Averaged Voronoi Polyhedron in the Equiaxed Solidification Modelling

Abstract

For the modelling of the equiaxed grain growth controlled by diffusion the spherical Elementary Micro-Diffusion Field (EMDF) is usually used. Unfortunately, deviation of the idealized spherical grain geometry from the real one increases with a distance from nuclei. The proposed model of the equiaxed solidification, controlled by diffusion, assumes that EMDF has non-spherical shape as a result of random contacts between the grains growing around the individual nuclei. To determine the geometry and characteristics of the proposed EMDF, Kolmogorov’s principle of the statistical theory of crystallization has been used. Modelling based on the non-spherical EMDF gives more accuracy of the solidification path prediction at the last stage of solidification. The results of simulation have been compared with experimental results obtained for near-peritectic Pb-Bi alloy.