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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

查看参考文献18篇

文摘 提出采用分形理论对泡沫金属的细现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,由于引入了表征细现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.
其他语种文摘 Meso structure of metallic foam, such as morphologies of cells, cell walls and pores, is very important to its mechanical properties. Unlike honeycombs and some other cellular solids which have sequential and periodical cell structures, metallic foams are inherently disordered in the cell level: non-equally sized and various shaped cells, non-equally dimensioned and curvy cell walls, random pores and cracks. It is impractical to extract a representative cell and build ordered models, and the simplified homogenous models can not reveal the importance of cell structures to the global mechanical properties. A common parameter in analytical models is relative density, which is a macroscopic value that cannot reveal the meso structure of metallic foam. In this paper, a fractal approach is introduced to bridge the morphological parameters of cell structures and the mechanical properties of metallic foams. Cell morphology of A1 foams is proved to be a fractal geometry of self-similar in a certain scale, using the slit island method proposed by Mandelbrot. A series of Al foams with different relative densities and meso structures were examined by the box-counting dimension method, the information dimension method and the slit island method. It is found that the fractal dimension is in direct proportion to the ratio of characteristic wall thickness to mean cell diameter. By mapping the cell morphology to the generalized Sierpinski carpet, the mechanical properties of Al foams are expressed as the function of fractal dimension. In addition, the fractal model is combined with the size effect model proposed by Onck et al, and the revised size effect model for metallic foams incorporates stochastic characteristic of meso structures. The results show that the fractal-based model can not only reveal the variation of yield strength with specimen size, but also bridge the meso structures and mechanical properties of A1 foams directly.
来源 力学学报 ,2009,41(3):370-375 【核心库】
关键词 泡沫金属 ; 分形 ; 尺寸效应 ; 细观结构 ; 力学性能
地址

中国科学院力学研究所, 北京, 100190

语种 中文
文献类型 研究性论文
ISSN 0459-1879
学科 力学
基金 国家自然科学基金 ;  王宽诚基金会卢嘉锡青年人才奖 ;  非线性国家重点实验室基金
文献收藏号 CSCD:3508101

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