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

Abstract

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.

Stochastic Nature of the Casting Solidification Displayed by Micro-Modelling and Cellular Automata Method

“…The numerical solution of the diffusion equation by the elementary balance method was proposed in [19] on the geometry of an averaged Voronoi cell. The method to determine the geometry of EDF and equations used in the solution are shown below.…”

“…Some results of the AVP using for the solidification modelling of the ductile iron solidification are presented below [19]. Changes in the distance of the "graphite-austenite" and "austenite-liquid" phase boundaries from the centre of eutectic grain are shown in Fig.…”

Using of the Averaged Voronoi Polyhedron for the Equiaxed Solidification Modeling

“…The model assumes that EMDF has non-spherical shape as a result of random contacts between the grains growing around the individual nuclei. The details of this mathematical model were presented in [19,20].…”

Micromodeling of the Diffusion‐Controlled Equiaxed Peritectic Solidification

“…Use of the Averaged Voronoi Polyhedron (AVP) concept was proposed in Refs . for the diffusion field simulation in the equiaxed grains during solidification.…”

“…Use of the Averaged Voronoi Polyhedron (AVP) concept was proposed in Refs. [20,21] for the diffusion field simulation in the equiaxed grains during solidification. Onedimensional distribution of the solute in the liquid and solid solutions was analyzed by means of the diffusion equations.…”