A. Burbelko

Modeling of Directional Solidification of Columnar Grain Structure in CMSX-4 Nickel-Based Superalloy Castings

The paper presents the analysis of numerical simulation of the Bridgman directional solidification process performed on CMSX-4 rods. The numerical simulation was studied applying the ProCAST software. The constitutive law parameters of the normal Gaussian distribution were used to describe the nucleation process. The coefficients of the equation were determined and used to calculate the growth rate of dendrite tip. The analysis of the as-cast microstructure was carried out with the use of Aphelion software in order to determine the average area of grains and their quantity. The experimental verification of both nucleation and grain growth coefficients used for the simulation of the directional solidification process confirmed that the model was correct and described well the investigated process of directional solidification using the Bridgman method.

Modelling of Grain Microstructure of IN-713C Castings

This paper provides an analysis of experimental research results and numerical simulation of grain microstructure of turbine blade castings made of the IN-713C nickel superalloy. The numerical simulation was carried out by applying the ProCAST program. The geometric description of model assemblies and three-dimensional ceramic mould enclosure was developed. The boundary conditions as well as the thermal and physical coefficients for alloy and ceramic shell mould were selected for simulation purposes. The parameters of nucleation law based on normal (Gaussian) distribution as well as the values of equation coefficients were established in order to determine the growth rate of dendrite tips for the IN-713C alloy, depending on the undercooling. The experimental verification of boundary conditions for numerical simulation was carried out by comparison with the results of temperature distribution measurements performed in the castings. The analysis of grain microstructure was conducted on the surface and cross-sections of castings. The forecasted grain microstructure was determined using the CAFE module (ProCAST software). The cast microstructure as well as the value of grain growth and nucleation coefficients, which were used for numerical simulation of solidification process, were experimentally verified.

Cellular automaton modelling of ductile iron microstructure in the thin wall casting

The mathematical model of the globular eutectic solidification in 2D was designed. Proposed model is based on the Cellular Automaton Finite Differences (CA-FD) calculation method. Model has been used for studies of the primary austenite and of globular eutectic grains growth during the ductile iron solidification in the thin wall casting. Model takes into account, among other things, non-uniform temperature distribution in the casting wall cross-section, kinetics of the austenite and graphite grains nucleation, and non-equilibrium nature of the interphase boundary migration.

Stochastic Nature of the Casting Solidification Displayed by Micro-Modelling and Cellular Automata Method

Some aspects of stochastic nature of the solidification processes are described. Firstly, the influence of the random grains nucleation on the cooling curves repeatability in the thin wall casting is presented. Secondly, the foundations of an average shape prediction for geometry of ele¬mentary diffusion field (concept of the Averaged Voronoi Polyhedron, AVP) are shown for the mi¬cro-modelling of the diffusion limited growth. Stochastic nature of the grains nucleation and growth is taken into account in the solidification modelling based on the Cellular Automaton technique (CA).

Undercooling, Cooling Curves and Nodule Count for Hypo-, Hyper- and Eutectic Thin-Walled Ductile Iron Castings

Solidification model and numerical calculations are presented describing the solidification of a thin wall ductile iron with hypo-, hyper- and eutectic composition. The principal assumptions of the kinetic nature of growth, depending on undercooling in respect of the equilibrium lines, have been adopted, disregarding the diffusion processes, which was justified by the rapid course of the crystallization process in a thin-walled casting. This kinetic model was operating in a correct mode when it was completed with adjusted calculations of the carbon amount diffusing through the austenite film around the graphite nodules. The applied model of diffusion determined jointly with the kinetic model of the growth of graphite and austenite resulted in high-speed calculation program. Quite interesting are the results showing distinct differences in the kinetics of solidification and final structure of the cast iron with the same degree of eutectic saturation, but different content of C and Si.

Stereological Analysis of the Statistical Distribution of the Size of Graphite Nodules in DI

The estimate of a distribution law of the nodule diameters in a volume of cast iron provides information about the graphite nucleation kinetics, and also about the crystallization kinetics. This information is essential for building more accurate mathematical models of the alloy crystallization. The mapping of a Cumulative Distribution Function (CDF3) of radii for graphite nodules in ductile iron is presented on the base of a Probability Density Function (PDF1) of the chord length distribution for random sections of the sample at the planar cross-section.

Modelling of the Density Changes of Nodular Cast Iron During Solidification by CA-FD Method

Formation of the shrinkage defects in ductile iron castings is far more complicated phenomenon than in other casting alloys. In the presented paper changes the ductile iron density during solidification is analyzed. During the solidification path the influence of the temperature, phase fractions and phase composition is taking into account. Computer model, using cellular automata method, for estimation of changes in density of ductile iron during its solidification is applied. Results of the solidification modeling for Fe-C binary alloys with different composition in the castings with a different wall thickness are presented. As a result of calculations it was stated that after undercooling ductile iron below liquidus temperature volumetric changes proceed in three stages: pre-eutectic shrinkage (minimal in eutectic cast iron), eutectic expansion and the last shrinkage.

Using of the Averaged Voronoi Polyhedron for the Equiaxed Solidification Modeling

For the characterization of the equiaxed polycrystalline structure the Dirichlet tessellation is often used. The results of this space decomposition Voronoi polyhedrons are convex but not necessarily bounded. Size, volume and other characteristics of these bodies are the random variables. Parameters of the Averaged Voronoi Polyhedron are used in the presented paper for the modeling of the diffusion controlled peritectic transformation. Proposed model takes into account decreasing of the transformation interface surface in the remote regions of the diffusion field due to the probabilistic grains impingements. The results of the modeling are compared with the microstructure of the Pb-32 wt.% Bi alloy and thermal analysis results.

Cellular Automata Diffusion-Kinetic Model of Dendritic Growth

A mathematical crystallization model in the meso scale (the intermediate dimension scale between interatomic distance in solids and grain size in metals and alloys) is presented with the use of a kinetic-diffusion cellular automaton model. The proposed model differs from other models by including the diffusion of elements and heat conductivity effects on the physical phenomena at the solid-liquid interface. The model considers the non-equilibrium character of real processes of phase transformation, where the kinetic undercooling of the solid-liquid interface is a measure of this non-equilibrium level. The anisotropy of interface mobility is assumed. The growth of individual dendrites was simulated for different initial conditions and growth parameters. The modelling results are compared to the experimental data.