球形破片侵彻多层板弹道极限的量纲分析

王雪; 智小琦; 徐锦波; 范兴华

doi:10.11858/gywlxb.20190757

球形破片侵彻多层板弹道极限的量纲分析

doi: 10.11858/gywlxb.20190757

王雪^1,,
智小琦^1,*, ,,
徐锦波²,
范兴华²

1.
中北大学机电工程学院，山西太原　030051
2.
晋西工业集团，山西太原　030027

详细信息

作者简介:
王　雪（1994－），女，硕士研究生，主要从事弹药工程与毁伤技术研究. E-mail：271976366@qq.com

通讯作者:
智小琦（1963－），女，博士，教授，主要从事武器毁伤与装药技术研究. E-mail：zxq4060@sina.com

中图分类号: TJ410.3
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出版历程
- 收稿日期: 2019-04-10
- 修回日期: 2019-05-05
- 发布日期: 2019-09-25

Dimensional Analysis of Ballistic Limit of Spherical Fragments Penetrating Multi-Layer Plate

WANG Xue^1
,,
ZHI Xiaoqi^{1,*
, ,},
XU Jinbo²,
FAN Xinghua²

1.
College of Mechatronic Engineering, North University of China, Taiyuan 030051, China
2.
Shanxi West Group, Taiyuan 030027, China

摘要

摘要: 为了研究Q235钢多层板的抗侵彻性能，进行了直径为9.45 mm的钨合金球形破片侵彻7.2 mm和(3.6+3.6)mm厚Q235钢双层板试验，获得了相应的弹道极限。在此基础上，建立数值仿真模型，研究了钨合金球侵彻接触式等厚3层、4层、5层、6层板的弹道极限。通过量纲分析方法，分析了分层数对靶板弹道极限的影响。结果表明：对于球形破片，总厚度为7.2 mm的等厚双层板的抗侵彻性能高于单层板；当分层数大于2时，接触式多层等厚靶板的弹道极限随着层数的增加而减小，即分层数越多，靶板的抗侵彻性能越低，通过量纲分析方法得到了靶板分层数与破片弹道极限的关系。研究结果可为未来装甲防护设计提供一定的参考。
- 球形破片 /
- 弹道极限 /
- 多层板 /
- 量纲分析
Abstract: In order to study the anti-penetration performance of Q235 steel multi-layer plate, we carried out a $\varnothing $9.45 mm spherical fragment of tungsten alloy to penetrate the 7.2 mm and (3.6+3.6) mm Q235 steel double-layer plates, and obtained the corresponding ballistic limits. On this basis, we established a numerical simulation model to study the ballistic limits of the laminated contact plates with three, four, five, and six layers of equal thickness penetrated by the tungsten ball. Through the dimensional method, we analyzed the effect of the number of layers on the ballistic limit of the target. The results show that for spherical fragments, the anti-penetration performance of the double-layer plate with a total thickness of 7.2 mm is higher than that of the single-layer plate; when the number of layers is greater than 2, the ballistic limit of the multi-layer target decreases with the increase of the number of layers. The relationship between the number of layers of the target and the ballistic limit of the fragment is obtained by the dimensional method. The results can provide a guidance for the design of armor protection in the future.
- spherical fragment /
- ballistic limit /
- multi-layer plate /
- dimensional analysis

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图 1 试验原理图

Figure 1. Experimental schematic

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图 2 弹托、破片及小药筒

Figure 2. Sabot, fragments and small cartridge

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图 3 单层板冲击试验后破片与冲塞状态

Figure 3. Fragmentation and plug after single layer impacting experiment

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图 4 试验后的单层板状态

Figure 4. Single-layer plate after experiment

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图 5 试验后的双层板状态

Figure 5. Double-layer plate after the test

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图 6 有限元模型

Figure 6. Finite element model

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图 7 数值模拟和试验得到的残余速度的比较

Figure 7. Comparison of residual velocity obtained by numerical simulation and experiment

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图 8 仿真结果

Figure 8. Simulation results

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图 9 多层板的数值模拟结果

Figure 9. Numerical simulation of multi-layer plate

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图 10 多层板残余速度的数值模拟

Figure 10. Numerical residual velocity of multi-layer plate

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表 1 破片侵彻试验结果

Table 1. Experimental results of fragment penetrating plate

Target type	Initial velocity/(m∙s⁻¹)	Residual velocity/(m∙s⁻¹)	Phenomenon
Single layer plate 7.2 mm	494.3		Embedment
	598.8	248.6	Penetration
	662.0	350.2	Penetration
	718.5	413.3	Penetration
	726.4	423.0	Penetration
	734.1	454.3	Penetration
	766.1	479.2	Penetration
	787.3	504.9	Penetration
	837.0	558.9	Penetration
Double layer plate (3.6+3.6) mm	455.3		Embedment
	532.7		Embedment
	604.0	194.2	Penetration
	619.0	224.4	Penetration
	631.4	246.1	Penetration
	652.5	281.8	Penetration
	738.0	400.7	Penetration
	819.0	493.2	Penetration

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表 2 钨合金球的材料模型参数

Table 2. Material model parameters of tungsten alloy ball

Density/(g·cm^–3)	Young modulus/GPa	Poisson’s ratio	Yield stress /MPa	ETAN/MPa
18.2	357	0.303	1 506	762

BETA	SRC	SRP	FS	VP
1	3.9	6	1.2	0

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表 3 Q235钢靶板的材料模型参数

Table 3. Material model parameters of Q235 steel plate

Density/(g·cm^–3)	G/GPa	A/MPa	B/MPa	c	m	n
7.8	77.3	300	347	0.1	0.55	0.08

T_m/K	T_r/K	D₁	D₂	D₃	D₄	D₅
1 795	300	0.3	0.9	2.8	0	0

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表 4 破片侵彻靶板的仿真结果

Table 4. Simulation results of fragmentation penetrating the plate

Target type	Initial velocity/(m∙s⁻¹)	Residual velocity/(m∙s⁻¹)		Relative error/%	Phenomenon
Target type	Initial velocity/(m∙s⁻¹)	Simulation	Experiment	Relative error/%	Phenomenon
Single-layer plate 7.2 mm	494.3				Embedment
	598.8	243.8	248.6	1.93	Penetration
	662.0	340.3	350.2	2.83	Penetration
	718.5	408.9	413.3	1.06	Penetration
	726.4	410.7	423.0	2.91	Penetration
	734.1	435.8	454.3	4.07	Penetration
	766.1	467.3	479.2	2.48	Penetration
	787.3	487.8	504.9	3.39	Penetration
	837.0	541.5	558.9	3.11	Penetration
Double-layer plate (3.6+3.6) mm	532.7				Embedment
	604.0	189.5	194.2	2.42	Penetration
	619.0	217.4	224.4	3.12	Penetration
	631.4	237.4	246.1	3.54	Penetration
	652.5	270.5	281.8	4.01	Penetration
	738.0	383.2	400.7	4.37	Penetration
	819.0	470.7	493.2	4.56	Penetration

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表 5 破片侵彻靶板的仿真结果

Table 5. Simulation results of fragmentation penetrating the plate

Target type	Initial velocity/(m∙s⁻¹)	Residual velocity/(m∙s⁻¹)	Phenomenon
Three-layer plate (2.4+2.4+2.4) mm	550	115	Penetration
	600	228	Penetration
	630	267	Penetration
	680	342	Penetration
	700	360	Penetration
	750	417	Penetration
Four-layer plate (1.8+1.8+1.8+1.8) mm	520	64	Penetration
	550	157	Penetration
	600	250	Penetration
	650	318	Penetration
	700	381	Penetration
	750	434	Penetration
Five-layer plate (1.44+1.44+1.44+1.44+1.44) mm	550	168	Penetration
	600	258	Penetration
	650	325	Penetration
	700	389	Penetration
	750	441	Penetration
Six-layer plate (1.2+1.2+1.2+1.2+1.2+1.2) mm	550	184	Penetration
	600	265	Penetration
	650	332	Penetration
	700	394	Penetration
	750	450	Penetration

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表 6 相关物理量与无量纲量

Table 6. Related physical quantities and dimensionless quantities

H/m	${{v_{{\rm{50}}}}}$/(m∙s⁻¹)	n	${\dfrac{H}{{{d_{\rm{p}}}}}}$	${\dfrac{{{v_{50}}\sqrt {{\rho _{\rm{t}}}} }}{{\sqrt {{\sigma _{{\rm{st}}}}} }}}$
0.002 40	527.9	3	0.254 0	0.003 041
0.001 80	512.7	4	0.190 5	0.002 954
0.001 44	507.2	5	0.152 4	0.002 922
0.001 20	500.7	6	0.127 0	0.002 885

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表 7 破片侵彻靶板的仿真结果

Table 7. Simulation results of fragment penetrating the plate

Target type	Initial velocity /(m∙s⁻¹)	Residual velocity/(m∙s⁻¹)	Phenomenon
Eight-layer plate (0.9+0.9+0.9+0.9+0.9+0.9+0.9+0.9) mm	550	196	Penetration
	600	284	Penetration
	650	356	Penetration
	700	410	Penetration
	750	472	Penetration

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