The paper presents a new numerical model of solidification processes in hypoeutectic alloys. The model combines stochastic elements, such as e.g. random nucleation sites and orientation of dendritic grains, as well as deterministic methods e.g. to compute velocity of dendritic tips and eutectic grains. The model can be used to determine the temperature and the size of structure constituents (of both, the primary solid phase and eutectics) and the arrangement of individual dendritic and eutectic grains in the consecutive stages of solidification. Two eutectic transformation modes, typical to modified and unmodified hypoeutectic alloys, have been included in the model. To achieve this, cellular automata and Voronoi diagrams have been utilized.
In Part I of this article, two-stage solidification model was presented. In this part we use our model to simulate solidification of the Al 7% Si alloy for two cooling rates and . Simulations have been performed for two eutectic transformation modes, typical for modified and unmodified alloys. Obtained cooling curves are qualitatively consistent with the typical cooling curves for modified and unmodified alloys. Moreover, evolution of cooling-curve characteristics is compared with the analytical model and found to be in close agreement.
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.