多弹丸协同冲击下柱壳装药响应特性数值模拟及试验

doi:10.12382/bgxb.2024.0356

摘要/Abstract

摘要：

为探究多弹目交汇条件下多爆炸成形弹丸(Multiple Explosively Formed Projectiles,MEFP)协同冲击柱壳装药响应特性,在冲击起爆试验基础上,采用理论计算和数值仿真相结合的方式,开展不同密集度MEFP群束协同冲击柱壳装药的响应特性分析研究。实验结果表明:MEFP群束密集度λ及柱壳壁厚h均会对响应特性产生影响;当λ相同时起爆用时t随h增大而同步增加,3种壁厚起爆用时分别增大2.00、2.50、1.88倍,当λ为8和5.33时,起爆用时t随h呈线性增长规律;当h相同时起爆用时t随λ减小同步增加,4种密集度MEFP群束起爆用时分别增大2.66、3.60、3.25、2.50倍,且当柱壳壁厚h为13mm时起爆用时t随λ同样呈线性变化规律。MEFP群束对柱壳装药的协同增强作用在h为13mm时发生分化,当λ为16和8时,MEFP群束对目标的冲击起爆用时均早于任意单EFP作用,最多分别提前约41.22%、8.61%,协同增强作用明显;当λ为4时,MEFP群束对柱壳装药起爆能力逐渐与单EFP趋同,协同增强作用减弱。

关键词: 多爆炸成形弹丸战斗部, 柱壳装药, 数值模拟, 响应特性

Abstract:

The response characteristics of cylindrical shell charge under the collaborative impact of multiple explosively formed projectiles (MEFPs) are studied. The response characteristics of cylindrical shell charges with different densities are analyzed by using a combination of theoretical calculation and numerical simulation based on impact detonation tests. The results indicate that the density of MEFPs, λ, and the thickness of cylindrical shell wall both affect the response characteristics. When λ is the same, the initiation time t increases synchronously with the increase in the thickness of cylindrical shell wall. The initiation time for the three wall thicknesses is increased by 2.00, 2.50, and 1.88 times, respectively. Especially when λ is 8 and 5.33, the initiation time shows a linear growth pattern; when h is the same, the initiation time t increases synchronously with the decrease in λ. The initiation time for the four spacings is increased by 2.66, 3.60, 3.25, and 2.50 times, respectively. Moreover, when h is 13mm, the initiation time also shows a linear pattern.The synergistic enhancement effect of MEFPs on cylindrical shell charges is differentiated when h is 13mm. When λ is 18 and 8, the impact initiation time of MEFP on a target is earlier than that of any single explosively formed projectile (EFP), with a maximum advance of about 41.22% and 8.61%, respectively, indicating a significant synergistic enhancement effect. When λ is adjusted to 4, the initiation ability of MEFPs on the cylindrical shell charges gradually converges with that of a single EFP, and the synergistic enhancement effect weakens.

Key words: multiple explosively formed projectiles warhead, cylindrical shell charge, numerical simulation, response characteristics

中图分类号:

TJ55

张琨, 赵长啸, 韩彪, 纪冲, 张波, 张凯凯, 唐蓉. 多弹丸协同冲击下柱壳装药响应特性数值模拟及试验[J]. 兵工学报, 2024, 45(S1): 70-80.

ZHANG Kun, ZHAO Changxiao, HAN Biao, JI Chong, ZHANG Bo, ZHANG Kaikai, TANG Rong. Numerical Simulation and Experimental Study on the Response Characteristics of Cylindrical Shell Charge under Collaborative Impact of Multiple Projectiles[J]. Acta Armamentarii, 2024, 45(S1): 70-80.

图/表 19

图1 组合式MEFP战斗部装配体及实物

Fig.1 Combined MEFP warhead assembly and physical object

图2 组合式MEFP战斗部冲击侵彻柱壳装药模拟目标

Fig.2 The simulated target of shell charge penetrated by a combined MEFP warhead in simulation

图3 组合式MEFP战斗部冲击引爆13mm厚柱壳装药模拟目标过程

Fig.3 Detonation process of 13mm-thick shell charge under the impact of the combined MEFP warhead in simulation

图4 回收的13mm厚柱壳装药模拟目标壳体残片

Fig.4 Recovered shell fragments of 13mm-thick cylindrical shell charge in simulation

图5 组合式MEFP战斗部攻击柱壳装药模型

Fig.5 Model of the combined MEFP warhead attacking a cylindrical shell charge

表1 8701炸药主要参数

Table 1 Main parameters of 8701 explosive

参数	ρ/(g·cm^-3)	D/(m·s^-1)	P_CJ/GPa	A	B	R₁	R₂	ω	V₀
数值	1.7	8315	29.5	8.545	20.49×10^-2	4.6	1.35	0.25	1.0

表2 高导无氧铜和6063铝合金主要参数

Table 2 Main parameters of high conductivity oxygen free copper and 6063 aluminum alloy

参数	ρ/(g·cm-³)	G/GPa	A₁	B₁	C	m	T_m/K	T_r/K	C_v
高导无氧铜	8.968	46	0.9×10^-3	2.92×10^-3	0.025	1.09	1356	300.15	2.83×10^-6
6063铝合金	2.7	27.6	2.65×10^-3	4.26×10^-3	0.015	1.09	775	294	8.75×10^-6

表3 45号钢主要参数

Table 3 Main parameters of 45# steel

参数	ρ/(g·cm³)	E/GPa	μ	σ_s/GPa	E_t/MPa	ε_s
数值	7.83	207	0.3	0.005	207	0.47

表4 TNT点火增长模型主要参数

Table 4 Main parameters of TNT ignition growth model

参数	ρ/(g·cm^-3)	D/(m·s^-1)	P_CJ/GPa	A	B	R₁	R₂	ω	T₀/K
数值	1.65	6930	18	171.01	-0.03745	9.8	0.98	0.3	298

表5 计算工况设定

Table 5 Calculation condition setting

λ	h/mm
λ	11	12	13
16	1-1'	1-2'	1-3'
8	2-1'	2-2'	2-3'
5.33	3-1'	3-2'	3-3'
4	4-1'	4-2'	4-3'

图6 θ=0°时MEFP攻击柱形带壳装药

Fig.6 Schematic diagram of MEFP attacking a cylindrical shell charge for θ=0°

表6 4种组合式MEFP各角度分布

Table 6 Angular distributions of four combined MEFPs

d/mm	2	4	6	8
θ₁/(°)	18°39'	19°52'	21°6'	22°20'
θ₂/(°)	9°12'	9°47'	10°22'	10°57'
θ_a/(°)	37°18'	39°44'	42°12'	44°40'

表7 各工况MEFP侵彻13mm厚柱壳前及穿透壳体后参数

Table 7 Comparison of parameter changes before and after MEFP penetrates a 13mm-thick cylindrical shell

参量		m₀/ g	m₁/ g	v₀/ (m·s^-1)	v₁/ (m·s^-1)
	中心弹丸	11.44	4.36	1773	965
1-3'	1号周边弹丸	11.48	4.27	1758	940
	2号周边弹丸	11.48	4.13	1758	953
	中心弹丸	11.52	4.22	1744	937
2-3'	1号周边弹丸	11.52	4.23	1742	923
	2号周边弹丸	11.52	4.21	1742	915
	中心弹丸	11.52	4.22	1741	935
3-3'	1号周边弹丸	11.46	4.17	1741	920
	2号周边弹丸	11.46	4.15	1741	918
	中心弹丸	11.52	4.21	1742	917
4-3'	1号周边弹丸	11.4	4.11	1741	922
	2号周边弹丸	11.4	4.12	1741	924

图7 4种计算工况下各弹丸冲击作用13mm厚柱壳装药时炸药内部最大压力变化曲线

Fig.7 Variation curves of maximum pressure inside the explosive during impact on a 13mm-thick cylindrical shell charge

表8 不同工况对不同厚度45号钢柱壳装药的冲击毁伤结果

Table 8 Impact damage results of 45# steel cylindrical shells with different thicknesses under different working conditions

d/mm	作用弹丸	h=11mm		h=12mm		h=13mm
d/mm	作用弹丸	毁伤状态	起爆机制	毁伤状态	起爆机制	毁伤状态	起爆机制
	所有弹丸	起爆	冲击引爆	起爆	冲击引爆	起爆	冲击引爆
2	中心弹丸	起爆	冲击引爆	起爆	冲击引爆	起爆	冲击引爆
	1号周边弹丸	起爆	冲击引爆	起爆	剪切引爆	未起爆	·
	2号周边弹丸	起爆	冲击引爆	起爆	冲击引爆	起爆	剪切引爆
	所有弹丸	起爆	冲击引爆	起爆	冲击引爆	起爆	冲击引爆
4	中心弹丸	起爆	冲击引爆	起爆	冲击引爆	起爆	剪切引爆
	1号周边弹丸	起爆	冲击引爆	起爆	剪切引爆	未起爆	·
	2号周边弹丸	起爆	冲击引爆	起爆	冲击引爆	起爆	剪切引爆
	所有弹丸	起爆	冲击引爆	起爆	冲击引爆	起爆	冲击引爆
6	中心弹丸	起爆	冲击引爆	起爆	剪切引爆	起爆	剪切引爆
	1号周边弹丸	起爆	冲击引爆	起爆	剪切引爆	未起爆	·
	2号周边弹丸	起爆	冲击引爆	起爆	剪切引爆	起爆	剪切引爆
	所有弹丸	起爆	冲击引爆	起爆	冲击引爆	起爆	剪切引爆
8	中心弹丸	起爆	冲击引爆	起爆	剪切引爆	起爆	剪切引爆
	1号周边弹丸	起爆	冲击引爆	起爆	剪切引爆	未起爆	·
	2号周边弹丸	起爆	冲击引爆	起爆	剪切引爆	起爆	剪切引爆

图8 工况1-3'中心弹丸与MEFP群束冲击13mm厚柱壳装药及起爆被发装药过程

Fig.8 Processes of central projectile and MEFP impacting 13mm-thick cylindrical shell charge and initiatiing a charge under Condition 1-3'

图9 冲击3种壁厚柱壳装药时炸药内部最大压力变化曲线

Fig.9 Variation curves of maximum pressure inside the explosive when impacting 3 cylindrical shell charges with different wall thicknesses

表9 4种密集度弹丸群束对3种厚度柱壳装药冲击起爆用时

Table 9 Impact initiation times of four projectiles on 3 cylindrical shell charges with different wall thicknesses μs

λ	h/mm
λ	11	12	13
16	3	3.6	8
8	3	6.5	10.8
5.33	4	9	13
4	6	9	15

图10 各工况MEFP群束冲击起爆3种壁厚柱壳装药用时曲面图

Fig.10 Curved surface diagram of 3 types of cylindrical shells with different wall thicknesses during MEFPs impact detonation under various working conditions

参考文献 23

[1]	ROSLUND L A. Initiation of warhead fragments I: normal impacts NOLTR 73-124[R]. White Oak,IL, US: Naval Surface Weapons Center,1973.
[2]	JAMES H R. Critical energy criterion for the shock initiation of explosives by projectile impact[J]. Propellants,Explosives,Pyrotechnics, 1988, 13(2): 35-41.
[3]	HELD M. Initiation phenomena with shaped charge jets[C]// Proceedings of the 9th International Symposium on Detonation. Oregon the Portland, the Netherlands: Materials Science, Engineering, Chemistry, 1989: 1416-1426.
[4]	QUIDOT M, HAMAIDE S, GROUX J, et al. Fragment impact initiation of cast PBXs in relation with shock sensitivity tests[C]// Proceedings of the 10th International Symposium on Detonation.Boston, MA, US: Office of Naval Research, ONR 33395—12, 1993: 113-121.
[5]	LLOYD R. Conventional warhead systems physics and engineering design[M]. Washington,US: American Institute of Aeronautics and Astronautics, Inc.,1998.
[6]	李文彬, 赵国志, 何勇, 等. 两破片同时撞击非均质炸药的冲击起爆[J]. 弹箭与制导学报, 2002, 22(3):147-149,152.
	LI W B, ZHAO G Z, HE Y, et al. Study on shock initiation of explosives by the impact of two fragments at the same time[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2002, 22(3):147-149,152. (in Chinese)
[7]	杨洋, 韩勇, 段英良, 等. 双钨球破片同时冲击柱壳装药起爆响应规律[J]. 兵工学报, 2021, 42(增刊1):46-52.
	YANG Y, HAN Y, DUAN Y L, et al. Initiation response law of cylindrical charge subjected to simultaneous impact of two tungsten ball fragments[J]. Acta Armamentarii, 2021, 42(S1):46-52. (in Chinese)
[8]	郭淳, 张先锋, 熊玮. 双EFP冲击引爆带盖板B炸药的累积毁伤效应[J]. 含能材料, 2023, 31(8):797-807.
	GUO C, ZHANG X F, XIONG W, et al. Cumulative damage effect on shock initiation of covered composition B by dual EFP impacts[J]. Chinese Journal of Energetic Materials, 2023, 31(8):797-807. (in Chinese)
[9]	郭淳, 郭尚生, 钱建平, 等. 多破片对柱壳装药冲击起爆速度阈值的数值模拟研究[J]. 爆炸与冲击, 2020, 40(6):24-32.
	GUO C, GUO S S, QIAN J P, et al. Numerical simulation on shock critical initiation velocity of cylindrical covered charge by multiple fragment impacts[J]. Explosion and Shock Waves, 2020, 40(6):24-32. (in Chinese)
[10]	郭淳, 郭尚生, 钱建平. 双球破片冲击柱壳装药的临界起爆条件[J]. 国防科技大学学报, 2022, 44(2):188-194.
	GUO C, GUO S S, QIAN J P, et al. Critical initiation condition of cylindrical covered charge by double spherical fragments impact[J]. Journal of National University of Defense Technology, 2022, 44(2):188-194. (in Chinese)
[11]	王昕, 蒋建伟, 王树有, 等. 钨球对柱面带壳装药的冲击起爆数值模拟研究[J]. 兵工学报, 2017, 38(8):1498-1505. doi: 10.3969/j.issn.1000-1093.2017.08.006
	WANG X, JIANG J W, WANG S Y, et al. Numerical simulation on the initiation of cylindrical covered charge impacted by tungsten sphere fragment[J]. Acta Armamentarii, 2017, 38(8):1498-1505. (in Chinese) doi: 10.3969/j.issn.1000-1093.2017.08.006
[12]	张广华, 韩秀凤, 沈飞, 等. 带壳装药在不同材质破片撞击下的响应特性[J]. 兵器装备工程学报, 2022, 43(8):1-6.
	ZHANG G H, HAN X F, SHEN F, et al. Reaction characteristic of covered charge impacted by different material fragments[J]. Journal of Ordnance Equipment Engineering, 2022, 43(8): 1-6. (in Chinese)
[13]	陈清畴, 刘刚, 马弢. 飞片初始形状对雷管起爆能力的影响[J]. 火工品, 2020(1):6-9.
	CHEN Q C, Liu G, MA T. Effects of the flyer shape on detonator output[J]. Initiators & Pyrotechnics, 2020(1):6-9. (in Chinese)
[14]	李一鸣, 杨晓红, 姚文进, 等. 背板材料及炸药厚度对破片冲击起爆8701炸药装药的影响[J]. 火炸药学报, 2020, 43(3):276-281. doi: 10.14077/j.issn.1007-7812.202001007
	LI Y M, YANG X H, YAO W J, et al. Effects of back plate materials and explosives thickness on the fragment impact initiation of 8701 explosives charge[J]. Chinese Journal of Explosives & Propellants, 2020, 43(3):276-281. (in Chinese)
[15]	贺翔, 董海平, 严楠. JO-9C(Ⅲ)炸药的飞片冲击起爆判据参数拟合[J]. 高压物理学报, 2023, 37(2):121-131.
	HE X, DONG H P, YAN N, et al. Parameter fitting of flyer impact initiation criteria of JO-9C(Ⅲ) explosive[J]. Chinese Journal of High Physics, 2023, 37(2):121-131. (in Chinese)
[16]	XU Y X, GAO P, Wang S S. Critical criterion for the shock initiation/ignition of cylindrical charges with thin aluminum shell impacted by steel fragment[J]. Propellants Explosives Pyrotechnics 42( 8), 921-931.
[17]	LI Y M, LI W B, ZHANG Q, et al. Shock initiation of covered flake JH-2 high explosive by simultaneous impact of multiple fragments[J]. Propellants Explosives Pyrotechnics, 45(7):1133-1144.
[18]	张琨, 刘永旭, 赵长啸, 等. MEFP协同冲击平面带壳装药数值模拟研究[J]. 兵器装备工程学报, 2022, 43(8):13-19.
	ZHANG K, LIU Y X, ZHAO C X, et al. Numerical simulation of MEFP collaborative impact planar shell charge[J]. Journal of Ordnance Equipment Engineering, 2022, 43(8): 13-19. (in Chinese)
[19]	LIU J F, LONG Y, JI C, et al. The influence of liner material on the dynamic response of the finite steel target subjected to high velocity impact by explosively formed projectile[J]. International Journal of Impact Engineering 109:264-275.
[20]	ZHANG K, ZHAO C X, JI C, et al. Numerical simulation and experimental study of the damage law of EFP warhead charging of cylindrical shells under different angles[J]. Latin American Journal of Solids and Structures, 2022, 19(4): e451.
[21]	HOWE P M. On the role of shock and shear mechanism in the initiation of detonation by fragment impact[C]// Proceedings of the 8th International Symposium on Detonation.Albuquerque, New Mexico, US: Department of the Navy, 1985:150-1160.
[22]	王礼立, 朱兆祥. 应力波基础[M]. 北京: 国防工业出版社, 2005:216-239.
	WANG L L, ZHU Z X. Foundation of stress waves[M]. Beijing: National Defence Industry Press, 2005:216-239. (in Chinese)
[23]	TIMOSHENKO S, GOODIER J N. Theory of elasticity[M]. NY, US: Mc Graw-Hill, 1951:56-83.