Fractal properties of dynamic recrysatallized grain boundaries

Microstructures (e.g., grain boundary structure) as manifestations of the mechanical behavior of deformed materials have several fractal properties. Here taking an example of grain boundary of recrystallized quartz shape produced under various deformation conditions (high temperature and strain rate), fractal properties of the boundary profiles are shown. Fractal analysis by using box-counting method for each grain gives an individual fractal dimension D_I of each profile, that by using area-perimeter method for various sizes of grains gives a collective fractal dimension D_C representing structural property. D_I shows larger variation as grain size decreased, and D_I converges to Dc as the grain size increases. Since the boundary serration during dynamic recrystallization should be determined by relative movement of its surrounded gains, D_I becomes to vary from grain to grain. On the collective fractal dimension D_c, D_c correlates positively, linearly to logarithmic of Zener-Hollomon parameter combining the strain rate and the temperature. Based on the fractal concepts, the relationship can be explained theoretically by a modified grain boundary migration model, and the number of cross points on the grain boundary sectioned by an Euclidian curve can be interpreted as the structural parameter related to the Zener-Hollomon parameter.