The study presents a mathematical model of the crystallisation of nodular graphite cast iron. The proposed model is based on micro- and macromodels, 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” phase boundaries was examined. Data on the microsegregation of carbon in the cross-section of an austenite layer in eutectic grains were obtained. Calculations were performed for different particle densities and different wall thicknesses. The calculation results were compared with experimental data.
The mathematical model of the globular eutectic solidification in 2D was designed. Proposed model is based on the Cellular Automaton Finite Differences (CA-FD) calculation method. Model has been used for studies of the primary austenite and of globular eutectic grains growth during the ductile iron solidification in the thin wall casting. Model takes into account, among other things, non-uniform temperature distribution in the casting wall cross-section, kinetics of the austenite and graphite grains nucleation, and non-equilibrium nature of the interphase boundary migration. Calculation of eutectic saturation influence (Sc = 0.9 - 1.1) on microstructure (austenite and graphite fraction, density of austenite and graphite grains) and temperature curves in 2 mm wall ductile iron casting has been done.