The Structural Parameters of Combined Liner for Tandem Explosively Formed Projectile

doi:10.12382/bgxb.2023.0911

Abstract

Abstract:

In order to improve the destructive power of shaped charge warhead to underwater targets, a combined liner warhead structure was proposed to form a tandem Explosively Formed Projectile (EFP). The velocity model of combined liner EFP was established by the formulas of plate driving and cylinder collapsing, the EFP molding and damage in water were simulated by AUTODYN-2D to study the influence of structural parameters of combined liner on tandem EFP molding and prove its efficient damage performance in water. The results show that the theoretical and simulated EFP speeds are basically consistent with the maximum error of less than 10%. The separation of the combined liner to form tandem EFP is caused by the large velocity difference between the liner elements from the interface due to the different material and structure combination of the inner liner and the outer liner. With the increase of the inner liner diameter, EFP velocity of the inner and outer liners decreases simultaneously, and aspect ratio of inner and outer EFP increases and decreases respectively; as the outer curvature radius and the top wall thickness of the inner or outer liner are increased separately, the performance of EFP molded by the current inner or outer liner is the same as that of the single liner, but the aspect ratio of EFP molded by the another outer liner decreases, while the aspect ratio of EFP molded by the another inner liner decreases or increases, and the change in the velocity of another EFP is small. After the tandem EFP of combined liner penetrates water with a diameter of 4 times the charge diameter, the kinetic energy decay rate and the residual velocity of combined liner EFP are reduced by 21.55% and increased by 5.77% compared to the double-layer liner, respectively, and the gap of kinetic energy decay rate and residual velocity further expands with the increase of penetration distance.

Key words: combined liner, tandem explosively formed projectile, forming regulation, underwater damage, numerical simulation

CLC Number:

YANG Guitao, GUO Rui, SONG Pu, GAO Guangfa, YU Yanghui. The Structural Parameters of Combined Liner for Tandem Explosively Formed Projectile[J]. Acta Armamentarii, 2024, 45(9): 3056-3070.

Figures/Tables 40

Fig.1 Schematic diagram of double-layer liner warhead structure[12]

Fig.2 Schematic diagram of combined liner warhead structure[20]

Fig.3 Schematic diagram of combined liner warhead structure

Fig.4 Effect of explosive driving on liner element

Fig.5 Schematic diagram of cylinder implosion control body

Table 1 Material parameters for numerical simulation

参数	4340钢	Ta2.5W	铜	参数	JH-2
ρ/(g·cm^-3)	7.83	16.65	8.96	ρ/(g·cm^-3)	1.70
G/GPa	77	70.37	46	D₀/(m·s^-1)	8315
A/GPa	0.792	0.211	0.09	p_C-J/GPa	29.5
B/GPa	0.51	0.381	0.292	A₁/GPa	854.5
n	0.26	0.75	0.31	B₁/GPa	20.94
C	0.014	0.068	0.025	R₁	4.60
m	1.03	0.38	1.09	R₂	1.35
$ε · 0$ /s^-1	1	0.001	1	ω	0.25
T_m/K	1793	3450	1356	E/GPa	8.50
T_r/K	293	298	293
Г	1.67	1.67	2.02
C₁/(m·s^-1)	4578	3410	3940
S₁	1.33	1.20	1.489
C_p/(J·kg^-1·K^-1)	477	135	383

Table 1 Material parameters for numerical simulation

参数	4340钢	Ta2.5W	铜	参数	JH-2
ρ/(g·cm^-3)	7.83	16.65	8.96	ρ/(g·cm^-3)	1.70
G/GPa	77	70.37	46	D₀/(m·s^-1)	8315
A/GPa	0.792	0.211	0.09	p_C-J/GPa	29.5
B/GPa	0.51	0.381	0.292	A₁/GPa	854.5
n	0.26	0.75	0.31	B₁/GPa	20.94
C	0.014	0.068	0.025	R₁	4.60
m	1.03	0.38	1.09	R₂	1.35
$ε · 0$ /s^-1	1	0.001	1	ω	0.25
T_m/K	1793	3450	1356	E/GPa	8.50
T_r/K	293	298	293
Г	1.67	1.67	2.02
C₁/(m·s^-1)	4578	3410	3940
S₁	1.33	1.20	1.489
C_p/(J·kg^-1·K^-1)	477	135	383

Fig.6 Simulation model of EFP forming for combined liner

Fig.7 Tandem EFP forming process of combined liner

Fig.8 Velocity distribution of combined and single liner elements

Table 2 Range of control parameters for combined liner

D_i/D_c	R_io/D_c	δ_i/D_c	R_oo/D_c	δ_o/D_c
0.45~0.70 Δ=0.05	0.8	0.045	1.4	0.040
0.6	0.7~1.2 Δ=0.1	0.045	1.4	0.040
0.6	0.8	0.035~0.05375 Δ=0.00375	1.4	0.040
0.6	0.8	0.045	1.1~1.6 Δ=0.1	0.040
0.6	0.8	0.045	1.4	0.03125~0.05 Δ=0.00375

Fig.9 Influence of liner structure on charge quantity

Fig.10 Feature size parameters of EFP

Fig.11 Variation of vi and vo with Di/Dc

Fig.12 Variation of EFP shape, li/di and lo/do with Di/Dc

Fig.13 Variation of vxi and vxo with Di/Dc

Fig.14 Variation of vyi and vyo with Di/Dc

Fig.15 Variation of vi and vo with Rio/Dc

Fig.16 Variation of EFP shape, li/di and lo/do with Rio/Dc

Fig.17 Variation of vxi and vxo with Rio/Dc

Fig.18 Variation of vyi and vyo with Rio/Dc

Fig.19 Variation of vi and vo with δi/Dc

Fig.20 Variation of EFP shape, li/di and lo/do with δi/Dc

Fig.21 Variation of vxi and vxo with δi/Dc

Fig.22 Variation of vyi and vyo with δi/Dc

Fig.23 Variation of vi and vo with Roo/Dc

Fig.24 Variation of EFP shape, li/di and lo/do with Roo/Dc

Fig.25 Variation of vxi and vxo with Roo/Dc

Fig.26 Variation of vyi and vyo with Roo/Dc

Fig.27 Variation of vi and vo with δo/Dc

Fig.28 Variation of EFP shape, li/di and lo/do with δo/Dc

Fig.29 Variation of vxi and vxo with δo/Dc

Fig.30 Variation of vyi and vyo with δo/Dc

Fig.31 Simulation model of EFP water-entry

Fig.32 Numerically calculated and experimental projectile trajectory and cavity shape

Fig.3 Numerically calculated and experimental results comparison of projectile entry into water

Table 3 Performance parameters of EFPs formed in water

结构	材料	速度/ (m·s^-1)	长径比	动能/ kJ	比动能/ (kJ·cm^-2)
组合	铜	2157.1	2.83	55.68	21.50	47.69
药型罩	Ta2.5W	1485.2	2.24	50.55	26.19
双层	铜	2064.8	2.59	59.76	32.66	50.97
药型罩	Ta2.5W	1610.3	1.69	49.99	18.31

Fig.34 Processes of EFPs penetrating into water

Fig.35 Variation of EFP Ek with L during penetrating water

Fig.36 Variation of EFP v with L during penetrating water

Table 4 Variation of Ek and vrt after EFP penetrating into 4Dc water

结构	初始状态		侵彻4D_c水		衰减率
结构	E_k/kJ	v_rt/ (m·s^-1)	E_k/kJ	v_rt/ (m·s^-1)	E_k/%
组合药型罩	106.23	1485.2	51.71	1471.1	51.32
双层药型罩	109.75	1610.3	29.77	1390.8	72.87

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