弹体高速侵彻花岗岩靶体的结构响应特性

韩明海; 刘闯; 李鹏程; 刘子涵; 张先锋

doi:10.11883/bzycj-2024-0145

弹体高速侵彻花岗岩靶体的结构响应特性

doi: 10.11883/bzycj-2024-0145

南京理工大学机械工程学院，江苏南京 210094

基金项目: 国家自然科学基金（12202205，12141202）；

详细信息

作者简介:
韩明海（2000－　），男，硕士研究生，minghaidadi@163.com

通讯作者:
张先锋（1978－　），男，博士，教授，博士生导师，lynx@njust.edu.cn

中图分类号: O385
计量
- 文章访问数: 151
- HTML全文浏览量: 28
- PDF下载量: 76
- 被引次数: 0
出版历程
- 收稿日期: 2024-05-17
- 修回日期: 2024-06-21
- 网络出版日期: 2024-06-24

A study on structural response characteristics of projectile penetrating on granite target

School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China

摘要

摘要: 为探究弹体斜侵彻花岗岩靶体的结构响应特性，基于30 mm弹道炮平台，开展了弹体斜侵彻花岗岩靶试验，获得了非正侵彻作用下弹体结构破坏参数。在此基础上，结合数值模拟方法研究了弹体斜侵彻花岗岩靶的弹体结构变形及断裂机制，分析了侵彻初始条件对弹体结构响应的影响规律。研究结果表明：弹体非正侵彻花岗岩靶体时，易发生弯曲和断裂；弹体头尾部所受非对称力是影响弹体响应特性的主要因素，弹体的变形破坏程度由弹体头尾部角速度差峰值大小决定；随着攻角的增大，弹体弯曲程度线性增大，攻角增大到8°时，弹体发生断裂；随着着角的增大，弹体弯曲程度先增大后减小再增大，着角为15°时，弹体弯曲程度最小，着角达到30°时，弹体发生断裂；与着角相比，攻角对弹体结构响应行为的影响更显著；攻角与着角联合作用时，着角的引入会增大弹体临界断裂正攻角，负攻角会削弱弹体抵抗弯曲变形和断裂的能力；撞击速度高于1600 m/s时，弹体撞击速度成为弹体产生不同响应行为的主控因素。
- 弹体 /
- 侵彻 /
- 岩石靶 /
- 结构响应
Abstract: In order to explore the structural response characteristics of projectile obliquely penetrating granite target, based on a 30 mm ballistic gun platform, the tests of projectile obliquely penetrating granite target were carried out, and the damage parameters of projectile structure under non-normal penetration were obtained. On this basis, combined with the numerical simulation, the deformation and fracture mechanism of the projectile structure of the projectile obliquely penetrating the granite target are studied, and the influence of the initial conditions of penetration on the structural response of the projectile is analyzed. The results show that the projectile is prone to bending and fracture when it is not penetrating the granite target. The asymmetric force on the head and tail of the projectile is the main factor affecting the response characteristics of the projectile. The degree of deformation and failure of the projectile is determined by the peak value of the angular velocity difference between the head and tail of the projectile. As the yaw increases, the bending degree of the projectile increases linearly, and the projectile breaks when the yaw increases to 8°. With the increase of the impact angle, the bending degree of the projectile increases first, followed by decrease and then increase again. When the impact angle is 15°, the bending degree of the projectile is the smallest. When the impact angle reaches 30°, the projectile breaks. Compared with the impact angle, the yaw has a more significant effect on the response behavior of the projectile structure. When the yaw and impact angle are combined, the introduction of the impact angle will increase the critical fracture positive yaw of the projectile, and the negative yaw will weaken the ability of the projectile to resist bending deformation and fracture. When the impact velocity is greater than 1600 m/s, the impact velocity of the projectile becomes the main controlling factor for the different response behaviors of the projectile.
- projectile /
- penetration /
- rock target /
- structural response

HTML全文

图 1 试验弹体

Figure 1. Projectile used in the experiment

下载: 全尺寸图片幻灯片

图 2 试验靶体

Figure 2. Targets used in the experiments

下载: 全尺寸图片幻灯片

图 3 试验布局

Figure 3. Experimental layout

下载: 全尺寸图片幻灯片

图 4 弹体侵彻条件示意图

Figure 4. Condition of penetration

下载: 全尺寸图片幻灯片

图 5 弹体飞行姿态分析

Figure 5. Flying attitude of projectile

下载: 全尺寸图片幻灯片

图 6 弹体侵彻岩石靶动态开坑过程

Figure 6. The dynamic process during the cratering stage of the projectile penetration into a granite target

下载: 全尺寸图片幻灯片

图 7 靶体典型破坏形貌

Figure 7. Photographs of typical destruction on the target

下载: 全尺寸图片幻灯片

图 8 不同初始速度下靶体的侵彻深度和开坑体积

Figure 8. Depth of penetration and crater volume of target under different velocity

下载: 全尺寸图片幻灯片

图 9 不同工况下试验前后弹体的对比

Figure 9. Comparison of the projectile before and after the experiment under different working condition

下载: 全尺寸图片幻灯片

图 10 有限元模型

Figure 10. Finite element model

下载: 全尺寸图片幻灯片

图 11 靶体开坑破坏对比

Figure 11. Experimental carter damage of target compared with numerical simulation

下载: 全尺寸图片幻灯片

图 12 试验4中的弹体头尾部角速度

Figure 12. Nose and tail angular velocity of the projectile in test 4

下载: 全尺寸图片幻灯片

图 13 试验4中的弹体典型时刻受力分析

Figure 13. Force analysis of typical moment of the projectile in test 4

下载: 全尺寸图片幻灯片

图 14 弹体头尾部角速度

Figure 14. Nose and tail angular velocity of projectile

下载: 全尺寸图片幻灯片

图 15 弹体破坏形貌对比

Figure 15. Comparisons between simulation and test results for deformation of projectiles

下载: 全尺寸图片幻灯片

图 16 侵彻深度结果对比

Figure 16. Comparison of the penetration depth results

下载: 全尺寸图片幻灯片

图 17 弹体头尾部角速度

Figure 17. Nose and tail angular velocity of projectile

下载: 全尺寸图片幻灯片

图 18 不同攻角角速度差

Figure 18. Angular velocity difference under different yaws

下载: 全尺寸图片幻灯片

图 19 弹体弯曲程度及量化方法

Figure 19. Bending degree of projectile and quantification method

下载: 全尺寸图片幻灯片

图 20 不同着角角速度差

Figure 20. Angular velocity difference under different impact angle

下载: 全尺寸图片幻灯片

图 21 35°着角弹体头尾部角速度

Figure 21. Nose and tail angular velocity of projectile under 35° impact angle

下载: 全尺寸图片幻灯片

图 22 35°着角弹体典型时刻受力分析

Figure 22. Force analysis of 35° impact angle projectile at typical moment

下载: 全尺寸图片幻灯片

图 23 弹体弯曲程度

Figure 23. Bending degree of projectile

下载: 全尺寸图片幻灯片

图 24 15°着角弹体头尾部角速度

Figure 24. Nose and tail angular velocities of projectile with 15° impact angle

下载: 全尺寸图片幻灯片

图 25 10°攻角和着角的弹体角速度差对比

Figure 25. Comparison of angular velocity difference of 10° yaw and impact angle

下载: 全尺寸图片幻灯片

图 26 增大着角时弹体的角速度差

Figure 26. Angular velocity difference varying with impact angle

下载: 全尺寸图片幻灯片

图 27 增大攻角时弹体的角速度差

Figure 27. Angular velocity difference varying with yaw

下载: 全尺寸图片幻灯片

图 28 弹体头尾部角速度

Figure 28. Nose and tail angular velocities of projectile

下载: 全尺寸图片幻灯片

图 29 增大着角弹体角速度差

Figure 29. Angular velocity difference varying with impact angle

下载: 全尺寸图片幻灯片

图 30 增大攻角弹体角速度差

Figure 30. Angular velocity difference varying with yaw

下载: 全尺寸图片幻灯片

图 31 弹体弯曲程度

Figure 31. Bending degree of projectile

下载: 全尺寸图片幻灯片

图 32 不同撞击速度弹体结构响应变化规律

Figure 32. A map characterizing the structural response of projectile under different impact velocities

下载: 全尺寸图片幻灯片

表 1 弹体主要参数

Table 1. Main parameters of projectile

材料	d/mm	l/mm	CRH	m/g	h_t/mm	HRC
30CrMnSiNi2A	30	180	3	550	5	45-50

下载: 导出CSV

表 2 弹靶交会初始条件

Table 2. Initial condition of projectile-target intersection

试验编号	v₀/(m·s⁻¹)	α/(°)	β/(°)
1	467	−1.1	1.1
2	666	−3.0	3.0
3	749	2.3	2.3
4	792	−10.6	10.6
5	834	9.0	9.0
6	892	−3.5	3.5

下载: 导出CSV

表 3 弹体侵彻花岗岩靶的试验结果

Table 3. Test results of projectile penetrating granite target

试验编号	v₀/(m·s⁻¹)	α/(°)	β/(°)	P/mm	V_c/cm³	弹体结构破坏
1	467	−1.1	1.1	90	1660	侵蚀
2	666	−3.0	3.0	128	4360	−
3	749	2.3	2.3	137	5143	弯曲
4	792	−10.6	10.6	82	2318	断裂
5	834	9.0	9.0	93	2784	断裂
6	892	−3.5	3.5	168	10440	弯曲

下载: 导出CSV

表 4 不同工况下弹体的质量损失率与长度缩短率

Table 4. Mass loss rate and length shortening rate of projectile body under different working condition

试验编号	v₀/(m·s⁻¹)	α/(°)	β/(°)	δ/%	γ/%
1	467	−1.1	1.1	0.8	0.3
2	666	−3.0	3.0	−	−
3	749	2.3	2.3	2.3	1.7
4	792	−10.6	10.6	22.3	55.6
5	834	9.0	9.0	−	61.1
6	892	−3.5	3.5	4.0	3.06

下载: 导出CSV

表 5 弹体材料参数^[41-42]

Table 5. Projectile material parameters^[41-42]

材料	ρ/(g·cm⁻³)	E/GPa	A/MPa	B/MPa	n	C	v
30CrMnSiNi2A	7.85	210	1314	1028	0.479	0.019	0.3

下载: 导出CSV

表 6 靶体材料参数^[43-45]

Table 6. Target material parameters^[43-45]

ρ/(g·cm⁻³)	G/GPa	f_c/MPa	f_t^*	f_s^*	A₁/GPa	A₂/GPa	A₃/GPa	B₀	B₁
2.66	21.9	167.8	0.04	0.21	25.7	37.84	21.29	1.22	1.22

T₁/GPa	P_el/MPa	P_co/GPa	α₀	n	A	N	Q₀	B	β_c
25.7	125	6.0	1.0	3.0	2.44	0.76	0.68	0.05	0.026

β_t	A_f	n_f	g^*_c	g^*_t	ξ	D₁	D₂	ε
0.007	1.78	0.80	0.53	0.7	0.5	0.04	1.0	0.015

下载: 导出CSV

参考文献(48)

[1]	任辉启, 穆朝民, 刘瑞朝, 等. 精确制导武器侵彻效应与工程防护 [M]. 北京: 科学出版社, 2016: 179–184. REN H Q, MU C M, LIU R C, et al. Penetration effects of precision guided weapons and engineering protection [M]. Beijing: Science Press, 2016: 179–184.
[2]	杨秀敏, 邓国强. 常规钻地武器破坏效应的研究现状和发展 [J]. 后勤工程学院学报, 2016, 32(5): 1–9. DOI: 10.3969/j.issn.1672-7843.2016.05.001. YANG X M, DENG G Q. The research status and development of damage effect of conventional earth penetration weapon [J]. Journal of Logistical Engineering University, 2016, 32(5): 1–9. DOI: 10.3969/j.issn.1672-7843.2016.05.001.
[3]	高杰, 何翔, 李磊, 等. 金属-岩石复合材料抗侵彻性能研究 [J]. 防护工程, 2016, 38(5): 11–16. GAO J, HE X, LI L, et al. Study on anti-penetration performance of metal-rock composite [J]. Protective Engineering, 2016, 38(5): 11–16.
[4]	吴飚, 杨建超, 刘瑞朝. 有限厚块石砌体钢筋混凝土结构板抗贯穿性能的实验研究 [J]. 爆炸与冲击, 2013, 33(1): 73–78. DOI: 10.11883/1001-1455(2013)01-0073-06. WU B, YANG J C, LIU R C. Experimental study on perforation resistance of composite targets composed by granite block masonry and reinforced concrete plates [J]. Explosion and Shock Waves, 2013, 33(1): 73–78. DOI: 10.11883/1001-1455(2013)01-0073-06.
[5]	ZHANG X Y, WU H J, et al. A constitutive model of concrete based on Ottosen yield criterion [J]. International Journal of Solids and Structures, 2020, 193–194. DOI: 10.1016/j.ijsolstr.2020.02.013.
[6]	何丽灵, 郭虎, 陈小伟, 等. 结构变形对深侵彻弹体偏转的影响 [J]. 爆炸与冲击, 2023, 43(9): 091404. DOI: 10.11883/bzycj-2023-0068. HE L L, GUO H, CHEN X W, et al. Influence of structural deformation on the deflection of penetrator into concrete target with deep penetration [J]. Explosion and Shock Waves, 2023, 43(9): 091404. DOI: 10.11883/bzycj-2023-0068.
[7]	李鹏程, 张先锋, 刘闯, 等. 攻角和入射角对弹体侵彻混凝土薄靶弹道特性影响规律研究 [J]. 爆炸与冲击, 2022, 42(11): 113302. DOI: 10.11883/bzycj-2021-0435. LI P C, ZHANG X F, LIU C, et al. Study on the influence of attack angle and incident angle on ballistic characteristics of projectiles penetration into thin concrete targets [J]. Explosion and Shock Waves, 2022, 42(11): 113302. DOI: 10.11883/bzycj-2021-0435.
[8]	HANCHAK S J, FORRESTAL M J, YOUNG E R, et al. Perforation of concrete slabs with 48 MPa (7 ksi) and 140 MPa (20 ksi) unconfined compressive strengths [J]. International Journal of Impact Engineering, 1992, 12(1): 1–7. DOI: 10.1016/0734-743X(92)90282-X.
[9]	FREW D J, HANCHAK S J, GREEN M L. Penetration of concrete targets with ogive-nose steel rods [J]. International journal of Impact Engineering, 1998, 21(6): 489–497. DOI: 10.1016/s0734-743x(98)00008-6.
[10]	张雪岩, 孙凯, 李元龙, 等. 基于Ottosen屈服条件的不同强度混凝土空腔膨胀模型及侵彻机理 [J]. 爆炸与冲击, 2023, 43(9): 091403. DOI: 10.11883/bzycj-2022-0511. ZHANG X Y, SUN K, LI Y L, et al. Cavity expansion model and penetration mechanism of concrete with different strengths based on the Ottosen yield condition [J]. Explosion and Shock Waves, 2023, 43(9): 091403. DOI: 10.11883/bzycj-2022-0511.
[11]	SHAH Q H, HAMDANI A. The damage of unconfined granite edge due to the impact of varying stiffness projectiles [J]. International Journal of Impact Engineering, 2013, 59: 11–17. DOI: 10.1016/j.ijimpeng.2013.03.004.
[12]	张德志, 张向荣, 林俊德, 等. 高强钢弹对花岗岩正侵彻的实验研究 [J]. 岩石力学与工程学报, 2005, 24(9): 1612–1618. DOI: 10.3321/j.issn:1000-6915.2005.09.024. ZHANG D Z, ZHANG X R, LING D J, et al. Penetration experiments for normal impact into granite targets with high-strength steel projectile [J]. Chinese Journal of Rock Mechanics and Engineering, 2005, 24(9): 1612–1618. DOI: 10.3321/j.issn:1000-6915.2005.09.024.
[13]	李艳, 范文, 赵均海, 等. 中低速长杆弹侵彻半无限岩石靶的动态响应研究 [J]. 工程力学, 2017, 34(9): 139–149. DOI: 10.6052/j.issn.1000-4750.2016.04.0334. LI Y, FAN W, ZHAO J H, et al. Dynamic response study for penetration of medium-low speed projectile on semi-infinite rock targets [J]. Engineering Mechanics, 2017, 34(9): 139–149. DOI: 10.6052/j.issn.1000-4750.2016.04.0334.
[14]	李干, 宋春明, 邱艳宇, 等. 超高速弹对花岗岩侵彻深度逆减现象的理论与实验研究 [J]. 岩石力学与工程学报, 2018, 37(1): 60–66. DOI: 10.13722/j.cnki.jrme.2017.0584. LI G, SONG C M, QIU Y Y, et al. Theoretical and experimental studies on the phenomenon of reduction in penetration depth of hyper-velocity projectiles into granite [J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(1): 60–66. DOI: 10.13722/j.cnki.jrme.2017.0584.
[15]	宋春明, 李干, 王明洋, 等. 不同速度段弹体侵彻岩石靶体的理论分析 [J]. 爆炸与冲击, 2018, 38(2): 250–257. DOI: 10.11883/bzycj-2017-0198. SONG C M, LI G, WANG M Y, et al. Theoretical analysis of projectiles penetrating into rock targets at different velocities [J]. Explosion and Shock Waves, 2018, 38(2): 250–257. DOI: 10.11883/bzycj-2017-0198.
[16]	LI J, WANG M Y, CHENG Y H, et al. Analytical model of hypervelocity penetration into rock [J]. International Journal of Impact Engineering, 2018, 122: 384–394. DOI: 10.1016/j.ijimpeng.2018.08.008.
[17]	高飞, 邓树新, 张国凯, 等. 缩比模型弹侵彻岩石靶尺寸效应试验研究与理论分析 [J]. 兵工学报, 2023, 44(12): 3601–3612. DOI: 10.12382/bgxb.2023.0014. GAO F, DENG S X, ZHANG G K, et al. Experimental study and theoretical analysis of the size effect for scale model projectile penetrating into rock target [J]. Acta Armamentarii, 2023, 44(12): 3601–3612. DOI: 10.12382/bgxb.2023.0014.
[18]	FORRESTAL M J, FREW D J, HANCHAK S J, et al. Penetration of grout and concrete targets with ogive-nose steel projectiles [J]. International Journal of Impact Engineering, 1996, 18(5): 465–476. DOI: 10.1016/0734-743x(95)00048-f.
[19]	SILLING S A, FORRESTAL M J. Mass loss from abrasion on ogive-nose steel projectiles that penetrate concrete targets [J]. International Journal of Impact Engineering, 2007, 34(11): 1814–1820. DOI: 10.1016/j.ijimpeng.2006.10.008.
[20]	CHEN X W, HE L L, YANG S Q. Modeling on mass abrasion of kinetic energy penetrator [J]. European Journal of Mechanics - A/Solids, 2010, 29(1): 7–17. DOI: 10.1016/j.euromechsol.2009.07.006.
[21]	ZHAO J, CHEN X W, JIN F N, et al. Depth of penetration of high-speed penetrator with including the effect of mass abrasion [J]. International Journal of Impact Engineering, 2010, 37(9): 971–979. DOI: 10.1016/j.ijimpeng.2010.03.008.
[22]	WEN H M, YANG Y, HE T. Effects of abrasion on the penetration of ogival-nosed projectiles into concrete targets [J]. Latin American Journal of Solids and Structures, 2010, 7(4): 413–422. DOI: 10.1590/S1679-78252010000400003.
[23]	欧阳昊, 陈小伟. 混凝土骨料对高速侵彻弹体质量侵蚀的影响分析 [J]. 爆炸与冲击, 2019, 39(7): 073102. DOI: 10.11883/bzycj-2018-0068. OUYANG H, CHEN X W. Analysis of mass abrasion of high-speed penetrator influenced by aggregate in concrete target [J]. Explosion and Shock Waves, 2019, 39(7): 073102. DOI: 10.11883/bzycj-2018-0068.
[24]	刘均伟, 张先锋, 刘闯, 等. 考虑摩擦因数变化的弹体高速侵彻混凝土质量侵蚀模型研究 [J]. 爆炸与冲击, 2021, 41(8): 083301. DOI: 10.11883/bzycj-2020-0250. LIU J W, ZHANG X F, LIU C, et al. Study on mass erosion model of projectile penetrating concrete at high speed considering variation of friction coefficient [J]. Explosion and Shock Waves, 2021, 41(8): 083301. DOI: 10.11883/bzycj-2020-0250.
[25]	BLESS S J, SATAPATHY S, NORMANDIA M J. Transverse loads on a yawed projectile [J]. International Journal of Impact Engineering, 1999, 23(1): 77–86. DOI: 10.1016/S0734-743X(99)00064-0.
[26]	WARREN T L. Simulations of the penetration of limestone targets by ogive-nose 4340 steel projectiles [J]. International Journal of Impact Engineering, 2002, 27(5): 475–496. DOI: 10.1016/S0734-743X(01)00154-3.
[27]	盛强. 椭圆截面战斗部高速侵彻混凝土靶壳体及装药响应研究 [D]. 南京: 南京理工大学, 2024: 62–74.
[28]	陈小伟. 动能深侵彻弹的力学设计(I): 侵彻/穿甲理论和弹体壁厚分析 [J]. 爆炸与冲击, 2005, 25(6): 499–505. DOI: 10.11883/1001-1455(2005)06-0499-07. CHEN X W, et al. Mechanics of structural design of EPW(Ⅰ): the penetration/Perforation theory and the analysis on the cartridge of projectile [J]. Explosion and Shock Waves, 2005, 25(6): 499–505. DOI: 10.11883/1001-1455(2005)06-0499-07.
[29]	皮爱国, 黄风雷. 大长细比弹体斜侵彻混凝土靶的动力学响应 [J]. 爆炸与冲击, 2007, 27(4): 331–338. DOI: 10.11883/1001-1455(2007)04-0331-08. PI A G, HUANG F L. Dynamic behavior of a slender projectile on oblique penetrating into concrete target [J]. Explosion and Shock Waves, 2007, 27(4): 331–338. DOI: 10.11883/1001-1455(2007)04-0331-08.
[30]	皮爱国, 黄风雷. 大长细比动能弹体弹塑性动力响应数值模拟 [J]. 北京理工大学学报, 2007, 27(8): 666–670. DOI: 10.3969/j.issn.1001-0645.2007.08.003. PI A G, HUANG F L. Numerical simulation of the elastic-plastic dynamic response of a slender kinetic energy penetrator [J]. Transactions of Beijing Institute of Technology, 2007, 27(8): 666–670. DOI: 10.3969/j.issn.1001-0645.2007.08.003.
[31]	皮爱国, 黄风雷. 大长细比结构弹体侵彻2024-O铝靶的弹塑性动力响应 [J]. 爆炸与冲击, 2008, 28(3): 252–260. DOI: 10.11883/1001-1455(2008)03-0252-09. PI A G, HUANG F L. Elastic-plastic dynamic response of slender projectiles penetrating into 2024-O aluminum targets [J]. Explosion and Shock Waves, 2008, 28(3): 252–260. DOI: 10.11883/1001-1455(2008)03-0252-09.
[32]	朱超, 张晓伟, 张庆明, 等. 弹体斜侵彻双层钢板的结构响应和失效研究 [J]. 爆炸与冲击, 2023, 43(9): 091408. DOI: 10.11883/bzycj-2023-0017. ZHU C, ZHANG X W, ZHANG Q M, et al. Structural response and failure of projectiles obliquely penetrating into double-layered steel plate targets [J]. Explosion and Shock Waves, 2023, 43(9): 091408. DOI: 10.11883/bzycj-2023-0017.
[33]	高飞, 张国凯, 纪玉国, 等. 卵形弹体超高速侵彻砂浆靶的响应特性 [J]. 兵工学报, 2020, 41(10): 1979–1987. DOI: 10.3969/j.issn.1000-1093.2020.10.007. GAO F, ZHANG G K, JI Y G, et al. Response characteristics of hypervelocity ogive-nose projectile penetrating into mortar target [J]. Acta Armamentarii, 2020, 41(10): 1979–1987. DOI: 10.3969/j.issn.1000-1093.2020.10.007.
[34]	LI P C, ZHANG X F, LIU C, et al. Trajectory characteristics of oblique penetration of projectile into concrete targets considering cratering effect [J]. International Journal of Impact Engineering, 2024, 185: 104864. DOI: 10.1016/j.ijimpeng.2023.104864.
[35]	张朝平, 张先锋, 谈梦婷, 等. 聚能杆式射流侵彻混凝土和岩石靶体试验与数值模拟 [J]. 含能材料, 2023, 31(8): 773–785. DOI: 10.11943/CJEM2023071. ZHANG C P, ZHANG X F, TAN M T, et al. Experimental and numerical simulation of shaped charge jet penetrating concrete and rock targets [J]. Chinese Journal of Energetic Materials, 2023, 31(8): 773–785. DOI: 10.11943/CJEM2023071.
[36]	薛建锋, 沈培辉, 王晓鸣. 弹体斜侵彻混凝土靶的实验研究及其数值模拟 [J]. 爆炸与冲击, 2017, 37(3): 536–543. DOI: 10.11883/1001-1455(2017)03-0536-08. XUE J F, SHEN P H, WANG X M. Experimental study and numerical simulation of projectile obliquely penetrating into concrete target [J]. Explosion and Shock Waves, 2017, 37(3): 536–543. DOI: 10.11883/1001-1455(2017)03-0536-08.
[37]	段建, 王可慧, 周刚, 等. 弹体侵彻混凝土的临界跳弹 [J]. 爆炸与冲击, 2016, 36(6): 797–802. DOI: 10.11883/1001-1455(2016)06-0797-06. DUAN J, WANG K H, ZHOU G, et al. Critical ricochet performance of penetrator impacting concrete targets [J]. Explosion and Shock Waves, 2016, 36(6): 797–802. DOI: 10.11883/1001-1455(2016)06-0797-06.
[38]	FRAS T, MURZYN A, PAWLOWSKI P. Defeat mechanisms provided by slotted add-on bainitic plates against small-calibre 7.62 mm×51 AP projectiles [J]. International Journal of Impact Engineering, 2017, 103: 241–253. DOI: 10.1016/j.ijimpeng.2017.01.015.
[39]	王维占, 赵太勇, 冯顺山, 等. 12.7 mm动能弹斜侵彻复合装甲的数值模拟研究 [J]. 爆炸与冲击, 2019, 39(12): 123301. DOI: 10.11883/bzycj-2018-0425. WANG W Z, ZHAO T Y, FENG S S, et al. Numerical simulation study on penetration of a 12.7 mm kinetic energy bullet into a composite armor [J]. Explosion and Shock Waves, 2019, 39(12): 123301. DOI: 10.11883/bzycj-2018-0425.
[40]	施德胜, 施冠银, 陈江瑛. RHT模型的改进与数值拟合 [J]. 宁波大学学报(理工版), 2014, 27(3): 93–96. SHI D S, SHI G Y, CHEN J Y. Improvement and numerical fitting of RHT model [J]. Journal of Ningbo University (NSEE), 2014, 27(3): 93–96.
[41]	李磊, 张先锋, 吴雪, 等. 不同硬度30CrMnSiNi2A钢的动态本构与损伤参数 [J]. 高压物理学报, 2017, 31(3): 239–248. DOI: 10.11858/gywlxb.2017.03.005. LI L, ZHANG X F, WU X, et al. Dynamic constitutive and damage parameters of 30CrMnSiNi2A steel with different hardnesses [J]. Chinese Journal of High Pressure Physics, 2017, 31(3): 239–248. DOI: 10.11858/gywlxb.2017.03.005.
[42]	周义清, 张治民. 30CrMnSiNi2A钢在不同应变率下的力学性能研究 [J]. 兵器材料科学与工程, 2010, 33(4): 46–50. DOI: 10.3969/j.issn.1004-244X.2010.04.013. ZHOU Y Q, ZHANG Z M. Mechanical property of 30CrMnSiNi2A steel under various strain rates [J]. Ordnance Material Science and Engineering, 2010, 33(4): 46–50. DOI: 10.3969/j.issn.1004-244X.2010.04.013.
[43]	XIE L X, LU W B, ZHANG Q B, et al. Analysis of damage mechanisms and optimization of cut blasting design under high in-situ stresses [J]. Tunnelling and Underground Space Technology, 2017, 66: 19–33. DOI: 10.1016/j.tust.2017.03.009.
[44]	聂铮玥. 三种典型岩石材料的RHT模型参数研究 [D]. 湖南: 国防科学技术大学, 2021: 60–65.
[45]	聂铮玥, 彭永, 陈荣, 等. 侵彻条件下岩石类材料RHT模型参数敏感性分析 [J]. 振动与冲击, 2021, 40(14): 108–116. DOI: 10.13465/j.cnki.jvs.2021.14.015. NIE Z Y, PENG Y, CHEN R, et al. Sensitivity analysis of RHT model parameters for rock materials under penetrating condition [J]. Journal of Vibration and Shock, 2021, 40(14): 108–116. DOI: 10.13465/j.cnki.jvs.2021.14.015.
[46]	ABDEL-KADER M. Modified settings of concrete parameters in RHT model for predicting the response of concrete panels to impact [J]. International Journal of Impact Engineering, 2019, 132: 103312. DOI: 10.1016/j.ijimpeng.2019.06.001.
[47]	YAN J, LIU Y, YAN J B, et al. Collapse of concrete target subjected to embedded explosion of shelled explosive [J]. Engineering Failure Analysis, 2024, 161: 108298. DOI: 10.1016/j.engfailanal.2024.108298.
[48]	姜安邦, 李典, 李永清, 等. 偏转式抗侵彻防护技术研究现状 [J]. 材料导报, 2023, 37(24): 22060150–9. DOI: 10.11896/cldb.22060150. JIANG A B, LI D, LI Y Q, et al. Research status of deflected anti-penetration protection technology [J]. Materials Reports, 2023, 37(24): 22060150–9. DOI: 10.11896/cldb.22060150.