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Presented paper is focused on volumetric hardening process using liquid low melting point metal as a coolant. Effect of convective motion of the coolant on material structure after hardening is investigated. Comparison with results obtained for model neglecting motion of liquid is executed. Mathematical and numerical model based on Finite Element Metod is described. Characteristic Based Split (CBS) method is used to uncouple velocities and pressure and finally to solve Navier-Stokes equation. Petrov-Galerkin formulation is employed to stabilize convective term in heat transport equation. Phase transformations model is created on the basis of Johnson-Mehl and Avrami laws. Continuous cooling diagram (CTPc) for C45 steel is exploited in presented model of phase transformations. Temporary temperatures, phases participation, thermal and structural strains in hardening element and coolant velocities are shown and discussed.
Czasopismo
Rocznik
Tom
Strony
39--44
Opis fizyczny
Bibliogr. 15 poz., rys., tab., wykr.
Twórcy
autor
- Technical University of Częstochowa, Institute of Mechanics and Machine Design, st. Dąbrowskiego 73, 42-200 Częstochowa, Poland
autor
- Technical University of Częstochowa, Institute of Mechanics and Machine Design, st. Dąbrowskiego 73, 42-200 Częstochowa, Poland
autor
- University of Częstochowa, Institute of Mathematics and Computer Science, st. Dąbrowskiego 73, 42-200 Częstochowa, Poland
Bibliografia
- [1] E. Węgrzyn-Skrzypczak, Modelling of solidification with motion of the fluid in liquid and mushy zone, PhD Thesis, Częstochowa 2005 (in Polish).
- [2] J. Orlich, A. Rose, P. Wiest, Atlas zur Wärmebehandlung von Stähle, III Zeit Temperatur Austenitisierung Schaubilder, Verlag Stahleisen MBH, vol 1 (1973).
- [3] M. J. Avrami, Chem. Phys. 7, 1939.
- [4] A. Bokota, A. Kulawik, Model and numerical analysis of hardening process phenomena for medium-carbon steel, Archives of Metallurgy and Materials, vol. 52 (2007) 337-346.
- [5] A. Kulawik, Numerical analysis of thermal and mechanical phenomena during hardening process of the 45 steel, PhD Thesis, Częstochowa 2005 (in Polish).
- [6] D. P. Koistinen, R. E. Marburger, A general equation prrescribing the extent of the autenite-martensite transformation in pure iron-carbon alloys and plain carbon steels, Acta Mettalica, vol 7 (1959) 59-60
- [7] K. J. Bathe, Finite element procedures in engineering analysis, Prentice-Hall, 1982.
- [8] P. Bochev, Finite element methods based on least squares and modified variational principles. COM2MAC Lecture Notes, Postech, Pohang, South Korea, 2001.
- [9] T. J. R. Hughes, Recent progress in the development and understanding of SUPG methods with special reference to the compressible Euler and Navier-Stokes equations, International Journal for Numerical Methods in Fluids , vol. 7 (1987) 1261-1275.
- [10] Z. Svoboda, The analysis the convective-conductive heat transfer in the building constructions, In: Proceedings of the 6th Building Simulation Conference, Kyoto (1999) 1: 329-335.
- [11] A. Bokota, A. Kulawik, Three dimensional model of thermal phenomena determined by moving heat source, Archives of Foundry vol. 2, No. 4 (2002) 74–79 (in Polish).
- [12] A. J. Chorin, Numerical solution of the Navier-Stokes equation, Math. Comput. (1968) 23:745-762.
- [13] O. C. Zienkiewicz, R. Codina, A general algorithm for compressible and incompressible flow, Part I. The split characteristic based scheme, International Journal for Numerical Metods in Fluids (1995) 20:869-885.
- [14] O. C. Zienkiewicz, R.L. Taylor, The finite element method, Volume 3: Fluid dynamics, Butterworth and Hienemann, 2000.
- [15] J. Chessa, T. Belytschko, An extended finite element method for two-phase fluids, Journal of Applied Mechanics, vol. 70 (2003) 10-17.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d249317d-828d-484d-8d61-1839a1efda37