Impact response of transparent ceramic sandwich structures and its prediction by BP neural network
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摘要: 首先，选择以蓝宝石陶瓷为迎弹层、二氧化硅无机玻璃和聚碳酸酯有机玻璃为吸能层和聚氨酯为胶结材料的透明夹层结构为研究对象，采用一级轻气炮对试样进行了冲击实验，试样呈现陶瓷层弯曲失效破坏主导和冲击压缩破坏主导的2种破坏模式，通过高速摄像详细记录裂纹动态扩展过程。然后，采用Abaqus 有限元软件对多组结构层厚度配比的透明夹层结构进行120、150、180 m/s 速度的弹体冲击模拟，针对陶瓷材料引入了基于JH-2 本构模型的子程序，并结合单元删除法，对裂纹扩展和碎片飞溅过程进行了数值模拟。模拟结果与实验结果吻合较好。最后，采用BP 神经网络算法对冲击点后侧位移峰值进行了预测，单层和多层神经网络模型平均计算耗时分别为1和3 min，与位移峰值的数值模拟结果相比，2种神经网络模型预测结果的平均相对误差分别为7.6% 和3.2%。该BP 神经网络模型计算时效和精度都满足要求，相比传统消耗5 h的有限元计算，节省大量时间，可对透明夹层结构的设计提供指导。Abstract: Transparent sandwich structures can combine the advantages of various materials, thus avoiding secondary damage caused by brittle material fragments. Therefore, they are widely used in various impact protection fields. However, the impact resistance of the structure is influenced by different material thicknesses in a complex manner, and there is a lack of quick and convenient design guidance. Artificial neural network has good applicability to the nonlinear problems of multi-material structures, and provides a novel approach to structural design. In this study, a transparent sandwich structure consisting of sapphire (Al2O3) ceramic as the impact-absorbing layer, silica inorganic glass, polycarbonate plexiglass as the energy absorption layers, and polyurethane as the bonding material was selected as the research subject. Impact experiments were conducted on samples using a first-stage light-gas gun. Two failure modes were observed in the samples: ceramic layer bending failure and impact compression failure. The dynamic crack propagation process was meticulously captured using high-speed cameras. Subsequently, Abaqus finite element software was employed to simulate projectile impact on transparent sandwich structures with varying layers thickness ratios at 120, 150, and 180 m/s. For ceramic materials, a subroutine based on the JH-2 constitutive model was introduced. The numerical simulation of crack propagation and debris splashing process was performed using the element deletion method. The simulation results exhibited good agreement with the experimental results. Finally, the BP neural network algorithm was utilized to predict peak displacement behind the impact point. The average calculation time for single-layer and multi-layer neural network models was 1 minute and 3 minutes, respectively. Compared with the numerical simulation results of displacement peak, the average relative error of the predicted results of the two neural network models was 7.6% and 3.2%, respectively. The BP neural network model fulfills the requirement for calculation time and accuracy, saving a substantial amount of time compared to the traditional 5-hour finite element calculations. It can provide valuable guidance for the design and development of transparent sandwich structures.
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图 4 冲击过程中不同时刻试样3的高速摄像图片
Figure 4. High-speed camera images of sample 3 at different times during impact
图 5 冲击过程中不同时刻试样6的高速摄像图片
Figure 5. High-speed camera images of sample 6 at different times during impact
图 10 结构层厚度配比为6 mm/3 mm/5 mm的试样在180 m/s速度弹体冲击下的破坏与裂纹扩展
Figure 10. Damage and crack propagation in the specimen with the structure layer thickness proportioningof 6 mm/3 mm/5 mm under the 180-m/s-bullet impact
图 12 在不同冲击载荷下透明夹层结构试样测点位移-时间曲线模拟结果
Figure 12. Simulated displacement-time curves of the two transparent sanwich structure specimens with different structure layer thickness proportions under different impact loads
图 14 单层、双层神经网络预测的测点峰值位移及有限元模拟结果
Figure 14. Peak displacements at measuring points predicted by single-layer and double-layer neural networks and the corresponding results by finite element simuations
表 1 实验条件及结果
Table 1. Experimental conditions and the corresponding results
试样编号 弹体速度/(m·s−1) 弹体质量/g 厚度/mm 破坏模式 陶瓷层 无机玻璃层 有机玻璃层 1 164.79 16.7 8 6 4 弯曲失效 2 193.38 16.7 8 6 4 压缩失效 3 186.28 16.7 8 6 10 弯曲失效 4 183.84 16.7 8 8 4 压缩失效 5 183.18 16.7 6 4 10 压缩失效 6 184.22 16.7 6 3 5 压缩失效 
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表 2 模拟工况
Table 2. Simulated conditions
工况 厚度/mm 弹体速度/(m·s−1) 陶瓷 无机玻璃 有机玻璃 1 6 3 5 120, 150, 180 2 6 4 4 120, 150, 180 3 6 5 5 120, 150, 180 4 8 4 4 120, 150, 180 5 6 8 4 120, 150, 180 6 8 6 4 120, 150, 180 7 6 4 10 120, 150, 180 8 8 8 4 120, 150, 180 9 6 6 10 120, 150, 180 10 8 10 4 120, 150, 180 11 6 6 10 120, 150, 180 12 8 6 10 120, 150, 180 13 6 6 6 120, 150, 180
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表 3 陶瓷JH-2本构参数
Table 3. Constitutive parameters of ceramic JH-2
A B C M N T/GPa G/GPa E/GPa K1/GPa K2/GPa 0.889 0.29 0.0045 0.53 0.764 0.2 120.34 295 184.560 185.870 K3/GPa $ {\sigma }_{\text{HEL}} $/GPa pHEL/GPa D1 D2 β $ {\sigma }_{\mathrm{i},\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{*}} $ $ {\sigma }_{\mathrm{f},\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{*}} $ $ \rho $/(kg·m−3) 157.540 6 3.268 0.005 1.0 1.0 0.2 1.0044 3700
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表 4 材料参数
Table 4. Material parameters
材料 密度/(kg·m−3) 弹性模量/GPa 泊松比 钨钢弹体 7800 210 0.30 二氧化硅无机玻璃 2450 68 0.23 聚碳酸酯有机玻璃 1200 23 0.35
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表 5 单层、双层神经网络模型计算效率的对比
Table 5. Comparison of computational efficiencies of single-layer and double-layer neural network models
计算方式 峰值位移/mm 峰值位移平均相对误差/% 平均计算时长 有限元模拟 0.41 5 h 单层BP神经网络 0.44 7.6 1 min 双层BP神经网络 0.42 3.2 3 min
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