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1
Content available Cellular automaton modeling of ductile iron density changes at the solidification time
Burbelko A. A., Gurgul D., Królikowski M., Wróbel M.
Archives of Foundry Engineering
|
2013
|
Vol. 13, iss. 4
9--14
EN
Formation of the shrinkage defects in ductile iron castings is far more complicated phenomenon than in other casting alloys. In the paper one of the aspects of formation of porosity in this alloy was considered – changes in cast iron's density during crystallization caused by varying temperature, phase fractions and phase's composition. Computer model, using cellular automata method, for determination of changes in density of ductile iron during crystallization was applied. Simulation of solidification was conducted for 5 Fe-C binarie alloys with ES from 0.9 to 1.1 for the estimation of the eutectic saturation influence on the ductile iron shrinkage and expansion. As a result of calculations it was stated that after undercooling ductile iron below liquidus temperature volumetric changes proceed in three stages: preeutectic shrinkage (minimal in eutectic cast iron), eutectic expansion (maximum value equals to about 1.5% for ES = 1.05) and last shrinkage (about 0.4% in all alloys regardless of ES).
2
Content available Application of averaged Voronoi polyhedron in the modelling of crystallisation of eutectic nodular graphite cast iron
Burbelko A. A., Początek J., Królikowski M.
Archives of Foundry Engineering
|
2013
|
Vol. 13, iss. 1
134--140
EN
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.
3
Content available Analiza rozkładu węgla w ziarnie eutektycznym żeliwa sferoidalnego metodą uśrednionego wielościanu Voronoia
Burbelko A. A., Początek J.
Archives of Foundry Engineering
|
2013
|
Vol. 13, iss. 2 spec.
29--34
PL
W pracy został przedstawiony model matematyczny krystalizacji żeliwa z grafitem kulkowym. W modelu uwzględniona została dyfuzja w skali mikro w kierunku promieniowym w obszarze elementarnego pola mikrodyfuzji (EPMD) odpowiadającego jednej komórce eutektycznej. Zaproponowano wykorzystanie EPMD o kształcie uśrednionego wielościanu Voronoia (UWV). Dla wyznaczenia geometrii EPMD zastosowano statystyczną teorię krystalizacji Kolmogorova. Przedstawiono zasady różnicowego sformułowania matematycznego omawianego zagadnienia. Zastosowanie geometrii wielościanu Voronoia pozwala uwzględnić zmniejszenie udziału objętościowego obszarów peryferyjnych ziaren równoosiowych na skutek losowych kontaktów pomiędzy sąsiednimi ziarnami. W modelowaniu uwzględniono wpływ dyfuzji pierwiastka stopowego w cieczy na końcowy rozkład jego stężenia w ziarnie eutektycznym. W wyniku symulacji wyznaczono rozkład składnika stopowego w różnych momentach czasu zarówno dla fazy pierwotnej jak i dla fazy ciekłej, co pozwoliło na otrzymanie danych dotyczących mikrosegregacji węgla w przekroju warstwy austenitu.
EN
The study presents the mathematical model of the carbon diffusion field in the growing eutectic grain during the ductile iron solidification. In the proposed model heat flow is analyzed at the macro level, while micro level is used for modeling of the diffusion field. The use of an averaged Voronoi polyhedron (AVP) geometry was proposed as a shape of the elementary diffusion field domain. To determine the geometry of the AVP, Kolmogorov’s statistical theory of the solidification was applied. The principles of a differential mathematical formulation of this problem were discussed. Application of the AVP geometry allows taking into account the reduced volume fraction of the peripheral areas of the equiaxial grains by random contacts between the adjacent grains. The model also takes into consideration an influence of a segregation of the solute in the liquid phase on the final distribution of this element in the eutectic grain. The distribution of the solute at different time instance in the liquid phase and eutectic austenite was calculated. It allows as to obtain data on the carbon distribution in the eutectic cell at the end of the solidification process. The cooling curve was determined as well.
4
Content available Parameters of the two-phase sand-air stream in the blowing process
Dańko J., Dańko R., Burbelko A. A., Skrzyński M.
Archives of Foundry Engineering
|
2012
|
Vol. 12, iss. 4
25-30
EN
Theoretical problems concerning the determination of work parameters of the two-phase sand-air stream in the cores making process by blowing methods as well as experimental methods of determination of the main and auxiliary parameters of this process decisive on the cores quality assessed by the value and distribution of their apparent density are presented in the paper. In addition the results of visualisations of the core-box filling with the sand-air stream, from the blowing chamber, obtained by the process filming by means of the quick-action camera are presented in the paper and compared with the results of simulation calculations with the application of the ProCast software.
5
Content available Modelling of eutectic saturation influence on microstructure in thin wall ductile iron casting using cellular automata
Burbelko A. A., Gurgul D., Kapturkiewicz W., Górny M.
Archives of Foundry Engineering
|
2012
|
Vol. 12, iss. 4
11-16
EN
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. Calculation of eutectic saturation influence (Sc = 0.9 - 1.1) on microstructure (austenite and graphite fraction, density of austenite and graphite grains) and temperature curves in 2 mm wall ductile iron casting has been done.
6
Content available remote Cellular automaton modeling of ductile iron microstructure in the thin wall
Burbelko A. A., Gurgul D., Kapturkiewicz W., Początek J., Wróbel M.
Archives of Foundry Engineering
|
2011
|
Vol. 11, iss. 4
13-18
EN
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 solidification of the ductile iron with different carbon equivalent 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. Solidification of the DI with different carbon equivalents was analyzed. Obtained results were compared with the solidification path calculated by CALPHAD method.
7
Content available remote Computer modelling of ductile iron solidification using FDM and CA methods
Kapturkiewicz W., Burbelko A. A., Fraś E., Górny M., Gurgul D.
Journal of Achievements in Materials and Manufacturing Engineering
|
2010
|
Vol. 43, nr 1
310--323
EN
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.
8
Content available remote Transformation kinetic for instantaneous nucleation in the finite volume - application of statistical theory of shielding
Burbelko A. A.
Archives of Metallurgy and Materials
|
2009
|
Vol. 54, iss. 2
358-367
EN
The framework of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory is applied usually for the study of transition kinetics when the processes are ruled by nucleation and growth. This theory accurately describes only the transitions with the identical convex shape of new nuclei with the identical growth velocity distribution at an interface of the growing grains. The infinite initial volume of the mother phase is one of the indispensable conditions for the above theory. The proposed earlier extension of KJMA theory (statistical theory of the shielding growth) enlarges the scope of its application and eliminates the above limitation. The model of the transformation kinetics in the space of finite volume has been analyzed and discussed.
PL
W badaniach kinetyki procesów kontrolowanych zarodkowaniem i wzrostem skutecznie wykorzystuje się statystyczną teorię krystalizacji, podwaliny której zostały założone przez Kołmogorova, Jonhsona, Mehla i Avramiego (teoria KJMA). Powyższa teoria opisuje badane zjawiska precyzyjnie w przypadku, gdy wszystkie nowopowstające obiekty mają identyczny rozkład prędkości wzrostu na powierzchni (podobny kształt geometryczny), są wypukłe, a w przypadku anizotropii kształtu są identycznie zorientowane w przestrzeni. Jednym z założeń powyższej teorii jest nieskonczona objetość zanikającego materiału. Zaproponowane wczesniej rozszerzenie teorii KJMA (statystyczna teoria ekranowanego wzrostu) zwiększa zakres zastosowania klasycznych równań, pokonując niektóre ograniczenia. W artykule przedstawiono badania kinetyki wzrostu ziaren nowej fazy w przypadku małej objętosci fazy macierzystej.
9
Content available remote Modeling the kinetics of solidification of cast iron with lamellar graphite
Kapturkiewicz W., Fraś E., Burbelko A. A.
Archives of Metallurgy and Materials
|
2009
|
Vol. 54, iss. 2
369-380
EN
The most important results of own studies on modeling the solidification kinetics in lamellar (flake) graphite cast iron were reviewed. A set of basic equations used for modeling the solidification process in macro- and micro-scales was given. A numerical solution of these model equations enables the determination of thermodynamic equilibrium temperature and actual temperature of cast iron solidification, the cooling rate, the heat flux generated during solidification, the fractions of the solidified structural constituents, the size of graphite eutectic grains and austenite dendrites, thickness of graphite lamellar, as well as the segregation of cast iron alloying constituents in liquid phase and in the forming grains. It has also been proved and confirmed by experiments that the grains of graphite eutectic are formed in a two-step process, that is, at the beginning and end of the solidification process. Some important differences in the size of graphite precipitates were observed to exist between the cast plate and cylinder.
PL
Zaprezentowano najistotniejsze rezultaty własnych prac, dotyczących modelowania komputerowego krystalizacji żeliwa z grafitem płatkowym. Przedstawiono zestaw podstawowych równań procesu, odnoszących się do mikro i makro skali. Rozwiązanie numeryczne zestawu równań w postaci programu symulacyjnego pozwoliło na wyznaczenie przebiegu temperatury w czasie stygnięcia odlewu wraz z rozkładem temperatury równowagowej, ciepła generowanego podczas krystalizacji, ilości frakcji zakrzepłej poszczególnych składników strukturalnych żeliwa, wymiaru ziaren austenitu i eutektyki grafitowej, wymiary płatków grafitu jak również mikrosegregacji składników stopu w ziarnach. Potwierdzono eksperymentalnie, że ziarna eutektyki grafitowej mogą zarodkować w dwóch etapach: na początku i pod koniec procesu krystalizacji. Istotne różnice zauważono w wymiarach grafitu w zależnosci od kształtu odlewu.
10
Content available remote Modeling of the dendrite arms behavior during solidification
Burbelko A. A., Kapturkiewicz W., Gurgul D., Stręk P.
Archives of Foundry Engineering
|
2009
|
Vol. 9, iss. 4
13-16
EN
Modelling was carried out to investigate the internal dendrite grains structure formation from a liquid two-component solution. For the simulation, our own model and computer program based on CAFD (Cellular Automata - Finite Differences) were used. In modelling, the effect of process conditions and material-related parameters on the nature of the dendritic grain growth was examined. It was demonstrated that increase of the secondary dendrite arm space may by a result of interruption of the arms growth as well as of overgrowing of concave regions. A local melting down of the grains of a solid phase due to the segregation of admixtures reducing the alloy point of liquidus is also possible.
11
Content available remote Kinetic model of ductile iron solidification with experimental verification
Kapturkiewicz W., Burbelko A. A., Górny M.
Archives of Foundry Engineering
|
2009
|
Vol. 9, iss. 4
95-102
EN
A solidification model for ductile iron, including Weibull formula for nodule count has been presented. From this model, the following can be determined: cooling curves, kinetics of austenite and eutectic nucleation, austenite and eutectic growth velocity, volume fraction, distribution of Si and P both in austenite and eutectic grain with distribution in casting section. In the developed model of nodular graphite iron casting solidification, the correctness of the mathematical model has been experimentally verified in the range of the 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.
12
Content available remote A full diffusion model of the graphite eutectic grain growth in liquid cast iron under non-equilibrium conditions
Kapturkiewicz W., Burbelko A. A., Górny M.
Archives of Foundry Engineering
|
2009
|
Vol. 9, iss. 1
107-112
EN
An extension of the full diffusion 1-D model developed by Tanzili & Heckel has been presented which now allows for both temperature variations (responsible for an equilibrium interface concentration of constituents) as well as variations in the density of phases participating in the process of solidification. Under boundary conditions, the well-known possibility of the formation of a diffusive layer has been taken into consideration, but - compared to previous solutions that assumed a steady flow of constituent through this layer - a variability of this process has been allowed for now. In this situation, the extended model is approaching the state when it finally becomes possible to solve some problems of the casting solidification under real conditions. The developed model enabled obtaining a control balance of the alloying constituent content (carbon) with an error below 1%. The attempts to neglect the elements newly introduced to the model (different phase densities, different interface concentrations) resulted in an error of several dozen percent and more.
13
Content available remote Screening effect during the growth of spheroidal grains vs deviations from Kolmogorov-Johnson-Mehl-Avrami equation
Burbelko A. A.
Archives of Foundry Engineering
|
2008
|
Vol. 8, iss. 1 spec.
35--40
EN
To forecast the kinetics of phase transformations which consist in nucleation and growth of the grains of a new phase, the well-known Kolmogorov-Johson-Mehl-Avrami (KJMA) equation has been used. It is generallly known that in the case of parallel grain growth in different phases proceeding at different velocities. the results of the calculations are burdened with an error. In this study. applying the assumptions of a statistical theory of the screened grain growth. an attempt has been made to estimate this error for the case of growth of the spheroidal grains of two types. The obtained results indicate that the value of an error in typical equations increases with increasing difference in the growth velocity of the particles of bath types.
PL
Dla prognozowania kinetyki przemian fazowych polegających na zarodkowaniu i wzroście ziaren nowej fazy używa się znane równanie Kolmogorova-Johsona-Mehla-Avramiego. Wiadomo, że w przypadku równoległego wzrostu ziaren różnych faz z różną prędkością wyniki obliczeń obarczone są błędem. W niniejszej pracy z wykorzystaniem założeń statystycznej teorii wzrostu ekranowanego podjęto próbę oszacowania tego błędu dla przypadku wzrostu ziaren kulistych dwu typów. Otrzymane wyniki wskazują, że wielkość błędu klasycznego równania wzrasta ze zwiększeniem różnicy prędkości wzrostu cząstek obu typów.
14
Content available remote Modelling the concentration and dimensional changes in the structural constituents of vermicular graphite cast iron on cooling within the range of solidus-eutectoid temperature
Kapturkiewicz W., Burbelko A. A., Fraś E.
Archives of Foundry Engineering
|
2008
|
Vol. 8, iss. 1 spec.
179--182
EN
A mathematical model and a simulation program have been developed to trace changes in the structure of Fe-C alloy on cooling from the solidus temperature to the temperature of eutectoid transformation. A simplified schematic representation of the process can be referred to the cast iron with vermicular graphite. The numerical experiments using the newly developed program have proved a significant effect of the cooling conditions and structure refinement degree (the dimensions of austenite) on the concentration field in austenite and, consequently, on the dimensional changes of graphite within the examined cooling range. The developed methods of modelling the process of transformation enable including the procedure into a complex software operating in a system reproducing in real manner the casting configuration, while the obtained results indicate an important effect of thermophysical parameters and heat transfer process on final alloy structure.
15
Content available remote Mathematical and numerical model of directional solidification including initial and terminal transients of the process
Kapturkiewicz W., Burbelko A. A., Fraś E.
Archives of Foundry Engineering
|
2008
|
Vol. 8, iss. 4
65-70
EN
The, developed in this study, simple model and numerical solution of diffusion growth of the solid phase under the conditions of directional solidification allow for the effect of constituent diffusion in both liquid and solid phase and assume the process run in which (like in reality) the preset parameter is the velocity of sample (pulling velocity) at a preset temperature gradient. The solid/liquid interface velocity is not the process parameter (like it is in numerous other solutions proposed so far) but a function of this process. The effect of convection outside the diffusion layer has been included in mass balance under the assumption that in the zone of convection the mixing is complete. The above assumptions enabled solving the kinetics of growth of the solid phase (along with the diffusion field in solid and liquid phase) under the conditions of diffusion well reflecting the process run starting with the initial transient state, going through the steady state period in central part of the casting, and ending in a terminal transient state. In the numerical solution obtained by the finite difference method with variable grid dimensions, the error of the mass control balance over the whole process range was 1- 2%.
16
Content available remote Concurrent growth of two phases in 2D space
Burbelko A. A., Kapturkiewicz W., Fraś E.
Archives of Foundry Engineering
|
2008
|
Vol. 8, iss. 4
23-26
EN
The kinetics of phase transformations has been studied within the framework of the Kolmogorov- Johnson-Mehl-Avrami (KJMA) theory. This theory accurately describes only the parallel growth of anisotropic products with identical convex shape. The identical growth velocity distribution at an interface is the indispensable condition for the above restriction. The proposed earlier extension of KJMA theory (statistical theory of the screened growth) enlarges the scope of its application and eliminates the above limitation. The results of the application of this extension were compared with the results obtained during modelling of the concurrent growth of the two types of circular particles on a plane, where the said particles were characterised by different growth rates and modelling was carried out by the method of cellular automata (CA).
17
Content available remote Computation of interface curvature in modelling of solidification by the method of cellular automaton
Burbelko A. A., Kapturkiewicz W., Gurgul D.
Archives of Foundry Engineering
|
2007
|
Vol. 7, iss. 1
41-46
EN
Modelling of solidification process by the method of cellular automaton (CA) requires determination of geometrical characteristics of the interface, i.e. of its direction and curvature. In previous studies the authors proposed a method to reduce the well-known effect of an artificial symmetry of the simulation results caused by the anisotropy of the CA computation grid (e.g. a preferred growth of the main dendrite arms along the grid lines or at an angle of 45° in the case of grids with square cells). The aim was achieved by application of the developed methods of computation of the transformation rate and front direction. In this study the authors examined the problem of an accuracy of the computations of an interface curvature. The obtained results show us that the error of the curvature computation introduced by some well-known methods exceeds by 100% a nominal value of this parameter. A method to estimate the accuracy of the applied solution has been proposed. Practical application of the proposed tests enables selection of a best solution, including the authors' own solutions, thus considerably improving an accuracy of the solidification modelling by the method of CA.
18
Content available remote Modelowanie odlewania ciągłego wlewków ze stopu AL
Kapturkiewicz W., Burbelko A. A., Dąbek P.
Archiwum Odlewnictwa
|
2006
|
R. 6, nr 18/1
137--142
PL
Na przykładzie oprogramowania komputerowego Calcosoft przedstawiono możliwości wykorzystania modeli matematycznych i systemów komputerowych do wirtualizacji procesów zachodzących podczas krystalizacji pionowego okrągłego wlewka ciągłego ze stopu Al. Wyniki modelowania zweryfikowano doświadczalnie.
EN
The possibility of mathematical models and using of the special computer software for virtualization of solidification of continuous Aluminum rod-shaped vertical casting has been presented on the example of Calcosoft program. The results of modeling were validated by the experimental results.
19
Content available remote Kalorymetria skaningowa przemian austenitu w ferrytycznym żeliwie sferoidalnym
Kapturkiewicz W., Czeppe T., Burbelko A. A.
Archiwum Odlewnictwa
|
2006
|
R. 6, nr 22
260-265
PL
Przeprowadzono próby wykorzystania kalorymetrii skaningowej (aparat SDT Q600 firmy Thermal Analysis) do oceny kinetyki przemian fazowych w żeliwie sferoidalnym w zakresie temperatury 600 - 1000°C. Celem było oszacowanie wpływu szybkości nagrzewania na położenie pików przemian fazowych dla żeliwa sferoidalnego o osnowie ferrytycznej, wyznaczenie entalpii przemian fazowych (ferryt - austenit, austenit - ferryt), porównanie kinetyki przemian fazowych podczas nagrzewania i studzenia próbki. Wyniki wskazują na istotny wpływ szybkości nagrzewania tworzywa na położenie punktów przemiany, jej kinetykę, a także na wartość ciepła przemiany.
EN
Ability of Differential Scanning Calorimetry (Q600 device of TA Instruments) was checked for the study of the phase transformation kinetics in the ductile cast iron in the temperature interval 600 - 1000°C. The main aims of this study are the estimation of heating rate influence on the temperature profile of transformation in the ferritic ductile cast iron, the estimation of the austenitisation and austenite decomposition enthalpy, comparison of the phase transformation rate during the heating and cooling processes. It was shown that the heating rate has an essential influence on the transformation rate, on the temperature of the transformation end and enthalpy of the transformation.
20
Content available remote Modelowanie odlewania półciągłego i ciągłego z wykorzystaniem oprogramowania własnego i profesjonalnego
Kapturkiewicz W., Burbelko A. A.
Archiwum Odlewnictwa
|
2001
|
R. 1, nr 2
185--192
PL
Rezultaty modelowania krystalizacji wlewka półciągłego Al, uzyskane z pomocą profesjonalnego programu Calcosoft zgodne są z wynikami uzyskanymi wcześniej w oparciu o potwierdzone eksperymentem własne oprogramowanie. Stwierdzono, że profesjonalny program charakteryzuje się dobrym dopracowaniem komunikacji pomiędzy programem i użytkownikiem, umożliwia automatyczne przygotowanie siatki obliczeniowej o zróżnicowanych parametrach, daje duże możliwości efektywnego opracowania wyników, a także uwzględnia przepływy cieczy spowodowane konwekcją wymuszoną i naturalną. Z tego też powodu do dalszych rozwiązań wykorzystano możliwości tego programu. Z przeprowadzonych cykli modelowania wynika, że ustawienie wlewów istotnie wpływa na kinetykę ruchu ciekłego metalu we wlewku. Głębokość jeziorka w przypadku ciągłego odlewania stali (COS) jest wielokrotnie większa niż dla wlewków Al wykonywanych technologią odlewania półciągłego.
EN
The results of modeling of solidification of Al semicontinuous casting, which have been were obtained by the professional program Calcosoft, agree with the results of the earlier results obtained from own program, confirmed by experiments. There have been affirmed that the professional program characterize very good communication between user and program, gives good possibility for elaboration of results, takes into consideration fluid flow by natural and forced convection. Because of that for further solutions this program has been used. From the results of modeling follows that the set-up of runners has a significant influence on the kinetics of fluid flow in solidified slab. The deep of liquid in case of continuous casting of steel is repeatedly higher than for Al semicontinuous casting.
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