钽合金EFP靶后破片的空间散布特性

位国旭; 徐宏伟; 郭锐; 李向东; 张磊; 姬龙

doi:10.11883/bzycj-2025-0326

钽合金EFP靶后破片的空间散布特性

doi: 10.11883/bzycj-2025-0326

位国旭^1,,
徐宏伟²,
郭锐^1, ,,
李向东¹,
张磊²,
姬龙²

1.
南京理工大学机械工程学院，江苏南京 210094
2.
西安现代控制技术研究所陆空基信息感知与控制全国重点实验室，陕西西安 710065

基金项目: 中央高校基本科研业务费专项资金（30925020102）

详细信息

作者简介:
位国旭（1997－　），男，博士研究生，wei_guoxu@163.com

通讯作者:
郭　锐（1980－　），男，博士，教授，guorui@njust.edu.cn

中图分类号: O389; TJ012.4
计量
- 文章访问数: 162
- HTML全文浏览量: 17
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- 被引次数: 0
出版历程
- 收稿日期: 2025-09-29
- 修回日期: 2025-12-26
- 网络出版日期: 2026-01-05

Spatial dispersion characteristics of behind-armor debris generated during the penetration of tantalum alloy explosively-formed projectile

1.
School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China
2.
National Key Laboratory of Land and Air Based Information Perception and Control, Xi’an Modern Control Technology Research Institute, Xi’an 710065, Shanxi, China

摘要

摘要: 为研究钽合金爆炸成型弹丸（explosively-formed projectile，EFP）侵彻靶板产生靶后破片的空间散布，首先开展了钽合金EFP侵彻45钢的X光及破片散布试验；其次，采用经试验验证的FE-SPH（finite element-smoothed particle hydrodynamics）固定耦合方法开展了多种弹、靶条件下EFP垂直侵彻靶板的数值模拟，获得了靶后破片空间散布的数据集；最后，采用基于贝叶斯优化的支持向量回归对靶后破片密集飞散角数据进行训练，得到了基于贝叶斯优化的支持向量回归模型。研究结果表明：从试验结果来看，靶后破片云形貌为典型的截椭球状，由于钽、钢密度差异导致不同材料破片径向膨胀能力不同，钢破片分布在椭球的外表面而钽破片分布在椭球的内表面，靶后破片主要集中在验证靶上中心穿孔处周围的圆形区域；采用FE-SPH固定耦合方法模拟再现了靶后破片的形成过程，得到的靶后破片云形貌与试验结果十分接近，靶后破片平均最大飞散角与试验结果相对误差不超过10%，验证了数值模拟结果的准确性；建立的基于贝叶斯优化的支持向量回归模型能够实现对不同靶板厚度、着靶速度条件下靶后破片的密集飞散角的准确预测，数值模拟结果与模型预测结果最大相对误差均小于10%，在此基础上可以实现对靶后一定距离内验证靶毁伤面积的快速预测。
- EFP /
- 靶后破片 /
- 空间散布 /
- 支持向量回归 /
- 贝叶斯优化
Abstract: To investigate the spatial dispersion characteristics of behind-armor debris (BAD) generated by the penetration of tantalum alloy explosively-formed projectile (EFP) into steel targets, a comprehensive study combining experimental testing, numerical simulation, and machine learning prediction was performed. First, X-ray imaging and fragment-distribution experiments were conducted on 45 steel targets penetrated by tantalum alloy EFP to obtain initial experimental data. Subsequently, the finite element-smoothed particle hydrodynamics (FE-SPH) fixed-coupling method, which had been validated by the experimental data, was employed to simulate the perforation process. These numerical simulations were carried out under a wide range of working conditions, specifically varying the projectile velocity and target thickness. Through this process, a comprehensive dataset describing the spatial dispersion of BAD was generated. Finally, to achieve rapid prediction capabilities, a support vector regression (SVR) model was established. The Bayesian optimization algorithm was utilized to train the model using the dense-fragment dispersion angle data extracted from the simulation dataset, thereby creating a robust predictive model for spatial dispersion of BAD. The experimental results indicate that the morphology of the BAD cloud exhibits a typical truncated-ellipsoidal shape. Due to the density difference between tantalum and steel, fragments composed of different materials display distinct radial expansion behaviors, i.e. steel fragments are distributed along the outer surface of the ellipsoid whereas tantalum fragments are concentrated on the inner surface. Spatially, the debris is primarily concentrated within a circular region surrounding the central perforation area of the witness plate. The FE-SPH fixed-coupling method successfully reproduced the BAD formation process, yielding debris-cloud morphologies that closely match the experimental results. The relative error between the simulated and measured mean maximum fragment dispersion angles is less than 10%, thereby confirming the accuracy of the numerical simulations. Furthermore, the analysis reveals that the Bayesian-optimized SVR model enables accurate prediction of dense-fragment dispersion angles under varying target thicknesses and EFP impact velocities, with maximum relative errors below 10%. Based on these predictions, the damage area on witness plates within a certain distance behind the target can be rapidly estimated.
- explosively formed projectile /
- behind-armor debris /
- spatial dispersion /
- support vector regression /
- bayesian optimization

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图 1 试验布置

Figure 1. Experimental setup

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图 2 EFP战斗部及成型后EFP

Figure 2. EFP warhead and EFP

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图 3 靶后破片的X光图像

Figure 3. X-ray image of the behind-armor debris

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图 4 验证靶毁伤情况

Figure 4. The image of the witness plate

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图 5 验证靶分区示意图

Figure 5. Schematic diagram of witness plate zoning

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图 6 EFP数值模拟模型的建立过程

Figure 6. The establishment process of the EFP simulation model

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图 7 数值模拟模型

Figure 7. Numerical simulation model

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图 8 不同粒子尺寸下EFP速度时程曲线对比

Figure 8. Comparison of EFP velocity-time curves for different particle sizes

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图 9 靶后破片云形貌对比

Figure 9. Comparison of the morphology of behind-armor debris clouds

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图 10 验证靶穿孔对比

Figure 10. Comparison of perforation results on the witness plate

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图 11 靶后破片在验证靶上的散布(v₀=1900 m/s，h₀=30 mm)

Figure 11. The dispersion of fragments on the witness plate (v₀=1900 m/s，h₀=30 mm)

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图 12 不同靶板厚度下破片在验证靶上的散布

Figure 12. The dispersion of fragments on the witness plate for different thicknesses of targets

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图 13 不同着靶速度下破片在验证靶上的散布

Figure 13. The dispersion of fragments on the witness plate for different impact velocities of EFP

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图 14 靶后破片密集飞散角预测结果

Figure 14. Prediction results of the dense scattering angle of BAD

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图 15 靶板毁伤区域示意图

Figure 15. Schematic diagram of the damaged area of the target plate

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图 16 验证靶上密集毁伤区域面积随靶板厚度变化情况

Figure 16. The variation of the area of densely damaged areas on the witness plate with the thickness of the target

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图 17 验证靶上密集毁伤区域面积随着靶速度变化情况

Figure 17. The variation of the area of densely damaged areas on the witness plate with the impact velocities of EFP

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表 1 Ta_2.5W及45钢基础力学性能

Table 1. The basic mechanical properties of Ta 2.5W and 45 steel

材料	屈服强度 σ_s/MPa	抗拉强度 σ_b/MPa	断后伸长率 δ/%	硬度
Ta_2.5W	223	354	50	130HV
45钢	≥ 355	≥ 600	≥ 16	≤ 229HBW

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表 2 钽钨合金材料参数^[7]

Table 2. Material parameters of tantalum-tungsten alloy^[7]

材料	ρ₀/(g·cm⁻³)	A/MPa	B/MPa	n	c	m	D₁	D₂	D₃	D₄	D₅
Ta_2.5W	16.70	211	381	0.75	0.068	0.38	1.355	1.833	-1.93	0.015	1.868
	P₁/GPa	c₀/(m·s⁻¹)	S₁	S₂	S₃	a	γ₀
	5.6	3410	1.2	0	0	0.42	1.67

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表 3 45钢^[23-25]材料参数

Table 3. Material parameters of 45 steel^[23-25]

材料	ρ₀/(g·cm⁻³)	A/MPa	B/MPa	n	c	m	D₁	D₂	D₃	D₄	D₅
45钢	7.85	507	320	0.28	0.064	1.06	0.1	0.76	1.57	0.005	-0.84
	P₁/GPa	c₀/(m·s⁻¹)	S₁	S₂	S₃	a	γ₀
	3.95	4569	1.49	0	0	0.46	2.17
注：45钢本构模型参数A、B、n、c、m取自文献[23]，失效参数D₁～D₅取自文献[24]，最大主应力P₁取自文献[25]，其余参数为常见参数。

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表 4 靶后破片云形貌特征尺寸数值模拟与试验对比

Table 4. Comparison of numerical simulation and experimental results of the morphological feature sizes of the behind-armor debris clouds

方法	长轴a/mm	短轴b/mm	a/b	轴向膨胀速度/(m·s⁻¹)
试验	111.4	72.2	1.54	1123
数值模拟	115.4	77.0	1.50	1060
相对误差/%	3.59	6.65	−2.60	−5.61

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表 5 用于训练的数值模拟工况

Table 5. Numerical simulation conditions used for training

设计变量	变量值	工况数
v₀/(m·s⁻¹)	1500，1600，1700，1800，1900，2000，2100，2200	8
h₀/mm	10，15，20，25，30	5

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表 6 BO-SVR模型的预测性能

Table 6. The predictive performance of the BO-SVR model

预测指标	R²	ε_MAPE/%	ε_RMSE
训练集性能	0.9678	4.2100	1.0428
交叉验证性能	0.9484	5.3612	1.2404

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