椭圆截面截锥弹体的高速穿甲特性及阻力模型

邓希旻; 武海军; 董恒; 田泽; 黄风雷

doi:10.11883/bzycj-2023-0074

椭圆截面截锥弹体的高速穿甲特性及阻力模型

doi: 10.11883/bzycj-2023-0074

北京理工大学爆炸科学与技术国家重点实验室，北京 100081

基金项目: 国家自然科学基金（12072039）;国家自然科学基金青年科学基金（12202067）

详细信息

作者简介:
邓希旻（1993－　），男，博士研究生，bitdengxm@bit.edu.cn

通讯作者:
武海军（1974－　）, 男, 教授, 博士生导师， wuhj@bit.edu.cn

中图分类号: O385
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- PDF下载量: 108
- 被引次数: 41
出版历程
- 收稿日期: 2023-03-01
- 修回日期: 2023-05-19
- 网络出版日期: 2023-06-21
- 刊出日期: 2023-09-11

A study of high-velocity penetration characteristics and resistance model of elliptical cross-section truncated ogive projectile

State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

摘要

摘要: 随着高超声速武器系统的发展，具有更大空间利用率的异型截面弹体开始受到广泛关注，异型弹体的高速穿甲特性及毁伤机理是当前亟需解决的关键问题。基于典型反舰战斗部的截锥形头部结构及椭圆截面弹体外形，通过数值仿真方法研究了椭圆截面截锥弹体高速正贯穿金属薄板的阻力特性及薄板损伤机理，将弹体载荷分为剪切冲塞和延性扩孔阻力两部分，结合数值仿真结果提出了适用于椭圆截面平头弹、尖卵形弹的高速穿甲阻力函数及剩余速度解析模型，采用微分面力法和刚体动力学相结合的方法构建了椭圆弹正穿甲模型，并通过数值仿真结果验证了理论模型的有效性。结果表明：椭圆截面截锥弹体正贯穿金属薄板的过程分为载荷作用的头部侵入阶段和无载荷作用的弹身贯穿阶段，头部侵入阶段弹体对薄板的破坏模式分解为截锥平台造成的剪切冲塞和头部弧面的延性扩孔；高速冲击条件下椭圆截面尖卵形弹/平头弹对薄板的损伤与低速冲击时不同，尖卵形弹体贯穿薄板时发生延性扩孔破坏，薄板受平头弹高速冲击时出现剪切冲塞-延性扩孔相耦合的破坏模式；椭圆截面弹体正穿甲过程中所受阻力与截面积相等的圆截面弹体相同，区别在于椭圆截面弹体非对称结构外形导致载荷非均匀分布。
- 椭圆截面弹体 /
- 剪切冲塞 /
- 延性扩孔 /
- 阻力函数 /
- 穿甲模型
Abstract: With the development of the hypersonic weapon system, the non-circular cross-section projectile with more space utilization has attracted extensive attention. The high-velocity penetration mechanism of the non-circular cross-section projectile is a crucial issue that must be solved. Based on the truncated conical head structure of a typical anti-ship warhead and the elliptical section projectile’s shape, the elliptical section’s resistance characteristics and damage mechanism of thetruncated cone projectile through the metal sheet at high velocity are studied by numerical simulation. The load applied on the projectile is divided into two parts: shear punching resistance and ductile enlargement resistance. Combined with the numerical simulation results, the high-velocity penetration resistance function and the analytical model of residual velocity are proposed, which are suitable for elliptic cross-section flat projectile and ogive projectile. The differential surface force method and rigid body dynamics are used to construct a normal penetration model, and numerical simulation results verify the validity of the theoretical model. The results show that the elliptical cross-section truncated cone projectile penetrating through the metal sheet can be divided into the head penetration stage under load and the body penetration stage without load. In the head invasion stage, the failure mode of the thin sheet due to project penetration is decomposed into the shear plugging caused by the truncated cone platform and the ductility enlargement of the curved surface of the head. Under high-velocity impact, the damage to the sheet caused by elliptic ogive projectile/blunt projectile is different from that caused by low-velocity impact. When the ogive projectile penetrates through the sheet, ductile enlargement failure occurs. When the sheet is impacted by blunt projectile at high velocity, the coupled failure mode of shear punching and ductile enlargement takes place. The resistance of the elliptical cross-section projectile is the same as that of the circular cross-section projectile with the same cross-sectional area. The difference is that the asymmetric structure of the elliptical cross-section projectile leads to non-uniform load distribution.
- elliptical cross section projectile /
- plugging /
- enlargement /
- resistance function /
- penetration model

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图 1 椭圆截面截锥弹体结构示意图

Figure 1. The geometry of the projectile

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图 2 网格敏感性验证

Figure 2. Grid sensitivity verification

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图 3 弹体正贯穿速度/加速度曲线

Figure 3. The velocity and acceleration curves of the projectile

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图 4 弹体加速度与塞块速度曲线

Figure 4. The plug velocity and acceleration curves of the projectile

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图 5 阶段I不同时刻弹靶速度分布

Figure 5. Velocity distributions at different times in phase I

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图 6 柱坐标中单元应力、应变分量示意图

Figure 6. Stress and strain components in cylindrical coordinates

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图 7 阶段Ⅰ靶板的塑性功率-时间曲线

Figure 7. Energy rate curves of the target in phase Ⅰ

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图 8 等效圆与椭圆的几何关系

Figure 8. Equivalent circle and ellipse

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图 9 尖卵形弹体结构示意图

Figure 9. The geometry of the ogive projectile

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图 10 相同速度下不同尖卵形弹体加速度对比

Figure 10. Ogive projectile’s acceleration at the same velocity

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图 11 不同速度下尖卵形弹体加速度对比

Figure 11. Ogive projectile’s acceleration at the different velocity

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图 12 椭圆空腔中的等效应力分布示意图

Figure 12. Stress distribution of elliptic cavity

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图 13 相同速度下不同平头弹加速度对比

Figure 13. Flat projectile’s acceleration at the same velocity

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图 14 不同速度下两类平头弹加速度对比

Figure 14. Flat projectile’s acceleration at the different velocities

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图 15 椭圆截面平头弹以不同速度撞击时靶板的破坏模式

Figure 15. Failure modes of the target at different impact velocities

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图 16 椭圆截面尖卵形弹体正贯穿薄靶示意图

Figure 16. Schematic of elliptical cross section ogive projectile penetrating thin target

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图 17 椭圆截面尖卵形弹体的速度分量及载荷分量示意图

Figure 17. Schematic diagram of velocity and load component

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图 18 延性扩孔过程中弹靶相对位置关系示意图

Figure 18. The relative position between a projectile and a target

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图 19 高速冲击下C-α曲线

Figure 19. C-α curves under high velocity impact

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图 20 椭圆截面弹体剪切冲塞金属薄靶示意图

Figure 20. Shearing process of thin metal target

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图 21 剩余速度-初速曲线

Figure 21. Residual velocity vs. initial velocity curves

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图 22 弹体表面单元划分示意图

Figure 22. Meshing of projectile surface

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图 23 计算流程图

Figure 23. Flow chart of computation

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图 24 弹体加速度曲线对比图

Figure 24. Comparison on the acceleration of projectile

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图 25 两类弹体正穿甲剩余速度曲线

Figure 25. Residual velocity of two types of projectiles

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表 1 945钢仿真材料参数统计

Table 1. Material parameters of 945 steel used in numerical simulation

A/MPa	B/MPa	n	C₁	C₂	E/GPa	ν	${\dot{\varepsilon }}_{0}/{\mathrm{s}}^{-1}$	T₀/K	T_m/K
451.6	797.73	0.75	−0.1589	0.012	210	0.33	3×10⁻⁴	293	1800

m_T	χ	ρ/（g·cm⁻³）	c_p/(J·kg⁻¹·K⁻¹)	D₁	D₂	D₃	D₄	${\varepsilon }_{\mathrm{f},\mathrm{t}}$
0.859	0.9	7.85	452	0.35	1.11	−0.806	0.10	0.996

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表 2 塑性冲击波速仿真结果

Table 2. Simulation results of the velocity of plastic shock wave

v₀/(m·s⁻¹)	x₁/mm	t₁/μs	c_s/(m·s⁻¹)
v₀/(m·s⁻¹)	x₁/mm	t₁/μs	H/t₁	式(32)	式(34)
700	0.376	0.542	5533.7	5497.1	4897.9
800	0.452	0.536	5600.6	5564.3	4968.6
900	0.480	0.537	5584.3	5547.4	5039.3
1000	0.511	0.515	5827.0	5788.5	5110.0

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表 3 模型误差

Table 3. Relative deviation of the model

长短轴之比	初速/(m·s⁻¹)	尖卵形弹			平头弹
		余速/(m·s⁻¹)		误差%	余速/(m·s⁻¹)		误差%
		仿真	模型	误差%	仿真	模型	误差%
1	700	688.8	685.9	−0.4	664.9	671.6	1.0
	800	787.8	786.0	−0.2	759.8	764.9	0.7
	900	887.1	885.9	−0.1	854.6	857.4	0.3
	1000	986.5	985.7	−0.1	949.4	949.3	0.0
2	700	688.7	688.9	0.0	665.2	671.6	1.0
	800	787.8	789.2	0.2	760.1	764.9	0.6
	900	887.2	889.3	0.2	855.0	867.4	1.5
	1000	986.8	989.2	0.2	949.8	949.2	−0.1

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表 4 剩余速度对比表

Table 4. Comparison of the residual velocity

初速 /(m·s⁻¹)	剩余速度/(m·s⁻¹)（λ=1.6，靶板厚度3 mm）		相对误差/%	剩余速度/(m·s⁻¹)（λ=2，靶板厚度5 mm）		相对误差/%
初速 /(m·s⁻¹)	本文模型	Recht-Ipson模型	相对误差/%	本文模型	Recht-Ipson模型	相对误差/%
100	91.0	22.5	−303.8	74.7	22.5	231.3
200	186.5	175.6	−6.2	158.1	97.5	62.2
300	284.1	282.7	−0.5	251.8	242.0	4.0
400	382.7	385.1	0.6	350.7	354.1	−1.0
500	482.0	485.9	0.8	453.1	459.0	−1.3
600	581.8	585.9	0.7	556.6	560.8	−0.7
700	681.8	685.5	0.5	658.4	661.1	−0.4
800	782.0	784.9	0.4	758.9	760.4	−0.2
900	881.4	884.1	0.3	858.6	859.1	−0.1
1000	980.6	983.1	0.3	957.7	957.5	0.0

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参考文献(33)

[1]	董恒. 椭圆截面弹体侵彻混凝土靶作用过程与结构响应研究 [D]. 北京理工大学, 2021. DONG H. Penetration mechanism and structural response of elliptical cross-sectional projectile penetrating into concrete target[D]. Beijing: Beijing Institute of Technology, 2021.
[2]	王浩. 椭圆变截面弹体贯穿加筋板破坏模式与偏转机理研究 [D]. 北京理工大学, 2020. WANG H. The failure mode and deflection mechanism of projectiles with tapered-elliptic cross-section perforation into stiffened plates[D]. Beijing: Beijing Institute of Technology, 2020.
[3]	DAI X H, WANG K H, LI M R, et al. Rigid elliptical cross-section ogive-nose projectiles penetration into concrete targets [J]. Defence Technology, 2021, 17(3): 800–811. DOI: 10.1016/j.dt.2020.05.011.
[4]	魏海洋, 张先锋, 熊玮, 等. 椭圆截面弹体斜侵彻金属靶体弹道研究 [J]. 爆炸与冲击, 2022, 42(2): 023304. DOI: 10.11883/bzycj-2021-0291. WEI H Y, ZHANG X F, XIONG W, et al. Oblique penetration of elliptical cross-section projectile into metal target [J]. Explosion and Shock Waves, 2022, 42(2): 023304. DOI: 10.11883/bzycj-2021-0291.
[5]	田泽, 王浩, 武海军, 等. 椭圆变截面弹体斜贯穿薄靶姿态偏转机理研究 [J]. 兵工学报, 2022, 43(7): 1537–1552. DOI: 10.12382/bgxb.2021.0367. TIAN Z, WANG H, WU H J, et al. Attitude deflection mechanism of projectiles with variable elliptical cross-sections obliquely perforating thin targets [J]. Acta Armamentarii, 2022, 43(7): 1537–1552. DOI: 10.12382/bgxb.2021.0367.
[6]	WU H J, DENG X M, DONG H, et al. Three-dimensional trajectory prediction and analysis of elliptical projectile [J]. International Journal of Impact Engineering, 2023, 174: 104497. DOI: 10.1016/j.ijimpeng.2023.104497.
[7]	LIU J W, LIU C, ZHANG X F, et al. Research on the penetration characteristics of elliptical cross-section projectile into semi-infinite metal targets [J]. International Journal of Impact Engineering, 2023, 173: 104438. DOI: 10.1016/j.ijimpeng.2022.104438.
[8]	邓希旻, 田泽, 武海军, 等. 上下非对称结构弹体侵彻金属薄板的特性及薄板破坏形式[J]. 兵工学报, 2022. DOI: 10.12382/bgxb.2022.0724. DENG X M, TIAN Z, WU H J, et al. Penetration characteristics and plate failure modes of asymmetric shaped projectiles penetrating thin metal targets[J]. Acta Armamentarii, 2022. DOI: 10.12382/bgxb.2022.0724.
[9]	BACKMAN M E, GOLDSMITH W. The mechanics of penetration of projectiles into targets [J]. International Journal of Engineering Science, 1978, 16(1): 1–99. DOI: 10.1016/0020-7225(78)90002-2.
[10]	RECHT R F, IPSON T W. Ballistic perforation dynamics [J]. Journal of Applied Mechanics, 1963, 30(3): 384. DOI: 10.1115/1.3636566.
[11]	AWERBUCH J, BODNER S R. Analysis of the mechanics of perforation of projectiles in metallic plates [J]. International Journal of Solids and Structures, 1974, 10(6): 671–684. DOI: 10.1016/0020-7683(74)90050-x.
[12]	CHEN X W, LI Q M. Shear plugging and perforation of ductile circular plates struck by a blunt projectile [J]. International Journal of Impact Engineering, 2003, 28(5): 513–536. DOI: 10.1016/S0734-743X(02)00077-5.
[13]	WEN H M, JONES N. Low-velocity perforation of punch-impact-loaded metal plates [J]. Journal of Pressure Vessel Technology-Transactions of the Asme, 1996, 118(2): 181–187. DOI: 10.1115/1.2842178.
[14]	ROSENBERG Z, DEKEL E. Revisiting the perforation of ductile plates by sharp-nosed rigid projectiles [J]. International Journal of Solids and Structures, 2010, 47(22/23): 3022–3033. DOI: 10.1016/j.ijsolstr.2010.07.003.
[15]	CHEN X W, HUANG X L, LIANG G J. Comparative analysis of perforation models of metallic plates by rigid sharp-nosed projectiles [J]. International Journal of Impact Engineering, 2011, 38(7): 613–621. DOI: 10.1016/j.ijimpeng.2010.12.005.
[16]	MASRI R. Practical formulae for predicting the ballistic limit velocity of armour perforation by ductile hole growth [J]. International Journal of Impact Engineering, 2022, 167: 104219. DOI: 10.1016/j.ijimpeng.2022.104219.
[17]	CHEN X W, LI Q M, FAN S C. Initiation of adiabatic shear failure in a clamped circular plate struck by a blunt projectile [J]. International Journal of Impact Engineering, 2005, 31(7): 877–893. DOI: 10.1016/j.ijimpeng.2004.04.011.
[18]	BORVIK T, HOPPERSTAD O S, LANGSETH M, et al. Effect of target thickness in blunt projectile penetration of Weldox 460 E steel plates [J]. International Journal of Impact Engineering, 2003, 28(4): 413–464. DOI: 10.1016/S0734-743x(02)00072-6.
[19]	RUSINEK A, RODRíGUEZ-MARTíNEZ J A, ZAERA R, et al. Experimental and numerical study on the perforation process of mild steel sheets subjected to perpendicular impact by hemispherical projectiles [J]. International Journal of Impact Engineering, 2009, 36(4): 565–587. DOI: 10.1016/j.ijimpeng.2008.09.004.
[20]	陈小伟, 梁冠军, 姚勇, 等. 平头弹穿透金属靶板的模式分析 [J]. 力学学报, 2009, 41(1): 84–90. DOI: 10.6052/0459-1879-2009-1-2007-572. CHEN X W, LIANG G J, YAO Y, et al. Perforation modes of metal plates struck by a blunt rigid projectile[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(1): 84–90. DOI: 10.6052/0459-1879-2009-1-2007-572.
[21]	MAE H, TENG X, BAI Y, et al. Comparison of ductile fracture properties of aluminum castings: Sand mold vs. metal mold [J]. International Journal of Solids and Structures, 2008, 45(5): 1430–1444. DOI: 10.1016/j.ijsolstr.2007.10.016.
[22]	李营. 反舰导弹舱内爆炸作用下舱室结构毁伤与防护机理 [D]. 武汉:武汉理工大学, 2017. LI Y. Damage and protective mechanism of cabins under anti-ship missile internal blast [D]. Wuhan: Wuhan University of Technology, 2017.
[23]	DONG H, LIU Z H, WU H J, et al. Study on penetration characteristics of high-speed elliptical cross-sectional projectiles into concrete [J]. International Journal of Impact Engineering, 2019, 132: 103311. DOI: 10.1016/j.ijimpeng.2019.05.025.
[24]	王浩, 潘鑫, 武海军, 等. 椭圆截面截卵形刚性弹体正贯穿加筋板能量耗散分析 [J]. 爆炸与冲击, 2019, 39(10): 103203. DOI: 10.11883/bzycj-2018-0350. WANG H, PAN X, WU H J, et al. Energy dissipation analysis of elliptical truncated oval rigid projectile penetrating stiffened plate[J]. Explosion and Shock Waves, 2019, 39(10): 69–80. DOI: 10.11883/bzycj-2018-0350.
[25]	DENG X M, WU H J, YANG X, et al. Preformed fragment velocity distribution of elliptical cross-section projectile [J]. Latin American Journal of Solids and Structures, 2022, 19(1): e423. DOI: 10.1590/1679-78256835.
[26]	TENG X, WIERZBICKI T. Dynamic shear plugging of beams and plates with an advancing crack [J]. International Journal of Impact Engineering, 2005, 31(6): 667–698. DOI: 10.1016/j.ijimpeng.2004.03.013.
[27]	VERSHININ V V. Validation of metal plasticity and fracture models through numerical simulation of high velocity perforation [J]. International Journal of Solids and Structures, 2015, 67/68: 127–138. DOI: 10.1016/j.ijsolstr.2015.04.007.
[28]	MASRI R. Ballistically equivalent aluminium targets and the effect of hole slenderness ratio on ductile plate perforation [J]. International Journal of Impact Engineering, 2015, 80: 45–55. DOI: 10.1016/j.ijimpeng.2015.01.003.
[29]	MASRI R, DURBAN D. Quasi-static cylindrical cavity expansion in an elastoplastic compressible Mises solid [J]. International Journal of Solids and Structures, 2006, 43(25/26): 7518–7533. DOI: 10.1016/j.ijsolstr.2006.03.012.
[30]	STANLEY M. Lasl shock hugoniot data [M]. Berkeley: University of California Press, 1980.
[31]	LI Q M, JONES N. Shear and adiabatic shear failures in an impulsively loaded fully clamped beam [J]. International Journal of Impact Engineering, 1999, 22(6): 589–607. DOI: 10.1016/s0734-743x(99)00013-5.
[32]	BØRVIK T, LANGSETH M, O. SHOPPERSTAD, et al. Perforation of 12 mm thick steel plates by 20 mm diameter projectiles with flat, hemispherical and conical noses: part I: experimental study [J]. International Journal of Impact Engineering, 2001, 27(1): 19–35. DOI: 10.1016/S0734-743X(01)00034-3.
[33]	BEN-DOR G, DUBINSKY A, ELPERIN T. Shape optimization of high-speed penetrators: a review [J]. Open Engineering, 2012, 2(4): 473–482. DOI: 10.2478/s13531-012-0022-4.

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