Investigation of the growth kinetics of c ? a in Fe–C–X alloys with a thick interface model Nataliya Perevoshchikova a , Benoît Appolaire b,⇑ , Julien Teixeira a , Elisabeth Aeby-Gautier a , Sabine Denis a a Institut Jean Lamour – SI2M, École des Mines, Parc de Saurupt, Nancy, France b LEM, CNRS/ONERA, 29 av. Division Leclerc - BP 72, F-92322 Châtillon Cedex, France article info Article history: Received 7 April 2013 Received in revised form 19 September 2013 Accepted 22 September 2013 Keywords: Austenite Ferrite Interface migration Dissipation Transformation kinetics abstract A thick interface model is proposed aiming at predicting the whole spectrum of conditions at an austen- ite/ferrite interface during ferrite growth in ternary Fe–C–X alloys, from full equilibrium to paraequilib- rium, with intermediate cases as the most interesting feature. It is shown that the different kinetics can be obtained by tuning only the ratio between the diffusivities inside the thick interface and in bulk aus- tenite. The predictions of the model for the kinetic transitions in different Fe–C–Ni alloys with a single value of this ratio are in good agreement with available measurements. In particular, sudden growth stops observed in alloys with high substitutional species contents are explained by the transition from paraequilibirium to local equilibrium non partitioning growth modes. Ó 2013 Elsevier B.V. All rights reserved. 1. Introduction Steels are an essential structural materials because a large spec- trum of mechanical properties can be achieved by suitable alloying and thermo-mechanical treatments. This large spectrum is permit- ted by the rich microstructures that steels can feature. Among all the transformation at the solid state in steels, the allotropic trans- formation of austenite c (fcc phase) into ferrite a (bcc phase) is very important because it gives rise to many microstructures, such as allotriomorphic ferrite, Widmanstätten ferrite, bainite and pearlite. This is why the c ? a transformation is the most studied diffusion controlled transformation in steel. Besides the works con- cerning the mechanisms at the atomic scale (growth ledges, dis- connections, etc., e.g. [1]), the most common approach for predicting the kinetics of diffusion controlled phase transformation relies on the so-called sharp interface concept: interfaces are re- duced to mathematical surfaces with intrinsic thermodynamic and kinetic properties, following the seminal work of Gibbs [2]. This type of models handle microstructures at the millimeter scale in the most practical way, i.e. in a Representative Volume Element (RVE) for structural mechanics (e.g. [3,4]). Two steps are intrinsi- cally implied by this approach. First, the transport problem in the bulk phases must be solved accounting for the moving interface through the local solute balances, relating the jumps in solute con- centrations, the velocity, and the jumps in the flux [5]. Second, some conditions must be prescribed at the interface (sometimes called response functions [6]) which are the necessary boundary conditions for the diffusion problem in the bulks. In many cases considering local equilibrium at the interface gives satisfying results, in particular in dilute binary metallic alloys exhibiting precipitation, e.g. [7]. This is also the case for transfor- mations in multicomponent alloys at high temperatures, i.e. not too far from equilibrium, and when all diffusivities are of the same order of magnitude, e.g. [8,9]. Moreover, it makes the moving boundary problem analytically tractable, because for some partic- ular simple geometries (plane, cylinder, sphere, etc.) the interface is a concentration level set. Hence, similarity solutions to the diffu- sion problems can be used to find solutions as pioneered by Stefan [10], Zener [11], Frank [12], Ivantsov [13] and Horvay and Cahn [14]. In other cases, the local equilibrium assumption fails to pre- dict the correct kinetics. Thus, different refinements have been pro- posed to the description of the diffusion processes in the bulks: diffusion in finite system with soft impingement [15], short circuit diffusion (e.g. by the collector plate mechanism) [16], or geometri- cal complexities (in that case by relying on numerical models) [17]. But all those refinements revealed to be not sufficient to explain many observed features, in particular slow kinetics and states at fractions below equilibrium [18]. The most promising way which would give a consistent account of all these puzzling features relies on the description of the interfacial phenomena. This is not a new trend, since interface controlled transformations have been put forward very early as the opposite case to diffusion controlled transformations [19]. In 0927-0256/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2013.09.047 ⇑ Corresponding author. E-mail address: benoit.appolaire@onera.fr (B. Appolaire). Computational Materials Science 82 (2014) 151–158 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci