Explosion Driving Characteristics of Shell Fragments Driven by Cylindrical Charge with Cavity

doi:10.12382/bgxb.2024.1089

Abstract

Abstract:

In order to study the explosion driving characteristics of shell fragments driven by cylindrical charge with cavity and reveal the mechanism of the influence of shaped charge structure on the initial velocity of shell fragments,the explosion driving process and initial velocity distribution of shell fragments under different cavity cone angles are studied through the numerical simulation.The initial velocity distribution function of shell fragment along the axial direction is fitted by analyzing the rarefaction wave propagation path,velocity loss coefficient and fragment acceleration process.The relative error between the calculated and simulated results is less than 15%.The results show that the earlier generation of rarefaction wave and the decrease in cross-section ratio of mass of charge to shell are the main factors contributing to the decrease in the initial velocity of fragments.The initial velocity of the fragments near the non-detonation end decreases with the decrease in the cone angle of cavity and the increase in the cone top height of cavity.The rarefaction wave reflected from the non-detonation end is an approximately planar wave and is at a certain angle to the cavity surface.The instant when rarefaction wave reaches shell is linearly and positively correlated with the axial position of the shell.The cross-section ratio of mass of charge to shell has a quadratic function relationship with k,where k is the ratio of the distance from the cross section to the non-initiating end to the height of cavity cone top.The velocity loss coefficient decays exponentially with the decrease in k.The research can provide a useful reference for the overall structural design,material selection and structural optimization of anti-armour and anti-personnel composite warheads and the deformable fragment warhead with cavity charge structure.

Key words: fragment warhead, shaped charge, numerical analysis, initial velocity distribution

CLC Number:

TJ410.1

WANG Chenxu, ZHANG Jiahao, CAI Yiqiang, ZHOU Sheng, GONG Jie, CHEN Pengwan, YU Qingbo. Explosion Driving Characteristics of Shell Fragments Driven by Cylindrical Charge with Cavity[J]. Acta Armamentarii, 2025, 46(9): 241089-.

Figures/Tables 32

Fig.1 Comparison of experimental and calculated results

Fig.2 Particle convergence analysis

Fig.3 Geometric model

Table 1 Johnson-Cook constitutive model of steel 45#[13,19,24]

ρ/(g·cm^-3)	A/MPa	B/MPa	C	n	m	T_melt	γ
7.83	507	320	0.064	0.28	1.06	1793	53.8

Table 2 EOS Gruneisen parameters of steel 45#[13]

c/(m·s^-1)	S₁	S₂	S₃	γ₀
4570	1.49	0	0	2.17

Table 3 Material model parameters of Comp B[26]

ρ/ (g·cm^-3)	D/ (m·s^-1)	p_CJ/ GPa	E/ (kJ·m^-3)	C₁/ GPa	C₂/ GPa	ω	R₁	R₂
1.717	7980	29	8.5×10⁶	542	7.68	0.24	4.2	1.1

Fig.4 Comparison of simulated and experimental results

Table 4 Parameters of samples in Refs.[11,16]

工况	装药长度/ mm	壳体外径/ mm	装药外径/ mm	空腔直径/ mm
1	77.3	29.68	23.6	0
2	90.0	54.00	45.0	0
3	90.0	54.00	45.0	18
4	90.0	54.00	45.0	27

Fig.5 3D calculation model

Fig.6 Propagation of detonation wave near detonation end

Fig.7 Propagation of detonation wave near non-detonation end

Fig.8 Location of gauge points

Fig.9 Shell acceleration process at gauge points

Fig.10 Shell acceleration process near non-detonation end

Fig.11 Analysis model of rarefaction wave propagation

Fig.12 Prediction for instants when rarefaction wave reaches shell

Fig.13 Initial velocity distribution of fragments under different cavity cone angles

Fig.14 Variation of cross-section ratio of mass of charge to shell with relative location

Fig.15 Fragment initial velocity loss coefficient distribution under different cavity cone angles

Table 5 Fitting values and goodness of G(α) and H(α)

序号	α/(°)	G(α)	H(α)	拟合优度
1	30	0.75060	2.2140	0.9968
2	40	0.66710	2.0940	0.9981
3	50	0.58530	1.9810	0.9934
4	60	0.51180	1.8690	0.9825
5	70	0.42330	1.6710	0.9786
6	80	0.33620	1.4390	0.9759
7	90	0.26560	1.2260	0.9733
8	100	0.20530	1.0200	0.9736
9	110	0.15910	0.8439	0.9758
10	120	0.12480	0.7036	0.9770
11	130	0.09588	0.5724	0.9788
12	140	0.07377	0.4653	0.9767
13	150	0.05210	0.3519	0.9771
14	160	0.03660	0.2304	0.9689
15	170	0.00700	0.1287	0.9675
16	180	0	0	1.0000

Fig.16 Fitting situation of parameters G and H

Fig.17 Fitting situation of velocity loss coefficient

Fig.18 Fitting situation of fragment initial velocity distribution

Fig.19 Relative error of fragment initial velocity

Fig.20 Bottom-cut cavity charge structure

Fig.21 Velocity loss coefficient distribution of bottom-cut structure

Fig.22 Velocity distribution of bottom-cut structure

Fig.23 Relative error of initial velocity distribution of bottom-cut structure

Fig.24 Top-cut cavity charge structure

Fig.25 Velocity loss coefficient distribution of top-cut structure

Fig.26 Velocity distribution of top-cut structure

Fig.27 Relative error of initial velocity distribution of top-cut structure

References 27

[1]	王利侠, 袁宝慧, 孙兴昀, 等. 破甲/杀伤多用途战斗部结构设计及试验研究[J]. 火炸药学报, 2016, 39(2):75-79. doi: 10.14077/j.issn.1007-7812.2016.02.016
	WANG L X, YUAN B H, SUN X Y, et al. Structural design and experimental research on the anti-armor and anti-personnel multi-purpose warhead[J]. Chinese Journal of Explosive & Propellants, 2016, 39(2):75-79. (in Chinese)
[2]	陈文刚. 小口径破榴多功能弹药终点效应影响因素研究[D]. 南京: 南京理工大学, 2011.
	CHEN W G. Study on the influencing factors of the terminal effect of small caliber anti-armor and anti-personnel multipurpose ammunition[D]. Nanjing: Nanjing University of Science & Technology, 2011. (in Chinese)
[3]	张俊, 刘荣忠, 郭锐, 等. 破甲杀伤复合战斗部仿真研究[J]. 计算机仿真, 2012, 29(12):34-37
	ZHANG J, LIU R Z, GUO R, et al. Simulation study on anti5armor and anti-personnel composite warhead[J]. Computer Simulation, 2012, 29(12):34-37. (in Chinese)
[4]	李兴隆, 陈科全, 路中华, 等. 装填系数对破甲杀伤复合战斗部威力影响的数值模拟[J]. 含能材料, 2019, 27(6):535-540.
	LI X L, CHEN K Q, LU Z H, et al. Numerical simulation of the influence of charge-shell mass ratio on the damage power of anti-armor and anti-personnel composite warhead[J]. Chinese Journal of Energetic Materials, 2019, 27(6):535-540. (in Chinese)
[5]	韩文斌, 张国伟, 邵彬, 等. 药型罩锥角对破片飞散的影响[J]. 爆破器材, 2020, 49(1):18-23.
	HAN W B, ZHANG G W, SHAO B, et al. Effect of cone angle of shaped liner on fragment dispersion[J]. Explosive Materials, 2020, 49(1):18-23. (in Chinese).
[6]	白晶, 张国伟, 陈京生, 等. 多功能战斗部药型罩结构参量研究[J]. 兵器装备工程学报, 2023, 44(1):96-101.
	BAI J, ZHANG G W, CHEN J S, et al. Research on the liner structural parameters of multi-functional warhead[J]. Journal of Ordnance Equipment Engineering, 2023, 44(1):96-101. (in Chinese)
[7]	周兰庭, 张庆明, 龙仁荣. 新型战斗部原理与设计[M]. 北京: 国防工业出版社, 2018:292-294.
	ZHOU L T, ZHANG Q M, LONG R R. Principle and design of the new warhead[M]. Beijing: National Defense Industry Press, 2018:292-294. (in Chinese)
[8]	GURNEY R W. The initial velocities of fragments from bombs,shell,grenades:BRL-405[R]. Aberdeen Proving Ground,MD, US: Ballistic Research Laboratories, 1943.
[9]	BOLA M S, MADAN A K, SINGH M. Expansion of metallic cylinders under explosive loading[J]. Defence Science Journal, 1992, 42(3):157-163.
[10]	KARPP R R, PREDEBON W W. Calculations of fragment velocities from naturally fragmenting munitions:BRL-MR-2509[R]. Aberdeen Proving Ground,MD, US: Ballistic Research Laboratory,1975.
[11]	HUANG G Y, LI W, FENG S S. Axial distribution of fragment velocities from cylindrical casing under explosive loading[J]. International Journal of Impact Engineering, 2015, 76:20-27.
[12]	LIU H, HUANG G Y, GUO Z W, et al. Fragments velocity distribution and estimating method of thin-walled cylindrical improvised explosive devices with different length-to-diameter ratios[J]. Thin-Walled Structures, 2022, 175:109212.
[13]	YIN Z Y, CHEN X W. Numerical study on the dynamic fracture of explosively driven cylindrical shells[J]. Defence Technology, 2023, 27:154-168.
[14]	GAO Y G, ZHANG B, YAN X M, et al. Axial distribution of fragment velocities from cylindrical casing with air parts at two ends[J]. International Journal of Impact Engineering, 2020, 140:103535.
[15]	NOH D, FAZILY P, SEO S, et al. Data driven prediction of fragment velocity distribution under explosive loading conditions[J]. Defence Technology, 2025, 43:109-119.
[16]	AN X Y, LIU J Y, YE P, et al. Axial distribution characteristics of fragments of the warhead with a hollow core[J]. International Journal of Impact Engineering, 2018, 122:10-22.
[17]	LI Y, REN T F, WEN Y Q, et al. Impact of aspect ratio on fragment velocity distribution for hollow charges[J]. Materials & Design, 2023, 228:111815.
[18]	LI W, HUANG G Y, FENG S S. Effect of eccentric edge initiation on the fragment velocity distribution of a cylindrical casing filled with charge[J]. International Journal of Impact Engineering, 2015, 80:107-115.
[19]	高月光, 冯顺山, 刘云辉, 等. 不同端盖厚度的圆柱形装药壳体破片初速分布[J]. 兵工学报, 2022, 43(7):1527-1536.
	GAO Y G, FENG S S, LIU Y H, et al. Initial velocity distribution of fragments from cylindrical charge shells with different thick end caps[J]. Acta Armamentarii, 2022, 43(7):1527-1536. (in Chinese) doi: 10.12382/bgxb.2021.0443
[20]	LIAO W, JIANG J W, MEN J B, et al. Effect of the end cap on the fragment velocity distribution of a cylindrical cased charge[J]. Defence Technology, 2021, 17(3):1052-1061. doi: 10.1016/j.dt.2020.06.024
[21]	YE P, DONG Y X, SUN Q T, et al. Double casing warhead with sandwiched charge:the axial distribution of fragments velocities[J]. Defence Technology, 2024, 34:201-216.
[22]	GAO Y G, FENG S S, XIAO X, et al. Fragment characteristics of cylinder with discontinuous charge[J]. International Journal of Impact Engineering, 2023, 173:104479.
[23]	崔秉贵. 弹药战斗部工程设计[M]. 北京: 北京理工大学,1995.
	CUI B G. Engineering design of ammunition warhead[M]. Beijing: Beijing Institute of Technology,1995. (in Chinese)
[24]	陈刚, 陈忠富, 陶俊林, 等. 45钢动态塑性本构参量与验证[J]. 爆炸与冲击, 2005, 25(5):69-74.
	CHEN G, CHEN Z F, TAO J L, et al. Investigation and validation on plastic constitutive parameters of 45 steel[J]. Explosion and Shock Waves, 2005, 25(5):69-74. (in Chinese)
[25]	KONG X S, WU W G, LI J, et al. A numerical investigation on explosive fragmentation of metal casing using smoothed particle hydrodynamic method[J]. Materials & Design, 2013, 51:729-741.
[26]	DYNAMICS C. Release 14.0 documentation for ANSYS AUTODYN[Z]. Canonsburg,PA, US: ANSYS Inc., 2011:150-151.
[27]	LIU M T, REN G W, FAN C, et al. Experimental and numerical studies on the expanding fracture behavior of an explosively driven 1045 steel cylinder[J]. International Journal of Impact Engineering, 2017, 109:240-252.