Application of Averaged Voronoi Polyhedron in the Modelling of Crystallisation of Eutectic Nodular Graphite Cast Iron

The study presents a mathematical model of the crystallisation of nodular graphite cast iron. The proposed model is based on micro- andmacromodels, in which heat flow is analysed at the macro level, while micro level is used for modelling of the diffusion of elements. The use of elementary diffusion field in the shape of an averaged Voronoi polyhedron [AVP] was proposed. To determine the geometry of the averaged Voronoi polyhedron, Kolmogorov statistical theory of crystallisation was applied. The principles of a differential mathematical formulation of this problem were discussed. Application of AVP geometry allows taking into account the reduced volume fraction of the peripheral areas of equiaxial grains by random contacts between adjacent grains.As a result of the simulation, the cooling curves were plotted, and the movement of "graphite-austenite" and "austenite-liquid” phaseboundaries was examined. Data on the microsegregation of carbon in the cross-section of an austenite layer in eutectic grains wereobtained. Calculations were performed for different particle densities and different wall thicknesses. The calculation results were compared with experimental data.