Simulation on the oblique penetration of an elliptical cross-section projectile into concrete
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摘要: 为了获取椭圆截面弹体斜侵彻混凝土的弹道特性，采用数值模拟方法开展了系统性研究。构建了可靠的数值模拟模型，对影响弹道偏转的倾角、攻角和滚转角进行了解耦，开展了不同落角下椭圆截面弹体斜侵彻混凝土的数值模拟，深入分析并揭示了弹道偏转、自旋转演变规律及机理。研究结果表明：倾角和攻角导致弹体上、下表面受力面积存在差异，且攻角还会造成弹体表面应力分布不对称，最终产生偏转力矩驱动弹体偏转；随着倾角和攻角的增大，弹体角速度、姿态角和弹道偏移总体上呈增大趋势。在带倾角斜侵彻情况下，竖姿弹体偏转慢、持续时间长，而平姿弹体偏转快、持续时间短，两者在弹道稳定性方面不存在绝对的优劣；在带攻角斜侵彻情况下，竖姿弹体的弹道稳定性相对平姿弹体更好。滚转角叠加倾角导致弹靶交会条件不对称，弹体除偏移和偏转外，还有绕轴的自旋转运动；当滚转角由0°向90°增大时，弹靶交会条件经历对称至不对称再至对称的转变，弹体在水平方向的偏移量和滚转角增量呈先增大后减小的趋势。研究成果可为椭圆截面弹体实际工程应用提供参考。Abstract: To obtain the ballistic characteristics of the oblique penetration of an elliptical cross-section projectile into concrete, a systematic study was carried out using numerical simulation. A reliable finite element numerical simulation model was constructed. The oblique angle, attack angle and axis spin angle that affect the ballistic deflection were decoupling. Numerical simulations of the oblique penetration of an elliptical cross-section projectile into concrete under different drop angles were carried out. The evolution laws of ballistic deflection and spin were deeply analyzed, and the mechanisms of ballistic deflection and spin were explained. The results show that the oblique angle and attack angle lead to the asymmetry of the force-bearing areas on the upper and lower surfaces of the projectile, and the attack angle also leads to the asymmetry of the surface stress of the projectile, eventually generating a deflection torque that prompts the deflection of the projectile. The angular velocity, attitude angle and ballistic offset of the projectile increase with the increases of the oblique angle and attack angle. In the case of oblique penetration with an oblique angle, the projectile in the upright position (γ=0°) deflects slowly and for a long time, while the projectile in the lying position (γ=90°) deflects quickly and for a short time. There is no absolute superiority or inferiority between the two positions in terms of ballistic stability. In the case of oblique penetration with an attack angle, the ballistic stability of the projectile in the upright position is better than that of the projectile in the lying position. The combined effects of the axis spin angle and oblique angle lead to the asymmetry of the projectile-target intersection. Besides offset and deflection, the projectile also has a self-rotating motion around the axis. When the axis spin angle increases from 0° to 90°, the projectile-target intersection condition undergoes a transformation from symmetry to asymmetry and then back to symmetry. The offset in the horizontal direction and the axis spin angle increment of the projectile first increase and then decrease. The research results provide important references for the practical engineering application of the elliptical cross-section projectile.
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图 1 椭圆截面弹体斜侵彻混凝土靶姿态示意图
Figure 1. Schematic diagram of the posture of an elliptical cross-section projectile oblique penetration into concrete target
图 4 竖姿弹体侵彻不同倾角靶板结果
Figure 4. The results of the upright position projectile penetration into concrete at different oblique angles
图 5 平姿弹体侵彻不同倾角靶板结果
Figure 5. The results of the lying position projectile penetration into concrete at different oblique angles
图 6 竖姿弹体弹道偏移时程曲线
Figure 6. Ballistic offset vs. time of the upright position projectile
图 10 竖姿弹体角速度时程曲线
Figure 10. Angular velocity vs. time of the upright position projectile
图 11 平姿弹体角速度时程曲线
Figure 11. Angular velocity vs. time of the lying position projectile
图 14 竖姿弹体在不同攻角下的侵彻结果
Figure 14. The results of the upright position projectile penetration into concrete at different attack angles
图 15 平姿弹体在不同攻角下的侵彻结果
Figure 15. The results of the lying position projectile penetration into concrete at different attack angles
图 16 竖姿弹体弹道偏移时程曲线
Figure 16. Ballistic offset vs. time of the upright position projectile
图 17 平姿弹体弹道偏移时程曲线
Figure 17. Ballistic offset vs. time of the lying position projectile
图 18 竖姿弹体姿态角时程曲线
Figure 18. Attitude angle vs. time of the upright position projectile
图 20 竖姿弹体角速度时程曲线
Figure 20. Angular velocity vs. time of the upright position projectile
图 21 平姿弹体角速度时程曲线
Figure 21. Angular velocity vs. time of the lying position projectile
图 24 椭圆截面弹体在不同滚转角条件下的侵彻结果
Figure 24. The results of the elliptical cross-section projectile penetration into concrete at different axis spin angles
图 25 弹尖X'方向偏移时程曲线
Figure 25. Ballistic offset vs. time of the projectile tip X' direction
图 26 弹尖X'方向偏移量随初始滚转角变化
Figure 26. Ballistic offset vs. initial axis spin angle of the projectile tip X' direction
图 27 椭圆截面弹体在X'方向的偏移速度
Figure 27. Offset velocity vs. time of the elliptical cross-section projectile in the X' direction
图 31 竖姿弹体侵彻过程受力分析
Figure 31. Force analysis during the penetration process of the upright position projectile
图 32 竖姿弹体侵彻过程受力分析
Figure 32. Force analysis during the penetration process of the upright position projectile
图 33 弹体侵彻初期应力云图
Figure 33. Stress cloud map in the early stage of projectile penetration
表 1 弹体材料Johnson-Cook本构模型参数[21]
Table 1. Parameters of steel 35CrMnSiA for Johnson-Cook constitutive model[21]
ρ/(g·cm−3) E/GPa $ \nu $ A/MPa B/MPa n C m Tmelt/K 7.85 210 0.29 1280 346 0.372 0.015 1.027 1775 
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ρ/(g·cm−3) fc/GPa A1 B1 C1 SF,max G/GPa D1 D2 N 2.4 0.035 0.79 1.60 0.007 7 14.8 0.04 1.0 0.61 EF,min T/GPa Pcrush/GPa μcrush μlock Plock/GPa K1/GPa K2/GPa K3/GPa $ {\dot{\varepsilon }}_{00} $ 0.01 0.004 0.016 0.001 0.1 0.8 85 −171 208 1E-6
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表 3 数值模拟结果与实验数据的对比
Table 3. Comparison of simulation results with experimental data
实验编号 弹体类型 侵彻速度/(m·s−1) 靶板倾角/° 初始滚转角/° 最终滚转角 侵彻深度 实验值/° 模拟值/° 误差/% 实验值/mm 模拟值/mm 误差/% 4 E1 840 30 54.0 67.0 61.4 8.4 554.4 596.0 7.5
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