Dynamic Mechanical Behavior of Graded Metallic Foams Based on Lagrangian Analysis Method
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摘要: 采用Lagrangian分析法，对梯度泡沫金属在高速冲击下的变形机理和应力响应进行研究。基于3D-Voronoi技术，构建了5种不同密度梯度的泡沫金属细观有限元模型，并进行了高速冲击下的Taylor数值实验，得到不同密度梯度泡沫金属的质点速度分布规律。采用Lagrangian分析法并结合数值实验结果，研究了高速冲击下密度梯度参数对泡沫金属的局部应变分布、应力分布以及冲击波传播与衰减规律的影响。结果表明：负密度梯度泡沫金属比正密度梯度泡沫金属具有更强的抵抗变形能力，且密度梯度参数越小，变形程度越小；负密度梯度泡沫金属的局部压实应力呈线性减小，最大局部压实应力随着密度梯度参数的减小而增大，在冲击端附近可以承受更大的载荷；正密度梯度泡沫金属的局部压实应力分布呈平台状，其最大局部压实应力小于负密度梯度泡沫金属。
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关键词:
- Lagrangian分析法 /
- 梯度泡沫金属 /
- 3D-Voronoi技术 /
- 密度梯度参数
Abstract: The Lagrangian analysis method was employed to investigate the deformation mechanism and stress response of graded metallic foams. The mesoscopic finite element models of the graded metallic foams with five different density gradient parameters were constructed by the 3D-Voronoi technique, and the corresponding Taylor numerical tests were performed under high-speed impact, and the particle velocity distributions of different graded foams were obtained. By combining the Lagrangian analysis method with the results of Taylor numerical tests, the effects of density gradient parameters on the local strain distribution, stress distribution, shock wave propagation and attenuation of metallic foams under high-speed impact were investigated. The results show that the metallic foams with negative density gradient have better resistance to vertical deformation than those with positive density gradient, and the deformation degree decreases with the decrease of the density gradient parameter. The local densification stress distribution of the metallic foams with negative density gradient decreases linearly, and the maximum local densification stress increases with the decrease of the density gradient parameter. The metallic foams with negative density gradient have high load bearing capability near the impact end. The local densification stress distribution of the metallic foams with positive density gradient has a plateau stage, and the maximum local densification stress is less than metallic foams with negative density gradient. -
图 2 Taylor数值实验(a)以及理论和实际密度分布(b)
Figure 2. Virtual Taylor impact test scenario (a) and theoretical and practical density distributions (b)
图 3 γ=–0.8的泡沫金属在Taylor撞击过程中的变形
Figure 3. Deformation of metallic foams with γ=–0.8 in the virtual Taylor impact test
图 4 质点速度时程曲线(a)和X=40 mm处的速度时程曲线(b)
Figure 4. Time histories of particle velocity (a) and velocity at X=40 mm (b)
图 6 局部动态应变时程曲线(a)和X=40 mm的动态应变时程曲线(b)
Figure 6. Local dynamic strain-time curves (a) and time histories of dynamic strain at X=40 mm (b)
图 8 局部动态应力时程曲线((a)～(c))和X=40 mm处的动态应力时程曲线(d)
Figure 8. Local dynamic stress-time curves ((a)–(c)) and time histories of dynamic stress atX=40 mm (d)
表 1 局部最大压实应变、压实应变、最大局部压实应力及其位置
Table 1. Maximum local locking strain, locking strain, and local maximum densification stress and its location
γ Maximum local locking strain Locking strain Maximum local densification stress Value/MPa Lagrangian location/mm –0.8 0.88 0.68 47.44 58 –0.4 0.91 0.70 39.72 56 0 0.92 0.72 34.77 58 0.4 0.93 0.74 30.08 35 0.8 0.96 0.76 30.75 37 
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