分形理论盒维数与第二相颗粒相体积的关系研究  

Research on relationship between value of box dimension in fractal theory and phase volume of the second phase particles

作　　者：何振娟[1] 王录全[1] 彭小明[1] 庾正伟[1] 冷茂林[1] 杨天华[1] 

机构地区：[1]中国核动力研究设计院第四研究所,成都市291信箱106分箱610005

出　　处：《粉末冶金技术》2016年第1期16-20,共5页Powder Metallurgy Technology

摘　　要：本文采用分形理论中的盒维数法开展了复合材料中第二相颗粒分布均匀性评价研究,理论计算了两种颗粒分布情况下(颗粒均匀分布、横向与纵向的颗粒间距比为1.5的分布)盒维数值与第二相颗粒相体积的关系。结果表明:两种分布情况下,不论第二相颗粒相体积值高或低,每种分布的盒维数均为同一值,但两种分布的盒维数值不相同,这说明盒维数法可评价出第二相颗粒的分布均匀性,与其相体积无关;且研究表明分形方程中的ln K与相体积的对数呈线性关系;第二相颗粒相体积相同时,横向与纵向颗粒间距比为1.5分布时的ln K与颗粒均匀分布时的ln K也呈线性关系。The distribution uniformity of second phase particles of composite materials was evaluated by box dimension method of fractal theory,and the relationship between value of box dimension of fractal theory and phase volume of the second phase particles for two kinds of particles ＇ distribution were theoretically calculated. The one distribution was uniformly distributed,the ratio of transverse and longitudinal spacing for the other distribution was1. 5. The results show that in the situation of two kinds of particles＇ distribution,regardless of value of phase volume of the second phase particles is big or small,each distribution ＇s box dimension is the same,but the value of box dimension are different,this indicates that the box dimension method can evaluate distribution uniformity of the second phase particles regardless of its phase volume; the study also shows that relationship between ln K in fractal equation and the logarithm of phase volume of the second phase particles is linear. The relationship between ln Kof the distribution in the condition that the particle volume of second phase is the same and the ratio of transverse and longitudinal spacing is 1. 5 and ln K of the distribution that particles are uniformly distributed also is linear.

关 键 词：分形理论 盒维数值 第二相颗粒 相体积 

分 类 号：O18[理学—数学]