RESEARCH ON DYNAMIC CRUSHING AND MECHANISM OF MITIGATION AND ENERGY ABSORPTION OF CELLULAR SACRIFICIAL LAYERS
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摘要: 本文对强动载荷下多孔泡沫牺牲层的动态压溃行为及缓冲吸能机理进行了研究. 基于刚性-理想塑性-锁定(R-PP-L)及刚性-塑性硬化(R-PH)两类多孔泡沫材料本构, 建立了强动载荷下多孔泡沫牺牲层动态响应的理论分析模型, 分析了一维冲击波在多孔泡沫牺牲层中的传播规律; 利用Voronoi方法建立了多孔泡沫牺牲层的二维细观有限元模型, 获得了冲击载荷下多孔泡沫牺牲层的变形模式和动态响应曲线, 讨论了多孔泡沫材料的层间界面效应对多孔泡沫牺牲层缓冲吸能的影响. 研究结果表明, 考虑多孔泡沫材料塑性硬化影响的理论分析模型能够预测入射波在远端的反射及对多孔泡沫牺牲层的二次压缩过程和端部应力增强现象; 相比较存在界面的多孔泡沫牺牲层, 连续设计的多孔泡沫牺牲层可增强其缓冲吸能能力, 但在界面处增加设计刚性面板则能够降低界面胞元不完整对缓冲吸能的影响; 相同冲量载荷下, 端部应力峰值随冲击能量增大而增大, 而端部冲击波的反射可能是端部应力增强的主要诱因.Abstract: In this paper, the dynamic crushing behavior and the mechanism of mitigation and energy absorption of the cellular sacrificial layers subjected to the intensive dynamic loading are investigated theoretically and numerically. Based on the rigid, perfectly plastic, locking (R-PP-L) and the rigid, plastic hardening (R-PH) constitutive models of the cellular materials, a theoretical model of the dynamic response of the cellular sacrificial layers subjected to the intensive dynamic loading is developed. The one-dimensional shock wave propagation in the cellular sacrificial layers is analyzed further. Finite element model is established by employing the Voronoi method and the numerical simulations are carried out to obtain the deformation modes and the response curves whilst the effect of interface on the mitigation and the energy absorption of the cellular sacrificial layers is discussed in detail. It is shown that the theoretical model considering the plastic hardening of cellular materials (R-PH model) can effectively predict the reflection of incident wave at the distal end and the secondary compression process of the cellular sacrificial layers as well as the enhancement phenomenon of the end stress than the R-PP-L model. Comparisons between the continuous and discontinuous interface models demonstrate that the continuous design of the cellular sacrificial layers can enhance the mitigation and the energy absorption while the interfaces separated by the rigid plates can decrease the effect of the incompleteness of interface cells. The peak stresses at the ends subjected to the same momentum increase with the increase of impact energy. It is possible that the reflection of the shock wave at the ends results in the stress enhancement at the ends.
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图 1 二维Voronoi有限元模型的准静态应力应变曲线及本构模型
Figure 1. Quasi-static stress-strain curve and constitutive laws of the two-dimensional Voronoi finite element model
图 2 欧拉坐标系下基于R-PP-L本构的冲击波传播示意图
Figure 2. Shock wave propagation model based on the R-PP-L constitutive law in Euler coordinate system
图 3 欧拉坐标系下基于R-PH本构的冲击波传播示意图
Figure 3. Shock wave propagation model based on the R-PH constitutive law in Euler coordinate system
5 不同界面类型的多边形细观有限元模型
5. Two-dimensional Voronoi meso-level finite element models of different interfaces
5 不同界面类型的多边形细观有限元模型(续)
5. Two-dimensional Voronoi meso-level finite element models of different interfaces (continued)
图 6 多孔泡沫牺牲层动态响应的理论预测值和有限元模拟结果对比
Figure 6. Comparison between the theoretical prediction result and the finite element simulation result of the dynamic response of the cellular sacrificial layers
图 7 入射波及反射波的波后应变及密度分布的理论预测值比较
Figure 7. Comparison of strain and density distributions based on different constitutive laws behind primary and reflected compaction wave fronts.
图 8 不同质量刚性板模型的远端应力比较
Figure 8. Comparison of distal stresses for inserted rigid plate models of different rigid plate masses
图 9 不同界面类型的多孔牺牲层的细观变形过程. (a)连续界面; (b)分离界面; (c)增加刚性板
Figure 9. Meso-deformation process of multicellular sacrificial layers with different interfaces. (a) Continuous interface; (b) Separated interface; (c) Added rigid plate
图 10 不同界面类型的多孔泡沫牺牲层的动态响应比较
Figure 10. Comparison of dynamic response of multi-cell sacrificial layers with different interfaces
图 11 不同冲击能量下多孔泡沫牺牲层的细观变形过程比较. (a)
${E_K} = 90\;{\rm{ J}}$ ; (b)${E_K} = 67.5\;{\rm{ J}}$ ; (c)${E_K} = 45\;{\rm{ J}}$ Figure 11. Comparison of the meso-deformation process of the multi-cell sacrificial layers under different impact energy. (a)
${E_K} = 90\;{\rm{ J}}$ ; (b)${E_K} = 67.5\;{\rm{ J}}$ ; (c)${E_K} = 45\;{\rm{ J}}$ 
图 12 不同冲击能量下多孔泡沫牺牲层的动态响应比较
Figure 12. Comparison of dynamic response of multi-cell sacrificial layers under different impact energy
表 1 模型参数
Table 1. The parameters of model
Impact plate mass
MP/gVoronoi foam mass
MF/gSeparated plate mass
MR/gL0/mm W/mm h/mm Relative density $\bar \rho $ 6.00 6.22 0.01 60 80 0.36 0.16 
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表 2 基体材料参数
Table 2. The parameters of the base material
Material Density$ {\rho _s} $/(kg·m−3) Young modulus${E_s}$/GPa Poisson ratio${\gamma _s}$ Yield stress${\sigma _{Ys}}$/MPa aluminum (L060) 2700 66 0.3 175
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