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何其健 宋宏伟 黄晨光. 基于分形的泡沫金属细观结构与尺寸效应研究[J]. 力学学报, 2009, 41(3): 370-375. DOI: 10.6052/0459-1879-2009-3-2008-034
引用本文: 何其健 宋宏伟 黄晨光. 基于分形的泡沫金属细观结构与尺寸效应研究[J]. 力学学报, 2009, 41(3): 370-375. DOI: 10.6052/0459-1879-2009-3-2008-034
Qijian He, Hongwei Song, Chengguang Huang. A fractal study on meso structures and size effect of metallic foams[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(3): 370-375. DOI: 10.6052/0459-1879-2009-3-2008-034
Citation: Qijian He, Hongwei Song, Chengguang Huang. A fractal study on meso structures and size effect of metallic foams[J]. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(3): 370-375. DOI: 10.6052/0459-1879-2009-3-2008-034

基于分形的泡沫金属细观结构与尺寸效应研究

A fractal study on meso structures and size effect of metallic foams

  • 摘要: 提出采用分形理论对泡沫金属的细观结构及尺寸效应进行研究的方法. 针对一系列具有不同相对密度和细观结构的泡沫铝,证明了其细观结构在一定尺度内符合分形特征,比较了小岛分维、计盒分维和信息分维等算法对泡沫金属分形表征的适用性,分析了细观结构特征对分维的影响. 结合推广的Sierpinski垫片模型研究了泡沫铝的屈服强度与分维的联系,建立了泡沫铝屈服强度的尺寸效应模型. 研究结果表明,由于引入了表征细观结构特征的分形维数,该模型除能表征屈服强度随试样尺寸的变化规律外,还在一定程度上直接反映了泡沫金属细观结构特征对力学性能的影响.

     

    Abstract: Meso structure of metallic foam, such as morphologies ofcells, cell walls and pores, is very important to its mechanical properties.Unlike honeycombs and some other cellular solids which have sequential andperiodical cell structures, metallic foams are inherently disordered in thecell level: non-equally sized and various shaped cells, non-equallydimensioned and curvy cell walls, random pores and cracks. It is impracticalto extract a representative cell and build ordered models, and thesimplified homogenous models can not reveal the importance of cellstructures to the global mechanical properties. A common parameter inanalytical models is relative density, which is a macroscopic value thatcannot reveal the meso structure of metallic foam. In this paper, a fractalapproach is introduced to bridge the morphological parameters of cellstructures and the mechanical properties of metallic foams. Cell morphologyof Al foams is proved to be a fractal geometry of self-similar in a certainscale, using the slit island method proposed by Mandelbrot. A series of Alfoams with different relative densities and meso structures were examined bythe box-counting dimension method, the information dimension method and theslit island method. It is found that the fractal dimension is in directproportion to the ratio of characteristic wall thickness to mean celldiameter. By mapping the cell morphology to the generalized Sierpinskicarpet, the mechanical properties of Al foams are expressed as the functionof fractal dimension. In addition, the fractal model is combined with thesize effect model proposed by Onck et al, and the revised size effect modelfor metallic foams incorporates stochastic characteristic of mesostructures. The results show that the fractal-based model can not onlyreveal the variation of yield strength with specimen size, but also bridgethe meso structures and mechanical properties of Al foams directly.

     

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