Composition dependence of the critical Rayleigh number curve for macrosegregation in multicomponent metal alloys

TL;DR

This study derives a composition-dependent Rayleigh number criterion for local remelting in mushy zones, linking convective instabilities to alloy composition and thermophysical properties.

Contribution

The paper introduces a new expression for the critical Rayleigh number that accounts for composition-dependent thermophysical properties in multicomponent alloys.

Findings

Critical Rayleigh number varies with local solid fraction.

Thermophysical properties significantly influence remelting conditions.

The criterion correlates with empirical data across different alloy compositions.

Abstract

Convective instabilities in the semi-solid mushy zone can trigger channel formation that leads to defects known as freckles, channel segregates and A-type segregates. In the present work, Flemings' model is used to determine conditions for the onset of local remelting when buoyancy-driven flow is suddenly triggered in an initially stagnant mushy zone. An expression in the form of a Rayleigh number $Ra$, and its associated critical value $Ra_{\rm crit}$, above which the local remelting condition is satisfied, are derived. Using thermophysical data from CALPHAD, these expressions are evaluated using results from benchmark experimental and numerical studies for the nickel-based superalloy SX-1 and Pb-Sn alloys. The correlation of this local-remelting criterion with previously reported empirical criteria is also tested for various steel compositions. It is found that $Ra_{\rm crit}$ varies with the local average solid fraction and several thermophysical properties. Since these properties can vary substantially within a relatively narrow composition range, it is suggested that $Ra_{\rm crit}$ is a strongly composition-dependent parameter.