Modelo analítico de microssegregação na solidificação de ligas binárias considerando o efeito Soret

Abstract

Currently, the mathematical models applicable to the solidification of metallic alloys, in their majority, disregard thermo diffusion (Soret effect). However, some studies have emerged indicating that there is a detectable influence of this effect under specific conditions. However, more comprehensive studies are needed in order to map the conditions in which the effect of thermodiffusion becomes important for the microstructure resulting from solidification. In this thesis, a mathematical model was proposed for microsegregation during the solidification of a binary alloy including the Soret effect. A micrometric control volume was defined between two secondary dendrite arms similar to the Gulliver-Scheil model. Unlike the closed system of Gulliver and Scheil, in the present work, the solute diffuses across the boundary of the system driven by a thermal gradient. Equations for thermal and solute diffusion, in transient regime, together with a set of hypotheses, constituted the present model and were solved analytically. A dimensionless number H was defined as a result of the proposed model in which it correlates thermodiffusion, heat transfer and the amount of solute secreted due to solidification, acting as an indicator of the intensity of segregation associated with thermodiffusion. In the case where H=0, that is, in the case in which the thermal diffusion is ignored in the micro-segregation, the proposed model is reduced to the Gulliver-Scheil model. Our model can be widely used in the study of the redistribution of solute and allows a direct analysis of the relevance of the contribution of thermodiffusion to the microegregation during the solidification of a binary alloy.