Spall Control in the Projectile Explosive Driving
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摘要: 在弹丸爆炸驱动过程中，对厚度大于一定尺寸的弹丸，为降低弹丸内部负压以避免其层裂，通常对弹丸前端进行封装。研究发现，在爆炸产生的加载脉冲下，封装后的弹丸可能产生两次负压。一次负压的产生仅与选择的封装材料有关，二次负压的产生同时还与封装材料的厚度有关。通过理论推导得到了在给定弹丸材料和封装材料的情况下，为使弹丸不产生一次负压，加载冲击波和卸载稀疏波波后压力应满足的临界条件；同时导出了一次负压为零时，在弹丸不产生二次负压的条件下，封装材料厚度的临界值。采用AUTODYN有限元软件，对钢、铝弹丸封装材料不同的情况进行数值模拟，验证理论解的正确性；另外还对比研究了三角形冲击波加载的情况。研究结果可为弹丸爆炸驱动过程中封装材料的设计提供参考。Abstract: In the process of projectile explosive driving, the front surface of the projectile whose thickness is larger than a certain size is usually packaged to reduce the negative pressure and prevent spalling.It is found that two negative pressures may be produced in the packaged projectile under the explosive load pulse.The first negative pressure is only relevant to the type of the package material, in addition to which, the second negative pressure also depends on the thickness of package material.With the given projectile and package material, the critical condition satisfied by loading pressure of shock wave and unloading pressure of rarefaction wave is derived.The first negative pressure is prevented under this condition.Furthermore, when the value of the first negative pressure is zero, in order to prevent the second negative pressure, the critical thickness of the package material is obtained in this paper.The projectile Fe, Al packaged by different materials are simulated by AUTODYN simulator and the analytical results are in good agreement with those of numerical results.Besides, the contrast of rectangular and triangular shock wave is given.This work will provide reference for engineering design of the package materials in the process of projectile explosive driving.
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Key words:
- projectile /
- explosive driving /
- negative pressure /
- spall /
- package
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图 3 不同封装材料下钢、铝弹丸不产生一次负压的临界条件曲线
Figure 3. Critical condition curve of not producing the first negative pressure for the Fe, Al projectile with different package materials
图 4 加载冲击波压力为40 GPa时封装材料临界厚度与弹丸长度的关系曲线
Figure 4. Relationship curves between critical thickness of package materials and projectile length when the load pressure is 40 GPa
图 5 弹丸长度为5 mm时封装材料临界厚度与加载冲击波压力的关系曲线
Figure 5. Relationship curves between critical thickness of package materials and load pressure when the projectile length is 5 mm
图 6 (a) 弹丸尾部加载脉冲(b)计算模型
Figure 6. (a) Load pulse at the rear of the projectile (b) The calculation model
图 7 不同卸载稀疏波波后压力下，封装材料为聚胺酯的钢、铝弹丸G1处的压力-时间曲线
Figure 7. Pressure-time histories of Fe, Al projectile with polyurethane package under different unload pressures at G1
图 8 封装材料聚胺酯厚度不同情况下，钢、铝弹丸G2处的压力-时间曲线
Figure 8. Pressure-time histories of Fe, Al projectile with different PU package thicknesses at G2
图 9(b) 钢、铝弹丸在两种冲击波下pb值对比
Figure 9(b). Unloaded pressure under two kinds of shock waves for the Fe, Al projectiles
图 10 两种冲击波作用下封装材料临界厚度与加载压力的关系
Figure 10. Relationship curves between critical thickness of package materials and load pressure of two kinds of shock waves
表 1 钢、铝弹丸和封装材料的Grüneisen状态方程参数
Table 1. Parameters of Grüneisen state equation of Fe, Al projectiles and package materials
Material ρ/(kg/m3) c/(m/s) λ Γ Steel 8 129 3 980 1.580 1.60 Aluminum 2 710 5 380 1.337 2.10 Polyurethane 1 265 2 486 1.577 1.55 Polycarbonate 1 200 1 933 2.650 0.61 Epoxy resin 1 186 2 730 1.493 1.13 Rubber polymer 1 010 852 1.865 1.50 Water 998 1 647 1.921 0 
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表 2 理论解与数值模拟给出的卸载稀疏波波后压力最小值对比
Table 2. Contrast of unload pressure minimum given by theoretical solution and simulation
(GPa) pa pb of steel projetile pb of Al projetile Polyurethane Rubber polymer Polyurethane Rubber polymer Theo. Simu. Theo. Simu. Theo. Simu. Theo. Simu. 20 14.3 14.9 16.6 16.8 8.0 8.3 11.0 11.4 40 25.9 27.5 30.1 31.2 12.3 13.2 16.5 17.7 60 35.9 37.8 41.7 44.0 15.3 16.9 20.2 22.3
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表 3 (7) 式与数值模拟给出的封装材料临界厚度的对比
Table 3. Contrast of package material critical thickness given by equation (7) and simulation
Package material H0 of steel projetile/(mm) H0 of Al projetile/(mm) Equation (7) Numerical simulation Equation (7) Numerical simulation Polyurethane 2.42 2.25 2.54 2.75 Rubber polymer 1.62 1.80 1.94 2.15
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