A mean field theory of grain growth: I

Abstract

The initial part of a theory of normal grain growth previously published by Saetre (2002 Acta Mater. 50 1539) contained a minimum grain size of uncertain physical interpretation. In this work, the previous derivation is modified in order to eliminate the minimum grain size. The present theory thus yields a quasi-stationary state size distribution function similar to the classical Hillert distribution in the range u ϵ [0, umax), where u is the relative grain size. This theory which, under certain conditions, is valid both for two and three dimensions, is compared to the Hillert theory and to experimental data. It is concluded that the present theory yields a size distribution, which is similar, although not identical, to the Hillert distribution. Hence, the present version of the theory fails to represent the experimental distribution in the same manner as the Hillert theory. However, the strength of the present theory is that it can be further modified, as will be shown in the accompanying paper, which is the third part of the theory. The accompanying paper offers a modification of the theory, which produces a much-improved agreement with experimental data.