High-angle grain-boundary migration was predicted to occur, by two types of mathematical model, during geometrical dynamic recrystallization. Both models considered the driving pressure due to curvature, plus a sinusoidal driving pressure due to sub-grain walls connected to the grain boundary. One model was based upon the finite difference solution of a kinetic equation, and the other upon a numerical technique in which the boundary was sub-divided into linear segments. The models showed that an initially flat boundary became serrated, with the peak and valley migrating into both adjacent grains, as observed during geometrical dynamic recrystallization. When the sinusoidal driving-pressure amplitude was smaller than 2π, the boundary ceased migrating; reaching an equilibrium shape. When the amplitude was greater than 2π, equilibrium was never reached and the boundary migrated indefinitely; causing the protrusions of two serrated parallel boundaries to impinge upon one another and create smaller equiaxed grains.

Modelling Grain Boundary Migration during Geometric Dynamic Recrystallization. M.A.Martorano, A.F.Padilha: Philosophical Magazine Letters, 2008, 88[9-10], 725-34