High Precision Simulation of the Influence of Pressing Ring on EFP Forming Properties

doi:10.12382/bgxb.2023.1193

Abstract

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

CLC Number:

TJ410.2

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-.

Figures/Tables 31

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

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

Fig.3 ALE model of EFP charge construction

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

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

Fig.4 Calculated results of FEM-SPH algorithm

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

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

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

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

Fig.8 Parameter definition

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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