box E, when the reflected sparse wave reaches the position of strain gauges for the first time, the compression “creep” caused by the transmitted wave is not completed, resulting in the superposition of the head of the sparse wave and the tail of the transmitted wave. It also can be seen that the transmitted wave does not immediately unload to 0, but directly changes from the compression wave to the stretch wave. From the time period between the arrival of transmitted wave and the arrival of the sparse wave, it can be found that the pulse width at X

_{4}is the largest and the pulse width at X

_{6}is the smallest.

#### 4.2. Stress–Strain Curves

#### 4.3. Energy Absorption

^{3}at the impact velocity of 22 m/s and is 5.1 times that in the quasi-static test. Specimen C5 has the lowest density, and its energy absorption capacity is the lowest in the quasi-static test; however, it has the second highest energy absorption capacity in the impact test, of 1.222 J/cm

^{3}at the impact velocity of 22 m/s, indicating the advantages of a stable structure in energy absorption under impact loading.

#### 4.4. Failure Mode

## 5. Conclusions

^{3}at the impact velocity of 22 m/s and was 5.1 times that in the quasi-static test. The energy absorption of C5 was 1.222 J/cm

^{3}at the impact velocity of 22 m/s and was 15.7 times that in the quasi-static test. C3 displayed the lowest flow stress and the weakest energy absorption capacity due to the half-reduced thickness of the oblique strut cross section (${t}_{2}$), which was 0.537 J/cm

^{3}at the impact velocity of 22 m/s and was 5.8 times that in the quasi-static test. It was found that the structural geometric parameters had a great effect on the peak yield stress, flow stress and energy absorption capacity of the impact specimen. In general, a smaller re-entrant angle (θ) can improve the yield stress, peak stress and energy absorption ability, such as C2. A longer horizontal length of the oblique strut (${L}_{0}$) is helpful to improve the peak stress and energy absorption capacity, such as C5. However, the obvious weakening of structural elements is detrimental to the strength and energy absorption capacity, such as C3. The test results can provide a reference for the structural optimization design of similar 3D auxetic structures under medium impact velocity. The trial specimens are limited and more works are required in the future to provide more accurate design predictions.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 6.**Stress–strain curves of the specimens under different working conditions. (

**a**) v0 = 14 m/s, (

**b**) v0 = 18 m/s, (

**c**) v0 = 22 m/s.

**Figure 7.**Comparison of stress–strain curves of specimens under different working conditions. (

**a**) C2, (

**b**) C3, (

**c**) C5.

**Figure 8.**Energy absorption curves of different specimens at different impact velocities. (

**a**) v0 = 14 m/s, (

**b**) v0 = 18 m/s, (

**c**) v0 = 22 m/s.

**Figure 9.**Comparison of the energy absorption of specimens under different impact velocities and quasi-static tests. (

**a**) C2, (

**b**) C3, (

**c**) C5.

**Figure 10.**Failure patterns of specimens. (

**a**) Impacted surface of impact specimen. (

**b**) Side surface of impact specimen. (

**c**) Compressed surface of quasi-static specimen. (

**d**) Side of quasi-static specimen.

**Table 1.**Material properties of polyamide [27].

Material | Young’s Modulus E (MPa) | Tensile Strength σ_{B} (MPa) | Elongation ε_{B} (%) | Density (g/cm^{3}) |
---|---|---|---|---|

PA 2200 | 1500~1650 | 48 | 18 | 0.93 |

Specimen | ${\mathit{t}}_{1}$$\left(mm\right)$ | ${\mathit{t}}_{2}$$\left(mm\right)$ | $\mathit{\theta}$ (°) | ${\mathit{L}}_{0}$$\left(mm\right)$ | ${\mathit{H}}_{0}$$\left(mm\right)$ | ${\mathit{L}}_{\mathit{x}}$$\left(mm\right)$ | ${\mathit{L}}_{\mathit{z}}$$\left(mm\right)$ | ${\mathit{N}}_{\mathit{x}},$${\mathit{N}}_{\mathit{y}}$ | ${\mathit{N}}_{\mathit{z}}$ |
---|---|---|---|---|---|---|---|---|---|

C1 | 1.2 | 1.0 | 70 | 2.6 | 5.4 | 6.4 | 7.22 | 7 | 3 |

C2 | 1.2 | 1.0 | 60 | 2.6 | 5.4 | 6.4 | 6.18 | 7 | 3 |

C3 | 1.2 | 0.5 | 50 | 2.6 | 6.0 | 6.4 | 7.34 | 7 | 3 |

C4 | 1.2 | 1.0 | 70 | 3.1 | 5.4 | 7.4 | 6.85 | 6 | 3 |

C5 | 1.2 | 1.0 | 70 | 3.6 | 5.4 | 8.4 | 6.49 | 5 | 3 |

**Table 3.**Comparison of the energy absorption (J/cm

^{3}) of the specimens under SHPB tests and quasi-static compression tests.

V | C1 | C2 | C3 | C4 | C5 |
---|---|---|---|---|---|

quasi-static | 0.109 | 0.333 | 0.092 | 0.145 | 0.078 |

14 m/s | 0.333/3.1 | 0.934/2.8 | 0.278/3.0 | 0.585/4.0 | 0.834/10.7 |

18 m/s | 0.509/4.7 | 1.389/4.2 | 0.438/4.8 | 0.378/2.6 | 0.773/9.9 |

22 m/s | 0.664/6.1 | 1.701/5.1 | 0.537/5.8 | 0.733/5.1 | 1.222/15.7 |

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**MDPI and ACS Style**

Chen, J.; Tao, W.; Pang, S.
Impact Testing of 3D Re-Entrant Honeycomb Polyamide Structure Using Split Hopkinson Pressure Bar. *Appl. Sci.* **2021**, *11*, 9882.
https://doi.org/10.3390/app11219882

**AMA Style**

Chen J, Tao W, Pang S.
Impact Testing of 3D Re-Entrant Honeycomb Polyamide Structure Using Split Hopkinson Pressure Bar. *Applied Sciences*. 2021; 11(21):9882.
https://doi.org/10.3390/app11219882

**Chicago/Turabian Style**

Chen, Jiangping, Weijun Tao, and Shumeng Pang.
2021. "Impact Testing of 3D Re-Entrant Honeycomb Polyamide Structure Using Split Hopkinson Pressure Bar" *Applied Sciences* 11, no. 21: 9882.
https://doi.org/10.3390/app11219882