Effect of Voids Arrangement on Behavior of PMMA Cellular Materials on Impact Loading
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摘要: 多孔材料具有轻质、缓冲减震、吸能等特点，在加载路径调控、爆炸或冲击防护领域具有广泛的应用前景。采用格点-弹簧模型（离散元方法），模拟多种孔洞排布方式的PMMA多孔材料在冲击加载过程中的早期孔洞塌缩破坏、应力分布与粒子速度等冲击响应行为。结果表明：在冲击加载过程中，裂纹萌发于孔洞侧向（垂直于冲击波方向）附近区域，孔洞破坏形式以剪切断裂为主；在不同的孔洞排列模型中，孔洞与孔洞之间均存在剪切裂纹相互贯通现象，促进孔洞体积压缩致密化，且孔洞排列方式不影响冲击波传播速度；四角点阵模型有效减缓孔洞附近区域的应力集中；四角点阵、三角点阵、锥形递减排列、锥形递增排列模型都显著影响PMMA多孔材料的冲击波阵面平整性；孔洞的随机排列模型对降低粒子速度最有效，四角点阵排列模型对降低波阵面后压力贡献最大。Abstract: Cellular materials, characterized by their light weight and energy absorbing, etc., have broad potential applications in the fields of loading-path control, explosion and impact protection. In this paper, the discrete element method of lattice-spring model is utilized to simulate the early impact response of PMMA cellular materials with different arrangement models of voids during the impact loading process. The early void collapse failure, stress distribution and particle velocity of materials with various arrangement models are investigated. Our results show that the arrangement of voids affect the particle velocity but not the shock wave velocity. The cracks are germinated in the area near the longitudinal direction of the void, and the failure mode of the void is mainly shear failure. In different arrangement models of voids, there is a phenomenon of shear cracks interpenetrating between the holes, which promotes the compression of the volume. The square lattice and triangular lattice arrangement models prominently slow the stress concentration and plastic deformation rate of voids in the nearby area. The square lattice, triangular lattice, decreasing arrangement and increasing arrangement significantly have a remarkable influence on the flatness of the shock wave front of PMMA cellular materials. The random arrangement is the most effective one to reduce the particle velocity, and the square lattice contributes most to the post-pressure reduction of the wave front.
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Key words:
- cellular materials /
- arrangement model of voids /
- shock wave /
- impact loading
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图 2 基于格点-弹簧模型的冲击压缩构型
Figure 2. Configuration of the shock compression model based on the lattice-spring model
图 4 不同时刻下5种孔洞排列模型的裂纹扩展
Figure 4. Crack growth patterns of five arrangement models of voids at various times
图 5 孔洞附近区域剪切裂纹(a)和颗粒破碎填充孔洞示意图(b)
Figure 5. Shear cracks in the area around the void (a) and schematic of particle-fragmentation-filled void (b)
图 6 不同时刻5种孔洞排列模型的应力分布云图
Figure 6. Stress distributions of five arrangement models of voids at various times
图 7 5种孔洞排列模型的粒子速度剖面
Figure 7. Particle velocity profiles of voids for five arrangement modes
表 1 模型各部分材料的物性参数
Table 1. Specific physical parameters of each part of the model
Material R/μm $\delta $/μm E/GPa $\;\mu$ $\;\rho$/(kg·m−3) $\gamma $/(J·m−2) Cu 200 110 0.25 8 960 50 000 PMMA 10 200 3 0.20 1 180 10 LiF 200 65 0.10 2 640 
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表 2 5种孔洞排列模型中的粒子速度与波阵面后应力
Table 2. Particle velocities and stresses in the five arrangements modes of void
Modes Particle velocity/(m·s−1) Stress/MPa Random lattice 142.6 56.11 Square lattice 155.0 29.74 Triangular lattice 151.5 62.84 Decreasing lattice 161.7 58.13 Increasing lattice 158.9 55.39
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