A model study of the impact of the transport of inoculant particles on microstructure formation during solidification M. Bedel a,⇑ , K.O. Tveito b , M. Zaloz ˇnik a,c , H. Combeau a,c , M. M’Hamdi b,d a Institut Jean Lamour, Dept. SI2M, CNRS – Université de Lorraine, F-54011 Nancy Cedex, France b Dept. of Materials Technology, NTNU, N-7491 Trondheim, Norway c Laboratory of Excellence on Design of Alloy Metals for low-mAss Structures (LabEx DAMAS), Université de Lorraine, France d SINTEF Materials and Chemistry, N-0314 Oslo, Norway article info Article history: Received 12 September 2014 Received in revised form 15 January 2015 Accepted 20 January 2015 Keywords: Solidification Modeling Microstructure Inoculant particles Aluminum alloys abstract We investigate the impact of the convective transport of inoculant particles on the distribution of the final microstructure (grain size) in grain-refined aluminum-alloy castings. We carry out numerical simulations of a casting experiment, considering the solidification of an Al–22 wt.%Cu alloy inoculated with Al–Ti–B in a side-cooled 76  76  254 mm sand mold. We use a fully coupled multiscale vol- ume-averaged two-phase model. At the macroscopic scale the transport of mass, heat and solute, as well as the transport of globular equiaxed grains and of inoculant particles are described by volume averaged transport equations. At the microscopic scale, nucleation and grain growth are accounted for. Nucleation is considered to be heterogeneous and athermal. Grains nucleate on polydisperse inoculant particles at an undercooling inversely proportional to the particle size. The growth of the globular solid grains is con- trolled by solute diffusion. We analyze the individual roles of the phenomena of transport of inoculant particles and of equiaxed grains for a range of process parameters (initial superheat, cooling rate, growth-restriction parameter). We show that the consideration of the transport of polydisperse inoculant particles has a strong impact on the prediction of the heterogeneity of the final microstructure across the casting. The transport of the inoculant particles considerably increases the heterogeneities of the microstructure and reduces the average grain size, and the grain motion reduces the microstructure heterogeneities. Ó 2015 Elsevier B.V. All rights reserved. 1. Introduction The control of microstructure formation during solidification continues to be one of the concerns for the aluminum industry. In order to relate the microscopic structures to the macroscopic solidification conditions, micro–macro models have been devel- oped for several decades. The review written by Rappaz [1] gives an overview of the microscopic mechanisms responsible for the microstructure formation and of their coupling with the macro- scopic transport phenomena. Nucleation is a key step in the formation of the microstructure. The modeling of nucleation is usually based on the heterogeneous nucleation theory, as it is energetically more favorable for grains to form on foreign particles [2]. In some industrial processes, grain refiners, which act as nucleation sites, are added to refine the microstructure. The consequences of an increase of the cooling rate [3] or of an increase of the growth-restriction parameter [4] on grain-refined alloys are well known. In both cases the final grain size is reduced. However, although these main tendencies are known, heterogeneous nucleation is a complex phenomenon that remains a subject of ongoing research. Already in 1950 Turnbull highlighted that the key parameter for grain formation was the undercooling [5]. He performed experi- ments of solidification of tin drops and he showed that no grain forms until a critical undercooling is reached; once the critical undercooling is exceeded, nucleation is very fast. Maxwell and Hellawell proposed a first model of nucleation on inoculant parti- cles, coupled with grain growth [6]. In their model they described the birth of new grains by an undercooling-dependent nucleation rate. They identified two distinct regimes of the nucleation-growth competition. For low inoculant densities the refinement is 100% efficient, which means that all the inoculants are used for the for- mation of grains. Then when the inoculant density becomes higher than a limit value, a virtually constant final grain density is obtained. Thus the final grain size can be refined only up to a http://dx.doi.org/10.1016/j.commatsci.2015.01.028 0927-0256/Ó 2015 Elsevier B.V. All rights reserved. ⇑ Corresponding author. E-mail address: marie.bedel@univ-lorraine.fr (M. Bedel). Computational Materials Science 102 (2015) 95–109 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci