Dynamic response of a metal target plate to simultaneous initiation of two charges
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摘要: 采用量纲分析的方法，分析了两装药同时爆炸加载下金属薄板动态响应过程中的相关独立变量，并使用有限元软件进行数值计算，研究了两装药同时起爆情况下装药量、装药间距及炸距对45钢靶板响应特性的影响。基于数值模拟和量纲分析的结果，分别建立了相关参量与金属靶板最大变形挠度的函数关系，获得了适用于一定范围的靶板挠度计算模型。该研究能够在一定程度上实现不同分布装药的爆炸效应快速计算。Abstract: To study the response law of a metal target plate under the simultaneous initiation of two charges and to construct a calculation model for the deformation and deflection of the target plate under the action of dual explosion source shock waves, the dynamic response of the metal plate under the action of double explosion sources was studied through dimensional analysis. Based on the numerical simulation calculation results using the finite element software, the influence of the charge quality, charge spacing, and vertical distance from the charge to the target plate of the double explosion source on the maximum deflection of the 45 steel target plate was summarized. The results show that the maximum deflection of the target plate increases linearly with the charge mass, decreases linearly with the charge spacing and decreases exponentially with the vertical distance from the charge to the target plate. The functional relationship between different parameters and the maximum deformation deflection of the target plate was fitted. This study can to some extent achieve rapid calculation of the explosion effect of charges with different distributions.
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Key words:
- simultaneous explosion /
- dimensional analysis /
- metal target plate /
- dynamic response
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图 2 两装药同时起爆冲击波传播
Figure 2. Propagation of shock waves caused by simultaneous initiation of two charges
图 3 靶板受双爆源冲击波载荷作用情况
Figure 3. Target plates subjected to the loading of shock waves from a double explosion source
图 4 金属靶板有限元模型及网格划分
Figure 4. A finite element model for the metal target plate and its grid division
图 5 靶板挠厚比与装药质量无量纲数的关系
Figure 5. Relationship of deflection-to-thickness ratio of the target plate with charge mass non-dimensional number
图 6 靶板挠厚比与炸距无量纲数的关系
Figure 6. Relationship of deflection-to-thickness ratio of the target plate with explosive distance non-dimensional number
图 7 靶板挠厚比与装药间距无量纲数的关系
Figure 7. Relationship of the deflection-to-thickness ratio of the target plate with the charge spacing non-dimensional number
图 8 靶板挠厚比与比例装药距离的关系
Figure 8. Relationship of deflection-to-thickness ratio of the target plate with proportional charge distance
图 9 靶板挠厚比与比例炸距的关系
Figure 9. Relationship of deflection-to-thickness ratio of the target plate with proportional explosive distance
图 10 靶板挠厚比与比例装药距离和比例炸距的关系
Figure 10. Relationships of deflection-to-thickness ratio of the target plate with proportional charge distance as well as proportional explosion distance
密度ρ/(g·cm−3) 杨氏模量E/GPa 泊松比υ A/MPa B/MPa N C 7.8 200 0.3 410 20 0.08 0.100 
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表 2 部分试验数据与仿真结果
Table 2. Partial test data and simulation results
序号 靶板厚度/mm TNT质量/g 炸距/cm 挠度/mm 挠度误差/% 试验 计算 1 1 700 98 79 71.132 10.0 2 1 708 80 102 91.946 9.9 3 1 1108 133 82 68.235 16.8 4 2 700 47 79 81.841 3.6
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密度ρ/(g·cm3) 杨氏模量E/GPa 泊松比υ A/MPa B/MPa N C 7.8 200 0.3 507 320 0.28 0.064
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表 4 不同药量下靶板的最大变形挠度
Table 4. The maximum deformation deflections of target plates under different charge amounts
序号 装药质量/kg 炸距/m 装药间距/m 靶板变形挠度/mm 装药1 装药2 1 1.0 1.0 2.0 1.5 9.815 2 1.5 1.5 13.561 3 2.0 2.0 17.016 4 2.5 2.5 20.36 5 3.0 3.0 23.61 6 5.0 5.0 35.852
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表 5 炸距不同时靶板的最大变形挠度
Table 5. The maximum deformation deflections of target plates with different explosive distances
序号 装药质量/kg 炸距/m 装药间距/m 靶板变形挠度/mm 装药1 装药2 1 2.0 2.0 2.0 1.5 17.020 2 2.1 15.653 3 2.2 14.349 4 2.3 13.235 5 2.4 12.268 6 2.5 11.324 7 2.6 10.522 8 2.7 9.704 9 2.8 8.972 10 2.9 8.331 11 3.0 7.869
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表 6 金属靶板的最大变形挠度计算结果
Table 6. Calculation results of the maximum deformation deflections of metal target plates
序号 装药质量/kg 炸距/m 两装药间距/cm 靶板变形挠度/mm 装药1 装药2 1 1.0 1.0 1.0 50 11.850 2 70 11.587 3 90 11.213 4 100 10.978 5 110 10.778 6 130 10.305 7 150 9.815 8 180 8.991 9 200 8.427 10 230 7.577 11 250 7.054
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表 7 不同比例装药间距下靶板的变形挠度
Table 7. Deformation deflections of target plates under different proportional charge spacings
序号 装药质量/kg 装药间距/m 炸距/m Z1 Z2 靶板变形挠度/mm 装药1 装药2 1 2.0 2.0 0.5 2.0 7.88709 31.54834 20.664 2 0.7 11.04192 20.155 3 0.9 14.19675 19.519 4 1.1 17.35159 18.767 5 1.3 20.50642 17.923 6 1.5 23.66126 17.016 7 1.7 26.81609 15.933 8 1.9 29.97093 15.074 9 2.0 31.54834 14.624
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表 8 不同比例炸距下靶板的变形挠度
Table 8. Deformation deflections of target plates at different proportional explosive distances
序号 装药质量/kg 装药间距/m 炸距/m Z1 Z2 靶板变形
挠度/mm装药1 装药2 1 2.0 2.0 1.5 2.0 23.66126 31.54834 17.02 2 2.1 33.12576 15.653 3 2.2 34.70318 14.349 4 2.3 36.28059 13.235 5 2.4 37.85801 12.268 6 2.5 39.43543 11.324 7 2.6 41.01285 10.522 8 2.7 42.59026 9.704 9 2.8 44.16768 8.972 10 2.9 45.16768 8.331 11 3.0 47.32251 7.869
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表 9 数值模拟结果与模型计算结果的对比
Table 9. Comparison of numerical simulation results with model calculation results
序号 TNT质量/kg 装药间距/m 炸距/m Z1 Z2 靶板挠度/mm 误差/% 装药1 装药2 仿真计算 模型计算 1 2.0 2.0 1.0 2.5 15.74061 39.35152 12.396 11.717 5.5 2 3.0 3.0 1.5 2.8 20.62603 38.50193 12.724 11.485 9.7 3 4.0 4.0 2.0 3.0 24.98666 37.47999 12.967 11.592 10.6 5 5.0 5.0 2.5 3.3 28.99445 38.27267 11.928 10.713 10.2 6 6.0 6.0 3.0 3.5 32.74179 38.19875 11.352 10.446 8.0
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