Abstract
Fractal analysis on experimentally recrystallized quartz grain boundaries has been employed to relate the grain boundary complexities with deformation conditions, such as strain rate and temperature. The fractal dimensional increment of the grain boundaries, defined as (D-1), and the degree of irregularity in grain boundaries, is proportional to the logarithmic of the Zener–Hollomon parameter that is defined by strain rate and temperature (the Arrhenius term). The physical mean of the empirical relationship can be explained theoretically by a new grain boundary migration model (GBM or cell dynamics model) extended by the fractal concepts and the dimension analysis. This is a more general model than the migration growth model for the fractal grain boundaries.
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