Comparative Study on Predictive Models for Radial Velocities of Fragments after PELE Impacting on Target Plates

doi:10.12382/bgxb.2024.0533

Abstract

Abstract:

In order to effectively predict the maximum radial velocity of fragments formecd after a penetrator with enhanced lateral effect (PELE) penetrating a metal target plate,the collision pressure,radial pressure,and fragment stop acceleration time when the PELE impacts the target plate are analyzed through numerical simulation and theoretical analysis method.The results show that the elastic wave theory underestimates the collision pressure when the PELE impacts the target plate,and the calculated results of the shock wave theory are more consistent with the actual situation.The axial pressure is all converted to radial pressure instead of a certain proportion.When the shell reaches the maximum failure strain,it starts to break and stops accelerating,which is more consistent with the actual situation.The radial velocity model is improved based on the above analysis,and compared with the elastic wave model,shock wave model and test results,respectively.When the collision pressure is high,the proposed model is able to effectively predict the maximum radial velocity of fragments after the PELE penetrates into the metal target plate.

Key words: penetrator, enhanced lateral effect, impact pressure, radial pressure, improved radial velocity model

CLC Number:

TJ410.3

WANG Zhanxuan, LI Xintian, XU Lizhi, DU Zhonghua. Comparative Study on Predictive Models for Radial Velocities of Fragments after PELE Impacting on Target Plates[J]. Acta Armamentarii, 2025, 46(6): 240533-.

Figures/Tables 22

Fig.1 Finite element model of PELE penetrating a thin metal target plate

Table 1 Material parameters

材料	ρ/(g·cm^-3)	c/(km·s^-1)	S₁	Grüneisen 常数	E/GPa	拉伸主应变	拉伸主应力/GPa	断裂软化算法	随机失效算法	侵蚀应变
钨合金	18.00	4.029	1237	0	360.0	0.035	2.8	是	是	0.6
A-G3铝	2.650	5.176	1.350	1.97	63.90			否	否	0.8
PE	9.200	2.187	1.481	1.64	1.060			否	否	0.8
尼龙^[33]	1.130	2.290	1.630	0.87	23.00			否	否	0.8
XC48钢	7.823	4.797	1.490	0.00	201.0			否	否
A-U4G铝	2.800	5.106	1.350	2.00	74.00			否	否

Fig.2 Comparison of simulated and experimental results of PELE ofragmentation patterns

Fig.3 Two selected metrics

Fig.4 Comparison of simulated and experimental results of fragment axial residual velocity behind the target

Fig.5 Comparison of simulated and experimental results of fragment radial velocity behind the target

Fig.6 Comparison of simulated and experimental results of residual length

Fig.7 Comparison of simulated and experimental results of maximum opening diameter

Table 2 Numerical model parameters

编号	弹芯材料	靶板材料	靶板厚度/mm	冲击速度/ (m·s^-1)
1	A-G3铝	A-U4G铝	3	300~2 700
2	A-G3铝	XC 48钢
3	PE	A-U4G铝
4	PE	XC 48钢
5	尼龙	A-U4G铝
6	尼龙	XC 48钢

Table 3 Impact pressure curve at different velocities(aluminium filling)

靶板材料	碰撞压力仿真结果	最终碰撞压力对比
A-U4G铝
XC 48钢

Table 4 Imapct pressure curves at different velocities(PE and nylon filling)

弹芯材料	靶板材料	碰撞压力仿真结果	最终碰撞压力对比
PE	A-U4G铝
PE	XC 48钢
尼龙	A-U4G铝
尼龙	XC 48钢

Table 5 Pressure of PELE impacting on target plate with nylon filling GPa

靶板材料	冲击速度/(m·s^-1)
靶板材料	300	2700
A-U4G铝	0.79	12.37
XC 48钢	0.87	15.84

Fig.8 The ratio of impact pressure to yield strength of core material

Fig.9 K values of two models and numerical simulations

Table 6 Two calculation models

模型	碰撞压力	径向压力	破片停止加速
3	p_b=ρ_ac_a(u_b-u_a)+ρ_as $(u b - u a) 2$	σ_r=σ_x_,_f	ε_r,lim(t)= $μ f σ x (t) (1 - μ f) E f$
4	p_b=ρ_ac_a(u_b-u_a)+ρ_as $(u b - u a) 2$	σ_r=σ_x_,f	ε_max=0.035

Table 6 Two calculation models

模型	碰撞压力	径向压力	破片停止加速
3	p_b=ρ_ac_a(u_b-u_a)+ρ_as $(u b - u a) 2$	σ_r=σ_x_,_f	ε_r,lim(t)= $μ f σ x (t) (1 - μ f) E f$
4	p_b=ρ_ac_a(u_b-u_a)+ρ_as $(u b - u a) 2$	σ_r=σ_x_,f	ε_max=0.035

Fig.10 Comparative results of maximum radial velocity

Table 7 Experimental condition parameters in Ref.[23]

编号	弹芯			靶板		冲击速度/ (m·s^-1)
编号	密度/ (g·cm^-3)	泊松比	弹性模量/GPa	密度/ (g·cm^-3)	厚度/ mm	冲击速度/ (m·s^-1)
7	1.09	0.45	10.7	7.85	2	632
8	1.09	0.45	10.7			711
9	1.09	0.45	10.7			811
10	1.09	0.45	10.7			890
11	0.96	0.40	28.3			775
12	1.40	0.33	68.1			802

Fig.11 Comparative results

Table 8 Experimental condition parameters in Ref.[21]

编号	弹芯			靶板			冲击速度/ (m·s^-1)
编号	材料	密度/ (g·cm^-3)	泊松比	密度/ (g·cm^-3)		厚度/ mm	冲击速度/ (m·s^-1)
13	6061铝	2.70	0.33		2.800	3	798
14	6061铝	2.70	0.33				806
15	聚四氟乙烯	2.15	0.41				802
16	聚四氟乙烯	2.15	0.41				809

Fig.12 Comparison of calculated results of improved radial velocity model,impact model,and elastic wave model,as well as experimental results[21]

Fig.13 Comparison of calculated results of improved radial velocity model,impact model,and elastic wave model, as well as experimental results[5]( A-U4G Al filling)

Fig.14 Comparison of calculated results of improved radial velocity model,impact model, and elastic wave model,as well as experimental results[5] (PE filling)

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