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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飞机在飞行过程中, 机翼、尾翼前缘、机身前段以及发动机吊舱等都容易受到冰雹撞击。复合材料在飞机结构中的应用日益广泛, 而冰雹撞击对复合材料结构所造成的损伤主要为目视不可检损伤, 这种内部损伤会大大降低结构的剩余强度, 对结构的承载能力造成很大影响。由于冰雹撞击实验费用高、难度大, 因此利用数值模拟手段模拟冰雹撞击过程, 评价影响结构性能的各项参数, 对复合材料结构的抗冰雹撞击设计具有重要的指导意义。
在冰雹撞击试验和数值模拟方面, 已有了大量研究并取得了较多成果。S.Singh等[1]设计了一种动态测量装置, 得到了冰雹撞击的撞击力。M.Lavoie等[2]建立了一个简单的冰的弹性光滑质点流体动力学(smoothed particle hydrodynamics, SPH)模型。H.Kim等[3]用球形冰模拟冰雹撞击碳/环氧树脂板件, 发现撞击力峰值与能量呈线性关系。H.Kim等[4]采用带失效的弹塑性材料模型模拟冰雹的力学性能。M.Anghileri等[5]发现, 相对于Lagrange模型和ALE模型, 冰雹的SPH模型能更好地描述冰雹撞击过程及其力学行为, 且具有最小的计算时间和较高的计算精度。T型接头是复合材料机翼或加筋板中最常见的结构单元。D.D.R.Cartié等[6]利用黏聚区模型(cohesive zone model, CZM)预测了复合材料T型接头在拉伸载荷下的失效。崔浩等[7]利用CZM模拟了T型结构根部填充区的随机裂纹扩展, 研究了T型接头的拉伸失效行为。但迄今为止, 对于冰雹撞击复合材料T型接头的研究仍然较少。
本文中, 利用高速空气炮进行冰雹撞击复合材料T型接头的实验, 采用SPH与CZM相结合的方法, 建立冰雹撞击复合材料T型接头的数值模型, 实验结果用于对数值模型结果的验证, 并运用验证后的数值模型研究影响复合材料T型接头损伤的因素。
1. 实验
T型接头由3个层合板共固化而成, 如图 1所示, 层合板材料为T700/ Q Y8911。接头长200 mm(x轴), 高120 mm(z轴), 宽50 mm(y轴)。接头根部填充区为圆弧过渡区, 内部由单向带填充。其中子层1与子层2的弧形区半径为5 mm, 铺层数为13层, 铺层间方向错开, 顺序为-45°、0°、45°、90°、-45°、0°、90°、0°、45°、90°、-45°、0°、45°, 子层3的铺层为16×2层, 铺层顺序为45°、0°、-45°、90°、0°、45°、0°、-45°、90°、0°、45°、0°、-45°、0°、45°、-45°, 复合材料单层厚度为0.125 mm。
接头夹持方式如图 2所示, T型接头沿x轴方向两端各有一个夹板, 用螺栓将接头与夹具固定于试验台上, 固支边界的长度为两端各25 mm。冰球直径为25.4 mm。撞击部位为T型接头子层3的中心位置, 运用载荷(压力)传感器、位移传感器、应变片分别测量试验件在撞击过程中的载荷、位移和应变。
2. 数值计算模型
2.1 冰雹的SPH模型
冰雹在高速撞击情况下会呈现流体特性, 所以冰雹的材料模型需要充分考虑冰雹在撞击变形后的流体性质。SPH是一种无网格算法, 基本思想是:将连续的流体(或固体)离散为多个相互作用具有质量的质点, 通过求解质点组的动力学方程及每个质点的运动轨道, 求得整个系统的力学行为。选用LS-DYNA中一种弹塑性流体动力学材料模型MAT10作为冰雹的本构模型, 材料的力学参数分别为[5]:密度为846 kg/m3, 剪切模量为3.46 GPa, 屈服强度为10.30 MPa, 塑性硬化模量为6.89 GPa, 拉伸失效应力为-4.00 MPa。汪洋[8]通过冰雹试验及数值模拟的结果对比, 证明了该材料模型的有效性。
2.2 黏聚区模型
近年来, 黏聚区模型越来越多地用于模拟复合材料结构层间分层损伤的起始和演化过程。黏聚区模型中, 将材料分为连续体及连续体之间的黏聚层, 层间失效由黏接面的分离即黏聚层单元的失效描述。在黏聚区模型中, 裂纹前端的黏聚区由损伤起始阶段和损伤扩展阶段两部分组成, 黏聚单元的应力随着裂尖张开位移的增大而逐渐增大, 当达到强度极限后开始出现刚度退化, 最终直至完全失去承载能力, 黏聚单元失效, 如图 3所示。
黏聚区模型的本构方程一般由黏聚单元的应力和裂尖张开位移的关系式给出。本文中采用双线性本构模型, 如图 4所示[9]:K为黏聚单元的初始刚度,
为材料的强度极限(即拉伸强度T、剪切强度S),
为单元达到强度极限时的位移,
为黏聚单元完全失效时的位移, (1-d)K为单元包含损伤后的刚度, 曲线下的面积GI/shear代表断裂过程中耗散的能量。
2.3 有限元模型
复合材料单层板采用八节点六面体实体单元(Solid 164), 雹撞击过程中T型接头内部的分层损伤, 可由各铺层之间的黏聚单元的失效及删除模拟, 分层面积可通过被删除的黏聚单元尺寸确定。观察试验件的失效模式发现:分层主要出现于填充区附近各子层与填充物以及各子层之间的胶接界面上, 因此只在上述界面定义厚度为0.01 mm的黏聚单元, 如图 5所示。在冰雹撞击区域及填充区内网格划分较密集, 其他区域网格逐渐变粗, 最终建立的有限元模型中八节点六面体实体单元数为336 735, SPH冰雹粒子数为17 256。复合材料单层板和黏聚单元的材料模型分别为增强复合材料损伤模型和黏聚混合材料模型, 具体的材料参数分别为:T700/QY8911复合材料单层板, ρ=1.6 t/m3, E11=125 GPa, E22=10.4 GPa, ν12=0.34, G12=6.120 GPa, G23=6.0 GPa, G31=6.0 GPa; 黏聚单元, ρ=1.24 t/m3, EN=108 MPa, ET =108 MPa, GIC=504 J/m, GIIC=1.33 kJ/m, T=15 MPa, S=25 MPa。填充物为单向带, 其力学性能与T700/QY8911单层板的材料参数一致。撞击过程中系统的沙漏能和系统阻尼能基本为零, 总能量基本保持不变, 从能量角度来看计算是收敛的。
3. 结果与讨论
3.1 接头损伤分析
通过对撞击后试验件的超声波C扫描, 可以得到结构内部的分层损伤情况。本文中通过x轴方向子层3与子层1、2以及填充物间胶接层损伤的长度, 描述分层损伤的尺寸, 图 6为某试验件在直径为25.4 mm的冰雹撞击后的C扫描图。
图 7给出了冰雹撞击T型接头的实验和数值模拟结果, 可见当速度低于74 m/s时, 冰雹撞击不会对接头造成明显分层损伤, 而随着冰雹速度的提高, 所造成的分层损伤尺寸也逐渐增大。冰雹速度为161 m/s时, 数值分析和实验得到的结果差别较大, 通过对相应C扫描图分析发现, 损伤缺陷在接头的筋条两侧分布明显偏向一侧, 说明实验中冰雹撞击位置出现偏差, 撞击能量多被接头的蒙皮吸收, 因此实验结果远大于数值模拟结果。
图 8为典型的黏聚单元失效删除过程, 可以看出在冰雹撞击下, 损伤最先出现于圆弧区, 随后扩展至填充物的边缘, 并沿着子层1、2与子层3的界面扩展, 在撞击时间0.445 ms后, 基本不再出现黏聚单元失效。
3.2 位移比较
实验中通过激光位移传感器记录了T型接头筋条顶点处的位移历程。图 9为上述试验件的实验和数值结果对比曲线。在实验中, 在t=0.44 ms时T型接头筋条顶点处的位移为3.01 mm, 在t=0.55 ms时位移达到最大值3.30 mm。在数值模拟中, 当t=0.44 ms时, T型接头筋条顶端的位移达到最大值3.31 mm。数值模拟的位移变化趋势及峰值与实验结果较一致, 只是数值模拟中峰值出现时间比实验中稍早一些。
图 9 试验件筋条顶点处z方向位移曲线Figure 9. Displacement in z direction at the top of fillet of the specimen3.3 影响冰雹撞击损伤的因素
有限元模拟结果与实验结果的比较表明, 采用所建立的分析模型能够较准确地模拟冰雹撞击复合材料T型接头的过程。因此, 可以应用该模型进一步研究冰雹的撞击能量和入射角度对T型接头分层损伤尺寸的影响。
3.3.1冰雹撞击能量
冰雹的撞击能量与冰雹的尺寸(质量)及初始撞击速度有关。图 10给出了直径为25.4和42.7 mm的冰雹在不同撞击能量下的数值模拟结果, 可以看出: T型接头内部在长度方向上的分层长度与冰雹的撞击能量之间呈近似线性关系, 分层长度随着撞击能量的增大而增大, 但当撞击能量在某一阈值以下时, 撞击不会产生明显的分层现象。相同撞击能量下, 尺寸较小速度较高的冰雹造成的分层面积相对更大, 损伤更严重, 这是因为冰雹的直径越小, 与T型接头的撞击区域越小, 应力会更加集中, 更容易产生分层。
图 10 冰雹接头在x方向的分层长度与撞击能量关系Figure 10. Delamination length in x direction versus impact energy3.3.2冰雹的入射角
冰雹与复合材料撞击面之间的夹角为入射角。飞机在实际飞行过程中, 很多情况下冰雹的入射角都小于90°, 因此有必要研究冰雹入射角对结构损伤的影响。由于T型接头形状的特殊性, 相同撞击角下不同形式的速度矢量对结构造成的损伤也有所差异, 因此在分析入射角的影响时, 将冰雹的入射速度矢量固定在yz平面内, 通过调整冰雹在y、z方向上的速度分量控制入射角度。模拟中采用的入射角分别为30°、45°、60°, 冰雹撞击速度固定为143 m/s。图 11给出了3种入射角下的计算结果, 撞击角越大, 分层面积也越大, 当撞击角为90°时达到最大值, 即正撞击对结构造成的损伤是最严重。图 12为撞击角为60°时T型接头的分层情况, 可看出沿y轴负向一侧的损伤远大于正向一侧。
图 12 撞击角为60°时黏聚单元失效情况Figure 12. The failure and deletion of cohesive elements when the impact angle is 60°4. 结论
(1) 进行了冰雹高速撞击复合材料T型接头结构的实验, 并在LS-DYNA中建立了相应的数值模型。针对T型接头在撞击后的内部分层损伤, 应用该数值模型可以获得与实验较吻合的结果, 这证实了该模型的准确性。
(2) 复合材料T型接头受到冰雹撞击后的损伤主要是分层损伤, 主要集中在填充区与3个子层的胶接界面处, 且损伤最早起始于填充区圆弧胶接面处。
(3) T型接头长度方向上的分层长度与撞击能量之间呈近似线性关系。撞击能量小于某阈值时, 并不会产生明显分层; 相同撞击能量下, 尺寸较小的冰雹造成的分层损伤更严重。
(4) 冰雹入射角越大, 分层尺寸也越大, 入射角为90°时对结构造成的损伤最严重。
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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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[1] FORRESTAL M J, ALTMAN B S, CARGILE J D, et al. An empirical equation for penetration depth of ogive-nose projectiles into concrete targets [J]. International Journal of Impact Engineering, 1994, 15(4): 395–405. DOI: 10.1016/0734-743X(94)80024-4. [2] KONG X Z, WU H, FANG Q, et al. Rigid and eroding projectile penetration into concrete targets based on an extended dynamic cavity expansion model [J]. International Journal of Impact Engineering, 2017, 100: 13–22. DOI: 10.1016/j.ijimpeng.2016.10.005. [3] LI Q M, CHEN X W. Dimensionless formulae for penetration depth of concrete target impacted by a non-deformable projectile [J]. International Journal of Impact Engineering, 2003, 28(1): 93–116. DOI: 10.1016/S0734-743X(02)00037-4. [4] YARIN A L, RUBIN M B, ROISMAN I V. Penetration of a rigid projectile into an elastic-plastic target of finite thickness [J]. International Journal of Impact Engineering, 1995, 16(5/6): 801–831. DOI: 10.1016/0734-743X(95)00019-7. [5] LI Q M, REID S R, WEN H M, et al. Local impact effects of hard missiles on concrete targets [J]. International Journal of Impact Engineering, 2005, 32(1/2/3/4): 224–284. DOI: 10.1016/j.ijimpeng.2005.04.005. [6] 王安宝, 邓国强, 张磊, 等. 混凝土侵彻公式的合理性分析 [J]. 防护工程, 2020, 42(6): 1–7. DOI: 10.3969/j.issn.1674-1854.2020.06.001.WANG A B, DENG G Q, ZHANG L, et al. Analysis on the rationality of concrete penetration formula [J]. Protective Engineering, 2020, 42(6): 1–7. DOI: 10.3969/j.issn.1674-1854.2020.06.001. [7] 张爽. 弹体侵彻/贯穿钢筋混凝土靶机理与弹道轨迹研究 [D]. 北京:北京理工大学, 2018. DOI: 10.26948/d.cnki.gbjlu.2018.000162.ZHANG S. Investigation on the mechanism and trajectory of projectile penetrating / perforating reinforced concrete target [D]. Beijing: Beijing Institute of Technology, 2018. DOI: 10.26948/d.cnki.gbjlu.2018.000162. [8] 程月华, 姜鹏飞, 吴昊, 等. 考虑尺寸效应的典型钻地弹侵彻混凝土深度分析 [J]. 爆炸与冲击, 2022, 42(6): 063302. DOI: 10.11883/bzycj-2021-0373.CHENG Y H, JIANG P F, WU H, et al. On penetration depth of typical earth-penetrating projectiles into concrete targets considering the scaling effect [J]. Explosion and Shock Waves, 2022, 42(6): 063302. DOI: 10.11883/bzycj-2021-0373. [9] 龚自明, 方秦, 张亚栋, 等. 混凝土靶体侵彻不贯穿系数的试验研究 [J]. 兵工学报, 2009,30 (9): 1181–1186. DOI: 10.3321/j.issn:1000-1093.2009.09.006.GONG Z M, FANG Q, ZHANG Y D, et al. Experimental investigation into coefficients of concrete targets to prevent perforation [J]. Acta Armamentarii, 2009,30 (9): 1181–1186. DOI: 10.3321/j.issn:1000-1093.2009.09.006. [10] WALTER T A, WOLDE-TINSAE A M. Turbine missile perforation of reinforced concrete [J]. Journal of Structural Engineering, 1984, 110(10): 2439–2455. DOI: 10.1061/(ASCE)0733-9445(1984)110:10(2439). [11] ACE. Fundamentals of protective structures: report AT120 AT1207821[R]. Office of the Chief of Engineers, Army Corps of Engineers, 1946. [12] NDRC. Effects of impact and explosion. summary technical report of division 2, vol. 1[S]. Washington D C: National Defence Research Committee, 1946. [13] LI Q M, REID S R, AHMAD-ZAIDI A M. Critical impact energies for scabbing and perforation of concrete target [J]. Nuclear Engineering and Design, 2006, 236(11): 1140–1148. DOI: 10.1016/j.nucengdes.2005.10.017. [14] CHEN X W, LI X L. Modeling of normal perforation of reinforced concrete slabs by a rigid projectile [J]. Transactions of Tianjin University, 2006,12 (S1): 107–111. [15] CHEN X W, FAN S C, LI Q M. Oblique and normal perforation of concrete targets by a rigid projectile [J]. International Journal of Impact Engineering, 2004, 30(6): 617–637. DOI: 10.1016/j.ijimpeng.2003.08.003. [16] PENG Y, WU H, FANG Q, et al. A note on the deep penetration and perforation of hard projectiles into thick targets [J]. International Journal of Impact Engineering, 2015, 85: 37–44. DOI: 10.1016/j.ijimpeng.2015.06.013. [17] FORRESTAL M J, TZOU D Y. A spherical cavity-expansion penetration model for concrete targets [J]. International Journal of Solids and Structures, 1997, 34(31/32): 4127–4146. DOI: 10.1016/S0020-7683(97)00017-6. [18] CHEN X W, LI Q M. Deep penetration of a non-deformable projectile with different geometrical characteristics [J]. International Journal of Impact Engineering, 2002, 27(6): 619–637. DOI: 10.1016/S0734-743X(02)00005-2. [19] FORRESTAL M J, FREW D J, HICKERSON J P, et al. Penetration of concrete targets with deceleration-time measurements [J]. International Journal of Impact Engineering, 2003, 28(5): 479–497. DOI: 10.1016/S0734-743X(02)00108-2. [20] ROSENBERG Z, DEKEL E. The penetration of rigid long rods–revisited [J]. International Journal of Impact Engineering, 2009, 36(4): 551–564. DOI: 10.1016/j.ijimpeng.2008.06.001. [21] ROSENBERG Z, DEKEL E. The deep penetration of concrete targets by rigid rods-revisited [J]. International Journal of Protective Structures, 2010, 1(1): 125–144. DOI: 10.1260/2041-4196.1.1.125. [22] ROSENBERG Z, DEKEL E, KOSITSKI R. A comment on “constant deceleration approach for the penetration analysis of rigid projectiles into concrete targets [J]. International Journal of Protective Structures, 2020, 11(3): 411–414. DOI: 10.1177/2041419620939117. [23] ROSENBERG Z, KOSITSKI R, DEKEL E. Comment on: “rigid and eroding projectile penetration into concrete targets based on an extended cavity expansion model [J]. International Journal of Impact Engineering, 2017, 100(104): A1–A3. DOI: 10.1016/j.ijimpeng.2017.03.004. [24] YANKELEVSKY D Z, FELDGUN V R. Constant deceleration approaches for penetration analysis of rigid projectile into concrete [J]. International Journal of Protective Structures, 2020, 11(4): 515–532. DOI: 10.1177/2041419620914646. [25] YANKELEVSKY D Z, FELDGUN V R. Response and closure to: a comment on “Constant deceleration approach for the penetration analysis of rigid projectiles into concrete targets [J]. International Journal of Protective Structures, 2020, 11(3): 415–420. DOI: 10.1177/2041419620939106. [26] 陈小伟, 李继承. 刚性弹侵彻深度和阻力的比较分析 [J]. 爆炸与冲击, 2009, 29(6): 584–589. DOI: 10.11883/1001-1455(2009)06-0584-06.CHEN X W, LI J C. Analysis on the penetration depth and resistive force in the deep penetration of a rigid projectile [J]. Explosion and Shock Waves, 2009, 29(6): 584–589. DOI: 10.11883/1001-1455(2009)06-0584-06. [27] KONG X Z, WU H, FANG Q, et al. Response to: comment on “rigid and eroding projectile penetration into concrete targets based on an extended cavity expansion model” by Kong et al. Int. J. Impact Eng. 2017 by Z. Rosenberg et al [J]. International Journal of Impact Engineering, 2017, 100(104): 150–153. DOI: 10.1016/j.ijimpeng.2017.03.003. [28] FREW D J, FORRESTAL M J, CARGILE J D. The effect of concrete target diameter on projectile deceleration and penetration depth [J]. International Journal of Impact Engineering, 2006, 32(10): 1584–1594. DOI: 10.1016/j.ijimpeng.2005.01.012. [29] FREW D J, HANCHAK S J, GREEN M L, et al. Penetration of concrete targets with ogive-nose steel rods [J]. International Journal of Impact Engineering, 1998, 21(6): 489–497. DOI: 10.1016/S0734-743X(98)00008-6. [30] TELAND J A, SJØL H. Penetration into concrete by truncated projectiles [J]. International Journal of Impact Engineering, 2004, 30(4): 447–464. DOI: 10.1016/S0734-743X(03)00073-3. [31] LI J Z, LV Z J, ZHANG H S, et al. Perforation experiments of concrete targets with residual velocity measurements [J]. International Journal of Impact Engineering, 2013, 57: 1–6. DOI: 10.1016/j.ijimpeng.2013.01.007. [32] FORRESTAL M J, FREW D J, HANCHAK S J, et al. Penetration of grout and concrete targets with ogive-nose steel projectiles [J]. International Journal of Impact Engineering, 1996, 18(5): 465–476. DOI: 10.1016/0734-743X(95)00048-F. [33] 吴飚, 任辉启, 陈力, 等. 弹体侵彻混凝土尺度效应试验研究与理论分析 [J]. 防护工程, 2020, 42(2): 1–10. DOI: 10.3969/j.issn.1674-1854.2020.02.001.WU B, REN H Q, CHEN L, et al. Experimental study and theoretical analysis of size effect on projectile penetrating concrete [J]. Protective Engineering, 2020, 42(2): 1–10. DOI: 10.3969/j.issn.1674-1854.2020.02.001. [34] WU H, LI Y C, FANG Q, et al. Scaling effect of rigid projectile penetration into concrete target: 3D mesoscopic analyses [J]. Construction and Building Materials, 2019, 208: 506–524. DOI: 10.1016/j.conbuildmat.2019.03.040. [35] 彭永, 卢芳云, 方秦, 等. 弹体侵彻混凝土靶体的尺寸效应分析 [J]. 爆炸与冲击, 2019, 39(11): 113301. DOI: 10.11883/bzycj-2018-0402.PENG Y, LU F Y, FANG Q, et al. Analyses of the size effect for projectile penetrations into concrete targets [J]. Explosion and Shock Waves, 2019, 39(11): 113301. DOI: 10.11883/bzycj-2018-0402. [36] CANFIELD J A, CLATOR I G. Development of a scaling law and techniques to investigate penetration in concrete [M]. United States Naval Weapons Laboratory, 1966. [37] ANDERSON JR C E, MULLIN S A, KUHLMAN C J. Computer simulation of strain-rate effects in replica scale model penetration experiments [J]. International Journal of Impact Engineering, 1993, 13(1): 35–52. DOI: 10.1016/0734-743X(93)90107-I. [38] HUANG X, KONG X, HU J, et al. Scaling the failure of concrete gravity dam subjected to underwater explosion shock loading [J]. Ocean Engineering, 2022, 261: 112176. DOI: 10.1016/j.oceaneng.2022.112176. [39] 徐建波. 长杆射弹对混凝土的侵彻特性研究 [D]. 长沙:国防科学技术大学, 2001. DOI: 10.7666/d.y480203.XU J B. Investigations on long projectiles penetrating into concrete targets [D]. Changsha: National University of Defense Technology, 2001. DOI: 10.7666/d.y480203. [40] O’NEIL E F, NEELEY B D, CARGILE J D. Tensile properties of very-high-strength concrete for penetration-resistant structures [J]. Shock and Vibration, 1999, 6(5/6): 237–245. DOI: 10.1155/1999/415360. [41] UNOSSON M, NILSSON L. Projectile penetration and perforation of high performance concrete: experimental results and macroscopic modelling [J]. International Journal of Impact Engineering, 2006, 32(7): 1068–1085. DOI: 10.1016/j.ijimpeng.2004.11.003. [42] 柴传国. 异形头部弹体对混凝土靶的侵彻效应研究 [D]. 北京:北京理工大学, 2014. DOI: CNKI:CDMD:1.1014.086790.CHAI C G. Study on the mechanism of penetration into concrete of nose headed projectile [D]. Beijing: Beijing Institute of Technology, 2014. [43] 栾晓岩, 贺虎成, 耿忠, 等. 弹丸侵彻混凝土的试验与仿真 [J]. 系统仿真学报, 2008, 20(13): 3571–3573. DOI: 10.16182/j.cnki.joss.2008.13.016.LUAN X Y, HE H C, GENG Z, et al. Simulation and experiment of projectile penetrating into concrete [J]. Journal of System Simulation, 2008, 20(13): 3571–3573. DOI: 10.16182/j.cnki.joss.2008.13.016. [44] GRAN J K, FREW D J. In-target radial stress measurements from penetration experiments into concrete by ogive-nose steel projectiles [J]. International Journal of Impact Engineering, 1997, 19(8): 715–726. DOI: 10.1016/S0734-743X(97)00008-0. [45] 周宁, 任辉启, 沈兆武, 等. 弹丸侵彻混凝土和钢筋混凝土的实验 [J]. 中国科学技术大学学报, 2006, 36(10): 1021–1027. DOI: 10.3969/j.issn.0253-2778.2006.10.001.ZHOU N, REN H Q, SHEN Z W, et al. Experimental on the projectile penetration concrete targets and reinforced concrete targets [J]. Journal of University of Science and Technology of China, 2006, 36(10): 1021–1027. DOI: 10.3969/j.issn.0253-2778.2006.10.001. [46] 石志勇, 汤文辉, 赵国民, 等. 混凝土靶中侵彻深度的相似性研究 [J]. 弹道学报, 2005, 17(1): 62–66. DOI: 10.3969/j.issn.1004-499X.2005.01.012.SHI Z Y, TANG W H, ZHAO G M, et al. Similarity study of the penetration depth for the concrete targets [J]. Journal of Ballistics, 2005, 17(1): 62–66. DOI: 10.3969/j.issn.1004-499X.2005.01.012. [47] 王德荣, 葛涛, 周泽平, 等. 钢纤维超高强活性混凝土(RPC)抗侵彻计算方法研究 [J]. 爆炸与冲击, 2006, 26(4): 367–372. DOI: 10.11883/1001-1455(2006)04-0367-06.WANG D R, GE T, ZHOU Z P, et al. Investigation of calculation method for anti-penetration of reactive power steel fiber concrete (RPC) [J]. Explosion and Shock Waves, 2006, 26(4): 367–372. DOI: 10.11883/1001-1455(2006)04-0367-06. [48] 顾晓辉, 王晓鸣, 陈惠武, 等. 动能侵彻体垂直侵彻半无限厚混凝土靶的试验研究 [J]. 实验力学, 2004, 19(1): 103–108. DOI: 10.3969/j.issn.1001-4888.2004.01.019.GU X H, WANG X M, CHEN H W, et al. Experimental study on the kinetic energy penetrations against semi-infinite concrete targets at normal incidence [J]. Journal of Experimental Mechanics, 2004, 19(1): 103–108. DOI: 10.3969/j.issn.1001-4888.2004.01.019. [49] DANCYGIER A N. Rear face damage of normal and high-strength concrete elements caused by hard projectile impact [J]. Structural Journal, 1998, 95(3): 291–304. DOI: 10.14359/547. [50] HANCHAK S J, FORRESTAL M J, YOUNG E R, et al. Perforation of concrete slabs with 48 MPa (7 ksi) and 140 MPa (20 ksi) unconfined compressive strengths [J]. International Journal of Impact Engineering, 1992, 12(1): 1–7. DOI: 10.1016/0734-743X(92)90282-X. [51] WU H, FANG Q, PENG Y, et al. Hard projectile perforation on the monolithic and segmented RC panels with a rear steel liner [J]. International Journal of Impact Engineering, 2015, 76: 232–250. DOI: 10.1016/j.ijimpeng.2014.10.010. [52] 薛建锋, 张鹏, 刘涛, 等. 不同靶板厚度对混凝土靶的抗侵彻性能研究 [J]. 兵器材料科学与工程, 2017, 40(5): 59–63. DOI: 10.14024/j.cnki.1004-244x.20170907.005.XUE J F, ZHANG P, LIU T, et al. Penetrating performance of concrete target with different thickness [J]. Ordnance Material Science and Engineering, 2017, 40(5): 59–63. DOI: 10.14024/j.cnki.1004-244x.20170907.005. [53] ZHANG S B, KONG X, FANG Q, et al. Numerical prediction of dynamic failure in concrete targets subjected to projectile impact by a modified Kong-Fang material model [J]. International Journal of Impact Engineering, 2020, 144: 103633. DOI: 10.1016/j.ijimpeng.2020.103633. [54] WANG Y, KONG X, FANG Q, et al. Modelling damage mechanisms of concrete under high confinement pressure [J]. International Journal of Impact Engineering, 2021, 150: 103815. DOI: 10.1016/j.ijimpeng.2021.103815. [55] 武海军, 黄风雷, 金乾坤, 等. 弹体贯穿钢筋混凝土数值模拟 [J]. 爆炸与冲击, 2003, 23(6): 545–550.WU H J, HUANG F L, JIN Q K, et al. Numerical simulation on perforation of reinforced concrete targets [J]. Explosion and Shock Waves, 2003, 23(6): 545–550. [56] 邓国强, 董军, 杨秀敏. 弹丸冲击下钢筋混凝土板的局部破坏形态分析 [C]//第十三届全国结构工程学术会议, 2004. [57] KONG X, FANG Q, CHEN L, et al. A new material model for concrete subjected to intense dynamic loadings [J]. International Journal of Impact Engineering, 2018, 120: 60–78. DOI: 10.1016/j.ijimpeng.2018.05.006. [58] 中华人民共和国住房和城乡建设部.GB/T 50107-2010, 混凝土强度检验评定标准 [S]. [59] 甄建伟, 曹凌宇, 孙福. 弹药毁伤效应数值仿真技术 [M]. 北京: 北京理工大学出版社, 2018. [60] 严平, 谭波, 苗润, 等. 战斗部及其毁伤原理 [M]. 北京: 国防工业出版社, 2020. -
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