• solidification modeling;
  • Voronoi polyhedron;
  • diffusion-controlled growth

Principles of the statistical solidification theory are used for the mathematical formulation of the micro-diffusion field modeling during the equiaxed grain growth controlled by diffusion. It is proposed to use the Averaged Voronoi Polyhedron concept for the representation of the domain of elementary diffusion field. This approach is applied for the peritectic transformation modeling with the assumption of a partial mixing of the intercrystalline liquid phase. The results of the evolution of the volume fractions of the liquid, austenite, and ferrite phases during primary solidification and the peritectic transformation simulation are presented as well as carbon concentration distribution along the grain radius in the ferrite and liquid phase at the instant of initiation of the peritectic solidification and in the austenite at the moment of peritectic solidification termination.