Microstructural Characterization and Mathematical Modeling for Determination of Volume Fraction of Eutectoid Mixture of the Cu-8.5wt% Sn Alloy Obtained by Unidirectional Upward Solidification

Abstract

The Cu-8.5wt % Sn alloy presents an extensive microsegregation during its solidification. That microsegregation results in the formation of a eutectoid mixture, which is detrimental to subsequent forming processes. This study deals with the influence of solidification time and cooling rate on the microstructure of that alloy. The unidirectional solidification technique allowed the acquisition of thermal data. The optical microscopy enabled the microstructural characterization of the material, the measurement of dendrite arm spacings and the quantification of the volume fraction of the eutectoid mixture. A semi-analytical mathematical model was proposed to estimate the volume fraction of the eutectoid mixture. The model expresses the volume fraction as an implicit function of the Fourier number. The results showed that the microstructure is dendritic and that the characteristic spacings increase with the solidification time between the liquidus and the peritectic temperatures. The data also showed that for higher cooling rates the dendrite arm spacings are smaller and that there is a tendency for the volume fraction of eutectoid mixture in the columnar zone to increase with the Fourier number and to decrease with the cooling rate. The proposed model allowed obtaining values of volume fraction with the same order of magnitude of the experimental data, but with behavior tendency opposite to that observed.