泡沫金属力学性能的跨尺度分析

发布时间：2018-03-06 03:14

本文选题：泡沫金属　切入点：尺度效应　出处：《江苏大学》2017年硕士论文　论文类型：学位论文

【摘要】：泡沫金属等多孔材料具有优异的力学性能,其特殊的细观结构特点对其跨尺度力学性能有重要影响。为了能更全面地阐释泡沫金属力学行为,本文采用梁链网模型作为泡沫金属的细观力学模型,并且结合应变梯度弹性理论的解析解给出泡沫金属宏观响应与细观参数的关系,最后研究了基体材料粘/超弹性和细观胞壁排布方式对材料力学响应的影响。具体研究内容包括:(1)借助有限元软件ANSYS构建梁链网模型来等效泡沫金属的各种细观结构,如胞孔形状为正三角形、正方形和正六边形的周期性规则模型,胞孔形状不规则的Voronoi模型(二维)和以六方最密堆积为基础的三维模型。采用应变能等效原理对二维的周期性模型做了宏观材料参数的标定,建立了基于应变梯度弹性理论的广义连续体和基体金属材料弹性参数与胞元尺寸和排布方式之间的关系。(2)泡沫金属的力学性能强烈依赖于内部结构。当构件特征尺寸与胞孔特征尺寸d处于相同数量级时,表现出明显的尺度效应。为了揭示这种尺度效应的力学机理,本文研究了泡沫金属试件的剪切、纯弯曲和单轴压缩试验。一方面,利用应变梯度弹性理论给出剪切和纯弯曲的解析解,其中包含了材料内禀尺寸lc这一关键模型参数。另一方面,选用正六边形梁链网模型模拟弯曲和剪切试验,选用三维梁链网模型模拟单轴压缩试验。发现材料内禀尺寸lc强烈相关于胞孔特征尺寸d,宏观力学响应随着样品特征尺寸与胞孔特征尺寸d的相对比值而改变。分析结果表明:剪切和纯弯曲试验中都表现出显著的尺度效应,即材料力学性能明显相关于样品尺寸。当样品尺寸与胞孔尺寸之比越小,尺度依赖性越强烈。并且,边界层的约束条件对泡沫金属的力学响应有重要影响。弯曲问题中,只有对离散模型上下表面施加恰当的附加转角约束后,应变梯度理论解与链网模型数值解才能够吻合。这为理解应变梯度理论中的非传统边界条件提供了一个直观的实例。通过数据拟合,得到了内禀尺寸lc与胞孔特征尺寸d之间的关系,与文献结论相符。单轴压缩的模拟结果与实验结果比较后发现,泡沫金属材料的杨氏模量表现出明显的尺度依赖性,随着样品尺寸的减小而减小,但压缩强度与样品尺寸无关。(3)研究了泡沫金属基体材料的粘弹性和超弹性对泡沫材料宏观力学响应的影响。另外,探讨了几种形式的非局部化链网,即相互作用不仅存在于最近邻节点之间,还存在于次近邻甚至次次近邻节点之间。该类链网模型本质上与近场动力学模型十分相似。链网模型的模拟结果表明,该材料具有比普通蜂窝材料更高的弹性模量和比刚度,且可以实现更多优异的复合性能。
[Abstract]:Porous materials such as foam metal have excellent mechanical properties, and their special meso-structure features have an important influence on their cross-scale mechanical properties. In this paper, the mesomechanical model of foamed metal is presented by using the beam-chain network model, and the relationship between the macroscopic response and the meso-parameters of the foamed metal is given by combining with the analytical solution of strain gradient elasticity theory. Finally, the effects of viscoelastic / hyperelastic matrix materials and the arrangement of mesoscale cell wall on the mechanical response of materials are studied. The specific research contents include: 1) using finite element software ANSYS to construct the mesoscale model of foamed metal to equivalent various meso-structures of foam metal. For example, the periodic regular model of the shape of the cell hole is triangular, square and hexagonal. The Voronoi model with irregular pore shape (2D) and the 3D model based on hexagonal most dense packing are used to calibrate the macroscopical material parameters of the two-dimensional periodic model by using the strain energy equivalent principle. Based on the strain gradient elasticity theory, the relationship between elastic parameters of generalized continuum and matrix metal material and cell size and arrangement mode is established. The mechanical properties of foam metal are strongly dependent on the internal structure. When the size is the same order of magnitude as the characteristic size d of the cell, In order to reveal the mechanical mechanism of the scale effect, the shear, pure bending and uniaxial compression tests of foam metal specimens are studied in this paper. Based on the strain gradient elasticity theory, the analytical solutions of shear and pure bending are given, which include the key parameters of material intrinsic size (LC). On the other hand, the hexagonal beam mesh model is used to simulate the bending and shear tests. Three-dimensional beam mesh model was used to simulate uniaxial compression test. It was found that the intrinsic size of the material was strongly related to the pore characteristic size d, and the macroscopic mechanical response varied with the relative ratio of the characteristic size of the sample to the characteristic size of the cell hole. The results show that both shear and pure bending tests show significant scale effect. That is, the mechanical properties of materials are obviously related to the sample size. When the ratio of sample size to cell size is smaller, the scale dependence becomes stronger. Moreover, the constraint conditions of boundary layer have an important effect on the mechanical response of foam metal. Only when appropriate additional angular constraints are applied to the upper and lower surfaces of the discrete model, The solution of strain gradient theory coincides with the numerical solution of chain network model, which provides an intuitionistic example for understanding the unconventional boundary conditions in strain gradient theory. The relationship between intrinsic size (LC) and pore characteristic size (d) was obtained, which was consistent with the results of literature. The results of uniaxial compression were compared with the experimental results, and it was found that the Young's modulus of foamed metal materials showed an obvious scale dependence. The influence of viscoelasticity and hyperelasticity of foamed metal matrix on the macroscopic mechanical response of foamed metal matrix was studied. In this paper, we discuss several forms of nonlocalized chain networks, that is, the interaction exists not only between the nearest neighbor nodes, but also between the nearest neighbor nodes. This kind of chain network model is essentially similar to the near field dynamic model. The simulation results of the chain network model show that the material has higher elastic modulus and higher specific stiffness than ordinary honeycomb material. And can achieve more excellent composite performance.
【学位授予单位】：江苏大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O341

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