The sections’ fractal dimension of grain boundary
The sections’ fractal dimension of grain boundary
复制标题
晶界截面分形维数
DOI：
10.1016/s0169-4332(01)00417-2
复制
发表时间：
2001
影响因子：
6.7
通讯作者：
H. Nagahama
中科院分区：
文献类型：
--
作者：
M. Takahashi;H. Nagahama
实验动态再结晶晶界的分形维数增量与Zener-Hollomon参数的对数成正比。分形维数增量定义为颗粒形状的分形维数减去一定截面的欧几里得维数。为了绘制分形维数增量的几何图形，介绍了剖面分形维数的基本规律。将分形维数增量的几何意义归结为以晶粒的等效面积为边界的圆或椭圆所横切的晶界上交叉点分布的分形维数，并得出了Zener-Hollomon参数与交叉点数之间的幂律关系。因此，综合Zener-Hollomon参数、差应力和晶界上的交叉点数目三者之间的幂次规律可知，交叉点数目可以响应差应力。
The fractal dimensional increment of the experimentally dynamic recrystallized grain boundary is proportional to logarithm of Zener–Hollomon parameter. The fractal dimensional increment is defined as the fractal dimension of the grain shape minus the Euclidean dimension of certain transection. To draw the geometrical image of the fractal dimensional increment, the basic rule of the sections’ fractal dimension is introduced. The geometrical implication of the fractal dimensional increment is concluded as the fractal dimension of the crossing point distribution on the grain boundary transected by the circumscribing circle or ellipse with the equivalent-area of the grain, and a power law relationship between the Zener–Hollomon parameter and the number of crossing points is found. Therefore, summarizing power laws among the Zener–Hollomon parameter, the differential stress and the number of the crossing points on the grain boundary, the number of crossing points could respond to the differential stress.