# Impact Testing of 3D Re-Entrant Honeycomb Polyamide Structure Using Split Hopkinson Pressure Bar
## 4 Results and Discussion
### Stress-Strain Curves  
The strain time-history curve at the position of the strain gauge of the PMMA bar was obtained from the voltage signal using the data acquisition system. The improved Lagrange analysis method [35] was used to process the strain data, and then the incident strain wave \(\epsilon_{I}(X_{1},t)\) at the interface \(X_{1}\) between the incident bar and the specimen, and the transmission strain wave \(\epsilon_{T}(X_{2},t)\) at the interface \(X_{2}\) between the transmission bar and the specimen, can be obtained. The stress and strain time-history curves of the tested specimen can be calculated by the traditional SHPB stress wave Equations (1) and (2). Figure 6 shows the stress-strain curves of each specimen at impact velocities of approximately 14, 18 and 20 m/s. Generally speaking, the stress of each specimen under impact loading includes three obvious stages, namely elastic growth, plastic growth and decline. Moreover, each specimen completes elastic growth and enters plastic growth within a very short time after loading. Among them, specimen C2 is the most impressive due to its appropriate re-entrant angle \(\theta\) and maximum density (please refer to [28]). Its peak stress is the largest in all working conditions, and the peak stress increases with the increase in impact velocity. Due to the stable structural configuration, namely the longest horizontal length of the oblique strut (\(L_{0}\)), specimen C5 exhibits obvious and long plateau stress. Because the thickness of the oblique strut cross section (\(t_{2}\)) of specimen C3 is reduced to half of that of other specimens, the plastic stress increases gently and the peak stress is relatively low. The stress of C4 was unstable at different impact velocities. The peak stress of specimen C1 is relatively low, and the peak stress increases with the increase in impact velocity. Comparing the stress-strain curves of specimens C1 to C2, it is found that when the re-entrant angle (\(\theta\)) changes from 70\({}^{\circ}\) to 60\({}^{\circ}\), it has a significant influence on the dynamic properties of the 3D RH structure under impact loading, which shows that the smaller re-entrant angle \(\theta\) lead to a larger Young's modulus (the slope at the elastic growth stage) and larger peak stress, indicating the importance of an appropriate \(\theta\) to the structure performance under impact loading. Compared with C1, C4 and C5, whose horizontal length of the oblique strut (\(L_{0}\)) are 2.6 mm, 3.1 mm and 3.6 mm, respectively, it can be found from Figure 6 that with the increase in \(L_{0}\), except for C4, which is unstable at v0 = 18 m/s, the peak stress increases and the plateau stress tends to be obvious. It is worth noting that C5 performs particularly well, although the density (please refer to [28]) of C5 is the smallest among all the specimens with different configurations; its stable structure causes it to perform well in both stress growth and energy absorption. Compared with C1, C2 and C3, whose re-entrant angle (\(\theta\)) changes from 70\({}^{\circ}\) to 60\({}^{\circ}\) and then to 50\({}^{\circ}\), and the fact that the thickness of the oblique strut cross section (\(t_{2}\)) of specimen C3 is reduced to half of that of other specimens, it shows that due to the half-reduced \(t_{2}\), the strength of specimen C3 is greatly reduced and C3 is vulnerable to shear failure, which indicates that the effect of decreasing \(t_{2}\) is greater than that of decreasing \(\theta\). Figure 5: Comparison of three transmitted waveforms. In order to compare the mechanical properties of specimens under quasi-static and different impact velocities, Figure 7 compares the stress-strain curves of representative specimens (C2, C3 and C5) under different working conditions.