Andriy A. Burbelko

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.

Multiscale Modeling of Ductile Iron Solidification With Continuous Nucleation by a Cellular Automaton

The solidification of metals and alloys is a typical example of multiphysics and multiscale engineering systems. The phenomenon of different time and spatial scales should be taken into consideration in the modeling of a microstructure formation: heat diffusion, the components diffusion in the liquid and solid phases, the thermodynamics of phase transformation under a condition of inhomogeneous chemical composition of growing and vanishing phases, phase interface kinetics, and grains nucleation. The results of a two-dimensional modeling of the microstructure formation in a ductile cast iron are presented. The cellular automaton model (CA) was used for the simulation. The model takes into account the nucleation of two kinds of grains that appear inside of the liquid during solidification: austenite and graphite. The six states of CA cells correspond to the above-mentioned three phases (liquid, austenite and graphite) and to the three two-phase interfaces. A numerical solution was used for the modeling of concentration and temperature fields. The parabolic nonlinear differential equations with a source function were solved by using the finite element method and explicit scheme. In the mono-phase cells the source function is equal to zero. In the interface cells the value of the source function varies depending on the local undercooling. The undercooling value depends on the front curvature, the local temperature and the local chemical composition of the phases. Overlapping lattices with the same spatial step were used for concentration field modeling and for the CA. The time scale of the temperature field for this lattice is about 104 times shorter. Due to the above reasons, another lattice was used with a multiple spatial step and the same time step. The new grain nucleation of solid phases from a liquid is a phenomenon which must be taken into account for correct simulation of a polycrystalline structure formation. The cumulative distribution curve approach was used to calculate the number of substrates on which nucleation takes place as a function of under-cooling below the equilibrium temperature. An algorithm of continuous nucleation modeling during solidification is presented. The undercooling of solid phase grain nucleation was calculated on the basis of the inverse function of the above-mentioned cumulative distribution curve (fractile) with the argument equal to the random number generated in the interval 0[[ellipsis]]1 with uniform density. The domain of correct usage of this algorithm was analyzed.Copyright

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.

The Application of Some Probability Density Functions on Heterogeneous Nucleation

Probability density functions of known statistical distributions (Gauss, Weibull, lognormal) have been used to describe the nucleation of grains during solidification. Empirical nucleation data for solidification of cast iron follow a model based on the lognormal distribution.