压环对爆炸成型弹丸成型影响的高精度仿真分析

doi:10.12382/bgxb.2023.1193

摘要/Abstract

摘要：

压环是爆炸成型弹丸(Explosively Formed Projectile,EFP)装药结构中紧固装药和药型罩不可缺少的部件。为研究其在爆炸驱动过程中对药型罩形成EFP特征的影响,选取典型球缺型紫铜药型罩基准装药结构,采用有限元分析软件的拉格朗日、任意拉格朗日-欧拉、光滑粒子流法(Smooth Particle Hydrodynamics,SPH)及有限元法(Finite Element Method,FEM)-SPH自适应耦合等算法分别建模和仿真计算,对各算法计算获得的EFP速度和形态特征与脉冲X光摄影拍摄的EFP图像进行对比,采用FEM-SPH算法获得高精度的EFP成型仿真结果。针对该基准装药结构,在压环与药型罩质量比M_R/M_L≤0.2范围,进行矩形及非矩形压环参数(如轴向、径向厚度及截面形状)和材料对EFP初速、质量转换比、长径比和气动特性(密实度及迎风面积)参数影响的仿真计算。研究结果表明:矩形截面压环的轴向、径向厚度及材料参数对EFP初速影响在3%以内;对EFP质量转换比呈递减趋势(最大可降低12.6%);对EFP长径比呈递减趋势(最大可降低19.2%);密实度呈递增趋势,钢环较无压环,EFP的密实度提高32.6%;迎风面积呈递减趋势。以上结果表明考虑压环有利于EFP翻转成型和形成更密实的杆式EFP,并减小其迎风阻力。所得研究结果可为EFP装药结构的优化设计提供指导。

关键词: 爆炸成型弹丸, 自适应耦合, 数值模拟, 压环

Abstract:

The pressing ring is an indispensable part of an explosively formed projectile (EFP) charge structure for fastening the liner on the charge.A typical EFP charge structure with a copper spherical segment liner is adopted to study the influence of pressing ring on the EFP formed by the liner during explosion.The Influence of pressing ring on EFP forming properties is modeled and simulated using 3D dynamic finite element software, including Lagrange algorithm, arbitrary Lagrangian-Eeulerian (ALE) algorithm, smoothed particle hydrodynamics (SPH) method, and finite element method and smooth particle hydrodynamics (FEM-SPH) adaptive coupling algorithm.The EFP’s velocity and shape characteristics calculated by each algorithm are compared with the EFP images captured by pulse X-ray photography, and the FEM-SPH algorithm is used to obtain the high precision simulation results of EFP formation.On this basis, for the basic EFP charge structure with mass ratio of pressing ring to liner M_R/M_L≤0.2, the influences of the pressing ring’s rectangular and non-rectangular parameters (axial and radial thicknesses, and sectional shape) and the materials of pressing ring on the EFP’s initial velocity, mass conversion ratio, aspect ratio, and aerodynamic characteristics (compactness and windward area) parameters are simulated and calculated.Results show that the influences of axial and radial thicknesses and material parameters on the initial velocity of EFP is within 3%.The mass conversion ratio of EFP gradually decreases (up to 12.6%), the aspect ratio of EFP shows a gradually decreasing trend (with maximum reduction of 19.2%), and the compactness of of EFP with pressing ring is increased by 32.6% compared with the case without a ring.The upwind area shows a decreasing trend, indicating that the increase of ring weight is beneficial to the formation of EFP and thus decreases its upwind resistance.The results of this study provide guidance for the optimal design of EFP charge structure.

Key words: explosively formed projectile, adaptive coupling, numerical simulation, pressing ring

中图分类号:

TJ410.2

刘贞娴, 蒋建伟, 李梅, 谢泓炜. 压环对爆炸成型弹丸成型影响的高精度仿真分析[J]. 兵工学报, 2025, 46(1): 231193-.

LIU Zhenxian, JIANG Jianwei, LI Mei, XIE Hongwei. High Precision Simulation of the Influence of Pressing Ring on EFP Forming Properties[J]. Acta Armamentarii, 2025, 46(1): 231193-.

图/表 31

图1 失效单元转换为SPH粒子原理[18]

Fig.1 Schematic diagram of conversion of failure unit to SPH particle[18]

图2 EFP装药结构[18]

Fig.2 Physical model of EFP charge construction[18]

图3 EFP流固耦合算法计算模型

Fig.3 ALE model of EFP charge construction

表1 金属材料J-C模型参数[21-22]

Table 1 J-C model parameters of liner[21-22]

参数	数值						参数		数值
参数	铜		钢		铝		参数		铜		钢		铝
ρ/ (g·cm^-3)		8.96		7.85		2.78		D₁		0.54		0.10		0.13
A/MPa		90		506		265		D₂		4.89		0.76		0.13
B/MPa		292		320		426		D₃		-3.03		1.57		-1.50
n		0.31		0.28		0.34		D₄		0.014		0.005		0.011
C		0.025		0.064		0.015		D₅		1.12		-0.84		0
m		1.09		1.06		1.70

表2 炸药JWL状态方程模型参数[23]

Table 2 JWL model parameters ofexplosives[23]

参数	数值	参数	数值
ρ_e/(kg·m^-3)	1.70	R₁	4.60
p_C-J/GPa	29.50	R₂	1.35
A_e/GPa	854.5	ω	0.25
B_e/GPa	20.49	E/GPa	8.50
D/(m·s^-1)	8315

图4 采用FEM-SPH算法获得典型时刻EFP图像

Fig.4 Calculated results of FEM-SPH algorithm

图5 EFP形态与脉冲X光照片不同算法结果对比(170μs时刻)

Fig.5 Comparison among calculated results of different algorithms and experimental results(170μs)

表3 170μs时刻EFP参数仿真结果与测试结果对比

Table 3 Comparisonamong calculated and test results of EFP characteristic parameter values

药型罩/压环算法以及试验值	长径比	初速v₀/(m·s^-1)
Lagrange	2.88	2072
ALE	2.80	2091
SPH	2.90	2159
FEM-SPH	3.06	2126
Lagrange/FEM-SPH	2.94	2147
FEM-SPH/Lagrange	3.09	2176
试验值	3.24	2120

图6 初速与试验值相对误差绝对值δ不同算法结果(170μs时刻)

Fig.6 Error rate of EFP velocity(170μs)

图7 长径比与试验值相对误差绝对值ξ不同算法结果(170μs时刻)

Fig.7 Error rate of EFP aspect ratio(170μs)

图8 尺寸参数定义

Fig.8 Parameter definition

图9 不同压环材料下EFP形态对比图(170μs时刻)

Fig.9 Simulated results of EFPs with and without pressing rings made of different materials(170μs)

表4 不同压环材料下EFP特征参数值(170μs时刻)

Table 4 Calculated results of characteristic parameter values of EFPs with and without pressing rings made of different materials (170μs)

压环材料	ρ/(g·cm^-3)	v/(m·s^-1)	λ	φ	A_r/mm²	η
钢压环	7.85	2126	3.06	0.83	254.47	0.88
铝压环	2.78	2091	3.38	0.67	232.35	0.91
无压环	0	2074	3.61	0.56	380.13	0.99

图10 不同压环材料下v/v0-ρ、λ/λ0-ρ曲线(170μs时刻)

Fig.10 v/v0-ρ、λ/λ0-ρ curves of EFPs with pressing rings made of different materials(170μs)

图11 不同压环材料下φ/φ0-ρ、Ar/Ar0-ρ曲线(170μs时刻)

Fig.11 φ/φ0-ρ、Ar/Ar0-ρ curves of EFPs with pressing rings made of different materials(170μs)

图12 不同压环材料下η-ρ曲线(170μs时刻)

Fig.12 η-ρ curves of EFPs with pressing rings made of different materials(170μs)

图13 不同压环径向厚度下EFP形态对比图(170μs时刻)

Fig.13 Simulated results of EFPs with different radial thicknesses of pressing ring(170μs)

表5 不同径向厚度下EFP特征参数值(170μs时刻)

Table 5 Calculated results of characteristic parametervalues of EFPs with different radial thicknessesof pressing ring(170μs)

h/D_c	v/(m·s^-1)	λ	φ	A_r/mm²	η
0.0089	2110	3.30	0.77	586.21	0.96
0.0178	2112	3.15	0.78	380.13	0.94
0.0267	2122	3.12	0.77	232.89	0.91
0.0357	2126	3.06	0.83	254.47	0.88

图14 不同压环径向厚度下v/v0-h/Dc、λ/λ0-h/Dc 曲线(170μs时刻)

Fig.14 v/v0-h/Dc、λ/λ0-h/Dc curves of EFPs different radial thicknesses of pressing ring(170μs)

图15 不同压环径向厚度下φ/φ0-h/Dc、Ar/Ar0-h/Dc 曲线(170μs时刻)

Fig.15 φ/φ0-h/Dcand Ar/Ar0-h/Dc curves of EFPs with different radial thicknessses of pressing ring(170μs)

图16 不同压环径向厚度下η-h/Dc曲线(170μs时刻)

Fig.16 η-h/Dccurve of EFP with different radial thicknesses of pressing ring(170μs)

图17 不同压环轴向厚度下EFP形态对比图(170μs时刻)

Fig.17 Simulated results of EFPs with different axial thicknesses of pressing ring(170μs)

表6 不同轴向厚度下EFP特征参数值(170μs时刻)

Table 6 Calculated results of EFP characteristic parameter values of EFPs with different axial thicknesses of pressing ring(170μs)

l/D_c	v/(m·s^-1)	λ	φ	A_r/mm²	η
0.0178	2084	3.65	0.56	346.36	0.98
0.0357	2098	3.38	0.73	226.98	0.91
0.0535	2120	3.07	0.79	240.53	0.88
0.0714	2126	3.06	0.83	254.47	0.88

图18 不同压环轴向厚度下v/v0-l/Dc、λ/λ0-l/Dc 曲线(170μs时刻)

Fig.18 v/v0-l/Dc and λ/λ0-l/Dc curves of EFPs with different axial thicknesses of pressing ring(170μs)

图19 不同压环轴向厚度下φ/φ0-l/Dc、Ar/Ar0-l/Dc 曲线(170μs时刻)

Fig.19 φ/φ0-l/Dcand Ar/Ar0-l/Dc curves of EFPs writh different axial thicknesses of pressing ring(170μs)

图20 不同压环轴向厚度下η-l/Dc曲线(170μs时刻)

Fig.20 η-l/Dc curve of EFP with different axial thicknesses of pressing ring(170μs)

图21 不同压环截面形状下EFP形态对比(170μs时刻)

Fig.21 Simulated results of EFPs with different sectional shapes of pressing ring(170μs)

表7 不同截面形状下EFP特征参数值(170μs时刻)

Table 7 Calculation results of EFP characteristic parameter valuesof EFPs with different sectional shapes of pressing ring(170μs)

截面形状系数ζ	v/(m·s^-1)	λ	φ	A_r/mm²	η
0.5	2124	3.39	0.71	431.89	0.89
0.75	2120	3.17	0.74	268.22	0.89
1	2126	3.06	0.83	254.47	0.88

图22 不同压环截面形状系数下v/v0-ζ、λ/λ0-ζ 曲线(170μs时刻)

Fig.22 v/v0-ζ、λ/λ0-ζ curves of EFP with different sectional shapes of pressing ring(170μs)

图23 不同压环截面形状系数下φ/φ0-ζ、Ar/Ar0-ζ 曲线(170μs时刻)

Fig.23 φ/φ0-ζ and Ar/Ar0-ζ curves of EFPs with different sectional shapes of pressing ring(170μs)

图24 不同压环截面形状系数下η-ζ曲线(170μs时刻)

Fig.24 η-ζ curve of EFP with different sectional shapes of pressing ring(170μs)

参考文献 23

[1]	隋树元, 王树山. 终点效应学[M]. 北京: 国防工业出版社,2000:233-237.
	SUI S Y, WANG S S. Terminal effects[M]. Beijing: National Defense Industry Press,2000:233-237. (in Chinese)
[2]	朱志鹏, 门建兵, 蒋建伟, 等. 大长径比钽爆炸成型弹丸控制研究[J]. 兵工学报, 2018, 39(增刊1):29-36.
	ZHU Z P, MEN J B, JIANG J W, et al. Forming control of tantalum EFP with large aspect ratio[J]. Acta Armamentarii, 2018, 39(S1):29-36. (in Chinese)
[3]	丁力, 蒋建伟, 王树有, 等. 钽爆炸成型弹丸成型及断裂特性[J]. 兵工学报, 2021, 42(增刊1):53-58.
	DING L, JIANG J W, WANG S Y, et al. Tantalum EFP’s forming and fracture characteristics[J]. Acta Armamentarii, 2021, 42(S1):53-58. (in Chinese)
[4]	杨绍卿. 灵巧弹药工程[M]. 北京: 国防工业出版社,2010:1-7.
	YANG S Q. Smart munition engineering[M]. Beijing: National Defense Industry Press,2010:1-7. (in Chinese)
[5]	李玉品, 周春桂, 王志军, 等. 夹层聚能装药EFP成型及侵彻数值模拟[J]. 兵器装备工程学报, 2019, 40(3):57-60.
	LI Y P, ZHOU C G, WANG Z J, et al. Numerical simulation of molding and penetration of interlayer shaped charge EFP[J]. Journal of Ordnance Equipment Engineering, 2019, 40(3):57-60. (in Chinese)
[6]	付恒, 蒋建伟, 王树有, 等. 爆炸成型弹丸药型罩用高密度合金选取准则[J]. 兵工学报, 2022, 43(9):2330-2338.
	FU H, JIANG J W, WANG S Y, et al. High-density alloy selection criteria for liners of explosively formed projectiles[J]. Acta Armamentarii, 2022, 43(9):2330-2338. (in Chinese) doi: 10.12382/bgxb.2021.0826
[7]	卞梁. 高速碰撞中的SPH方法及其应用研究[D]. 合肥: 中国科学技术大学, 2011.
	BIAN L. The SPH method and its application in hypervelocity impact[D]. Hefei: University of Science and Technology of China, 2011.( in Chinese)
[8]	门建兵, 蒋建伟, 王树有. 爆炸冲击数值模拟技术基础[M]. 北京: 北京理工大学出版社, 2015.
	MEN J B, JIANG J W, WANG S Y. Fundamentals of numerical simulation for explosion and shock problems[M] Beijing: Beijing Institute of Technology Press, 2015. (in Chinese)
[9]	黄正祥. 聚能装药理论与实践[M]. 北京: 北京理工大学出版社, 2014.
	HUANG Z X. Theory and practice of shaped charge[M]. Beijing: Beijing Institute of Technology Press, 2014. (in Chinese)
[10]	丁力, 蒋建伟, 门建兵, 等. 爆炸成型弹丸成型过程中的断裂数值模拟及机理分析[J]. 兵工学报, 2017, 38(3):417-423. doi: 10.3969/j.issn.1000-1093.2017.03.001
	DING L, JIANG J W, MEN J B, et al. Numerical simulation and mechanism analysis of EFP’s fracture in forming process[J]. Acta Armamentarii, 2017, 38(3):417-423. (in Chinese) doi: 10.3969/j.issn.1000-1093.2017.03.001
[11]	郑元枫, 王仕鹏, 李培亮, 等. 活性/金属串联爆炸成型弹丸侵爆耦合毁伤行为[J]. 兵工学报, 2023, 44(8):2273-2282. doi: 10.12382/bgxb.2022.0356
	ZHENG Y F, WANG S P, LI P L, et al. Combined damage behavior of penetration and blast of reactive /metal tandem EFPs[J]. Acta Armamentarii, 2023, 44(8):2273-2282. (in Chinese)
[12]	LI Y B, WANG J X, LIU Z T, et al. Orthogonal optimization design and experiments on explosively formed projectiles with fins[J]. International Journal of Impact Engineering, 2023, 173(3):104462.
[13]	YANG G T, GUO R, WEI G X, et al. Study on theinfluence of retaining ring on the formation of wings of explosively formed penetrator[C]//Proceedings of the 33rd International Symposium on Ballistics.Bruges, Belgium: Royal Military Academy,2023:700-710.
[14]	胡德安, 韩旭, 肖毅华, 等. 光滑粒子法及其与有限元耦合算法的研究进展[J]. 力学学报, 2013, 45(5):639-652. doi: 10.6052/0459-1879-13-092
	HU D A, HAN X, XIAO Y H, et al. Research developments of smoothed particle hydrodyamics method and its coupling with finite element method[J]. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(5):639-652.( in Chinese)
[15]	吴嘉炜, 王新峰, 古兴瑾, 等. 基于FEM-SPH自适应耦合方法的蓝宝石DOP性能研究[J]. 南京航空航天大学学报, 2023, 55(4):711-717.
	WU J W, WANG X F, GU X J, et al. A FEM-SPH adaptive coupled model for sapphire DOP performance[J]. Journal of Nanjing University of Aeronautics & Astronautics, 2023, 55(4):711-717.( in Chinese)
[16]	HALLQUIST J O. LS-DYNA keyword user’s manual V971[J]. Livermore,CA, US:Livermore Software Technology Corporation, 2007.
[17]	SOMNATH K, AMIT S. Response of R.C. plates under blast loading using FEM-SPH coupled method[J]. Engineering Failure Analysis, 2021, 125(3):105409.
[18]	王昕, 蒋建伟, 王树有, 等. 爆炸成型弹丸侵彻钢靶的后效破片云实验研究[J]. 兵工学报, 2018, 39(7):1284-1290. doi: 10.3969/j.issn.1000-1093.2018.07.005
	WANG X, JIANG J W, WANG S Y, et al. Experimental research on fragments after explosively-formed projectile penetrating into steel target[J]. Acta Armamentarii, 2018, 39(7):1284-1290. (in Chinese) doi: 10.3969/j.issn.1000-1093.2018.07.005
[19]	JOHNSON G R, COOK W H. A constitutive model and data for metals subjected to large strains,high strain rates and high temperatures[J]. Engineering Fracture Mechanics, 1983,21:541-548.
[20]	COOK J W H. Fracture characteristics of three metals subjected to various strains,strain rates,temperatures and pressures[J]. Engineering Fracture Mechanics, 1985.DOI:10.1016/0013-7944(85)90052-9.
[21]	陈刚, 陈忠富, 徐伟芳, 等. 45钢的J-C损伤失效参量研究[J]. 爆炸与冲击, 2007, 27(2):131-135.
	CHEN G, CHEN Z F, XU W F, et al. Investigation on the J-C ductile fracture parameters of 45 steel[J]. Explosive and Shock Waves, 2007, 27(2):131-135.( in Chinese)
[22]	BUYUK M, KURTARAN H, MARZOUGUI D, et al. Automated design of threats and shields under hypervelocity impacts by using successive optimization methodology[J]. International Journal of Impact Engineering, 2008, 35(12):1449-1458.
[23]	林加剑. EFP成型及其终点效应研究[D]. 合肥: 中国科学技术大学, 2009.
	LIN J J. Research on the formability of EFP and its terminal effect[J]. Hefei:University of Science and Technology of China, 2009. (in Chinese)