Ballistic Performance of Perforated Array Ceramic Armor Using FEM-SPH Adaptive Algorithm

doi:10.12382/bgxb.2025.0531

Abstract

Abstract:

The perforated array ceramic plate is a new type of protective armor. The projectiles are deflected by the asymmetric forces caused by the holes in the plates, reducing the stability and penetration ability of the projectiles. In this paper, FEM-SPH adaptive algorithm was used to model the penetration of a 7.62mm armor-piercing incendiary projectile into a perforated array boron carbide ceramic target plate. The effects of impact points, angles, and projectile rotation on the ballistic performance of the perforated array ceramic plate were analyzed. It is shown that the impact points have significant influence on the projectile-target interaction, the failure mode and the ballistic performance of the perforated array ceramic plate. The active failure mode of the projectile for the impact point located at the hole edge is deflected due to asymmetric forces, resulting in the enhancement of the ballistic performance of the plate. For the oblique impact, the projectile stability is further reduced by the plate, giving rise to the enhancement of the ballistic performance and expansion of the damage area on the plate. Comparing to non-rotating projectiles, the plate has greater advantages against the rotating projectiles.

Key words: perforated array armor, B₄C ceramic, penetration, FEM-SPH adaptive algorithm, ballistic performance

HE Zhifan, CHEN Tianming, LU Chengfa, YANG Yang, LIANG Bo, WANG Zhipeng, CHEN Aijun, CAO Jianwu, QIN Qinghua. Ballistic Performance of Perforated Array Ceramic Armor Using FEM-SPH Adaptive Algorithm[J]. Acta Armamentarii, 2025, 46(10): 250531-.

Figures/Tables 13

Table 1 Parameters of constitutive model of steel core and brass jacket

参数	钢弹芯	黄铜弹壳
ρ/(g·cm^-3)	7.85	8.96
E/GPa	208	124
ν	0.3	0.34
G/GPa	80	46
A/MPa	1.976	0.090
B/MPa	2.856	0.292
n	0.2072	0.310
C	0.005	0.025
m	1	1.09
T_m/K	1800	1356
T_r/K	300	300
${\stackrel{·}{\epsilon }}_{0}$/S^-1	0.008	1
C_p/(J·kg^-1·K^-1)	450	386
D₁		0.540
D₂	主应力: 3.6/GPa	4.89
D₃		-3.03
D₄	主应变:0.1	0.0014
D₅		1.12
c/(m·s^-1)		3940
S₁		1.49
S₂		0
S₃		0
γ₀		1.99
α		0

Table 2 Parameters of constitutive model of ceramic plate

参数	数值	参数	数值
ρ/(g·cm^-3)	2.51	σ_fmax	0.2
G/GPa	197	HEL/GPa	19
A	0.927	P_hel/GPa	8.71
B	0.7	β	1
C	0.005	D₁	0.001
m	0.85	D₂	0.5
n	0.67	K₁/GPa	233
${\stackrel{·}{\epsilon }}_{0}$/s^-1	1.0	K₂/GPa	-593
T/GPa	0.26	K₃/GPa	2800

Fig.1 Geometric model of projectile-target system

Fig.2 Finite element model of 1/4 target plate

Fig.3 Five typical impact points

Fig.4 Penetration process for different impact points

Fig.5 Damage modes of target plate and projectile core at different impact points

Fig.6 Yaw angle of projectile core

Fig.7 Kinetic energy-time curves of projectile core and eroded energy-time curves of target plate at different impact points

Fig.8 Contact forces between target plate and projectile core at different impact points

Fig.9 Effect of oblique angle on the ballistic performance of target plates

Table 3 Effect of oblique angle on damage modes of target plate

Fig.10 Effect of projectile rotation on the ballistic performance of target plates at different impact points

References 27

[1]	KILIÇ N, EKICI B, BEDIR S. Optimization of high hardness perforated steel armor plates using finite element and response surface methods[J]. Mechanics of Advanced Materials and Structures, 2017, 24(7): 615-624. doi: 10.1080/15376494.2016.1196771 URL
[2]	BEN-MOSHE D, TARSI Y, ROSENBERG G. An armor assembly for armored vehicles: Israel, 209221[P]. 1986-05-13.
[3]	MISHRA B, RAMAKRISHNA B, JENA P K, et al. Experimental studies on the effect of size and shape of holes on damage and microstructure of high hardness armour steel plates under ballistic impact[J]. Materials & Design, 2013, 43: 17-24. doi: 10.1016/j.matdes.2012.06.037 URL
[4]	秦庆华, 崔天宁, 施前, 等. 孔结构金属装甲抗弹能力的数值模拟[J]. 高压物理学报, 2018, 32(5): 135-143.
	QIN Q H, CUI T N, SHI Q, et al. Numerical study on ballistic resistance of metal perforated armor to projectile impact[J]. Chinese Journal of High Pressure Physics, 2018, 32(5): 135-143. (in Chinese)
[5]	肖毅华, 吴和成, 朱爱华, 等. 旋转对卵形弹侵彻钢板影响的FEM-SPH耦合模拟[J]. 高压物理学报, 2019, 33(5): 156-165.
	XIAO Y H, WU H C, ZHU A H, et al. Effect ofrotation on penetration of steel plate by ogival projectile using coupled FEM-SPH simulation[J]. Chinese Journal of High Pressure Physics, 2019, 33(5): 156-165. (in Chinese)
[6]	崔天宁, 秦庆华. 轻质多孔夹芯结构的弹道侵彻行为研究进展[J]. 力学进展, 2023, 53(2): 395-432.
	CUI T N, QIN Q H. Ballistic performance of lightweight cellular sandwich structures :a review[J]. Advances In Mechanics, 2023, 53(2): 395-432. (in Chinese)
[7]	YU Y, WU Y, WANG B, et al. Review of the penetration resistance performance of lightweight ceramic composite armor under high-speed impact[J]. Mechanics of Advanced Materials and Structures, 2025, 32(9): 2056-2078. doi: 10.1080/15376494.2024.2374442 URL
[8]	WILKINS M, HONODEL C, SAWLE D. Approach to the study of light armor[R]. Berkeley: Lawrence Radiation Laboratory, 1967.
[9]	余毅磊, 王晓东, 任文科, 等. 陶瓷/金属复合靶受12.7mm穿甲燃烧弹侵彻时弹靶破碎特征[J]. 兵工学报, 2022, 43(9): 2307-2317.
	YU Y L, WANG X D, RENG W K, et al. Fragmentation characteristics of 12.7mm armor-piercing incendiary projectile and ceramic/metal composite terget during penetration[J]. Acta Armamentarii, 2022, 43(9): 2307-2317. (in Chinese)
[10]	MARSHALL A, KARANDIKAR P, GIVENS B, et al. Geometrical effect on damage in reaction bonded ceramic composites having experienced high strain rate impact[J]. Ceramic Engineering and Science Proceedings, 2014, 34: 41-52.
[11]	KARANDIKAR P, GIVENS B, LISZKIEWICZ A, et al. Effects of novel geometric designs on the ballistic performance of ceramics[C]//Proceedings of the advances in Ceramic Armor X: A Collection of Papers Presented at the 38th International Conference on Advanced Ceramics and Composites. Hoboken, State of New Jersey, USA, John Wiley & Sons, 2014, 35: 13-22.
[12]	DENG Y, REN Y, LIU X, et al. Protection performance of aluminum matrix ceramic ball composite materials plate for hypervelocity impact based on FE-SPH adaptive method[J]. Compos Structures, 2024, 338: 118103. doi: 10.1016/j.compstruct.2024.118103 URL
[13]	王积锐, 王诚鑫, 王艺霓, 等. 长杆高速侵彻下装甲钢靶的等效强度[J]. 兵工学报, 2023, 44(12): 3755-3770. doi: 10.12382/bgxb.2023.0619
	WANG J R, WANG C X, WANG Y N, et al. Equivalent stength of armor steel against high-velocity pentration of long-rod projectile[J]. Acta Armamentarii, 2023, 44(12): 3755-3770. (in Chinese)
[14]	李鹏飞, 夏洪利, 侯川玉, 等. 基于光滑粒子流体动力学数值仿真方法的武器系统冲击损伤虚拟试验[J]. 兵工学报, 2024, 45(S2): 208-214. doi: 10.12382/bgxb.2024.0959
	LI P F, XIA H L, HOU C Y, et al. Thevirtual test of impact damage on weapon system based on sph numerical simulation method[J]. Acta Armamentarii, 2024, 45(S2): 208-214. (in Chinese)
[15]	王志远, 王凤英, 刘天生, 等. 基于FEM/SPH算法弹丸侵彻多孔陶瓷板的数值模拟[J]. 高压物理学报, 2017, 31(1): 35-41.
	WANG Z Y, WANG F Y, LIU T S, et al. Numerical simulation of projectile penetration into porous ceramic plates based on FEM/SPH algorithm[J]. Chinese Journal of High Pressure Physics, 2017, 31(1): 35-41. (in Chinese)
[16]	章杰, 苏少卿, 郑宇, 等. 改进SPH方法在陶瓷材料层裂数值模拟中的应用[J]. 爆炸与冲击, 2013, 33(4): 401-407.
	ZHANG J, SU S Q, ZHENG Y, et al. Application of modified SPH method to numerical simulation of ceramic spallation[J]. Explosion And Shock Waves, 2013, 33(4): 401-407. (in Chinese)
[17]	卞梁, 王肖钧, 章杰. SPH/FEM耦合算法在陶瓷复合靶抗侵彻数值模拟中的应用[J]. 高压物理学报, 2010, 24(3): 161-167.
	BIAN L, WANG X J, ZHANG J. Numericalsimulations of anti-penetration of confined ceramic targets by sph/fem coupling method[J]. Chinese Journal of High Pressure Physics, 2010, 24(3): 161-167. (in Chinese)
[18]	MU D R, QU H G, ZENG Y S, et al. An improved SPH method for simulating crack propagation and coalescence in rocks with pre-existing cracks[J]. Engineering Fracture Mechanics, 2023, 282: 109148. doi: 10.1016/j.engfracmech.2023.109148 URL
[19]	HE Q G, CHEN X, CHEN J F. Finite element-smoothed particle hydrodynamics adaptive method in simulating debris cloud[J]. Acta Astronautica, 2020, 175: 99-117. doi: 10.1016/j.actaastro.2020.05.056 URL
[20]	JOHNSON G R, STRYK R A. Conversion of 3D distorted elements into meshless particles during dynamic deformation[J]. International Journal of Impact Engineering, 2003, 28(9): 947-966. doi: 10.1016/S0734-743X(03)00012-5 URL
[21]	位国旭, 崔浩, 周昊, 等. 钨合金弹丸侵彻钢靶的数值模拟方法[J]. 爆炸与冲击, 2025, 45(8): 160-176.
	WEI G X, CUI H, ZHOU H, et al. Research on numerical simulation method of tungsten alloy projectile penetrating steel target[J]. Explosion and Shock Waves, 2025, 45(8): 160-176. (in Chinese) doi: 10.1007/s10573-009-0021-9 URL
[22]	JOHNSON G R, COOK W H. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures[J]. Engineering Fracture Mechanics, 1983, 21: 541-548.
[23]	BURIAN W, ZOCHOWSKI P, GMITRZUK M, et al. Protection effectiveness of perforated plates made of high strength steel[J]. International Journal of Impact Engineering, 2019, 126: 27-39. doi: 10.1016/j.ijimpeng.2018.12.006 URL
[24]	KILIÇ N, BEDIR S, ERDIK A, et al. Ballistic behavior of high hardness perforated armor plates against 7.62mm armor piercing projectile[J]. Materials & Design, 2014, 63: 427-438. doi: 10.1016/j.matdes.2014.06.030 URL
[25]	JOHNSON G R, HOLMQUIST T J. An improved computational constitutive model for brittle materials[J]. AIP Conference Proceedings, 1994, 309(1): 981-984.
[26]	JOHNSON G R, HOLMQUIST T J. Response of boron carbide subjected to large strains, high strain rates, and high pressures[J]. Journal of Applied Physics, 1999, 85(12): 8060-8073. doi: 10.1063/1.370643 URL
[27]	RADISAVLJEVIC I, BALOS S, NIKACEVIC M, et al. Optimization of geometrical characteristics of perforated plates[J]. Materials & Design, 2013, 49: 81-89. doi: 10.1016/j.matdes.2012.12.010 URL