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Macrotransport-solidification kinetics modeling of equiaxed dendritic growth: Part I. Model development and discussion

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Abstract

An analytical model that describes solidification of equiaxed dendrites has been developed for use in solidification kinetics-macrotransport modeling. It relaxes some of the assumptions made in previous models, such as the Dustin-Kurz, Rappaz-Thevoz, and Kanetkar-Stefanescu models. It is assumed that nuclei grow as unperturbed spheres until the radius of the sphere becomes larger than the minimum radius of instability. Then, growth of the dendrites is related to morphological instability and is calculated as a function of melt undercooling around the dendrite tips, which is controlled by the bulk temperature and the intrinsic volume average concentration of the liquid phase. When the general morphology of equiaxed dendrites is considered, the evolution of the fraction of solid is related to the interdendritic branching and dynamic coarsening (through the evolution of the specific interfacial areas) and to the topology and movement of the dendrite envelope (through the tip growth velocity and dendrite shape factor). The particular case of this model is the model for globulitic dendrite. The intrinsic volume average liquid concentration and bulk temperature are obtained from an overall solute and thermal balance around a growing equiaxed dendritic grain within a spherical closed system. Overall solute balance in the integral form is obtained by a complete analytical solution of the diffusion field in both liquid and solid phases. The bulk temperature is obtained from the solution of the macrotrasport-solidification kinetics problem.

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Author notes

  1. L. Nastac (Graduate Research Assistant, Senior Staff Engineer)

    Present address: the Department of Metallurgical and Materials Engineering, The University of Alabama, 35487, Tuscaloosa, AL

Authors and Affiliations

  1. Concurrent Technologies Corporation, 15904, Johnstown, PA

    L. Nastac (Graduate Research Assistant, Senior Staff Engineer)

  2. the Department of Metallurgical and Materials Engineering, The University of Alabama, 35487, Tuscaloosa, AL

    D. M. Stefanescu (University Research Professor and Director of the Solidification Laboratory)

Authors
  1. L. Nastac
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  2. D. M. Stefanescu
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Nastac, L., Stefanescu, D.M. Macrotransport-solidification kinetics modeling of equiaxed dendritic growth: Part I. Model development and discussion. Metall Mater Trans A 27, 4061–4074 (1996). https://doi.org/10.1007/BF02595655

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  • DOI: https://doi.org/10.1007/BF02595655

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