Experiments and dimensional analysis ofhigh-speed projectile penetration efficiency
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摘要: 为了研究高速侵彻时弹体撞击速度、材料强度等对质量侵蚀特性和侵彻效率的影响规律，开展了不同材料强度和长径比的弹体高速侵彻半无限厚素混凝土靶实验，弹体撞击速度为880~1 900 m/s，弹头形状为尖卵型(半径口径比为3)，口径为30 mm。由实验发现：弹体撞击速度对侵彻效率的影响呈抛物线分布，最大侵彻效率时的弹体特征撞击速度约1 400 m/s；高速侵彻时弹体的质量侵蚀主要发生在卵形头部，弹身及尾部损伤极少；速度超过特征撞击速度时，弹体侵蚀严重，甚至弯曲变形或解体；弹体强度提高至约2倍时，质量侵蚀率降低约80%。基于实验，利用量纲分析原则建立了量纲一侵彻效率和量纲一弹体撞击速度的函数关系式，可估算出最大侵彻效率对应的弹体撞靶速度，为高速侵彻效应模拟实验提供理论指导。Abstract: This paper carried out high-speed penetration experiments using semi-infinite plain concrete targets with different projectile materials and aspect ratios to investigate the effects of striking velocity and material strength on projectile loss and penetration efficiency. Characterized with caliber-radius-head (CRH) 3.0 and 30-mm diameter, the ogive-nose projectiles were launched at high-speed striking velocities between 880-1 900 m/s to impact the concrete target. The measured experiment data indicates that the penetration efficiency is in parabolic relation with the striking velocity, i.e. the maximum penetration efficiency corresponds to an impact velocity of about 1 400 m/s. The main abrasion occurs around the projectile nose while only negligible erosion is observed at the projectile shank and end cap. When the speed exceeds the characteristic impact velocity, the projectile's mass loss is so serious that even bending deformation or disintegration occurs. When the projectile strength is nearly doubled, the mass loss is reduced by about 80%. Based on the experimental data, the relationship function of dimensionless penetration efficiency and impact velocity was achieved using dimensional analysis. The dimensionless model obtained in this paper is capable of predicting the corresponding impact speed for the maximum penetration efficiency, thereby providing theoretical guidance for high-speed simulated penetration experiments.
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图 9 质量损失率和长度缩短率随撞击速度的变化
Figure 9. Variation of mass loss and length shorteningwith impact velocity
图 10 量纲一侵彻效率随量纲一速度的变化
Figure 10. Variation of dimensionless penetration efficiencywith dimensionless impact velocity
表 1 实验前弹体参数
Table 1. Parameters of projectiles before experiments
弹体 m0/g l0/mm d0/mm σp/MPa μ 33-01 285.8 89.76 29.91 856 3 33-02 287.1 90.06 29.87 856 3 33-03 286.5 90.02 29.88 856 3 33-04 287.3 90.10 29.93 856 3 5-01 322.6 90.23 30.00 1 650 3 5-02 322.0 90.02 29.98 1 650 3 5-03 323.4 90.13 29.97 1 650 3 5-04 322.8 90.01 29.88 1 650 3 5-05 322.2 90.02 29.98 1 650 3 6-01 313.1 107.39 26.91 1 650 4 6-02 318.1 107.88 26.95 1 650 4 6-03 315.8 107.05 26.82 1 650 4 
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表 2 实验后弹靶参数
Table 2. Parameters of projectiles and targets after experiments
弹体 v0/(m·s-1) α/(°) β/(°) (Δl/l0)/% (Δm/m0)/% d/mm γ/(°) H/mm 33-01 924.0 0.55 -3.13 6.20 2.80 29.94 15.0(向右) 247.85 33-02 1 087.9 0.59 1.64 13.60 5.05 30.19 6.5(向上) 321.19 33-03 1 174.8 - - - - - - 230.00 33-04 1 320.0 - - - - - - 170.00 5-01 885.3 1.00 1.00 1.36 1.77 29.92 5.0(向左) 310.00 5-02 1 385.0 6.00 2.00 3.35 2.82 29.78 23.7(向上) 775.00 5-03 1 286.3 0 1.30 1.93 3.12 29.91 6.3(向下)30.0(向左) 630.00 5-04 1 595.6 0 -1.59 14.74 7.00 29.89 14.4(向上) 780.00 5-05 1 851.7 0 5.79 22.76 13.38 29.91 5.5(向下)8.4(向左) 639.53 6-01 1 303.3 0 7.59 2.08 3.80 26.93 21.1(向上) 747.00 6-02 1 580.6 0 3.59 40.96 37.06 26.89 4.4(向下)7.1(向右) 508.69 6-03 1 872.3 0 21.56 - - - - 340.00
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表 3 侵彻实验数据
Table 3. Penetration experiment data
v0/(m·s-1) H/mm η/μs $\frac{{{v_0}}}{{\sqrt {f_{\rm{c}}^\prime /{\rho _{\rm{t}}}} }}$ $\frac{\eta }{{{d_0}\sqrt {{\rho _{\rm{t}}}/f_{\rm{c}}^\prime } }}$ 885.3 310.00 350.164 6.661 41 1.551 22 1 286.3 630.00 489.777 9.678 73 2.169 70 1 385.0 775.00 559.567 10.421 39 2.478 88 1 595.6 780.00 488.847 12.005 97 2.165 59 1 851.7 639.53 345.382 13.932 76 1.530 04
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