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International Journal for Multiscale Computational Engineering
Impact-faktor: 1.016 5-jähriger Impact-Faktor: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Druckformat: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v8.i3.30
pages 259-266

Generalized Micro/Macro Model of Crystallization and Its Numerical Realization

Bohdan Mochnacki
Czestochowa University of Technology, Dabrowskiego 69, 42-201 Czestochowa, Higher School of Labour Safety Management, Bankowa 8, 40-007 Katowice, Poland
Romuald Szopa
Czestochowa University of Technology, 42-200 Czestochowa, Dabrowskiego 73, Poland


In this paper considerations concerning the mathematical micro/macro model of pure metals solidification are presented. A generalized approach close to the Mehl-Johnson-Avrami-Kolmogoroff theory is applied. The differential equation leading to the well-known linear and exponential models of crystallization is generalized by the introduction of an additional parameter n. In this way the power-type model is obtained (the linear and exponential models correspond to n = 0 and n = 1). On a stage of numerical simulation the course of nucleation and nuclei growth are simulated using the procedure based on the registration of successive grain family growth. Obtained in this way, the local capacities of internal heat sources are taken into account on a stage of solution corresponding to macroscale. A macro heat transfer is described by the Fourier-type equation. Finally, examples of numerical simulations and the results concerning the influence of model parameters on a course of solidification are shown.