基于键基近场动力学对防弹插板在步枪弹侵彻下的力学响应仿真

doi:10.12382/bgxb.2024.0275

摘要/Abstract

摘要：

针对当前防弹插板在枪弹冲击下的力学响应研究尚有不足,采用键基近场动力学方法和传统拉格朗日方法相结合的方式对5.56mm SS109步枪弹侵彻NIJ Ⅲ级SiC/超高分子量聚乙烯(Ultra-High Molecular Weight Polyethylene,UHMWPE)防弹插板这一过程进行数值模拟,并与基于三维数字图像相关法的防弹插板侵彻试验结果对比,验证数值模型的准确性。研究结果表明:弹丸在侵彻防弹插板50μs后速度从810m/s衰减至157.57m/s,防弹插板与弹丸接触的陶瓷片严重碎裂;键基近场动力学方法可以很好地跟踪枪弹冲击陶瓷插板时裂纹的演化过程,SiC陶瓷插板受810m/s的SS109枪弹冲击时产生的放射性径向裂纹在10μs内基本向外扩展完毕,其重度损伤面积在30μs内就基本定型,最终在压力波的复杂作用下产生径向裂纹、环向裂纹以及平行碰撞面的层裂纹;防弹插板背凸量最大值为18.41mm,由于UHMWPE层合板具有正交各向异性,此时背面等效应变以弹着点为中心呈L形分布,发生的位置在鼓包边界约±45°处,等效应力场呈现菱形分布,应力集中发生在菱形的4个角上。

关键词: 防弹插板, 近场动力学, 碳化硅陶瓷, 裂纹扩展

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

中图分类号:

TJ012.4

王纪龙, 温垚珂, 刘东旭, 王会成, 沈周宇, 罗小豪. 基于键基近场动力学对防弹插板在步枪弹侵彻下的力学响应仿真[J]. 兵工学报, 2024, 45(11): 4094-4105.

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.

图/表 24

图1 5.56mm SS109弹丸有限元模型

Fig.1 FEM of 5.56mm SS109 bullet

图2 防弹插板有限元模型

Fig.2 FEM of body armor

表1 SiC陶瓷ELASTIC_PERI本构参数[12-13]

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

图3 键基PD本构力函数及示意图

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

表2 SS109各部分Johnson-Cook本构参数[15-16]

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

表3 UHMWPE层合板本构参数[18]

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

图4 牵引-分离关系

Fig.4 Traction-separation relationship

表4 固连断开面面接触option 9参数[19]

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

图5 测试系统组成

Fig.5 Test system components

表5 试验结果数据汇总

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

表6 单元尺寸敏感性验证

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

图6 试验和仿真防弹插板BFS高度对比

Fig.6 Comparison of heights of experimental and simulated BFSs

图7 700μs试验和仿真防弹插板BFS形态对比

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

图8 试验和数值模型沿对称轴方向鼓包轮廓变化历程

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

图9 弹芯速度变化及弹丸变形情况

Fig.9 Change of core velocity and deformation of bullet

图10 仿真结果和试验收集弹丸对比

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

图11 陶瓷裂纹形貌试验X光图和仿真对比

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

图12 半剖俯视45°视角陶瓷损伤形貌

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

表7 5μs内陶瓷裂纹演化形貌

Table 7 The morphology of ceramic crack evolution within 5μs

图13 10μs时陶瓷损伤和压力情况

Fig.13 Ceramic damage and pressure situation at 10μs

表8 10~30μs内陶瓷裂纹演化形貌

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

图14 陶瓷受冲击产生的径向裂纹、环向裂纹和层裂纹

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

图15 340μs时层合板最外层应变场

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

图16 340μs层合板最外层等效应力分布

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

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