Mosbah, Salem (2008) Multiple Scales Modeling of Solidification Grain Structures and Segregation in Metallic Alloys. PhD thesis Sciences et Génie des Matériaux, CEMEF - Centre de Mise en Forme des Matériaux, ENSMP p.125.

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Abstract

This work first presents a new multi-scales modeling approach of grain structures solidification and its associated segregation pattern in the as-cast state. It is based upon a semi-analytical description of the chemical length scales built in the solid and outside the envelope of the grains. Originality lies in the account of both the primary and the eutectic structure nucleation undercooling. The model has been applied for Al–Cu sample with spontaneous nucleation processed by the Electromagnetic Levitation (EML) technique. The EML technique is used as an experimental model to process Aluminum–Copper spherical samples with different copper compositions. For each sample, nucleation has been either spontaneous or triggered using an alumina plate. Various degrees of undercooling have been measured prior to the primary and the eutectic structure nucleation events. Extensive metallurgical characterizations have been performed over a median cutting plane for each sample using a scanning electron microscope(SEM) equipped with energy–dispersive X-ray spectrometry and analyses of SEM images. A complete set of data has been elaborated consisting of the distribution maps drawn for the average copper composition, the volume fraction of the eutectic structure, the dendrite arm spacing and their averaged values over the same cutting plane. Segregation has been measured and found to be strongly correlated with the eutectic and the dendrite arm spacing maps. Application of the model shows that the nucleation undercooling of the eutectic structure is a key parameter for a quantitative prediction of the fraction of phases in the solidified samples. In addition, a two-dimensional Cellular Automaton - Finite Element (2D CAFE) model is developed to investigate the segregation maps and the non-equilibrium temperature evolution for samples with spontaneous and triggered nucleation. The model integrates the microsegregation model in each CA cell taking into account the primary phase nucleation undercooling and back diffusion in the solid phase. Additional microstructural features considered are the primary and the secondary dendrite arm spacing. Heat, mass and momentum conservation equations over the simulation domain are solved using the finite element model. A new coupling scheme between the finite element and the cellular automaton model is developed allowing finite element mesh adaptation. A geometrical error estimator has been integrated in the finite element model to control the mesh size and orientation in order to increase the accuracy of the finite element solution. New interpretations of the experimental observations are accessible thanks to the new 2D CAFE model. The 2D CAFE model is also successfully applied to a benchmark solidification test developed recently for a rectangular cavity experiment. Comparisons with maps of temperature, macrosegregation and grains structures have been performed demonstrating the model capabilities to deal with heat and mass exchanges at micro and macro scales.

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