W. Kapturkiewicz

Modelling of Dendritic Growth during Unidirectional Solidification by the Method of Cellular Automata

Modelling was carried out to investigate the internal dendrite grains structure formation from a liquid two-component solution in the area adjacent to a mould wall. For the simulation, our own model and computer program based on CAFD (Cellular Automata Finite Differences) were used. In modelling, the effect of process conditions and material-related parameters, e.g. nucleation temperature, heat exchange rate, interfacial energy, crystal orientation with respect to the casting wall, etc. on the nature of the dendritic grain growth was examined. It was demonstrated that the profile of concentration field in a near-mould-wall zone impedes the growth of the solid phase in the direct vicinity of the wall. A local melting down of the grains of a solid phase due to the segregation of admixtures reducing the alloy point of liquidus is also possible.

Nonequilibrium Kinetics of Phase Boundary Movement in Cellular Automaton Modelling

A mathematical crystallization model in the meso scale (the intermediate dimension scale between interatomic distance in solids and grain size in metals and alloys) is presented with the use of a kinetic-diffusion cellular automaton model. The model considers the non-equilibrium character of real processes of phase transformations, where the kinetic undercooling of the solid-liquid interface is a measure of this non-equilibrium level. Anisotropy of the interface mobility is assumed. The modelling results are compared to the experimental data.

Simulation of the Ductile Iron Solidification Using a Cellular Automaton

The mathematical model of the globular eutectic solidification in 2D was designed. Pro¬posed model is based on the Cellular Automaton Finite Differences (CA-FD) calculation method. Model has been used for studies of the primary and of globular eutectic grains growth during the ductile iron (DI) solidification. A hyper-eutectic composition has been analyzed but this model can be used in the solidification modeling of hypo- and eutectic DI. The proposed model makes possible to trace the unrestricted growth of primary grains of two phases from the liq¬uid, transition from free to cooperative solidification, and cooperative growth of globular eutectic.

Cellular automaton modelling of ductile iron microstructure in the thin wall casting

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.

Chilling tendency and chill of cast iron

Abstract An analytical expression is presented for the susceptibility of liquid cast iron to solidify according to the Fe-C-X metastable system (also known as the chilling tendency of cast iron, CT). The analysis incorporates the nucleation and growth processes associated with the eutectic transformation. The CT is related to the physicochemical state of the liquid, the eutectic cells in the flake graphite, and the number of nodules in nodular cast iron. In particular, the CT can be related to the critical wall thickness, scr, or the chill width, Wcr, in wedge shaped castings. Finally, this work serves as a guide for understanding the effect of technical factors such as the melt chemistry, the spheroidizing and inoculation practice, and the holding time and temperature on the resultant CT and chill of the cast iron. Theoretical calculations of scr and Wcr compare well with experimental data for flake graphite and nodular cast iron.

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

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).

Undercooling, Cooling Curves and Nodule Count for Hypo-, Hyper- and Eutectic Thin-Walled Ductile Iron Castings

Solidification model and numerical calculations are presented describing the solidification of a thin wall ductile iron with hypo-, hyper- and eutectic composition. The principal assumptions of the kinetic nature of growth, depending on undercooling in respect of the equilibrium lines, have been adopted, disregarding the diffusion processes, which was justified by the rapid course of the crystallization process in a thin-walled casting. This kinetic model was operating in a correct mode when it was completed with adjusted calculations of the carbon amount diffusing through the austenite film around the graphite nodules. The applied model of diffusion determined jointly with the kinetic model of the growth of graphite and austenite resulted in high-speed calculation program. Quite interesting are the results showing distinct differences in the kinetics of solidification and final structure of the cast iron with the same degree of eutectic saturation, but different content of C and Si.

Measurement of the Kinetics of Thermal Effects during Phase Transformations in ADI

The heat generation rate during austempering of ADI (Austempered Ductile Iron) for process temperatures of 250, 265, 280 and 293°C has been presented. A special measuring device was constructed. Thermal effects were quantified by analysis of the experimental temperature curves during the austempering process.

Stereological Analysis of the Statistical Distribution of the Size of Graphite Nodules in DI

The estimate of a distribution law of the nodule diameters in a volume of cast iron provides information about the graphite nucleation kinetics, and also about the crystallization kinetics. This information is essential for building more accurate mathematical models of the alloy crystallization. The mapping of a Cumulative Distribution Function (CDF3) of radii for graphite nodules in ductile iron is presented on the base of a Probability Density Function (PDF1) of the chord length distribution for random sections of the sample at the planar cross-section.

Modelling of the Density Changes of Nodular Cast Iron During Solidification by CA-FD Method

Formation of the shrinkage defects in ductile iron castings is far more complicated phenomenon than in other casting alloys. In the presented paper changes the ductile iron density during solidification is analyzed. During the solidification path the influence of the temperature, phase fractions and phase composition is taking into account. Computer model, using cellular automata method, for estimation of changes in density of ductile iron during its solidification is applied. Results of the solidification modeling for Fe-C binary alloys with different composition in the castings with a different wall thickness are presented. As a result of calculations it was stated that after undercooling ductile iron below liquidus temperature volumetric changes proceed in three stages: pre-eutectic shrinkage (minimal in eutectic cast iron), eutectic expansion and the last shrinkage.