Critical ricochet angle of cylindrical tungsten fragment impacting aluminum target
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摘要: 采用理论计算、数值模拟与实验相结合的方法，研究了直径5.7 mm、长6.7 mm的圆柱形破片以800~1 200 m/s的速度撞击2~10 mm厚铝靶时的跳飞特性。建立了破片斜侵彻有限厚靶板的跳飞临界角理论模型，计算得到破片跳飞临界角与破片入射速度、靶板厚度的关系，并与模拟值、实验值对比，三者吻合较好。结果表明：破片撞靶速度相同时，随着靶板厚度的增加，破片的跳飞临界角减小。靶板厚度相同的情况下，在所计算的速度范围内，入射速度越大，破片跳飞临界角越大。速度在800~1 200 m/s时，破片撞击2 mm厚靶板的跳飞临界角为81°~81.25°；撞击4 mm厚靶板的跳飞临界角为72.5°~76.25°。Abstract: In the present study, we performed theoretical calculation, numerical simulation and experimental test to investigate the ricochet performance of cylindrical fragments. The fragment, 5.7 mm in diameter and 6.7 mm in length, impacted aluminum plates 2-10 mm in thickness at speeds of 800-1 200 m/s. A theoretical model of the ricochet was established, the relation between the critical angle and the initial velocity and the thickness of the target plate were obtained. The results of theoretical calculation agreed well with both the simulation and experiment. The results show that the higher the impacting velocity, the larger the critical ricochet angle; and the thicker the target, the smaller the critical ricochet angle. When a fragment impacts a 2 mm target plate at 800-1 200 m/s, the critical ricochet angle is 81°-81.25°; when a fragment impacts a 4 mm target plate at 800-1 200 m/s, the critical ricochet angle is72.5°-76.25°.
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图 2 破片斜侵彻有限厚靶板示意图
Figure 2. Fragment obliquely penetrating target of limited thickness
图 6 破片轴线与靶板平面的夹角随时间的变化
Figure 6. Variation of angle between fragment axis and target with time
图 7 破片跳飞临界角与入射速度、靶板厚度的关系
Figure 7. Relation of critical ricochet angle with incident speed and target thickness
图 12 理论计算值、实验值、模拟值的对比
Figure 12. Comparison of calculated, experimental, and simulated results
表 1 计算得到的破片侵彻靶板跳飞临界角
Table 1. Calculated results of critical ricochets of penetrators impacting targets
靶板厚度/mm αcr/(°) 800 m/s 1 000 m/s 1 200 m/s 2 81 82 83 4 75 77 78 6 70 72 74 8 69 71 73 10 68 70 72 
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表 2 Johnson-Cook材料参数
Table 2. Johnson-Cook material parameters
材料 ρ/(g·cm-3) E/GPa μ A/MPa B/MPa C n m Tm/K Tr/K 钨 18.3 350 0.28 1 806 177 0.016 0.12 1.0 1 450 294 2A12 T4铝 2.797 69.6 0.33 265 426 0.015 0.34 1.0 775.5 294
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表 3 破片撞击靶板实验结果
Table 3. Experimental results of fragment impacting target
靶板厚度/mm 入射角/(°) 入射速度/(m·s-1) 是否跳飞 2 80.0 812 否 2 80.0 980 否 2 82.0 822 是 2 82.5 997 是 2 82.5 1 015 是 2 82.5 1 042 是 2 85.0 1 059 是 2 80.0 1 064 否 4 70.0 862 否 4 72.5 907 否 4 73.8 833 是 4 73.8 921 否 4 75.0 868 是 4 75.0 1 060 否 4 77.5 970 是 4 77.5 1 053 是
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表 4 破片撞击靶板跳飞临界角对比
Table 4. Results of critical ricochets of fragment impacting target
靶板厚度/mm 2 2 2 4 4 4 入射速度/(m·s-1) 800~900 900~1 000 1 000~1 100 800~900 900~1 000 1 000~1 100 跳飞角度/(°) 81.00 81.25 81.25 72.5 76.25 76.25
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