Numerical study on the prediction of microstructure parameters by multi-scale modeling of directional solidification of binary aluminum–silicon alloys

Abstract

In order to create a model to predict microstructural quantities like grain size, primary and secondary dendrite arm spacing a multi-phase and multi-scale model based on the work of Wang and Beckermann [C. Wang, C. Beckermann, Metallurgical and Materials Transactions A 27A (1996) 2754–2764] was combined with a front tracking technique [A. Wu, A. Ludwig, in: C.-A. Gandin, M. Bellet (Eds.), Modeling of Casting, Welding, and Advanced Solidification Processes – XI, TMS, 2006, pp. 291–298], micro-models for nucleation [M. Rappaz, P. Thevoz, Acta Metallurgica 35 (7) (1987) 1487–1497], primary [J. Hunt, S.-Z. Lu, Metallurgical and Materials Transactions A 27A (1996) 611–623], secondary [W. Kurz, D. Fisher, Fundamentals of Solidification, Trans Tech Publication, 1986, ISBN 0-87849-522-3] dendrite arm spacing and a control volume based finite element solver for axial-symmetric problems. As most of the micro-models are just valid for pure diffusive conditions, the model just takes into account macroscopic diffusion in the melt and thus neglects the influence of melt flow. The new software was used for a comprehensive comparison to several test cases. The validation includes investigation of the correlation of calculated and measured grain size distributions for inoculated alloys. Experimental and numerical data for the primary and secondary dendrite arm spacing for steady state and transient directional solidification were compared in a second step. A good correlation is found for all test cases.