Modelling of crystallization process using the interval boundary element method

Ewa Majchrzak; Alicja Piasecka-Belkhayat

Ewa Majchrzak Silesian University of Technology,
Alicja Piasecka-Belkhayat Silesian University of Technology,

Abstract

The mathematical model of solidification process can be formulated using the macro or micro-macro approach. In this paper the second generation model (micro-macro one) is considered. The driving force of crystallization is the local and temporary undercooling below solidification point Tcr . The nucleation and nuclei growth are proportional to the second power of undercooling. Formulas determining the phenomena previously mentioned contain coefficients called the nucleation coefficient and nuclei growth one. These coefficients are assumed to be interval values. For above assumptions the problem has been solved bymeans of interval boundary element method. In the final part of the paper the results of computations are shown.

Keywords

interval boundary element method, interval arithmetic, crystallization,

References

[1] C.A. Brebbia, J.C.F. Telles, L.C. Wrobel. Boundary Element Techniques. Springer-Verlag, 1984.
[2] T. Burczyński, J. Skrzypczyk. The fuzzy boundary element method: A new solution concept. Proc. of XII Polish Conference on Computer Methods in Mechanics, Warsaw-Zegrze, Poland, May 9-13, 1995, pp. 65-66.
[3] E. Fraś. Crystallization of Metals and Alloys (in Polish). AKAPIT, Cracow, 2003.
[4] W. Kapturkiewicz. Modelling of Cast Iron Crystallization (in Polish). AKAPIT, Cracow, 2003.
[5] E. Majchrzak, A. Piasecka. The numerical micro/macro model of solidification process. Journal of Materials Processing Technology, 64: 267-276, 1997.