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铜基复合材料组织形态分形特征的统计分析与研究
引用本文:马润波,许世蒙,杜建华,邱健彬.铜基复合材料组织形态分形特征的统计分析与研究[J].数学的实践与认识,2012,42(7):155-162.
作者姓名:马润波  许世蒙  杜建华  邱健彬
作者单位:1. 装甲兵工程学院数学室,北京,100072
2. 装甲兵工程学院装备再制造系,北京,100072
摘    要:通过对铜基复合材料显微组织结构相图的分析和研究,根据分形理论,计算了不同实验条件下铜基复合材料横截面和平行压制力面的显微组织结构相图的分形维数,同时结合统计方法分析了铜基复合材料分形维数的一些统计特性,结果表明,分形维数反映了石墨在样品中的分布规律,分形维数越大,组织结构相图越复杂,石墨分布越不规则,故石墨分布的不规则性可用分形维数来刻画,分形维数可作为材料组织形态分析的一个表征参数,通过统计分析可知,铜基复合材料横截面和平行压制力面的组织结构相图的分形维数服从正态分布,且横截面和平行压制力面的分形维数随石墨含量变化的情况互不影响。

关 键 词:复合材料  分形维数  概率分布  Monte-Carlo方法  显微组织

Statistical Analysis and Research on the Microstructure Fractal Characteristics of Copper Matrix Composites
MA Run-bo , XU Shi-meng , DU Jian-hua , QIU Jian-bin.Statistical Analysis and Research on the Microstructure Fractal Characteristics of Copper Matrix Composites[J].Mathematics in Practice and Theory,2012,42(7):155-162.
Authors:MA Run-bo  XU Shi-meng  DU Jian-hua  QIU Jian-bin
Institution:1 (1.Section of Mathematics,Academy of Armored Force Engineering,Beijing 100072,China) (2.Department of Equipment Remanufacturing,Academy of Armored Force Engineering,Beijing 100072, China)
Abstract:Through the analysis and research on images of microstructure of the copper matrix composites,according to the fractal theory,calculated the fractal dimension of images of microstructure on cross section and parallel pressed power side of copper matrix composite materials under different experimental conditions.Meanwhile combined with statistics method analyzing some statistics characteristics of fractal dimension of copper matrix composites. The results show that,fractal dimension of graphite in the sample reflects the distribution, the fractal dimension is more larger,the organization chart is more complex,the distribution of graphite is more irregular,so the irregular distribution of free graphite can be described by fractal dimension,fractal dimension can be used as a material characterization parameters of organizational form.Through statistics analyses we can get that the fractal dimension of microstructure of reinforced copper matrix composite materials on cross section and parallel pressed power side combining to normal distribution,and the fractal dimension of cross section and parallel pressed power side that changed with graphite content doesn’t affect each other.
Keywords:composite materials  fractal dimension  probability distribution  Monte-Carlomethod  microstructure
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