Practical engineering calculation models for rigid projectile penetrating and perforating into concrete target
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摘要: 准确计算钻地弹对混凝土材料的侵彻深度和临界贯穿厚度是防护工程领域重点关注的问题。现有侵彻深度计算公式对于大口径钻地弹的预测精度较差，且临界贯穿厚度的计算方法缺乏理论依据。针对上述问题，基于145组刚性卵弹侵彻混凝土试验数据和32组贯穿混凝土试验数据，对刚性卵弹侵彻和贯穿混凝土靶体的实用化计算模型进行了研究。首先基于对刚性弹侵彻混凝土靶体的阻力分析，提出线性上升-恒定的两阶段阻力模型，建立了考虑尺寸效应影响的侵彻深度实用化计算模型，通过与15组大口径、大长径比的侵彻试验数据及ACE和NDRC公式的对比分析，验证了提出公式的可靠性和优越性；然后基于后坑由拉伸破坏引起的基本假定，给出了临界贯穿厚度、弹道极限和残余速度的计算模型；最后通过与现有的贯穿试验数据对比分析，验证了计算模型的正确性。Abstract: Accurate predictions of the penetration depth and critical perforation thickness of earth penetration weapons into concrete materials are key issues in the field of protective engineering. However, the widely-used formulas have limited predictive accuracy for penetration depth when earth penetration weapons have a large diameter and a high aspect ratio, and are lack of theoretical basis for critical perforation thickness. To resolve the two issues above, the engineering calculation models of rigid ogive-nose shape projectile penetrating and/or perforating into concrete targets are investigated in this paper on the basis of 145 sets of penetration data and 32 sets of perforation data. Firstly, based on the resistance analysis of rigid projectile penetrating into concrete target, a two-stage resistance model is proposed, and then a practical calculation model of penetration depth with the consideration of scaling effect is proposed. The reliability of the proposed model is verified by comparing it with 15 sets of penetration data with large diameter and high aspect ratio as well as the predictions by widely-used ACE formula and NDRC formula. The results show that the average errors of the proposed formula, ACE formula and NDRC formula are 5.5%, 15.7% and 24.9%, respectively. Secondly, based on the assumption that the scabbing is caused by the tensile failure of concrete, a formula for the scabbing height is derived based on the force equilibrium between the stress produced by the projectile and the tensile strength of concrete target. Then, the formulas for the critical perforation thickness, ballistic limit and residual velocity are deduced, which are validated by the relevant experimental data. Besides, the coefficients of concrete targets in preventing perforation for four typical earth penetration weapons are compared and analyzed. The accuracy of proposed calculation models for penetration depth and critical perforation thickness shows a great improvement, providing reliable reference for engineering design.
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Key words:
- rigid projectile /
- concrete target /
- penetration /
- perforation
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图 3 线性上升-恒定的侵彻阻力模型
Figure 3. A linear increasing-constant penetration resistance model
图 5 式（5）预测值和试验值的对比
Figure 5. Comparison of penetration depth predicted by Eq. (5) with test data
图 6 弹体贯穿混凝土厚靶的3个阶段试验照片
Figure 6. Post-test pictures of three stages for projectile penetrating into thick concrete target
图 9 残余速度和弹道极限的预测结果和试验数据的对比
Figure 9. Comparison of residual velocity and ballistic limit between predictions and test data
图 10 四种典型战斗部的侵彻不贯穿系数
Figure 10. Coefficients of concrete targets in preventing perforation for four typical warheads
表 1 弹径修正系数取值表
Table 1. Correction factor for projectile diameter
弹径/mm <40 60 80 100 >130 λd 0.95 1.05 1.15 1.25 1.55 
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表 2 大口径弹体侵彻混凝土靶体试验数据及各公式预测误差
Table 2. Test data and formulas error for projectile penetrating into concrete targets with large projectile diameters
来源 弹重/kg 弹径/mm 弹头长/mm 强度/MPa 初速度/（m·s−1） 试验侵深/mm 公式误差/% ACE NDRC 本文公式 周宁等[45] 25 100 193.6 35 456 1000 −7.21 −19.41 11.09 25 100 193.6 35 310 590 −8.13 −23.32 −1.95 25 100 193.6 35 387 750 −1.82 −16.62 11.20 25 100 193.6 35 455 1100 −15.91 −26.99 0.60 25 100 193.6 35 468 1190 −19.10 −29.44 −2.21 程月华等[8] 17.3 100 165.0 40 503 860 −17.64 −24.98 3.18 17.3 100 165.0 100 357 350 −14.59 −18.28 3.79 20.1 105 162.0 40 325 515 −19.10 −28.29 −9.88 145.0 203 335.4 100 360 870 −19.71 −25.81 6.56 874.0 370 571.0 100 325 1400 −11.27 −19.78 2.07 吴飚等[33] 25.62 100 132.3 40 450 1070.0 −18.23 −28.90 −5.40 25.62 100 132.3 60 450 906.0 −20.13 −29.42 −5.59 89.99 152 201.1 40 450 1810.3 −19.99 −31.27 5.41 214.35 203 268.5 40 450 2468.5 −16.88 −29.17 3.23 王德荣等[47] 307 300 540 176 320 740 −25.99 −21.24 9.92
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表 3 后坑高度预测值和试验值的对比
Table 3. Comparison of scabbing depth predicted by Eq. (11) with test data
来源 靶体厚度/mm 靶体抗压强度/MPa 靶体抗拉强度/MPa 阻力系数 后坑角度/(°) 无量纲后坑高度 试验值 公式(11) 误差/% Hanchak等[50] 178 48 4 10.06 65 2.33d 2.34d 0.43 178 140 5 5.62 2.33d 2.70d −15.88 Wu等[51] 200 41 3.71* 10.96 65 2.57d 2.34d 8.95 200 2.37d 1.27 200 1.98d −18.18 200 2.17d −7.83 150 2.57d 8.95 150 2.77d 15.52 150 2.57d 8.95 150 2.37d 1.27 Li等[31] 300 34.26 3.22* 12.08 65 2.03d 2.42d −19.21 400 2.84d 14.79 500 3.83d 36.81 600 4.77d 49.27 700 4.25d 43.06 注：*表示在试验中未实际测量靶体的抗拉强度，是通过规范[58]估计得到。
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