Numerical Simulation of Crack Propagation and Damage Behavior of Glass Plates under Impact Loading
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摘要: 裂纹的萌生和扩展是计算力学领域长期存在的难点和热点，也是玻璃、岩石、混凝土等脆性材料中常见的工程实际问题。为了探究冲击载荷下平板钠钙玻璃的损伤破坏行为和细观裂纹扩展规律，分别采用单元删除法、不连续伽辽金近场动力学法（discontinuous Galerkin peridynamic, DG-PD）和无网格粒子近场动力学法（meshless peridynamic, M-PD），研究其裂纹扩展行为。单元删除法采用JH-2材料模型，同时添加最大主应力和最大主应变失效准则；DG-PD法采用节点分离操作，并施加临界能量释放率准则；M-PD法采用自编程序粒子离散方法，选择合适的计算域，并施加临界伸长率准则。模拟结果表明：(1) 单元删除法可大致模拟出玻璃在冲击载荷下的损伤形貌，但在捕捉裂纹分叉和贯通等方面略显不足，未见玻璃碎片的飞溅，无法通过碎片飞溅速度评估其安全性能；(2) DG-PD法中环状裂纹和径向裂纹明显，裂纹具有很高的对称性，冲击点和边框处有大量玻璃碎片飞溅；(3) M-PD法中能捕捉到径向裂纹和环向裂纹，且裂纹的对称性较好，近场域和冲击速度对平板玻璃的动态响应有着重要的影响，就损伤形态而言，M-PD法和DG-PD法具有很高的一致性。Abstract: Crack initiation and propagation is a long-standing difficult problem in solid mechanics, especially for elastic-brittle material. To explore the damage and crack propagation behavior of glass plates under impact loading, the element deletion, discontinuous Galerkin peridynamic (DG-PD), and meshless peridynamic (M-PD) methods are used to conduct numerical simulations, respectively. The JH-2 material model, and the maximum principal stress and maximum principal strain failure criteria are adopted in the element deletion method. The node separation operation and the critical energy release rate criterion are used in the DG-PD method. In the M-PD method, a self-programmed particle discretization method is utilized along with an appropriate computational domain, and a critical elongation criterion is imposed. The simulation results show that: (1) the element deletion method can roughly simulate the damage morphology of glass under impact loading, but it is insufficient in capturing crack bifurcation and penetration. (2) In the DG-PD method, circumferential cracks and radial cracks are observed, and the cracks are of high symmetry. In addition, there are a lot of glass fragments splashing at the impact point and the frame. (3) Radial cracks and circumferential cracks can be captured in the M-PD method, and the symmetry of the cracks is good. The size of horizon and the impact velocity show great influence on the dynamic responses of the glass plates. As far as the damage form is concerned, the M-PD method and the DG-PD method yield consistent results.
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Key words:
- impact loading /
- glass plates /
- crack propagation /
- element deletion method /
- peridynamic /
- meshless method
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图 3 不同冲击速度下平板玻璃的最终损伤模态
Figure 3. Final damage of glass plates at different impact velocities
图 4 不同冲击速度下损伤参数的对比
Figure 4. Comparison of damage parameters at different impact velocities
图 5 二维有限单元断裂前后的节点分离示意图
Figure 5. Node separation before and after fracture of 2D finite elements
图 6 5 m/s冲击速度下迎撞面的损伤演化
Figure 6. Damage evolution of the impact face at the impact velocity of 5 m/s
图 9 50 m/s冲击速度下迎撞面的损伤演化
Figure 9. Damage evolution of the impact face at the impact velocity of 50 m/s
图 7 15 m/s冲击速度下迎撞面的损伤演化
Figure 7. Damage evolution of the top face at the impact velocity of 15 m/s
图 8 30 m/s冲击速度下迎撞面的损伤演化
Figure 8. Damage evolution of the top face at the impact velocity of 30 m/s
图 10 采用DG-PD法得到的不同冲击速度下中心点单元的速度变化
Figure 10. Velocity change of center element obtained by DG-PD method at different impact velocities
图 13 30 m/s冲击速度下迎爆面的损伤演化
Figure 13. Damage evolution images of the top face at the impact velocity of 30 m/s
图 15 不同冲击速度下平板玻璃的最终损伤破坏
Figure 15. Final damage of glass plate at different impact velocities
$ \;\rho $/(kg·m−3) G/GPa A B C M N $ \dot{\varepsilon }_{\rm s} $ T/GPa 2530 24 0.93 0.2 0.003 1 0.77 1 0.05042 σf,max σe/GPa pHEL/GPa β D1 D2 k1/GPa k2/GPa k3/GPa 0.5 5.95 2.92 1 0.043 0.85 45.4 −138 290 
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表 2 边框和弹头刚体材料模型参数
Table 2. Rigid body material model parameters of frame and bullet
$ \,\rho $/(kg·m−3) $\,\nu$ E/GPa 7850 0.28 200
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表 3 玻璃材料DG-PD材料模型参数
Table 3. DG-PD material model parameters of glass material
$ \,\rho $/(kg·m−3) E/GPa Gt/(J·m−2) HSFAC 2530 72 15.47 0.8
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表 4 玻璃材料M-PD材料模型参数
Table 4. M-PD model parameters of glass
$ \,\rho $/(kg·m−3) E/GPa G/GPa S0 $ \Delta x $/mm $ \delta $/mm 2530 72 24 $ 7.17\times 1{0}^{-5} $ 3 9.03
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