A new treatment of transient grain growth

The grain radius R distribution ftmction f(R, t) with R-c(t) as critical grain radius is formulated, inspired by the Hillert self-similar solution concept, as product of 1/R-c(4) and of a shape function g(rho, t) as function of the dimension-free radius rho = R/R-c and time t, contrarily to the Hillert self-similar solution concept with time-independent g(rho). The evolution equations for R-c(t) as well as for g(rho, t) are derived, guaranteeing that the total volume of grains remains constant. The solution of the resulting integro-differential equations for R-c(t) and g(rho, t) is performed by standard numerical tools. Remarkable advantages of this semi-analytical concept are: (i) the concept is a deterministic one, (ii) its computational treatment is very efficient and (iii) the shape function g(rho, t) remains localized in a fixed interval of rho. The shape function g(rho, t) evolves towards the well-known Hillert self-similar distribution, which is demonstrated for two initial shape functions (one of them is triangular). Also a study on nearly self-similar distribution functions proposed as useful approximations of experimental data is presented. (C) 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.