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Purpose: The typical mathematical descriptions of pure metal solidification (micro/macro approach) base on the linear or exponential (Kolmogoroff) models. In the paper the possibilities of such models modification are presented. This new model can be called a power type one. The approach proposed can be usefull on the stage of numerical simulation of solidification on the micro/macro scale. Design/methodology/approach: The local and temporary volumetric fraction of solid state is described by the equation from which both the linear and exponential model can be obtained. Introducing the additional parameter to this equation the new solidification model is found. Findings: The method here presented allows to determine the transient temperature field in a non-homogeneous system casting-mould and to observe the course of metal solidification. The obtained cooling curves allow to observe (contrary to macro models) the recalescence effect. Practical implications: The solidification model in a version presented in this paper can be an effective tool for numerical simulation of solidification process. Originality/value: The concept of introduction of power-type function for the mathematical description of micro/macro solidification model is original and gives the new possibilities numerical methods application in a thermal theory of foundry processes.
Wydawca
Rocznik
Tom
Strony
65--68
Opis fizyczny
Bibliogr. 15 poz., rys.
Twórcy
autor
autor
- Institute of Mathematics and Computer Science, Czestochowa University of Technology, ul. Dąbrowskiego 73, 42-200, Czestochowa, Poland, moch@imi.pcz.pl
Bibliografia
- [1] В. Mochnacki, J.S. Suchy, Numerical Methods in Computations of Foundry Processes, PFTA, Cracow, 1995.
- [2] R. Szopa, Macro and macro/micro models of solidification Numerical aspects of process simulation, Materials Science Forum 539-543 (2007) 2564-2569.
- [3] R. Szopa, Modelling of Solidification and Crystallization using the Combined Variant of the BEM, Publication of the Silesian University of Technology, Metallurgy, 54, Gliwice, 1999 (in Polish).
- [4] E. Majchrzak, M. Jasinski, G. Kaluza, Application of shape sensitivity analysis in numerical modelling of solidification process, Archives of Foundry 5/15 (2005) 259-264.
- [5] S. Chang, D.M. Stefanescu, D. Shangguan, Modelling of the liquid/solid and eutectoid transformation in spherical graphite cast iron, Metallurgical Transactions A/23 A (1992) 1333-1346.
- [6] E. Majchrzak, J.S. Suchy, R. Szopa, Linear model of crystallization: - identification of nuclei density, Giessereiforschung, International Foundry Research 2 (2006) 29-32.
- [7] B. Mochnacki, E. Pawlak, Micro/macro models of crystallization process. Comparison of the results of numerical simulations, Proceedings of Numerical Methods in Continuum Mechanics, Zilina, Slovak Republic (2005) 1-7.
- [8] E. Majchrzak, A. Piasecka, The numerical micro/macro model of solidification process, Journal of Materials Processing Technology 64 (1997) 267-276.
- [9] E. Majchrzak, M. Dziewonski, A. Metelski, Estimation of nuclei density in solidifying casting using the Kolmogorff model, Archives of Foundry 5/15 (2005) 253-258.
- [10] T.A. Walasek, Experimental verification of Monte Carlo recrystallization model, Journal of Materials Processing Technology 157-158 (2004) 262-267.
- [11] I. Sinha, R.K. Kandal, Two dimensional analysis of Kolmogorov-Johnson-Mehl-Avrani isothermal kinetics, Proceedings of the „International Conference on Computational & Experimental Engineering and Sciences” ICCES'07, Miami, 2007, 1-6.
- [12] E. Fras, W. Kapturkiewicz, H.F. Lopez, Macro and micro modelling of the solidification kinetics of casting, AFS Transactions 92-48 (1993) 583-591.
- [13] W. Kapturkiewicz, Modelling of Cast Iron Crystallization, AKAPIT, Cracow, 2003 (in Polish).
- [14] B. Mochnacki, E. Majchrzak, R. Szopa, J.S. Suchy, Inverse problems in the thermal theory of foundry processes, Scientific Research of the Institute of Mathematics and Computer Science of Technical University of Częstochowa, 1 (5), Częstochowa, 2006, 154-169.
- [15] С. Cho, W. Kim, В. Choi, S. Kwak, W. Pan, A management on mesh modelling for finite element analysis in casting simulation, Journal of Achievements in Materials and Manufacturing Engineering 20 (2007) 335-338.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BOS3-0017-0019