Study on Similarity and Equivalent Design Method of Steel Plate Targets with Different Materials Based on Modified Compensation Model

doi:10.12382/bgxb.2022.1255

Abstract

Abstract:

The penetration test of ship plate frame structure is often used to assess the penetration ability of projectile into ship. Due to the high purchasing and processing costs of special steel, it is necessary to carry out research on the similarity law and material equivalent method of projectile penetrating into metal target plate. The similarity of the residual velocities of three kinds of projectiles during vertical penetration into steel plates made of different materials is studied based on the similarity theory. The dimensionless residual velocities are expressed as the function of dimensionless plate thickness and dimensionless dynamic yield stress of target plate. The correction and compensation model method is applied for the different materials of model and the prototype target plates. A similarity design method is established to achieve the same residual velocity as the prototype by changing the thickness of model plate,And the equivalent coefficients of two materials is obtained through the fitting of numerically simulated results, which are 0.5047 for blunt-nosed projectiles, 0.3943 for pointed nose projectiles, and 0.3845 for truncated-oval-shaped projectiles.

Key words: armor piercing mechanics, penetration, similarity theory, correction and compensation model, material equivalence

CLC Number:

TJ012.4

ZHANG Jianwei, WU Ziqi, ZHANG Fengchao, XING Chengcheng, MENG Fanxing. Study on Similarity and Equivalent Design Method of Steel Plate Targets with Different Materials Based on Modified Compensation Model[J]. Acta Armamentarii, 2024, 45(4): 1297-1310.

Figures/Tables 28

References 22

[1]	JONES N, BIRCH R S. On the scaling of low-velocity perforation of mild steel plates[J]. Journal of Pressure Vessel Technology - Transactions of the ASME, 2008, 130(3):031207.
[2]	SONG Q, DONG Y X, CUI M, et al. A similarity method for predicting the residual velocity and deceleration of projectiles during impact with dissimilar materials[J/OL]. Advances in Mechanical Engineering, 2017, 9(7) (2017-07-21). https://doi.org/10.1177/168781401770559
[3]	蒋东, 黄瑞源, 余道建, 等. 侵彻试验尺度效应和相似准则[J]. 力学与实践, 2017, 39(6): 561-565.
	JIANG D, HUANG R Y, YU D J, et al. Scale effect and similarity criterion of equal penetration test[J]. Mechanics and Practice, 2017, 39(6): 561-565. (in Chinese)
[4]	刘源, 皮爱国, 杨荷, 等. 非等比例缩比侵彻/贯穿相似规律研究[J]. 爆炸与冲击, 2020, 40(3): 63-75.
	LIU Y, PI A G, YANG H, et al. Study on scaling penetration/penetration similarity law of unequal cases[J]. Explosion and Shock, 2020, 40(3): 63-75. (in Chinese)
[5]	黄蒙, 欧卓成, 段卓平, 等. 刚性弹体侵彻混凝土的相似性研究[J]. 兵工学报, 2016, 37(增刊2):176-180.
	HUANG M, OU Z C, DUAN Z P, et al. Research on the similarity of rigid projectiles penetrating concrete[J]. Journal of Military Engineering, 2016, 37(S2): 176-180. (in Chinese)
[6]	蒋东, 史文卿, 黄瑞源, 等. 高速/超高速侵彻的尺度效应及相似规律[J]. 中国科学:物理学力学天文学, 2021, 51(10):106-113.
	JIANG D, SHI W Q, HUANG R Y, et al. Scale effect and similarity law of high-speed/hypervelocity penetration[J]. Chinese Science: Physics, Mechanics and Astronomy, 2021, 51(10): 106-113. (in Chinese)
[7]	李建广, 尹建平, 任杰, 等. 超高速半穿甲战斗部侵彻多层间隔板缩比实验设计方法[J]. 兵器装备工程学报, 2019, 40(10): 21-25.
	LI J G, YIN J P, REN J, et al. Design method of scaled experiment for hypervelocity semi armor piercing warhead penetrating multilayer spacer[J]. Journal of Weapon Equipment Engineering, 2019, 40(10): 21-25. (in Chinese)
[8]	XU Z W, GUAN Z W, CANTWELL W J. An experimental study of scaling effects in the perforation resistance of woven CFRP laminates[J]. Composite Structures, 2017, 181:285-293.
[9]	罗刚, 谢伟, 李德聪, 等. 亚音速平头弹体侵彻船用钢板结构相似律研究[J]. 武汉理工大学学报(交通科学与工程版), 2022, 46(1):66-70.
	LUO G, XIE W, LI D C, et al. Study on similarity law of subsonic flat nosed projectile penetrating ship steel plate structure[J]. Journal of Wuhan University of Technology (Transportation Science and Engineering Edition), 2022, 46(1): 66-70. (in Chinese)
[10]	MULLIN S A, LITTLEFIELD D L, ANDERSON C E, et al. An examination of velocity scaling[J]. International Journal of Impact Engineering, 1995, 17(4/5/6): 571-581.
[11]	MULLIN S A, JR C E A, WILBECK J S. Dissimilar material velocity scaling for hypervelocity[J]. Impact International journal of impact engineering, 2003, 29(1-10): 469-485.
[12]	徐挺. 相似理论与模型试验[M]. 北京: 中国农业机械出版社, 1982.
	XU T. Similarity theory and model test[M]. Beijing: China Agricultural Machinery Publishing House, 1982. (in Chinese)
[13]	王逸南, 张建伟, 王治, 等. 基于板厚补偿的921A钢与Q345钢靶板在截卵形弹体侵彻下的等效方法[J]. 兵工学报, 2021, 42(11): 2465-2475. doi: 10.3969/j.issn.1000-1093.2021.11.020
	WANG Y N, ZHANG J W, WANG Z, et al. Equivalent method of 921A steel and Q345 steel target plate based on plate thickness compensation under truncated oval projectile penetration[J]. Journal of Military Industry, 2021, 42(11): 2465-2475. (in Chinese)
[14]	谢晖, 龚宣丞, 程威, 等. 基于正交实验的弹丸高速侵彻金属装甲数值分析[J]. 兵器装备工程学报, 2019, 40(6): 19-23.
	XIE H, GONG X C, CHENG W, et al. Numerical analysis of projectile penetrating metal armor at high speed based on orthogonal experiment[J]. Journal of Weapon Equipment Engineering, 2019, 40(6): 19-23. (in Chinese)
[15]	周岩, 唐平, 常敬臻, 等. 舰舷结构与均质靶板等效关系的基本方法[J]. 弹道学报, 2008, 20(1): 30-34.
	ZHOU Y, TANG P, CHANG J Z, et al. Basic method of equivalent relationship between equal ship side structure and homogeneous target[J]. Journal of Ballistics, 2008, 20(1): 30-34. (in Chinese)
[16]	任辉启, 穆朝民, 刘瑞朝. 精确制导武器侵彻效应与工程防护[M]. 精确制导武器侵彻效应与工程防护, 2016.
	REN H Q, MU C M, LIU R C. Penetration effect and engineering protection of precision guided weapons[M]. Penetration Effect and Engineering Protection of Precision Guided Weapons, 2016. (in Chinese)
[17]	钱伟长. 穿甲力学[M]. 北京: 国防工业出版社, 1984.
	QIAN W C. Mechanics of perforation[M]. Beijing: Nation Defense Industry Press, 1984. (in Chinese)
[18]	段卓平. 半穿甲弹丸对加筋靶板侵彻的终点弹道的实验和理论研究[J]. 爆炸与冲击, 2005, 25(6): 547-552.
	DUAN Z P. Experimental and theoretical studies on the terminal trajectory of the semi armor piercing projectile penetrating the stiffened target[J]. Explosion and Shock, 2005, 25(6): 547-552. (in Chinese)
[19]	段卓平, 张中国, 李金柱, 等. 半穿甲战斗部对加筋靶板侵彻的靶场实验[C]// 第三届全国爆炸力学实验技术交流会论文集. 合肥: 中国力学学会, 2004:368-373.
	DUAN Z P, ZHANG Z G, LI J Z, et al. Shooting range experiment of semi armor piercing warhead penetrating reinforced target[C]// Proceedings of the Third National Symposium on Experimental Technology of Explosive Mechanics. Hefei: Chinese Society of Theoretical and Applied Mechanics, 2004:368-373. (in Chinese)
[20]	黄涛. 大型水面舰艇舷侧板架结构穿甲过程数值计算研究[D]. 武汉: 武汉理工大学, 2009.
	HUANG T. Numerical calculation study on armor piercing process of side grillage structure of large surface ship[D]. Wuhan: Wuhan University of Technology, 2009. (in Chinese)
[21]	王海坤. 水下爆炸下水面舰船结构局部与总体耦合损伤研究[D]. 北京: 中国舰船研究院, 2018.
	WANG H K. Study on local and overall coupling damage of surface ship structure under underwater explosion[D]. Beijing: China Shipbuilding Research Institute, 2018. (in Chinese)
[22]	姚熊亮, 王治, 叶墡君, 等. 舰船靶标设计中的材料等效方法[J]. 哈尔滨工程大学学报, 2021, 42(8):1110-1116.
	YAO X L, WANG Z, YE S J, et al. Material equivalence method in ship target design[J]. Journal of Harbin Engineering University, 2021, 42(8): 1110-1116. (in Chinese)

符号	量纲	符号	量纲
D	[L]	H	[L]
L	[L]	ρ_t	[M] [L]^-3
N		E_ty	[M] [L]^-1 [T]^-2
D_p	[L]	E_tt	[M] [L]^-1 [T]^-2
ρ_p	[M] [L]^-3	σ_t	[M] [L]^-1 [T]^-2
E_py	[M] [L]^-1 [T]^-2	σ_td	[M] [L]^-1 [T]^-2
E_pt	[M] [L]^-1 [T]^-2	μ_t
σ_p	[M] [L]^-1 [T]^-2	ε_tf
σ_pd	[M] [L]^-1 [T]^-2	v₀	[L] [T]^-1
μ_p		α
ε_pf		β

符号	量纲	符号	量纲
D	[L]	H	[L]
L	[L]	ρ_t	[M] [L]^-3
N		E_ty	[M] [L]^-1 [T]^-2
D_p	[L]	E_tt	[M] [L]^-1 [T]^-2
ρ_p	[M] [L]^-3	σ_t	[M] [L]^-1 [T]^-2
E_py	[M] [L]^-1 [T]^-2	σ_td	[M] [L]^-1 [T]^-2
E_pt	[M] [L]^-1 [T]^-2	μ_t
σ_p	[M] [L]^-1 [T]^-2	ε_tf
σ_pd	[M] [L]^-1 [T]^-2	v₀	[L] [T]^-1
μ_p		α
ε_pf		β

结构	密度/(kg·m^-3)	弹性模量/GPa	泊松比	屈服应力/MPa	硬化模量/MPa
弹体壳体(30CrMnSiNi2A钢)	7850	517	0.28	1600	594
填充物	1800	10	0.30

结构	密度/(kg·m^-3)	弹性模量/GPa	泊松比	屈服应力/MPa	硬化模量/MPa
弹体壳体(30CrMnSiNi2A钢)	7850	517	0.28	1600	594
填充物	1800	10	0.30

材料	密度/(kg·m^-3)	弹性模量/GPa	泊松比	A/MPa	B/MPa	n	c
921A钢	7850	205	0.28	898.6	356	0.022	0.586
Q345B钢	7850	210	0.28	425.0	680	0.520	0.300
材料	m	η₁	η₂	η₃	η₄	η₅
921A钢	1.05	0.80	2.1000	0	0.0020	0.6
Q345B钢	1.03	0.28	0.3352	-0.54	-0.0123	0