Numerical simulation on ground shock waves induced by hypervelocity penetration of a projectile into a limestone target
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摘要: 为探究超高速动能武器的对地破坏效应及其影响因素，采用数值模拟方法对弹体超高速侵彻的地冲击规律进行了研究。首先，基于石灰岩静动态力学性能实验数据对材料模型参数进行了标定，并对已有弹体大范围着速侵彻石灰岩靶体进行了模拟，验证了所采用材料模型和数值模拟方法的合理性。随后，开展了钨合金长杆弹超高速侵彻石灰岩靶体的数值模拟，细致分析了地冲击传播的现象和机理：弹体超高速侵彻靶体时，弹靶交界面处会产生瞬时高压，并以应力波的形式在靶体中传播，对靶体内部造成破坏，且当弹体初速度高于3.0 km/s时，地冲击显著增强。最后，进一步研究了不同弹靶参数对地冲击的影响，发现从相对深度来看，弹体参数（弹体长径比、密度）对地冲击规律影响不大；而靶体特征特别是孔隙率对地冲击传播具有较大影响。Abstract: With the advancement of hypervelocity weapons such as the “Rods-from-God”, the damage and failure in targets induced by the hypervelocity penetrators have been a topic of current research, which is still not fully understood. To address this issue, numerical investigation was carried out on ground shock induced by hypervelocity penetration of projectiles into limestone targets. As the material model and corresponding parameters are crucial for the accurate numerical predictions, the parameters for the p-α equation of state and the Kong-Fang material model recently proposed to describe the limestone were firstly calibrated based on a large amount of dynamic tests. The smooth particle hydrodynamics (SPH) method was employed for simulating the target and the axisymmetric numerical model was used to improve the computational efficiency. The calibrated parameters and numerical algorithm were validated by numerically simulating a series of penetration tests on limestone targets with a broad range of striking velocities. Then, based on the validated numerical model, the penetration of long-rod tungsten projectile into a limestone target was simulated and the mechanism of the corresponding ground shock was discussed. It was found that a high pressure in the target was induced by the hypervelocity impact of the projectile, which then propagated into the target as a stress wave, leading to the damage and failure in the target. The induced ground shock wave increased with the increase of the initial projectile velocity, especially when the initial projectile velocity is over 3.0 km/s. Finally, parametric study was conducted to investigate the effects of the parameters related to the projectiles and targets on the ground shock wave. The parameters related to the projectiles, for example, the length-to-diameter ratio and density, which can influence on the damage area of the targets by influencing the depth of penetration, has limited influence on the ground shock wave from the view of the relative depth (the ratio of the depth to the penetration depth). While the target parameters, especially the porosity which can affect the wave propagation, have a great effect on the ground shock wave.
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Key words:
- hypervelocity penetration /
- ground shock wave /
- limestone /
- material model
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图 1 最大强度面模型与实验数据的拟合
Figure 1. Fitting of the maximum strength surface model to the experimental data
图 2 石灰岩应力-应变曲线的数值模拟结果与实验数据的对比
Figure 2. Comparison of stress-strain curves of limestone between experimental data and numerical simulation
图 3 石灰岩动态强度增强因子随应变率的变化曲线
Figure 3. Changes of the dynamic increase factors with strain rate for limestone
图 4 石灰岩状态方程曲线与实验数据的拟合
Figure 4. Equation of state of limestone fitted to experimental data
图 5 数值模拟的侵彻深度与实验数据的对比
Figure 5. Simulated depths of penetration at different initial projectile velocities compared with experimental data
图 7 数值模拟得到不同撞击速度下的的侵彻深度
Figure 7. Simulated depths of penetration at different initial projectile velocities
图 8 超高速侵彻过程中的破坏现象及压力波传播
Figure 8. Damage and pressure wave propagation in the target during hypervelocity penetration
图 10 不同弹体初速度下应力峰值随深度的变化趋势
Figure 10. Change of peak stress with depth at different initial projectile velocities
图 11 侵彻深度与弹体长径比的关系（弹径不变）
Figure 11. Depth of penetration versus length-to-diameter ratio at a constant projectile diameter
图 14 不同孔隙率岩石材料的状态方程
Figure 14. Equations of state for limestones with different porosities
表 1 石灰岩的强度模型参数
Table 1. Parameters of the strength surface models for limestone
最大强度面 残余强度面 屈服强度面 损伤参数 a1 a2 a3 a1y a2y λm 0.877 0.022 0.80 0.890 0.046 3×10−5 
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表 2 石灰岩的动态强度增强因子参数
Table 2. Parameters for dynamic increase factors of limestone
动态强度增强因子 Fm Wx S Wy DIFC 9 1.8 1.2 5.0 DIFT 10 1.6 1.6 5.5
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表 3 石灰岩的状态方程参数
Table 3. Equation of state parameters for limestone
pcrush/MPa plock/GPa n A1/GPa A2/GPa A3/GPa 100 1.44 3 22.53 –175.0 495.0
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表 4 不同弹体密度情况下的侵彻深度
Table 4. Depths of penetration at different projectile densities
材料 ρs/（kg∙m−3） （ρs/ρt）1/2 hp/m 铝 2785 1.10 2.58 钢 7830 1.85 4.69 钨 17000 2.73 6.20
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