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Abstract
High-angle grain boundary migration is predicted during geometric dynamic recrystallization (GDRX) by two types of mathematical models. Both models consider the driving pressure due to curvature and a sinusoidal driving pressure owing to subgrain walls connected to the grain boundary. One model is based on the finite difference solution of a kinetic equation, and the other, on a numerical technique in which the boundary is subdivided into linear segments. The models show that an initially flat boundary becomes serrated, with the peak and valley migrating into both adjacent grains, as observed during GDRX. When the sinusoidal driving pressure amplitude is smaller than 2π, the boundary stops migrating, reaching an equilibrium shape. Otherwise, when the amplitude is larger than 2π, equilibrium is never reached and the boundary migrates indefinitely, which would cause the protrusions of two serrated parallel boundaries to impinge on each other, creating smaller equiaxed grains.
Acknowledgements
The authors appreciate the opportunity to work with Professor M.A. Fortes, a brilliant scientist whose enthusiasm and kindness astonished us many times during the development of our research work. We also thank him for pointing out the existence of the analytical solution written in Equation (Equation5). M.A. Martorano thanks Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) for financial support (grant 03/08576-7). Finally, the authors thank the anonymous reviewer for the very interesting and comprehensive analysis of the submitted manuscript.