Modeling of primary and eutectic solidification by using CAFD method

Andriy Burbelko, Daniel Gurgul

AGH University of Science and Technology, Foundry Faculty,23 Reymonta Str., 30-059 Krakow, Poland.

DOI:

https://doi.org/10.7494/cmms.2011.1.0323

Abstract:

The results of a two-dimensional modeling of the microstructure formation in an eutectic ductile cast iron are presented. The cellular automaton model (CA) was used for the simulation. The model takes into account the nucleation of two kinds of grains that appear inside of the liquid during solidification: austenite and graphite. A numerical solution was used for the modeling of concentration and temperature fields. The parabolic nonlinear differential equations with a source function were solved by using the finite differences method (FD) and explicit scheme. In the interface cells the value of the source function varies depending on the local undercooling. The undercooling value depends on the front curvature, the local temperature and the local chemical composition of the phases. Overlapping lattices with the same spatial step were used for concentration field modeling and for the CA. Another lattice for temperature field was used with a multiple spatial step and the same time step. The new grain nucleation of solid phases from a liquid is a phenomenon which must be taken into account for correct simulation of a polycrystalline structure formation. An algorithm of continuous nucleation modeling during solidification is presented. The undercooling of solid phase grain nucleation was calculated on the basis of the inverse function of the above cumulative distribution curve (fractile) with the argument equal to the random number generated in the interval 0…1 with uniform density. The domain of correct usage of this algorithm was analyzed.

Cite as:

Burbelko, A., & Gurgul, D. (2011). Modeling of primary and eutectic solidification by using CAFD method. Computer Methods in Materials Science, 11(1), 128 – 134. https://doi.org/10.7494/cmms.2011.1.0323

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