含损伤的无机防弹玻璃的JH2本构模型

史刘彤; 黄友奇; 高玉波; 贾哲; 李志豪

doi:10.11858/gywlxb.20240704

含损伤的无机防弹玻璃的JH2本构模型

doi: 10.11858/gywlxb.20240704

史刘彤^1,,
黄友奇²,
高玉波^1,*, ,,
贾哲³,
李志豪¹

1.
中北大学航空宇航学院, 山西太原　030051
2.
中国建筑材料科学研究总院有限公司, 北京　100024
3.
中国航天科工集团第六研究院, 内蒙古呼和浩特　010010

基金项目: 国家自然科学基金（12172337）；山西省基础研究计划（20210302123022）；中北大学研究生科技立项（20231976）

详细信息

作者简介:
史刘彤（1999－），女，硕士研究生，主要从事防弹玻璃的本构关系及损伤机理研究. E-mail：1456185422@qq.com

通讯作者:
高玉波（1986－），男，博士，副教授，主要从事穿甲动力学、材料本构关系与损伤机理研究. E-mail：gaoyb@nuc.edu.cn

中图分类号: O345; TB321
计量
- 文章访问数: 40
- HTML全文浏览量: 17
- PDF下载量: 18
出版历程
- 收稿日期: 2024-01-03
- 修回日期: 2024-02-04
- 录用日期: 2024-03-15
- 刊出日期: 2024-07-25

JH2 Constitutive Model of Inorganic Bulletproof Glass with Damage

SHI Liutong^1
,,
HUANG Youqi²,
GAO Yubo^{1,*
, ,},
JIA Zhe³,
LI Zhihao¹

1.
School of Aerospace Engineering, North University of China, Taiyuan 030051, Shanxi, China
2.
China Building Materials Academy, Beijing 100024, China
3.
The Sixth Academy of China Aerospace Science and Industry Corporation Limited, Hohhot 010010, Inner Mongolia, China

摘要

摘要: 防弹玻璃具有良好的抗冲击性能，能够抵御枪弹、爆炸碎片以及其他高速飞行物体的攻击性威胁，广泛应用于安全防护领域。为探究防弹玻璃的无机玻璃层在冲击加载下的动态力学性能及本构关系，首先，采用电子万能试验机和分离式霍普金森压杆（split Hopkinson pressure bar, SHPB）试验装置，获得了不同应变率下材料的拉伸和压缩力学性能，结果表明，无机玻璃具有明显的应变率效应，材料强度随应变率的升高而增大。其次，借鉴土力学三轴围压试验，设计了适用于本研究的高强围压套筒，测试了完全损伤条件下玻璃颗粒的力学性能，发现其强度明显低于完整状态下无机玻璃的强度。最后，结合试验数据构建了含损伤无机玻璃的JH2本构模型，采用非线性有限元软件 LS-DYNA 模拟了材料在SHPB加载下的压缩过程，通过对比试验结果与模拟结果，验证了本构模型的有效性。
- 无机玻璃 /
- 力学性能 /
- 本构关系 /
- 损伤
Abstract: Bulletproof glass exhibits excellent impact resistance and protective capabilities against bullets, explosive fragments, high-speed projectiles, and various other aggressive threats, making it extensively utilized in the field of safety and security. To investigate the dynamic mechanical properties and constitutive relation of the inorganic glass layers in bulletproof glass under impact loading, we firstly employed an electronic universal testing machine and a split Hopkinson pressure bar (SHPB) test setup to obtain the tensile and compressive mechanical properties of the material at different strain rates. Results reveal a noticeable strain rate effect that the material’s strength increases with the strain rate. Secondly, drawing on the experience of geotechnical triaxial compression tests, we designed a high-strength confinement sleeve suitable for assessing the mechanical properties of glass particles under conditions of complete damage. Results show a significantly lower strength compared to that of the intact state of inorganic glass. Finally, by integrating test data, an JH2 constitutive model for inorganic glass with damage was established. By using the non-linear finite element software LS-DYNA, the SHPB test process was simulated. The effectiveness of the constitutive model was verified by comparing test and simulated results.
- bulletproof glass /
- mechanical properties /
- constitutive relation /
- damage

HTML全文

图 1 准静态试验设置

Figure 1. Quasi-static test setup

下载: 全尺寸图片幻灯片

图 2 动态压缩试验装置

Figure 2. Setup of dynamic compression tests

下载: 全尺寸图片幻灯片

图 3 三轴围压试验装置

Figure 3. Triaxial confining pressure test device

下载: 全尺寸图片幻灯片

图 4 无机玻璃的拉伸应力-应变曲线

Figure 4. Tensile stress-strain curves of inorganic glass

下载: 全尺寸图片幻灯片

图 5 不同应变率下典型应力-应变曲线

Figure 5. Typical stress-strain curves at different strain rates

下载: 全尺寸图片幻灯片

图 6 三轴围压试验轴向应力-应变曲线

Figure 6. Axial stress-strain curves of triaxial confining pressure test

下载: 全尺寸图片幻灯片

图 7 无机玻璃的Hugoniot曲线

Figure 7. Hugoniot curve of inorganic glass

下载: 全尺寸图片幻灯片

图 8 应变率敏感系数C的拟合过程

Figure 8. Fitting process of strain rate sensitivity coefficient C

下载: 全尺寸图片幻灯片

图 9 材料完整强度模型的拟合曲线

Figure 9. Fitting curve of complete strength model of material

下载: 全尺寸图片幻灯片

图 10 无机玻璃颗粒的无量纲静水压力与无量纲强度的关系

Figure 10. Relation between dimensionless hydrostatic pressure and dimensionless strength for inorganic glass particles

下载: 全尺寸图片幻灯片

图 11 玻璃试样和SHPB的有限元模型

Figure 11. Glass specimen and finite element model of SHPB

下载: 全尺寸图片幻灯片

图 12 模拟得到的无机玻璃的失效历程

Figure 12. Failure process of inorganic glass obtained by simulation

下载: 全尺寸图片幻灯片

图 13 试验与数值模拟结果对比

Figure 13. Comparison of test and simulation results

下载: 全尺寸图片幻灯片

表 1 玻璃的基本力学性能参数

Table 1. Basic mechanical parameters of glass

$ \overline{\rho} $/(kg∙m⁻³)	E_p/GPa	ν	G/GPa	K₁/GPa
2468	72	0.23	29.3	44.4

下载: 导出CSV

表 2 准静态和动态压缩试验得到的参考参数

Table 2. Parameters obtained by quasi-static and dynamic compression test

Test	${ \dot{{ \varepsilon }}}\text{/}{\text{s}}^{{-1}} $	σ/GPa	p/GPa	$\sigma^{*}$	$p^{*}$
Quasi-static compression	10⁻⁴	0.760	0.253	0.127	0.0719
SHPB	420	0.930	0.310	0.156	0.0881

下载: 导出CSV

表 3 根据动态压缩试验数据拟合得到的完整强度参数

Table 3. Complete strength parameters obtained by dynamic compression test data fitting

No.	${ \dot{{ \varepsilon }}}^{*} $	σ/GPa	$ {\sigma}^{{*}} $	$ p^{{*}} $	X	Y
1	230	0.864	0.1447	0.0818	−2.0393	−1.9576
2	280	0.893	0.1496	0.0846	−2.0184	−1.9255
3	350	0.917	0.1536	0.0868	−2.0015	−1.9000
4	420	0.933	0.1563	0.0884	−1.9903	−1.8835

下载: 导出CSV

表 4 三轴围压试验数据

Table 4. Triaxial confining pressure test data

Particle size/mm	$ {\sigma _{\textit{zz}}} $/GPa	$ {{\varepsilon} _{\text{c}}}/10^{-3} $	$ {E_{\text{c}}} $/GPa	$ {\sigma _{{\theta \theta }}} $/GPa	p/GPa	$ {\sigma _{\rm f}} $/GPa	$ {p ^*} $	$ \sigma_{\mathrm{f}}^* $
0–0.1	0.533	7.00	192	0.089	0.237	0.222	0.067	0.037
0.3–0.5	0.408	4.75	192	0.058	0.175	0.175	0.050	0.029

下载: 导出CSV

表 5 钢杆和垫块的线弹性材料参数

Table 5. Linear elastic material property parameters of steel bar and block

ρ_s/(kg∙m⁻³)	E_p/GPa	ν
7850	200	0.30

下载: 导出CSV

表 6 试验拟合得到的玻璃材料的JH2本构模型参数

Table 6. Parameters of JH2 constitutive model of glass material fitted by the test

ρ/(kg∙m⁻³)	G/GPa	K₁/GPa	K₂/GPa	K₃/GPa	T/GPa	σ_HEL/GPa	p_HEL/GPa
2468	29.3	44.4	−145	244	0.07	7.5	3.52

A	B	C	M	N	D₁	D₂	S_fmax
3.10	0.36	0.00256	0.83	1.51	0.005	0.85	0.2

下载: 导出CSV

表 7 数值模拟和试验获得的不同应变率下的单轴压缩强度

Table 7. Uniaxial compression strength at different strain rates obtained by simulation and test

${ \dot{{ \varepsilon }}}\text{/}{\text{s}}^{{-1}} $	Uniaxial compression strength/MPa		Error/%
${ \dot{{ \varepsilon }}}\text{/}{\text{s}}^{{-1}} $	Test	Simulation	Error/%
220	874	837	4.2
350	917	885	3.5
425	939	911	3.0

下载: 导出CSV

参考文献(21)

[1]	刘志海. 夹层玻璃的发展现状及趋势 [J]. 中国建材, 2003(9): 64–66. LIU Z H. Current situation and future trends of laminated glass [J]. China Building Materials, 2003(9): 64–66.
[2]	SHIM G I, KIM S H, EOM H W, et al. Improvement in ballistic impact resistance of a transparent bulletproof material laminated with strengthened soda-lime silicate glass [J]. Composites Part B: Engineering, 2015, 77: 169–178. doi: 10.1016/j.compositesb.2015.03.035
[3]	SHIM G I, EOM H W, KIM S H, et al. Fabrication of lightweight and thin bulletproof windows using borosilicate glass strengthened by ion exchange [J]. Composites Part B: Engineering, 2015, 69: 44–49. doi: 10.1016/j.compositesb.2014.09.023
[4]	ZHANG X H, HAO H, MA G W. Dynamic material model of annealed soda-lime glass [J]. International Journal of Impact Engineering, 2015, 77: 108−119.
[5]	葛彦鑫. Al₂O₃/SiC复相陶瓷冲击失效机理研究 [D]. 太原: 中北大学, 2022: 52−54. GE Y X. Study on impact failure mechanism of Al₂O₃/SiC composite [D]. Taiyuan: North University of China, 2022: 52−54.
[6]	JOHNSON G R, HOLMQUIST T J. An improved computational constitutive model for brittle materials [J]. AIP Conference Proceedings, 1994, 309(1): 981–984.
[7]	HOLMQUIST T J, JOHNSON G R, GRADY D E, et al. High strain rate properties and constitutive modeling of glass [C]//The 15th International Symposium on Ballistics. Jerusalem, Isreal, 1995: T14929.
[8]	ALEXANDER C S, CHHABILDAS L C, TEMPLETON D W. The hugoniot elastic limit of soda-lime glass [J]. AIP Conference Proceedings, 2007, 955(1): 733–738.
[9]	RENGANATHAN P, DUFFY T S, GUPTA Y M. Hugoniot states and optical response of soda lime glass shock compressed to 120 GPa [J]. Journal of Applied Physics, 2020, 127(20): 205901.
[10]	杨震琦, 庞宝君, 王立闻, 等. JH-2模型及其在Al₂O₃陶瓷低速撞击数值模拟中的应用 [J]. 爆炸与冲击, 2010, 30(5): 463–471. YANG Z Q, PANG B J, WANG L W, et al. JH-2 model and its application to numerical simulation on Al₂O₃ ceramic under low-velocity impact [J]. Explosion and Shock Waves, 2010, 30(5): 463–471.
[11]	高玉波. TiB₂-B₄C复合材料动态力学性能及抗侵彻机理研究 [D]. 哈尔滨: 哈尔滨工业大学, 2016: 29−42. GAO Y B. Study of dynamic mechanical property and anti-penetration mechanism of TiB₂-B₄C composites [D]. Harbin: Harbin Institute of Technology, 2016: 29−42.
[12]	MEYER L W, FABER I. Investigations on granular ceramics and ceramic powder [J]. Journal De Physique Ⅳ, 1997, 7: C3-565–C3-570.
[13]	ASTM. Standard test method for tensile strength estimate by disc compression of manufactured graphite: D8289-2020 [S]. 2020.
[14]	贾哲. 弹道冲击下防弹玻璃的损伤机理和抗侵彻性能研究 [D]. 太原: 中北大学, 2023: 12−36. JIA Z. Study on damage mechanism and anti-penetration performance of bulletproof glass under ballistic impact [D]. Taiyuan: North University of China, 2023: 12−36.
[15]	JOHNSON G R, COOK W H. A constitutive model and data for metals subjected to large strains, high strain rates, and high temperatures [C]//The 7th International Symposium on Ballistics. The Hague, The Netherlands, 1983.
[16]	JOHNSON G R, COOK W H. Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures [J]. Engineering Fracture Mechanics, 1985, 21(1): 31–48. doi: 10.1016/0013-7944(85)90052-9
[17]	HOLMQUIST T J, JOHNSON G R, GERLACH C A. An improved computational constitutive model for glass [J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2017, 375(2085): 20160182. doi: 10.1098/rsta.2016.0182
[18]	OSNES K, HOLMEN J K, GRUE T, et al. Perforation of laminated glass: an experimental and numerical study [J]. International Journal of Impact Engineering, 2021, 156: 103922. doi: 10.1016/j.ijimpeng.2021.103922
[19]	GRADY D E, CHHABILDAS L C. Shock-wave properties of soda-lime glass [R]. Albuquerque: Sandia National Laboratories, 1996: 4−6.
[20]	DANDEKAR D P. Index of refraction and mechanical behavior of soda lime glass under shock and release wave propagations [J]. Journal of Applied Physics, 1998, 84(12): 6614−6622.
[21]	SIMHA C H M, GUPTA Y M. Time-dependent inelastic deformation of shocked soda-lime glass [J]. Journal of Applied Physics, 2004, 96(4): 1880−1890.