No abstract

For the characterization of the equiaxed polycrystalline structure the Dirichlet tessellation is often used. The results of this space decomposition Voronoi polyhedrons are convex but not necessarily bounded. Size, volume and other characteristics of these bodies are the random variables. Parameters of theAveraged Voronoi Polyhedronare used in the presented paper for the modeling of the diffusion controlled peritectic transformation. Proposed model takes into account decreasing of the transformation interface surface in the remote regions of the diffusion field due to the probabilistic grains impingements. The results of the modeling are compared with the microstructure of the Pb-32 wt.% Bi alloy and thermal analysis results.

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.

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.

Some aspects of stochastic nature of the solidification processes are described. Firstly, the influence of the random grains nucleation on the cooling curves repeatability in the thin wall casting is presented. Secondly, the foundations of an average shape prediction for geometry of ele¬mentary diffusion field (concept of the Averaged Voronoi Polyhedron, AVP) are shown for the mi¬cro-modelling of the diffusion limited growth. Stochastic nature of the grains nucleation and growth is taken into account in the solidification modelling based on the Cellular Automaton technique (CA).