Velocity Variation Law of Limited Targets during Dislocated Sequential Penetration by Two Projectiles

XU Baowen; ZHANG Dingshan; LYU Yongzhu; ZHANG Bo; QUAN Jialin

doi:10.19554/j.cnki.1001-3563.2026.09.002

PDF(1067 KB)

Packaging Engineering ›› 2026, Vol. 47 ›› Issue (9) : 14-22. DOI: 10.19554/j.cnki.1001-3563.2026.09.002

Special Topic on Ammunition Response and Protection Technology under Intensive Dynamic Loading

Velocity Variation Law of Limited Targets during Dislocated Sequential Penetration by Two Projectiles

XU Baowen, ZHANG Dingshan^*, LYU Yongzhu, ZHANG Bo, QUAN Jialin

Author information +

History +

Abstract

The work aims to investigate the effects of dislocation distance and projectile diameter on the velocity variation of the second projectile during the dislocated sequential penetration of a concrete target, to provide theoretical support for the evaluation of damage effectiveness and the optimization design of combat strategies in the dislocated sequential penetration process. A theoretical model was developed to characterize the energy loss and velocity change during the dislocated sequential penetration process. A comparison was made between theoretical calculations and numerical simulations. Under test conditions involving penetration of a 1 m thick C40 concrete target at an initial velocity of 600 m/s, the critical dislocation distances for projectile diameters of 50 mm, 80 mm, and 100 mm were approximately 8, 10, and 14 times of the projectile diameter, respectively. The theoretical calculation result of the velocity variation of the second projectile differed from the simulation result by a maximum of about 6.6%. The results indicate that dislocated sequential penetration reduces the velocity decay of the second projectile, thereby enhancing its penetration depth. As the dislocation distance increases, the beneficial influence of the first projectile on the second projectile's velocity retention diminishes. Beyond a critical dislocation distance, this effect becomes negligible. A larger diameter of the first projectile corresponds to a greater critical dislocation distance.

Key words

penetration / dislocated penetration / velocity variation / numerical simulation

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

XU Baowen, ZHANG Dingshan, LYU Yongzhu, ZHANG Bo, QUAN Jialin. Velocity Variation Law of Limited Targets during Dislocated Sequential Penetration by Two Projectiles[J]. Packaging Engineering. 2026, 47(9): 14-22 https://doi.org/10.19554/j.cnki.1001-3563.2026.09.002

References

[1] ANTOUN T H, LOMOV I N, GLENN L A.Simulation of the Penetration of a Sequence of Bombs into Granitic Rock[J]. International Journal of Impact Engineering, 2003, 29(1/2/3/4/5/6/7/8/9/10): 81-94.
[2] 刘双喜, 徐小平, 黄伟, 等. 国外多弹协同项目发展及关键技术展望[J]. 航空兵器, 2024, 31(6): 1-13.
LIU S X, XU X P, HUANG W, et al.Development and Key Technologies Outlook of Foreign Multi-Missile Collaborative Projects[J]. Aero Weaponry, 2024, 31(6): 1-13.
[3] 赵鸿燕. 美国面向未来战争的导弹协同作战概念发展研究[J]. 航空兵器, 2019, 26(4): 1-9.
ZHAO H Y.Research on the Concept Development of the United States Missile Cooperative Operations for Future War[J]. Aero Weaponry, 2019, 26(4): 1-9.
[4] 宗香华, 王银, 孔祥振, 等. 错位多次打击下UHPC靶体损伤破坏效应的数值模拟研究[J]. 高压物理学报, 2024, 38(3): 158-170.
ZONG X H, WANG Y, KONG X Z, et al.Numerical Investigation on Damage and Failure of UHPC Targets Subjected to Dislocation Multi-Attacks[J]. Chinese Journal of High Pressure Physics, 2024, 38(3): 158-170.
[5] 邓国强, 杨秀敏. 工程岩体中多弹重复打击效应的数值模拟分析[J]. 爆炸与冲击, 2014, 34(3): 361-366.
DENG G Q, YANG X M.Numerical Simulation of the Effect of Multiply EPW into Engineering Rock[J]. Explosion and Shock Waves, 2014, 34(3): 361-366.
[6] 邓国强, 杨秀敏. 钻地弹重复打击效应现场试验研究[J]. 防护工程, 2012, 34(5): 1-5.
DENG G Q, YANG X M.Experimental Investigation into Damage Effects of Repeated Attacks of Precision-Guided Penetration Weapons[J]. Protective Engineering, 2012, 34(5): 1-5.
[7] GOMEZ J T, SHUKLA A.Multiple Impact Penetration of Semi-Infinite Concrete[J]. International Journal of Impact Engineering, 2001, 25(10): 965-979.
[8] 李金城. 射弹两次打击混凝土介质的累积侵彻效应研究[D]. 南京: 南京理工大学, 2018.
LI J C.Study on the Cumulative Penetration Effect of Two Projectiles Striking Concrete Media[D]. Nanjing: Nanjing University of Science and Technology, 2018.
[9] 张丁山, 全嘉林, 付良, 等. 侵彻弹体尖卵形头部形状对偏转力矩的影响[J]. 火炸药学报, 2023, 46(9): 834-839.
ZHANG D S, QUAN J L, FU L, et al.Effect of Sharp Oval-Nose Factor on Deflection Moment of the Penetration Projectile[J]. Chinese Journal of Explosives & Propellants, 2023, 46(9): 834-839.
[10] 薛建锋, 沈培辉, 王晓鸣. 弹体斜侵彻混凝土靶的跳弹及其规律研究[J]. 火炸药学报, 2016, 39(2): 54-58.
XUE J F, SHEN P H, WANG X M.Research on Ricochet and Its Regularity of Projectiles Obliquely Penetrating into Concrete Targets[J]. Chinese Journal of Explosives & Propellants, 2016, 39(2): 54-58.
[11] 武海军, 张爽, 黄风雷. 钢筋混凝土靶的侵彻与贯穿研究进展[J]. 兵工学报, 2018, 39(1): 182-208.
WU H J, ZHANG S, HUANG F L.Research Progress in Penetration/Perforation into Reinforced Concrete Targets[J]. Acta Armamentarii, 2018, 39(1): 182-208.
[12] 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.
[13] CHEN X W, LI X L, HUANG F L, et al.Normal Perforation of Reinforced Concrete Target by Rigid Projectile[J]. International Journal of Impact Engineering, 2008, 35(10): 1119-1129.
[14] 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.
[15] 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.
[16] 王可慧, 周刚, 李明, 等. 弹体高速侵彻钢筋混凝土靶试验研究[J]. 爆炸与冲击, 2021, 41(11): 89-96.
WANG K H, ZHOU G, LI M, et al.Experimental Research on the Mechanism of a High-Velocity Projectile Penetrating into a Reinforced Concrete Target[J]. Explosion and Shock Waves, 2021, 41(11): 89-96.
[17] 薛建锋, 沈培辉, 王晓鸣. 弹体侵彻混凝土开坑阶段阻力的计算[J]. 高压物理学报, 2016, 30(6): 499-504.
XUE J F, SHEN P H, WANG X M.Resistance during Cratering for Projectile Penetrating into Concrete Target[J]. Chinese Journal of High Pressure Physics, 2016, 30(6): 499-504.
[18] LIU J, LI J, FANG J G, et al.Ultra-High Performance Concrete Targets Against High Velocity Projectile Impact-A-State-of-the-Art Review[J]. International Journal of Impact Engineering, 2022, 160: 104080.
[19] YU R, SPIESZ P, BROUWERS H J H. Energy Absorption Capacity of a Sustainable Ultra-High Performance Fibre Reinforced Concrete (UHPFRC) in Quasi-Static Mode and under High Velocity Projectile Impact[J]. Cement and Concrete Composites, 2016, 68: 109-122.
[20] 刘志林, 史文卿, 蒋东, 等. 基于混凝土拉伸损伤的侵彻混凝土数值模拟研究[J]. 弹道学报, 2023, 35(3): 55-60.
LIU Z L, SHI W Q, JIANG D, et al.Numerical Study on Penetrating Concrete Targets Using Dynamic Constitutive Considering Tensile Damage[J]. Journal of Ballistics, 2023, 35(3): 55-60.
[21] 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.
[22] 马天宝, 武珺, 宁建国. 弹体高速侵彻钢筋混凝土的实验与数值模拟研究[J]. 爆炸与冲击, 2019, 39(10): 81-91.
MA T B, WU J, NING J G.Experimental and Numerical Study on Projectiles’ High-Velocity Penetration into Reinforced Concrete[J]. Explosion and Shock Waves, 2019, 39(10): 81-91.
[23] 聂铮玥, 彭永, 陈荣, 等. 侵彻条件下岩石类材料RHT模型参数敏感性分析[J]. 振动与冲击, 2021, 40(14): 108-116.
NIE Z Y, PENG Y, CHEN R, et al.Sensitivity Analysis of RHT Model Parameters for Rock Materials under Penetrating Condition[J]. Journal of Vibration and Shock, 2021, 40(14): 108-116.
[24] 郭锦炎, 阮文俊, 张丁山, 等. 半无限厚混凝土靶侵彻损伤的实验与仿真[J]. 弹箭与制导学报, 2012, 32(3): 103-106.
GUO J Y, RUAN W J, ZHANG D S, et al.Experimental and Simulation Study on Damage of Penetrating Half-Infinite Concrete Target[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2012, 32(3): 103-106.