Penetration depth of hypervelocity tungsten alloy projectile penetrating concrete target
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摘要: 为探索钨合金柱形弹超高速撞击水泥砂浆靶的侵彻深度随撞击速度变化规律，利用二级轻气炮开展了
$\varnothing $ 3.45 mm×10.5 mm的克级93 W钨合金柱形弹以1.82～3.66 km/s的速度撞击水泥砂浆靶的实验，利用CT图像诊断技术获得了侵彻深度和残余弹长随撞击速度的变化规律，对超高速撞击过程进行了数值模拟，结合数值模拟结果进一步分析了超高速撞击物理过程。结果表明：（1）超高速撞击条件下成坑是弹坑+弹洞型；（2）侵深-速度曲线呈现先增大后减小的现象，在弹速2.6 km/s附近存在侵彻深度极大值，约为8.5倍弹长，相对于中低速侵彻的深度并没有显著优势。（3）通过基于数值模拟得到的弹靶界面压力时程曲线将侵彻过程分为4个阶段，其中准定常侵彻阶段和第三侵彻阶段是决定总侵深的主要阶段。（4）随撞击速度增加，弹体侵蚀逐渐剧烈，此时准定常侵彻阶段的侵深变化不大，而第三侵彻阶段中的刚体侵彻部分大幅降低，导致总侵深大幅降低，使总侵深曲线呈现先增大后减小的现象。Abstract: In this paper we carried out experiments using two-stage light gas gun with Gram-grade cylindrical tungsten alloy projectiles, impacting concrete targets at velocity from 1.82 km/s to 3.66 km/s ton investigate the cratering mechanism of concrete targets in hypervelocity impact conditions. We obtained the penetration depth and residual length of the projectiles using computerized tomography (CT) and used the numerical simulation results conducted by Euler algorithm to further examine the mechanism of hypervelocity impact, and achieved the following results: (1) The craters were structured by spalling areas and bullet holes; (2) The penetration depth increases at first and then decreases with the increase of the impact velocities, and the maximum penetration depth was 8.5 times that of the projectile length, which showed no significant advantage over low velocity penetration; (3) According to the pressure of the interface of the projectiles and targets, the penetration processes were divided into four stages, of which the quasi-steady stage and the third stage were crucial in determining the total penetration depth; (4) When the projectiles were completely eroded with the increase of the impact velocities, the penetration depth of the quasi-steady stages almost remained the same and the penetration depth of the third stage decreased so that the total penetration depth was observed to increase at first and then decrease. -
图 2 93W钨合金柱形弹体和水泥砂浆靶
Figure 2. Cylindrical tungsten alloy projectiles and concrete targets
图 4 超高速撞击条件下靶板破坏CT图像和成坑示意图
Figure 4. CT photographs and illustration of hypervelocity impacted crater
图 7 残余弹体长度随撞击速度变化规律
Figure 7. Variation of residual projectiles length with impact velocities
图 8 侵深随速度变化规律的数值模拟结果与实验结果的对比
Figure 8. Penetration depth as compared between experiments and numerical simulations
图 9 数值模拟得到的残余弹体长度与实验结果的对比
Figure 9. Residual projectile length as compared between experiments and numerical simulations
图 10 弹体尾部速度、界面速度、界面压力、侵彻深度随时间的变化关系（
${v_0} $ =3 km/s）Figure 10. Time histories of projectile tail velocity, interface velocity, interface pressure and the penetration depth (
${v_0} $ =3 km/s)
图 11 数值模拟得到的准定常侵彻阶段和第三侵彻阶段的侵彻深度和总侵彻深度的关系
Figure 11. Relationship of penetration depth between quasi-steady stage, phase three stage and the total penetration obtained by simulation
表 1 钨合金弹体超高速撞击水泥砂浆靶的成坑数据
Table 1. Cratering data of hypervelocity impact of tungsten alloy projectiles penetrating concrete target
编号 弹速/
（km·s−1）侵彻深度 /mm 弹丸余长/
mm弹丸余长误差/
mm编号 弹速/
（km·s−1）侵彻深度 /mm 弹丸余长/
mm弹丸余长误差/
mm1-1 1.82 67.0 − − 1-9 2.90 76.8 3.2 1.4 1-2 1.97 69.8 6.2 1.1 1-10 3.08 66.5 0 0 1-3 2.02 80.58 6.7 1.2 1-11 3.19 68.0 0 0 1-4 2.35 84.15 4.9 1.4 1-12 3.36 63.8 0 0 1-5 2.39 82.5 5.6 0.1 1-13 3.36 61.0 0 0 1-6 2.61 85.9 4.5 1.1 1-14 3.46 65.0 0 0 1-7 2.66 84.0 4.2 0.1 1-15 3.66 58.3 0 0 1-8 2.86 84.1 4.4 1.3 
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表 2 水泥砂浆的材料模型参数
Table 2. Material parameters of concrete
G0/GPa fc/MPa ft/fc fs/fc A B ρ/(kg·m−3) M D1 D2 εf,min N 16.7 42.7 0.1 0.18 1.4 1.4 2.2 0.5 0.04 1 0.01 0.5
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表 3 不同初始速度条件下的弹体速度、成坑深度和弹体长度的数值模拟结果
Table 3. Simulated projectiles velocity, penetration depth and residual projectile length at different impact velocities
初始速度/
（m·s−1）准定常侵彻阶段结束时
弹体速度/（m·s−1）准定常侵彻阶段结束时
弹体余长/mm准定常侵彻阶段侵彻
深度/mm第三侵彻阶段侵彻
深度/mm总侵深/
mm1 700 1 050 6.5 28.0 38.5 66.5 2 000 1 101 5.5 30.7 42.3 73.0 2 300 1 201 4.5 32.3 46.2 78.5 2 650 1 243 3.5 35.2 44.8 80.0 3 000 1 277 0 34.9 42.6 77.5 3 300 1 325 0 38.5 35.0 73.5 3 460 1 374 0 36.1 33.0 69.1 4 000 1 394 0 40.5 22.0 62.5
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