JH2 Constitutive Model of Inorganic Bulletproof Glass with Damage
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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。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.
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Key words:
- bulletproof glass /
- mechanical properties /
- constitutive relation /
- damage
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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) Ep/GPa ν G/GPa K1/GPa 2468 72 0.23 29.3 44.4 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 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 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 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
ρs/(kg∙m−3) Ep/GPa ν 7850 200 0.30 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 σHEL/GPa pHEL/GPa 2468 29.3 44.4 −145 244 0.07 7.5 3.52 A B C M N D1 D2 Sfmax 3.10 0.36 0.00256 0.83 1.51 0.005 0.85 0.2 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/% Test Simulation 220 874 837 4.2 350 917 885 3.5 425 939 911 3.0 -
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