Analysis of grain topology and volumetric growth rate relation in three-dimensional normal grain growth

Abstract

The volumetric growth rate of individual grains as a function of their number of sides, as well as the average normalized volumetric growth rate for a given topological class are studied based on large-scale phase-field simulations of normal grain growth. For all cases, where different initial grain size distributions are considered, the same averaged normalized volumetric growth rate for a given topological class was obtained with the averaged normalized volumetric growth rate approximately zero for grains with Fo≈15 sides. The normalized average grain size as a function of topological class becomes constant within the transient regime and the relation in the transient and steady-state regime is similar and independent of initial grain structure. The relation does however not match Mullins' analytical model [W. Mullins, Acta Metall. 37 (1989) 2979–2984]. The effect of the average number of sides of the neighbouring grains on the average volumetric growth rate for a given topological class is analyzed, as well. Moreover, tracking of the evolution of four grains suggests that the normalized volumetric growth rate of a grain is strongly linked with the number of sides of the grain at the given time.