Scaling of intragranuiar dendritic microstructure in ingot solidification

Abstract

Analytic scaling formulas of complete constitutional generality for forced velocity cells and dendrites were in earlier research perfected forin situ steady-state solidification conditions involving binary organic alloys. As a further test, these were used, given the velocity and gradient control parameters, to predict the primary and secondary dendrite arm spacings of unidirectionally cooled Al-Cu alloys for which a large data set is available. Numerical methods were employed to determine the control parameters that exist under unsteady-state ingot solidification conditions according to the Scheil formulation. Primary and secondary arm spacings, corrected empirically for ripening, that by and large agree with the Al-Cu experimental data were obtained, demonstrating that the formulas are adequate for the prediction of dendrite scales in steady and unsteady-state conditions. The predictions have been incorporated into a computer program that displays the time-dependent columnar microstructure and mushy zone in an ingot cross section of an oriented single crystal together with the thermal and liquid-solid distributions.