Numerical Simulation of Damage Characteristics of Multi-Layer Protective Structure under Hypervelocity Impact of Kinetic Energy Block
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摘要: 基于有限元-光滑粒子流体动力学（FEM-SPH）自适应算法，采用有限元软件LS-DYNA对动能块超高速碰撞多层防护结构的毁伤特性进行了数值模拟，并结合量纲分析方法，分析了动能块的质量和撞击速度对多层防护结构穿孔特性的影响。结果表明：保持其他参数不变，在所研究的质量和撞击速度范围内，所有的动能块均可以穿透全部17层铝合金板，并在靶后形成碎片云，在撞击过程中动能块和铝合金板内部出现层裂现象；第1层铝合金板的穿孔直径随着动能块质量的增大近似呈幂函数增大，拟合误差在5%以内；第2层铝合金板的穿孔直径随着撞击速度的提升也呈幂函数增大，拟合误差在10%以内；碎片云的头部速度随着撞击速度的提升近似呈线性增大。研究结果可为后期分析靶后碎片云的质量与速度分布、建立冲击载荷模型奠定基础。Abstract: Based on finite element method-smoothed particle hydrodynamics (FEM-SPH) adaptive algorithm of finite element software LS-DYNA, the damage characteristics of a multi-layer protective structure caused by the hypervelocity impact of a kinetic energy block are numerically simulated. Combined with the dimensional analysis method, the effects of the mass and the impact velocity of the kinetic energy block on the perforation characteristics of the multi-layer protective structure are analyzed. The results show that when other parameters remain unchanged and within the range of mass and impact velocity studied in this paper, all kinetic energy blocks can penetrate 17 layers of aluminum alloy plates and form debris clouds behind the target. During the impact process, spallation occurs in the kinetic energy blocks and the aluminum alloy plates. The perforation diameter of the first layer of the aluminum alloy plate increases approximately as a power function with the increase of the mass of the kinetic energy block, and the fitting error is within 5%. The perforation diameter of the second layer of the aluminum alloy plate also increases approximately as another power function with the increase of impact velocity, and the fitting error is less than 10%. The head velocity of the debris cloud increases linearly with the increase of impact velocity. The research results can lay a foundation for analyzing mass and velocity distribution of debris cloud behind target and establishing impact load model.
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图 4 工况A1～A7的数值模拟结果
Figure 4. Numerical simulation results of different conditions (Case A1–A7)
图 5 动能块和铝合金板内部的冲击波传播（剖视图）
Figure 5. Propagation of shock wave in kinetic energy block and aluminum alloy plate (sectional view)
图 6 各层铝合金板的穿孔直径统计（工况A1～A7）
Figure 6. Statistics of perforation diameter of each layer of aluminum alloy plate (Case A1–A7)
图 7 工况B1～B5的数值模拟结果
Figure 7. Numerical simulation results of different conditions (Case B1−B5)
图 8 碎片云头部速度随动能块速度的变化曲线
Figure 8. Variation of debris cloud head velocity with impact velocity
图 9 各层铝合金板的穿孔直径统计（工况B1～B5）
Figure 9. Statistics of perforation diameter of each layer of aluminum alloy plate (Case B1−B5)
Material $\, \rho $/(g·cm–3) $ \,\mu $ E/GPa G/GPa A/GPa B/GPa n Tungsten alloy 17.000 0.28 409.6 160.0 1.506 0.177 0.12 Al2024-T351 2.785 0.33 73.4 27.6 0.265 0.426 0.34 Material C m Tm/K Tr/K D1 D2 D3 Tungsten alloy 0.016 1.0 1723 300 1.5 0 0 Al2024-T351 0.015 1.0 775 300 1.0 0 0 Material D4 D5 c/(km·s−1) S1 ${\gamma }{_{0}}$ a ${\sigma }{_{\mathrm{p} }}$/GPa Tungsten alloy 0 0 4.029 1.237 1.54 0.134 3.5 Al2024-T351 0 0 5.328 1.338 2.00 0.875 2.6 
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表 2 15.9 μs时的数值模拟结果与实验数据[24]的比较
Table 2. Comparison between numerical simulation and experimental result[24] at 15.9 μs
Method dh/cm va/(m·s−1) vr/(m·s−1) Ld/cm dd/cm Simulation 2.00 5320 1860 8.16 6.57 Experiment 1.89 5296 1913 8.11 6.56 Error/% 5.82 0.45 2.77 0.62 0.15
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表 3 数值模拟工况
Table 3. Conditions of numerical simulation
Group No. mp/g dp/mm vp/(km·s−1) Group No. mp/g dp/mm vp/(km·s−1) A 1 5 8.16 3 B 1 5 8.16 3 2 45 16.96 3 2 5 8.16 4 3 85 20.98 3 3 5 8.16 5 4 125 23.84 3 4 5 8.16 6 5 165 26.16 3 5 5 8.16 7 6 205 28.12 3 7 250 30.04 3
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表 4 第1层铝合金板的穿孔直径
Table 4. Perforation diameter of the first layer of aluminum alloy plate
Case ${d}{_{\mathrm{p} } }$/mm ${d}{_{\mathrm{h},\mathrm{m}\mathrm{a}\mathrm{x} }}$/mm ${d}{_{\mathrm{h},\mathrm{m}\mathrm{i}\mathrm{n} } }$/mm ${d}{_{\mathrm{h} } }$/mm ${d}{_{\mathrm{h} } }/{d}{_{\mathrm{p} } }$ A1 8.16 22.72 22.68 22.70 2.7819 A2 16.96 39.08 39.00 39.04 2.3019 A3 20.98 47.12 45.98 46.55 2.2188 A4 23.84 51.34 50.96 51.15 2.1456 A5 26.16 56.80 56.72 56.76 2.1697 A6 28.12 58.50 57.74 58.12 2.0669 A7 30.04 62.08 59.62 60.85 2.0256
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表 5 第1层铝合金穿孔直径的计算数据与数值模拟结果的对比
Table 5. Comparison between calculation and simulation of perforation diameter of the first layer of aluminum alloy plate
mp/g ${d} {_{\mathrm{h} } }/{d}{_{\mathrm{p} } }$ Error/% Calc. Sim. 25 2.4437 2.4835 −1.60 65 2.2683 2.2320 1.63 105 2.1854 2.0982 4.16 145 2.1312 2.0571 3.60 185 2.0912 2.1155 −1.15 225 2.0594 2.0255 1.67
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表 6 第2层铝合金板的穿孔直径（
${d}_{\mathrm{p}}$ =8.16 mm）Table 6. Perforation diameter of the second layer of aluminum alloy plate (
${d}_{\mathrm{p}}$ =8.16 mm)Case ${v}{_{\mathrm{p} } }$/(km·s−1) ${d}{_{\mathrm{h},\mathrm{m}\mathrm{a}\mathrm{x} } }$/mm ${d}{_{\mathrm{h},\mathrm{m}\mathrm{i}\mathrm{n} } }$/mm ${d}{_{\mathrm{h} } }$/mm ${d}{_{\mathrm{h} }}/{d}{_{\mathrm{p} } }$ B1 3 36.50 36.48 36.49 4.4718 B2 4 46.08 45.94 46.01 5.6385 B3 5 54.86 52.84 53.85 6.5993 B4 6 61.16 57.84 59.50 7.2917 B5 7 65.94 61.54 63.74 7.8113
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表 7 第2层铝合金板穿孔直径的计算结果与数值模拟结果的对比
Table 7. Comparison between calculation and simulation of perforation diameter of the second layer of aluminum alloy plate
${v}{_{\mathrm{p} } }$/(km·s−1) ${d}{_{\mathrm{h} }}/{d}{_{\mathrm{p} }}$ Error/% Calc. Sim. 3.5 5.0670 4.7426 6.84 4.5 5.9888 6.0515 −1.04 5.5 6.8405 6.4877 5.44 6.5 7.6414 7.3627 3.79
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