A COMBINED MODEL FOR THE DESCRIPTION OF AUSTENITIZATION, HOMOGENIZATION AND GRAIN GROWTH IN HYPOEUTECTOID Fe±C STEELS DURING HEATING A. JACOT{ and M. RAPPAZ{ Laboratoire de MeÂtallurgie Physique, Ecole Polytechnique FeÂdeÂrale de Lausanne, MX-G Ecublens, CH-1015 Lausanne, Switzerland (Received 17 August 1998; accepted 14 December 1998) AbstractÐA combined model which allows one to simulate all the steps of the reaustenitization process of ferrito-pearlitic plain carbon steel has been developed. The dissolution of pearlite, the transformation of fer- rite into austenite and the homogenization of the carbon distribution is described with a ®nite volume method. The simulation is performed on a bidimensional domain where ferrite (a), pearlite (P) and austenite (g) grains are represented. The dissolution of pearlite is described by the growth of spherical grains and simple nucleation and growth laws. The movement of a/g interfaces is calculated by solving the diusion equation for carbon in the a and g phases and accounting for the solute ¯ux balance at the interface using a pseudo-front tracking method. The diusion model is coupled with a Monte Carlo simulation which describes the grain growth occurring in austenite at a later stage of austenitization. The evolution of the volume fractions of pearlite and ferrite, the maximum and minimum carbon concentrations in the domain and the mean austenite grain size are represented as a function of the temperature for a typical case of con- stant heating rate. The in¯uence of the dierent steps of the austenitization process on the global kinetics is discussed. # 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. 1. INTRODUCTION Reaustenitization in hypoeutectoid steels in the fer- rito-pearlitic condition occurs in several steps [1]. The ®rst one is the transformation of pearlite into austenite. Nucleation of austenite grains takes place just above the eutectoid temperature and generally at the interfaces between pearlite colonies. The dis- solution of pearlite is then very fast since the diu- sion distances for carbon are relatively small (of the order of the interlamellar spacing). The second step is the transformation of proeutectoid ferrite into austenite. This transformation occurs at higher tem- peratures and is only completed above the (a + g)/g line in the phase diagram (the Ac 1 line). The for- mation of austenite is followed by homogenization of the carbon distribution and ®nally grain growth which is predominant at high temperature or long austenitization times. Dierent models have been proposed for the description of reaustenitization [2, 3], homo- genization [4] and grain growth [5±12]. However, these models are generally restricted to one or two steps of the process. Recently, the present authors have proposed a bidimensional model that describes the transformation of ferrite into austenite and homogenization [13]. In this model, it was assumed that the kinetics of pearlite dissolution was much faster than the dissolution of ferrite. Therefore, the ®rst step of reaustenitization was not described, and the initial microstructure was composed of ferrite and austenite zones, the latter corresponding to the former carbon-rich pearlitic regions. This model has been re®ned in order to account for the formation of austenite from pearlite as well. The present con- tribution describes the modi®cations that have been carried out in the ®nite volume model of Ref. [13] in order to account for the dissolution of pearlite. It also contains a short description of a Monte Carlo (MC) model that has been used to simulate the grain growth in austenite. Finally, a typical result obtained with the diusion model coupled with the MC model is shown. 2. DIFFUSION MODEL The model is mainly based on the two-dimen- sional ®nite volume method presented in Ref. [13] for the resolution of the diusion equation in the presence of two phases. The calculation domain is subdivided into hexagonal cells that can have ®ve dierent states: ferrite (a), pearlite (P), austenite (g), ferrite/pearlite interface (a/P) or ferrite/austenite interface (a/g), as illustrated in Fig. 1. There is no Acta mater. Vol. 47, No. 5, pp. 1645±1651, 1999 # 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 1359-6454/99 $20.00 + 0.00 PII: S1359-6454(99)00005-1 {Present address: Department of Metals and Materials Engineering, University of British Columbia, 309-6350 Stores Road, Vancouver, V6T 1Z4, Canada. {To whom all correspondence should be addressed. 1645