Application of Averaged Voronoi Polyhedron in the Modelling of Crystallisation of Eutectic Nodular Graphite Cast Iron

Journal title

Archives of Foundry Engineering




No 1

Publication authors


Cast iron with nodular graphite ; modelling ; Averaged Voronoi polyhedron

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.


The study presents a mathematical model of the crystallisation of nodular graphite cast iron. The proposed model is based on micro- and macromodels, in which heat flow is analysed at the macro level, while micro level is used for modelling of the diffusion of elements. The use of elementary diffusion field in the shape of an averaged Voronoi polyhedron [AVP] was proposed. To determine the geometry of the averaged Voronoi polyhedron, Kolmogorov statistical theory of crystallisation was applied. The principles of a differential mathematical formulation of this problem were discussed. Application of AVP geometry allows taking into account the reduced volume fraction of the peripheral areas of equiaxial grains by random contacts between adjacent grains. As a result of the simulation, the cooling curves were plotted, and the movement of "graphite-austenite" and "austenite-liquid” phase boundaries was examined. Data on the microsegregation of carbon in the cross-section of an austenite layer in eutectic grains were obtained. Calculations were performed for different particle densities and different wall thicknesses. The calculation results were compared with experimental data.


The Katowice Branch of the Polish Academy of Sciences




Artykuły / Articles


ISSN 2299-2944