A study of high-velocity penetration characteristics and resistance model of elliptical cross-section truncated ogive projectile
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摘要: 随着高超声速武器系统的发展，具有更大空间利用率的异型截面弹体开始受到广泛关注，异型弹体的高速穿甲特性及毁伤机理是当前亟需解决的关键问题。基于典型反舰战斗部的截锥形头部结构及椭圆截面弹体外形，通过数值仿真方法研究了椭圆截面截锥弹体高速正贯穿金属薄板的阻力特性及薄板损伤机理，将弹体载荷分为剪切冲塞和延性扩孔阻力两部分，结合数值仿真结果提出了适用于椭圆截面平头弹、尖卵形弹的高速穿甲阻力函数及剩余速度解析模型，采用微分面力法和刚体动力学相结合的方法构建了椭圆弹正穿甲模型，并通过数值仿真结果验证了理论模型的有效性。结果表明：椭圆截面截锥弹体正贯穿金属薄板的过程分为载荷作用的头部侵入阶段和无载荷作用的弹身贯穿阶段，头部侵入阶段弹体对薄板的破坏模式分解为截锥平台造成的剪切冲塞和头部弧面的延性扩孔；高速冲击条件下椭圆截面尖卵形弹/平头弹对薄板的损伤与低速冲击时不同，尖卵形弹体贯穿薄板时发生延性扩孔破坏，薄板受平头弹高速冲击时出现剪切冲塞-延性扩孔相耦合的破坏模式；椭圆截面弹体正穿甲过程中所受阻力与截面积相等的圆截面弹体相同，区别在于椭圆截面弹体非对称结构外形导致载荷非均匀分布。Abstract: With the development of the hypersonic weapon system, the non-circular cross-section projectile with more space utilization has attracted extensive attention. The high-velocity penetration mechanism of the non-circular cross-section projectile is a crucial issue that must be solved. Based on the truncated conical head structure of a typical anti-ship warhead and the elliptical section projectile’s shape, the elliptical section’s resistance characteristics and damage mechanism of thetruncated cone projectile through the metal sheet at high velocity are studied by numerical simulation. The load applied on the projectile is divided into two parts: shear punching resistance and ductile enlargement resistance. Combined with the numerical simulation results, the high-velocity penetration resistance function and the analytical model of residual velocity are proposed, which are suitable for elliptic cross-section flat projectile and ogive projectile. The differential surface force method and rigid body dynamics are used to construct a normal penetration model, and numerical simulation results verify the validity of the theoretical model. The results show that the elliptical cross-section truncated cone projectile penetrating through the metal sheet can be divided into the head penetration stage under load and the body penetration stage without load. In the head invasion stage, the failure mode of the thin sheet due to project penetration is decomposed into the shear plugging caused by the truncated cone platform and the ductility enlargement of the curved surface of the head. Under high-velocity impact, the damage to the sheet caused by elliptic ogive projectile/blunt projectile is different from that caused by low-velocity impact. When the ogive projectile penetrates through the sheet, ductile enlargement failure occurs. When the sheet is impacted by blunt projectile at high velocity, the coupled failure mode of shear punching and ductile enlargement takes place. The resistance of the elliptical cross-section projectile is the same as that of the circular cross-section projectile with the same cross-sectional area. The difference is that the asymmetric structure of the elliptical cross-section projectile leads to non-uniform load distribution.
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Key words:
- elliptical cross section projectile /
- plugging /
- enlargement /
- resistance function /
- penetration model
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图 4 弹体加速度与塞块速度曲线
Figure 4. The plug velocity and acceleration curves of the projectile
图 6 柱坐标中单元应力、应变分量示意图
Figure 6. Stress and strain components in cylindrical coordinates
图 10 相同速度下不同尖卵形弹体加速度对比
Figure 10. Ogive projectile’s acceleration at the same velocity
图 11 不同速度下尖卵形弹体加速度对比
Figure 11. Ogive projectile’s acceleration at the different velocity
图 14 不同速度下两类平头弹加速度对比
Figure 14. Flat projectile’s acceleration at the different velocities
图 15 椭圆截面平头弹以不同速度撞击时靶板的破坏模式
Figure 15. Failure modes of the target at different impact velocities
图 16 椭圆截面尖卵形弹体正贯穿薄靶示意图
Figure 16. Schematic of elliptical cross section ogive projectile penetrating thin target
图 17 椭圆截面尖卵形弹体的速度分量及载荷分量示意图
Figure 17. Schematic diagram of velocity and load component
图 18 延性扩孔过程中弹靶相对位置关系示意图
Figure 18. The relative position between a projectile and a target
表 1 945钢仿真材料参数统计
Table 1. Material parameters of 945 steel used in numerical simulation
A/MPa B/MPa n C1 C2 E/GPa ν $ {\dot{\varepsilon }}_{0}/{\mathrm{s}}^{-1} $ T0/K Tm/K 451.6 797.73 0.75 −0.1589 0.012 210 0.33 3×10−4 293 1800 mT χ ρ/（g·cm−3） cp/(J·kg−1·K−1) D1 D2 D3 D4 $ {\varepsilon }_{\mathrm{f},\mathrm{t}} $ 0.859 0.9 7.85 452 0.35 1.11 −0.806 0.10 0.996 
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表 2 塑性冲击波速仿真结果
Table 2. Simulation results of the velocity of plastic shock wave
v0/(m·s−1) x1/mm t1/μs cs/(m·s−1) H/t1 式(32) 式(34) 700 0.376 0.542 5533.7 5497.1 4897.9 800 0.452 0.536 5600.6 5564.3 4968.6 900 0.480 0.537 5584.3 5547.4 5039.3 1000 0.511 0.515 5827.0 5788.5 5110.0
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表 3 模型误差
Table 3. Relative deviation of the model
长短轴之比 初速/(m·s−1) 尖卵形弹 平头弹 余速/(m·s−1) 误差% 余速/(m·s−1) 误差% 仿真 模型 仿真 模型 1 700 688.8 685.9 −0.4 664.9 671.6 1.0 800 787.8 786.0 −0.2 759.8 764.9 0.7 900 887.1 885.9 −0.1 854.6 857.4 0.3 1000 986.5 985.7 −0.1 949.4 949.3 0.0 2 700 688.7 688.9 0.0 665.2 671.6 1.0 800 787.8 789.2 0.2 760.1 764.9 0.6 900 887.2 889.3 0.2 855.0 867.4 1.5 1000 986.8 989.2 0.2 949.8 949.2 −0.1
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表 4 剩余速度对比表
Table 4. Comparison of the residual velocity
初速
/(m·s−1)剩余速度/(m·s−1)（λ=1.6，靶板厚度3 mm） 相对误差/% 剩余速度/(m·s−1)（λ=2，靶板厚度5 mm） 相对误差/% 本文模型 Recht-Ipson模型 本文模型 Recht-Ipson模型 100 91.0 22.5 −303.8 74.7 22.5 231.3 200 186.5 175.6 −6.2 158.1 97.5 62.2 300 284.1 282.7 −0.5 251.8 242.0 4.0 400 382.7 385.1 0.6 350.7 354.1 −1.0 500 482.0 485.9 0.8 453.1 459.0 −1.3 600 581.8 585.9 0.7 556.6 560.8 −0.7 700 681.8 685.5 0.5 658.4 661.1 −0.4 800 782.0 784.9 0.4 758.9 760.4 −0.2 900 881.4 884.1 0.3 858.6 859.1 −0.1 1000 980.6 983.1 0.3 957.7 957.5 0.0
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