The paper presents the cellular automaton (CA) model for tracking the development of dendritic structure in non-equilibrium solidification conditions of binary alloy. Thermal, diffusion and surface phenomena have been included in the mathematical description of solidification. The methodology for calculating growth velocity of the liquid-solid interface based on solute balance, considering the distribution of the alloy component in the neighborhood of moving interface has been proposed. The influence of solidification front curvature on the equilibrium temperature was determined by applying the Gibbs Thomson approach. Solute and heat transfer equations were solved using the finite difference method assuming periodic boundary conditions and Newton cooling boundary condition at the edges of the system. The solutal field in the calculation domain was obtained separately for solid and liquid phase. Numerical simulations were carried out for the Al-4 wt.% Cu alloy at two cooling rates 15 K/s and 50 K/s. Microstructure images generated on the basis of calculations were compared with actual structures of castings. It was found that the results of the calculations are agreement in qualitative terms with the results of experimental research. The developed model can reproduce many morphological features of the dendritic structure and in particular: generating dendritic front and primary arms, creating, extension and coarsening of secondary branches, interface inhibition, branch fusion, considering the coupled motion and growth interaction of crystals.
A numerical model of binary alloy crystallization, based on the cellular automaton technique, is presented. The model allows to follow the
crystallization front movement and to generate the images of evolution of the dendritic structures during the solidification of a binary
alloy. The mathematic description of the model takes into account the proceeding thermal, diffusive, and surface phenomena. There are
presented the results of numerical simulations concerning the multi-dendritic growth of solid phase along with the accompanying changes
in the alloying element concentration field during the solidification of Al + 5% wt. Mg alloy. The model structure of the solidified casting
was achieved and compared with the actual structure of a die casting. The dendrite interaction was studied with respect to its influence on
the generation and growth of the primary and secondary dendrite arms and on the evolution of solute segregation both in the liquid and in
the solid state during the crystallization of the examined alloy. The morphology of a single, free-growing dendritic crystal was also
modelled. The performed investigations and analyses allowed to state e.g. that the developed numerical model correctly describes the
actual evolution of the dendritic structure under the non-equilibrium conditions and provides for obtaining the qualitatively correct results
of simulation of the crystallization process.