Modeling of Growth and Impingement of Spherical Grains

Abstract

A model was developed to simulate the growth and impingement of spherical grains, which are frequently encountered in the solidification, recrystallization and other processes in association with phase transformations. The initial grain was assumed as spherically approximated 128 faces polyhedron. Various cases were investigated under different conditions of final number of grains, nucleation and spatial distribution. The validity of the Kolmogorov, Johnson-Mehl and Avrami (KJMA) equation was examined for various cases.The results proved that KJMA equations are valid for the real volume and the effective surface area (effective for later growth) calculations under the conditions of site saturation/constant growth rate and the conditions of constant nucleation rate/constant growth rate. When the grain shape is not maintained same throughout the process, the results show that the effective surface area deviate largely from the KJMA equation even though the KJMA equation is approximately valid to calculate the real volume. Finally, when the spatial distribution of grains is non-random, clustered or ordered, the KJMA equation is not valid and the deviation from it is large especially at the end of transformation both for the real volume and for the effective surface. Even when the KJMA equation is not valid for the effective surface area, Rath’s empirical equation is effectively applicable for it, though the physical meaning of the parameters used in it is not clear.