Numerical determination of equiaxed grain radii arising in the casting during 3D simulation of solidification
Robert Dyja, Elżbieta Gawrońska, Andrzej Grosser, Piotr Jeruszka, Norbert Sczygiol
The Faculty of Mechanical Engineering and Computer Science, 42-201 Czestochowa, Dabrowskiego 69, Poland.
DOI:
https://doi.org/10.7494/cmms.2016.1.0567
Abstract:
The knowledge of material structure allows to predict the mechanical properties of alloy casting. Such structure can be modelled in micro- and mesoscale. The first way is connected with alloy morphology and enables one to find out the shape of grains emerging during the solidification process. The second way allows to define the magnitude and distribution of these grains in the casting structure. Learning both of these ways greatly enhances one’s knowledge about such mechanical phenomena as emerging stresses, strains, hot cracking and many others. This information makes it possible for one to predict the behaviour of castings during the cooling process or the further product exploitation. The one of the most difficult issues in the numerical and computer simulations of solidification is the modelling of the structure evolving in the casting. These simulations are extremely important in the work of an engineer in the foundry industry. The paper deals with a numerical modelling of equiaxed microstructure formation during the solidification of two-component alloys. The basic enthalpy formulation was applied to model the solidification. The equiaxed grain size depends on the average cooling velocity at the moment when the liquid metal reaches the liquidus temperature. The experimentally determined dependence between grain radius and cooling velocity was used in the calculation of average grain radii distribution.
Cite as:
Dyja, R., Gawrońska, E., Grosser, A., Jeruszka, P., Sczygiol, N. (2016). Numerical determination of equiaxed grain radii arising in the casting during 3D simulation of solidification. Computer Methods in Materials Science, 16(1), 27 – 36. https://doi.org/10.7494/cmms.2016.1.0567
Article (PDF):
Keywords:
Grain radius, Microstructure, Casting, FEM, Solidification modelling, Computer simulation
References:
Balay, S., Abhyankar S., Adams M., Brown J., Brune P.,Buschelman K., Dalcin L., Eijkhout V., Gropp W.,Karpeyev D., Kaushik D., Knepley M., Curfman McInnesL., Rupp K., Smith B., Zampini B., Zhang H., 2014,PETSc Users Manual, Argonne National Laboratory.
Date, A. W., 1994, A novel enthalpy formulation for multidimensionalsolidification and melting of a pure substance,Sadhana-Academy Proceedings in Engineering Sciences,19, 833–850.
Duan, Q., Tan, F. L., Leong, K. C., 2002, A numerical study ofsolidification of n-hexadecane based on the enthalpyformulation, Journal of Materials Processing Technology,120, 1-3, 249-258.
Dyja, R., Gawroska, E., Grosser, A., Jeruszka, P., Sczygiol, N.,2015a,Comparison of different heat capacity approximationin solidification modeling, in Lecture Notes in Engineeringand Computer Science, World Congress onEngineering and Computer Science, WCECS 2015, 21-23 October, San Francisco, USA, 2, 875-879.
Dyja, R., Gawronska, E., Sczygiol, N., 2015b, The Effect ofmechanical interactions between the casting and themold on the conditions of heat dissipation: a numericalmodel, Archives of Metallurgy and Materials, 609 (3),1901-1909.
Dyja, R., Sczygiol, N., Domanski, Z., 2014, The effect of cavityformation on the casting heat dissipation rate, IAENGTransactions on Engineering Sciences, 341-347.
Famouri, M., Jannatabadi, M., Ardakani, H. T. F., 2013, Simultaneousestimations of temperature dependent thermalconductivity and heat capacity using a time efficientnovel strategy based on mega-nn, Applied Soft Computing,13(1), 201-210.
Ganguly, S., Chakraborty, S., 2006, A generalized formulationof latent heat functions in enthalpy based mathematicalmodels for multicomponent alloy solidification systems,Metallurgical and Materials Transactions B – ProcessMetallurgy and Materials Processing Science, 37(1),143-145.
Gawronska, E., Sczygiol, N., 2010, Application of mixed timepartitioning methods to raise the efficiency of solidificationmodeling, 12th International Symposium on Symbolicand Numeric Algorithms For Scientific Computing(SYNASC), 99-103.
Gawronska, E., Sczygiol, N., 2015, Numerically Stable ComputerSimulation of Solidification: Association BetweenEigenvalues of Amplification Matrix and Size of TimeStep, in Transactions on Engineering Technologies,Springer Netherlands, 17-30.
Gawronska, E., Sczygiol, N., Dubow, E., 2016, Numericalmodeling of equiaxed structure forming in the cast duringalloy solidification, 20th International Slovak-PolishConference on Machine Modeling and Simulations(MMS),Terchova, Slovakia, Procedia Engineering, 136,101-107.
Gawronska, E., Wodo, O., 2012, Modeling of two-stage solidification:Part I Model development, Archives of FoundryEngineering, 12(4), 151-156.
Gawronska, E., Wodo, O., 2013, Modeling of two-stage solidification:Part II Computational verification of the model,Archives of Foundry Engineering, 13(1), 125-130.
Ghoneim, A., Ojo, O. A., 2011, Numerical modeling and simulationof a diffusion-controlled liquid solid phase changein polycrystalline solids, Computational Materials Science,50(3), 1102-1113.
Jamaly, N., Haghdadi, N., Phillion, A. B., 2015, Microstructure,macrosegregation, and thermal analysis of direct chillcast aa5182 aluminum alloy, Journal of Materials Engineeringand Performance, 24(5), 2067-2073.
Kim, J. W., Sandberg, R. D., 2012, Efficient parallel computingwith a compact finite difference scheme, Computers &Fluids, 58, 70-87.
Kodali, H. K., Ganapathysubramanian, B., 2012, A computationalframework to investigate charge transport in heterogeneousorganic photovoltaic devices, ComputerMethods in Applied Mechanics and Engineering, 247,113-129.
Michalski, G., Sczygiol, N., 2015, Using Modern Multi-/ManycoreArchitecture for the Engineering Simulations,Transactions on Engineering Technologies, SpringerNetherlands, 55-67.
MPI: A Message Passing Interface, available online at:http://www.mpi-forum.org, accessed: 15.03.2016.
Sczygiol, N., 2000, Modelowanie numeryczne zjawisk termomechanicznychw krzepnącym odlewie i formie odlewniczej,Monografie 71, Politechnika Częstochowska (inPolish).
Sczygiol, N., Szwarc, G., 2001, Application of enthalpy formulationfor numerical simulation of castings solidification,Computer Assisted Mechanics and Engineering Sciences,8, 99-120.
Stefanescu, D. M., 2001, Science and Engineering of CastingSolidification, Kluwer Academic, New York.
Stefanescu, F., Neagu, G., Mihai, A., Stan, I., Nicoara, M.,Raduta, A., Opris, C., 2012, Controlled temperature distributionand heat transfer process in the unidirectionalsolidification of aluminium alloys, Advanced Materialsand Structures, 188, 314-317.
Wodo, O., Ganapathysubramanian B., 2011, Computationallyefficient solution to the Cahn–Hilliard equation: Adaptiveimplicit time schemes, mesh sensitivity analysis andthe 3D isoperimetric problem, Journal of ComputationalPhysics, 230, 6037-6060.
Wołczyński, W., 2015, Back-diffusion in crystal growth. Eutectics.Archives of Metallurgy and Materials, 60(3), 2403-2407.
Wood, L. W., 1990, Practical Time-stepping Schemes. Oxford:Clarendon Press.Wyrzykowski, R., Szustak, L., Rojek, K., 2014, Parallelizationof 2d mpdata eulag algorithm on hybrid architectureswith gpu accelerators, Parallel Computing, 40(8), 425-447.
Yang, N., Li, D. W., Zhang, J., Xi, Y. G., 2012, Model predictivecontroller design and implementation on FPGA withapplication to motor servo system, Control EngineeringPractice, 20(11), 1229-1235.
Zienkiewicz, O.C., Taylor, R. L., 2000, The Finite ElementMethod, Fifth Edition, Butterworth – Heinemann, Oxford.