Mechanical Response of Body Armor during Rifle Bullet Penetration Based on Bond-based Peridynamic Method

doi:10.12382/bgxb.2024.0275

Abstract

Abstract:

At present, there is still a lack of research on the mechanical response of body amor under the impact of bullets. In this paper, a bond-based peridynamic method combined with the traditional Lagrangian method is used to numerically simulate the process of a 5.56mm SS109 rifle bullet penetrating a NIJ level III SiC/ultra-high molecular weight polyethylene (UHMWPE) body amor. The accuracy of the numerical model is verified by comparing it with the penetration test results of body amor based on the three-dimensional digital image correlation method. The research results show that the velocity of bullet decreases from 810m/s to 157.57m/s after penetrating the body armor for 50μs, and the ceramic block contacting with the bullet severely fractures.The bond-based peridynamics method can effectively track the evolution of cracks when the bullet impacts the ceramic insert plate. The radial cracks generated by the impact of an SS109 bullet at 810m/s on the SiC ceramic insert plate are outwardly expanded basically within 10μs, and the severely damaged area is essentially shaped within 30μs. Ultimately, the radial cracks, hoop cracks, and delamination cracks parallel to the impact surface are formed under the complex action of pressure wave. The maximum back face signature (BFS) value of body armor is 18.41mm. Due to the orthotropic nature of UHMWPE laminate, the effective strain on the back side is distributed in an “L-shaped” pattern centered around the point of impact and the maximum effective strain occurs at about ±45° on the bulge boundary. The equivalent stress field presents a “diamond-shaped” distribution, and the stress concentration occurs at the four corners of the “diamond”.

Key words: body armor, peridynamics, SiC ceramic, crack propagation

CLC Number:

TJ012.4

WANG Jilong, WEN Yaoke, LIU Dongxu, WANG Huicheng, SHEN Zhouyu, LUO Xiaohao. Mechanical Response of Body Armor during Rifle Bullet Penetration Based on Bond-based Peridynamic Method[J]. Acta Armamentarii, 2024, 45(11): 4094-4105.

Figures/Tables 24

Fig.1 FEM of 5.56mm SS109 bullet

Fig.2 FEM of body armor

Table 1 ELASTIC_PERI constitutive parameters for SiC ceramics[12-13]

参数	密度ρ/ (g·cm^-3)	杨氏模量 E/GPa	断裂能量释放率 G_t/(N·m^-1)
数值	3.21	420	27.3

Fig.3 Deformation of bonds in bond-based PD model and bond-based PD constitutive force function

Table 2 Johnson-Cook constitutive parameters for SS109 parts[15-16]

部件	ρ/(g·cm^-3)	A/MPa	B/MPa	n	C	m
被甲	8.45	90	292	0.01	0.025	1.09
钢芯	7.85	792	510	0.28	0.014	1.03
铅柱	11.2	14	18	0.685	0.035	1.68

Table 3 Constitutive parameters for UHMWPE laminated plates[18]

参数	数值	参数	数值
ρ/(g·cm^-3)	0.97	AOPT MACF	3 1
E_a/GPa	70	X_t/GPa	3
E_b/GPa	70	Y_t/GPa	3
E_c/GPa	8	Z_t/GPa	3
ν_ba	0.006	X_c/MPa	2
ν_ca	0.06	Y_c/MPa	2
ν_cb	0.706	Z_c/MPa	2
G_ab/MPa	0.05	S_ba/MPa	700
G_bc/MPa	5	S_ca/MPa	900
G_ca/MPa	5	S_cb/MPa	9

Fig.4 Traction-separation relationship

Table 4 Bonded contact with separation option 9 parameters[19]

参数	数值	参数	数值
T/MPa	1	S/MPa	3
E_N/(MPa·mm^-1)	70	E_T/(MPa·mm^-1)	3
G_IC/(MPa·mm)	70	G_IIC/(MPa·mm)	3
ΔN/mm	1	ΔS/mm	1.27

Fig.5 Test system components

Table 5 Summary of experimental results

试验编号	入靶速度/ (m·s^-1)	防弹插板面密度/ (kg·m^-2)	最大BFS值/ mm
1	817.4	29.34	18.99
2	805.7	28.69	19.30
3	811.7	28.75	19.72
4	803.2	29.52	19.50

Table 6 Validation of unit size sensitivity

最小单元尺寸/mm	模型单元总数	最大BFS值/mm	误差/%
0.20	1 750 148	19.75	1.91
0.25	1 004 134	18.41	-5.00
0.30	689 282	17.53	-9.54

Fig.6 Comparison of heights of experimental and simulated BFSs

Fig.7 Comparison of test and simulated BFS morphologies at 700μs

Fig.8 Evolution of bulging contours along the axis of symmetry in the experiment and numerical models

Fig.9 Change of core velocity and deformation of bullet

Fig.10 Comparison between simulated results and experimental data on projectile collection

Fig.11 Comparison between X-ray images and simulations of ceramic crack morphology in experiments

Fig.12 Semi-cutaway oblique 45°-view of ceramic damage morphology

Table 7 The morphology of ceramic crack evolution within 5μs

Fig.13 Ceramic damage and pressure situation at 10μs

Table 8 The morphology of ceramic crack evolution within 10~30μs

Fig.14 Radial cracks, circumferential cracks, and delamination cracks generated by impact on ceramics

Fig.15 The strain field of the outermost layer of laminated panel at 340μs

Fig.16 Distribution of equivalent stress in the outermost layer at 340μs

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