Computer modelling of ductile iron solidification using FDM and CA methods

Purpose: The purpose of the work was the presentation of tool for modelling of solidification process, for prediction of some structure parameters in DI by the given chemical composition of alloy and for given boundary condition of casting. Design/methodology/approach: Two mathematical models and methods developed by authors have been presented: micromodelling with using of finite difference method (FDM) and mesomodelling with using of cellular automaton method (CA). Findings: The FDM was used for solving the DI solidification model, including heat conductivity equation with source function, boundary condition for casting, equations for austenite and eutectic grains nucleation depended on the changing undercooling, the Weibull’s formula for graphite nodule count, Kolmogorov’s equation for calculation of volume fraction of phases (eutectics and austenite). A set of equations, after transformation to a difference form, were solved by the finite difference method, using an iteration procedure. The correctness of the mathematical model has been experimentally verified in the range of most significant factors, which include temperature field, the value of maximum undercooling, and the graphite nodule count interrelated with the casting cross-section. Literature offers practically no data on so confronted process model and simulation program. The CA model was used for the simulation of the grains’ shapes in connection with FD for temperature field and solute redistribution in the grain scale. Practical implications: FDM modeling gives the possibility of statistical description of microstructure but the geometrical shape of grains is assumed a priori. In CA modeling the grain shape is not assumed, but this is the result of modeling. The use of FDM gives results quantitatively comparable to the process in real casting, particularly according to temperature fields and number of graphite spheroids. Originality/value: The CA method gives on the present stage credible qualitative results but this method is more perspective for good reproducing of the real process of solidification.