Theoretical analysis of projectiles penetrating into rock targets at different velocities
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摘要: 随着撞击速度的增加，弹体对岩石类靶体的侵彻机制会发生显著变化，由刚体侵彻逐步转变为半流体侵彻和流体侵彻，3种侵彻机制各自适用的理论模型完全不同。在半流体侵彻阶段，弹体质量损失开始显著增加，造成侵彻效率严重下降，侵彻深度随撞击速度的增加急剧减小。基于提出的弹体质量与速度的理论模型以及弹体刚体段的侵彻阻抗，推导出考虑弹体质量损失的半流体侵彻深度计算公式。对于超高速撞击时的流体动力学侵彻段，通过对流体区和刚性区进行假定，建立动量守恒和伯努利方程，推导给出该阶段弹体的侵彻阻抗，结合弹体质量变化方程推导出侵彻深度的表达式。最后将3个阶段的理论计算结果与花岗岩侵彻试验数据进行了对比验证，侵深和弹体质量变化规律均吻合良好，而且各阶段模型计算结果反映出的侵彻变化规律与实验结果完全一致。Abstract: As the impact velocity increases, the penetration mechanism varies from rigid penetration to semi-liquid penetration and fluid penetration, each of which follows a wholly different analytical model. In the semi-liquid penetration stage, the mass loss of the projectile body begins to increase obviously, leading to serious decrease of the penetration efficiency and the penetration depth at the increase of the impact velocity. The intrinsic analytical model of rigid penetration was deducted by analysis of the real deformation and stress states of different damage zones. Based on the proposed relationship between penetration and velocity, we established the equation of penetration depth in account of the projectile mass loss, proposed the hypothesis of fluid and rigid region of fluid penetration under hypervelocity impact and, by adopting the laws of conservation of momentum and Bernoulli equation, presented the formulas for penetration resistance, and deduced the corresponding equations of penetration depth using the relational expression of the projectile mass loss. By comparison of the result of calculation with experimental data of penetration into granite, we proved the reliability of the formulas for the three stages, showing them in good compatibility in penetration depth and mass loss of the projectile with each other, and verifying a full agreement between their variation and experimental results.
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Key words:
- impact mechanics /
- penetration /
- high-velocity penetration /
- rock target /
- penetration mechanism
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表 1 侵彻深度及弹体剩余质量情况
Table 1. Penetration depth and residual mass of projectile
序号 撞击速度/(m·s-1) 侵彻深度/mm 弹体残余质量/g 1 1 196 118.80 31.65 2 1 426 146.02 31.42 3 1 430 155.80 31.32 4 1 600 163.90 30.83 5 1 654 134.00 30.83 6 1 752 87.40 10.17 7 1 789 83.10 9.35 8 1 808 93.40 10.25 9 2 067 105.47 6.36 10 2 165 104.73 5.19 11 2 356 109.84 5.13 12 2 378 101.48 3.79 
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