Modelling of the Dendritic Crystallization by the Cellular Automaton Method

Journal title

Archives of Foundry Engineering




No 1

Publication authors


Numerical modelling ; Crystallization ; Cellular automata ; Binary alloys ; Structure modeling

Divisions of PAS

Nauki Techniczne


Archives of Foundry Engineering continues the publishing activity started by Foundry Commission of the Polish Academy of Sciences (PAN) in Katowice in 1978. The initiator of it was the first Chairman Professor Dr Eng. Wacław Sakwa – Corresponding Member of PAN, Honorary Doctor of Czestochowa University of Technology and Silesian University of Technology. This periodical first name was „Solidification of Metals and Alloys” , and made possible to publish the results of works achieved in the field of the Basic Problems Research Cooperation. The subject of publications was related to the title of the periodical and concerned widely understand problems of metals and alloys crystallization in a casting mold. In 1978-2000 the 44 issues have been published. Since 2001 the Foundry Commission has had patronage of the annually published “Archives of Foundry” and since 2007 quarterly published “Archives of Foundry Engineering”. Thematic scope includes scientific issues of foundry industry:

  • Theoretical Aspects of Casting Processes,
  • Innovative Foundry Technologies and Materials,
  • Foundry Processes Computer Aiding,
  • Mechanization, Automation and Robotics in Foundry,
  • Transport Systems in Foundry,
  • Castings Quality Management,
  • Environmental Protection.


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.


The Katowice Branch of the Polish Academy of Sciences




Artykuły / Articles


ISSN 2299-2944


Zhan (2008), Cellular automaton simulation of grain growth with different orientation angles during solidification process of Materials Processing Technology, Journal, 208. ; Zhang (2012), A three - dimensional cellular automaton model for dendritic growth in multi - component alloys, Acta Materialia, 2249, ; Gandin (1994), A coupled finite element cellular automaton model for the prediction of dendritic grain structures in solidification processes, Acta Metallurgica et Materialia, 2233, ; Zhu (2007), Modeling of Microstructure and Microsegregation in Solidification of Multi - Component Alloys of Phase Equilibria and Diffusion, Journal, 130. ; Michelic (2010), Polydimensional modelling of dendritic growth and microsegregation in multicomponent alloys, Acta Materialia, 2738, ; Kuangfei (2010), Simulation of microstructural evolution in directional solidification of Ti at Al alloy using cellular automaton method, China Foundry, 45, 7. ; Yin (2011), Simulation of a dendritic microstructure with the lattice Boltzmann and cellular automaton methods, Acta Materialia, 3124, ; Wie (2012), Orientation selection of equiaxed dendritic growth by three - dimensional cellular automaton model, Physica B, 407. ; Zhu (2007), Virtual front tracking model for the quantitative modeling of dendritic growth in solidification of alloys, Acta Materialia, 1741, ; Yan (2002), Computational and Experimental Investigation of Microsegregation in an Al - rich Al - Mg - Si Quaternary Alloy, Acta Materialia, 2199,