The sections' fractal dimension of grain boundary

The fractal dimensional increment of the experimentally dynamic recrystalli zed 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 dr aw the geometrical image of the fractal dimensional increment, the basic ru le of the sections' fractal dimension is introduced. The geometrical implic ation of the fractal dimensional increment is concluded as the fractal dime nsion of the crossing point distribution on the grain boundary transected b y the circumscribing circle or ellipse with the equivalent-area of the grai n, and a power law relationship between the Zener-Hollomon parameter and th e number of crossing points is found. Therefore, summarizing power laws amo ng the Zener-Hollomon parameter. the differential stress and the number of the crossing points on the grain boundary, the number of crossing points co uld respond to the differential stress. (C) 2001 Elsevier Science B.V. All rights reserved.