Influence of Stiffened Structure of Steel Plate on the Hypervelocity Penetration Ability of Cylindrical Projectile

doi:10.12382/bgxb.2022.0420

Abstract

Abstract:

In order to further study the influence of stiffened structure on the penetration ability of the projectile based on the problem of cylindrical projectile impacting the target plate at hypervelocity. In numerical simulations, the GRAY solid-liquid phase equation of state model, the JC strength model and the JC failure model are collectively taken as the metal constitutive model. The typical problems are calculated by the smooth particle hydrodynamics method. In the experiment, the single-layer stiffened steel plate and the three-layer stiffened steel plate are impacted by the cylindrical projectile at hypervelocity. Combined with the simulation and experimental results, the physical mechanism of the cylindrical projectile impacting the stiffened structure at hypervelocity is analyzed. The influence of the oblique angle, the attack angle, the type of stiffener, the radio of the projectile diameter and the stiffener thickness on the penetration ability of the cylindrical projectile is investigated. The lateral displacement of the trajectory of the cylindrical projectile as it impacts the stiffened steel plates at hypervelocity is analyzed. The results show that: in the case of symmetric impact, adding a main stiffener or auxiliary stiffener in the vertical direction on the basis of the single main stiffener has little effect on the erosion length of the projectile, and the radio of projectile erosion length to stiffener width decreases exponentially with the increase of the ratio of projectile diameter to stiffener thickness; in the case of asymmetric impact, the large angle between the axis of the projectile and the middle plane of the main stiffener is the main reason for the obvious attitude change of the projectile and even the fracture of the projectile, and the lateral motion velocity of the remaining projectile is small relative to the residual velocity in the impact direction; in the case of the projectile impacting the three-layer stiffened steel plate at hypervelocity, when the ratio of the main stiffener boundary far from the projectile axis to the projectile boundary relative to the projectile axis is within 0.6, the projectile can still maintain a good penetration ability. The penetration trajectory will not deviate greatly even if the projectile has an initial lateral displacement relative to the main stiffener.

Key words: hypervelocity impact, stiffened steel plate, cylindrical projectile, terminal ballistic effect

CLC Number:

TJ012.4

MA Kun, LI Mingrui, CHEN Chunlin, YIN Lixin, FENG Na, SHEN Zikai. Influence of Stiffened Structure of Steel Plate on the Hypervelocity Penetration Ability of Cylindrical Projectile[J]. Acta Armamentarii, 2023, 44(8): 2441-2452.

Figures/Tables 26

Table 1 Strength model parameters of 93W and Q345 steel

材料	A/10⁸Pa	B/10⁸Pa	n	c	m	T_m/K	$ε · 0$ /s^-1
93钨合金	6.008	1.2	0.4944	0.059	0.8203	3683	0.001
Q345钢^[18]	3.74	7.957	0.4545	0.01586	0.8856	1795	0.001

Table 1 Strength model parameters of 93W and Q345 steel

材料	A/10⁸Pa	B/10⁸Pa	n	c	m	T_m/K	$ε · 0$ /s^-1
93钨合金	6.008	1.2	0.4944	0.059	0.8203	3683	0.001
Q345钢^[18]	3.74	7.957	0.4545	0.01586	0.8856	1795	0.001

Table 2 Failure model parameters of 93W and Q345 steel

材料	密度/(kg·m^-3)	D₁	D₂	D₃	D₄	D₅	$ε · 0$ /s^-1
93钨合金	17600	0.091	0.409	-2.460	-0.218	1.613	0.001
Q345钢	7830	-0.589	1.300	-0.616	0.0164	0.240	0.001

Table 2 Failure model parameters of 93W and Q345 steel

材料	密度/(kg·m^-3)	D₁	D₂	D₃	D₄	D₅	$ε · 0$ /s^-1
93钨合金	17600	0.091	0.409	-2.460	-0.218	1.613	0.001
Q345钢	7830	-0.589	1.300	-0.616	0.0164	0.240	0.001

Table 3 Comparison of experimental and simulation results of residual projectile length and fragments parameters

序号	L/mm			v_x/(m·s^-1)			v_r/(m·s^-1)
序号	实验值	计算值	误差/%	实验值	计算值	误差/%	实验值	计算值	误差/%
1	12.53	12.75	1.76	2953	2889	-2.17	738	735	-0.41
2	18.90	19.63	3.86	2457	2453	-0.16	482	530	9.96

Fig.1 Comparison of simulated fragment morphology with the first round experimental results (33.4μs)

Fig.2 Comparison of simulated fragment morphology with the second round experimental results (39.3μs)

Fig.3 Simulation model of cylindrical projectile impacting stiffened steel plate

Table 4 Results of the mechanical parameters of the residual projectile at different oblique angles

序号	代号	剩余长度/mm	侵蚀长度/mm	剩余速度/ (m·s^-1)	是否断裂	挠度/ mm	攻角/ (°)
1	Z0	61.08	23.92	1939.7	否	0	0
2	Q-y5	65.28	19.72	1939.5	是	13.1	1.0
3	Q-y10	70.82	14.18	1952.3	是	10.9	1.0
4	Q-z5	60.71	24.29	1940.8	否	0	0.3
5	Q-z10	60.44	24.56	1942.0	否	0	0.3

Fig.4 Morphology of projectile and target before, during and after impact of Q-y5 model

Fig.5 Morphology of projectile and target before, during and after impact of Q-y10 model

Fig.6 Morphology of projectile and target before, during and after impact of Q-z10 model

Table 5 Results of the mechanical parameters of the residual projectile under different attack angles

序号	代号	剩余长度/mm	侵蚀长度/mm	剩余速度/ (m·s^-1)	是否断裂	挠度/ mm	攻角/ (°)
1	Z0	61.08	23.92	1939.7	否	0	0
2	G-y5	61.53	23.47	1937.1	否^*	6.68	2.5
3	G-y10	60.06	24.94	1921.5	是	21.57	10.5
4	G-z5	60.96	24.04	1931.2	否	0.18	1.5
5	G-z10	62.17	22.83	1896.6	是	8.01	9.5

Fig.7 Morphology of projectile and target before, during and after impact of G-z10 model

Fig.8 Morphology of projectile and target before, during and after impact of G-y10 model

Table 6 Results of the mechanical parameters of the residual projectile under different stiffener conditions

序号	代号	加筋情况	剩余长度/ mm	侵蚀长度/ mm	剩余速度/ (m·s^-1)
1	Z0	十字筋(一主、一副)	61.08	23.92	1939.7
2	ZK-d8.5	一条主筋	61.60	23.40	1942.7
3	SK-d8.5	十字主筋	57.93	27.07	1927.4
4	ZZ0	一条副筋	72.90	12.10	1971.0

Table 7 Results of residual projectile under different ratios of projectile diameter to stiffener thickness

序号	代号	剩余长度/ mm	侵蚀长度/ mm	剩余速度/ (m·s^-1)
1	ZK-d2	49.34	35.66	1938.3
2	ZK-d4.5	57.77	27.23	1940.5
3	ZK-d8.5	61.60	23.40	1942.7
4	ZK-d12.5	63.20	21.80	1947.6
5	ZK-d16	63.67	21.33	1949.4
6	H-43.5	43.25	41.75	1852.4

Fig.9 Relationship between the ratio of projectile erosion length to stiffener width and the ratio of projectile diameter to stiffener thickness

Fig.10 Experimental arrangement and failure morphology of single stiffened steel plate impacted by a cylindrical projectile

Fig.11 Experimental and simulation results of the morphology of fragments scattering produced by the projectile impacting the stiffener

Fig.12 Failure morphology of the following layer of steel plate caused by fragments produced by hypervelocity impact on the stiffener

Fig.13 Failure morphology of the main stiffener after projectile impact obtained by experiment and numerical simulation

Fig.14 Diagram of relative position relationship between five kinds of cylinderical projectiles and the first stiffened steel plate

Table 8 Comparison of the residual projectile parameters after each layer of stiffened steel plate under different impact conditions

撞击情况	第1层				第2层				第3层
撞击情况	L₁/mm	ΔL₁/mm	v₁/(m·s^-1)	挠度/mm	L₂/mm	ΔL₂/mm	v₂/(m·s^-1)	攻角/(°)	L₃/mm	ΔL₃/mm	v₃/(m·s^-1)	攻角/(°)
1	61.08	23.92	1939.7	0	36.24	24.84	1836	0	14.51	21.73	1589.4	0
2	61.6	23.4	1942.7	0	38.12	23.48	1844.1	1	16.15	21.97	1622.8	0
3	72.9	12.1	1971	0	61.73	11.17	1933.2	1	48.69	13.04	1886.4	0.5
4	61.41	23.59	1949.1	4.5	39.31	22.1	1876.6	19	23.61	15.7	1784.9	10
5	52.63^*	32.37	1947.4	22.9	16.16	36.47	1876.7	8	0	16.16	0	0

Fig.15 Numerical simulation results of hypervelocity impact of projectile on three-layer stiffened steel plate under Condition 4

Fig.16 Numerical simulation results of hypervelocity impact of projectile on three-layer stiffened steel plate under Condition 5

Fig.17 Failure morphology of the back of each layer of stiffened steel plate of Experiment No. 1

Fig.18 Failure morphology of the back of each layer of stiffened steel plate in Experiment No. 2

References 19

[1]	HILL S A. Determination of an empirical model for the prediction of penetration hole diameter in thin plates from hypervelocity impact[J]. International Journal of Impact Engineering, 2004, 30(3): 303-321. doi: 10.1016/S0734-743X(03)00079-4 URL
[2]	SCHONBERG W P. Hypervelocity impact penetration phenomena in aluminum space structures[J]. Journal of Aerospace Engineering, 1990, 3(3): 173-185. doi: 10.1061/(ASCE)0893-1321(1990)3:3(173) URL
[3]	王金涛, 余文力, 王涛. 长杆弹侵彻多层间隔靶的破片云研究[J]. 固体力学学报, 2013, 33(增刊1): 84-90.
	WANG J T, YU W L, WANG T. On fragments cloud produced by long rod impacting multilayer targets[J]. Chinese Journal of Solid Mechanics, 2013, 33(S1): 84-90. (in Chinese)
[4]	汪庆桃, 吴克刚, 陈志阳. 圆柱形长杆超高速正碰撞薄板结构破碎效应[J]. 振动与冲击, 2017, 36(5): 54-60.
	WANG Q T, WU K G, CHEN Z Y. Fragmentation effect of a long cylindrical rod with a hypervelocity normally impacting a thin plate structure[J]. Journal of Vibration and Shock, 2017, 36(5): 54-60. (in Chinese)
[5]	WANG Q T, ZHANG Q M, HUANG F L, et al. An analytical model for the motion of debris clouds induced by hypervelocity impact projectiles with different shapes on multi-plate structures[J]. International Journal of Impact Engineering, 2014, 74: 157-164. doi: 10.1016/j.ijimpeng.2014.06.006 URL
[6]	张新伟, 涂建平, 尹晓春, 等. 离散杆对钢板的高速侵彻效应[J]. 航空兵器, 2007(3): 38-41.
	ZHANG X W, TU J P, YIN X C, et al. Effects of oblique penetration on plates by rod[J]. Aero Weaponry, 2007(3): 38-41. (in Chinese)
[7]	YANG T H, LEE Y S. A study of impact reduction characteristics of hat-shaped stiffened panel under hypervelocity impact[J]. Transactions of the Korean Society of Mechanical Engineers A, 2013, 37(7): 929-935. doi: 10.3795/KSME-A.2013.37.7.929 URL
[8]	SILNIKOV M V, GUK I V, NECHUNAEV A F, et al. Numerical simulation of hypervelocity impact problem for spacecraft shielding elements[J]. Acta Astronautica, 2018(150): 56-62.
[9]	ZHANG C B, CHEN X W, YUAN Y. Characterization of the non-ideal debris cloud in yaw hypervelocity impact by cylindrical projectile[J]. International Journal of Impact Engineering, 2021(155): 103908.
[10]	李名锐, 冯娜, 蔡青山, 等. 93W杆式弹超高速撞击多层Q345钢靶毁伤及微观分析[J]. 爆炸与冲击, 2021, 41(2): 021408.
	LI M R, FENG N, CAI Q S, et al. Damage of a multi-layer Q345 target under hypervelocity impact of a rod-shaped 93W projectile[J]. Explosion and Shock Waves, 2021, 41(2): 021408. (in Chinese)
[11]	马坤, 陈春林, 冯娜, 等. 柱形93钨弹体超高速撞击薄钢板穿孔及破片群扩展特征[J]. 兵工学报, 2021, 42(11): 2350-2359. doi: 10.3969/j.issn.1000-1093.2021.11.008
	MA K, CHEN C L, FENG N, et al. Characteristics of perforation and fragment group expansion of steel sheet impacted by cylindrical 93 tungsten projectile at hypervelocity[J]. Acta Armamentarii, 2021, 42(11): 2350-2359. (in Chinese)
[12]	SHANG C, REN T F, ZHANG Q M, et al. Experimental research on damage characteristics of multi-spaced plates with long rods of steel and W-Zr reactive material at hypervelocity impact[J]. Materials & Design, 2022, 216: 110564.
[13]	FENG N, MA K, CHEN C L, et al. Study of the axial density/impedance gradient composite long rod hypervelocity penetration into a four-layer Q345 target[J/OL]. Defence Technology, 2023(2023-02-23). https://www.sciencedirect.com/science/article/pii/S2214914723000387
[14]	ZHANG X T, LI X G, LIU T, et al. Element fracture technique for hypervelocity impact simulation[J]. Advances in Space Research, 2015, 55(9): 2293-2304. doi: 10.1016/j.asr.2015.01.040 URL
[15]	ZHANG D Z, JAYARAMAN B. Equations and closure models for material pulverization and debris flow[J]. International Journal of Multiphase Flow, 2013(56): 149-159.
[16]	BEISSEL S R, GERLACH C A, JOHNSON G R. A quantitative analysis of computed hypervelocity debris clouds[J]. International Journal of Impact Engineering, 2008(35): 1410-1418.
[17]	SEKINE H, ITO R, SHINTATE K. A single energy-based parameter to assess protection capability of debris shields[J]. International Journal of Impact Engineering, 2007(34): 958-972.
[18]	于文静. 导管架海洋平台钢结构在爆炸和火灾作用下的力学性能研究[D]. 上海: 上海交通大学, 2012.
	YU W J. Study on mechanical properties of steel jacket offshore platform in blast and fire[D]. Shanghai: Shanghai Jiao Tong University, 2012. (in Chinese)
[19]	马坤, 李名锐, 陈春林, 等. 93钨合金弹体超高速撞击钢板破片群分布数值模拟[J]. 兵工学报, 2019, 40(10): 2022-2031. doi: 10.3969/j.issn.1000-1093.2019.10.007
	MA K, LI M R, CHEN C L, et al. Simulation analysis of distribution of fragments of hypervelocity 93W projectile impacting on a steel plate target[J]. Acta Armamentarii, 2019, 40(10): 2022-2031. (in Chinese) doi: 10.3969/j.issn.1000-1093.2019.10.007