Modelling of the Dendritic Crystallization by the Cellular Automaton Method

Abstract

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.

Copper droplets agglomeration/coagulation in the conditions similar to industrial ones

“…2). The appearance of some Cu(Fe) dendrites is also possible, [4]. Then, the de-oxidation with calcium carbide melts is recommended, [5].…”

Some Similarities / Differences between Steel Static and Virtual Brass Static Casting

“…The static ingot solidification was the subject of some simulations in order to predict the "A" -segregates formation, [5], and the CET appearance, [6]- [22]. Generally, the different numerical method of the temperature field simulation were applied in the these models, [6], [12], [14], [17], [19], [21].…”

“…Generally, the different numerical method of the temperature field simulation were applied in the these models, [6], [12], [14], [17], [19], [21]. Particularly some attempts were made to describe the difference between columnar and equiaxed grains creation, [7]- [11], [13], [15]- [16], [18], [20], [22]. In the current model the temperature field is calculated and transformed into thermal gradient field.…”

Archives of Foundry Engineering

“…The analytical models developed in the last century were focused on the mathematical description of the dendrite tip movement and the determination of the relationship between its velocity and melt undercooling. Current numerical models can realistically simulate dendritic growth on a micro scale, reproducing many morphological features such as: curvature of the dendrite tip, the length of incubation before the generation of second-order arms, the dendrites arms spacing and the shape and size of the branches [4][5][6][7][8][9].…”

“…During solidification simulation can to observe the subsequent stages of dendrite growth, multi-dendritic interactions, as well as the formation and development of eutectic grains. Furthermore, based on the concentration fields obtained from the modeling, it is possible to determine the degree of solute segregation at the different cooling rates of the castings [5][6][7][8][9][10][11][12][13][14].…”