Simulation of Dendritic Growth in Multicomponent Aluminium Alloys by Point Automata Method

Abstract:

A numerical model is developed to describe the dendritic growth of multicomponent aluminium alloys, based on a coupled deterministic continuum mechanics heat and species transfer model and a stochastic localized growth model that takes into account the undercooling temperature, curvature, kinetic, and thermodynamic anisotropy. The stochastic model receives temperature and concentration information from the deterministic model and the deterministic heat and species diffusion equations receive the solid fraction information from the stochastic model. The heat and species transfer models are solved on a regular grid by the standard explicit Finite Difference Method (FDM). The dendritic growth model of multicomponent alloy [1,2] is solved by a novel Point Automata (PA) approach [3,4] where the regular cells of the Cellular Automata (CA) method are replaced by the randomly distributed points and neighborhood configuration, similar as appears in meshless methods. The PA method was developed in order to circumvent the mesh anisotropy problem, associated with the classical CA method. The present paper extends our previous developments of Pa method to multicomponent alloys. A comparison of the results, obtained by the PA and CA method is shown for Al-5.3% Zn-2.35% Mg-1.35% Cu-0.5% alloy.

• Periodical: Materials Science Forum (Volumes 790-791)
• Pages: 115-120
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.790-791.115
• Online since: May 2014
• Authors: Agnieszka Zuzanna Guštin, Božidar Šarler*
• Keywords: Aluminium Alloy, Dendritic Growth, Microstructure, Point Automata Method

References

[1] M. Rappaz, W.J. Boettinger, On dendritic solidification of multicomponent alloys with unequal liquid diffusion coefficients. Acta Mater. 47 (1999) 3205-3219.

DOI: 10.1016/s1359-6454(99)00188-3

[2] D.K. Sun, M.F. Zhu, T. Dai, W.S. Cao, S.L. Chen, D. Raabe, C.P. Hong, Modelling of dendritic growth in ternary alloy solidification with melt convection. Int. J. Cast Met. Res. 24 (2011) 177-183.

DOI: 10.1179/136404611x13001912813988

[3] A.Z. Lorbiecka, B. Šarler, Simulation of dendritic growth with different orientation by using the point automata method, CMC: Computers, Materials & Continua 18 (2010) 69-104.

[4] A.Z. Lorbiecka, B. Šarler, Point automata method for dendritic growth, in: A. Salcido (Ed. ), Cellular Automata Innovative Modelling for Science and Engineering, InTech, Rijeka, 2011, pp.197-220.

DOI: 10.5772/16139

[5] J.A. Dantzig, M. Rappaz, Solidification, EPFL Press, Lausanne, (2009).

[6] Y.H. Shin, C.P. Hong, Modelling of dendritic growth with convection using a modified cellular automaton model with diffuse interface. ISIJ Int. 42 (2011) 359-367.

DOI: 10.2355/isijinternational.42.359

[7] Q. Liu, B. Šarler, Non-singular method of fundamental solutions for two-dimensional isotropic elasticity problems. CMES: Computer Modeling in Engineering & Sciences. 91 (2013) 235-267.

[8] C.Y. Wang, C. Beckermann, A unified diffusion model for columnar and equiaxed dendritic alloy solidification. Mater. Sci. Eng. A171 (1993) 199-211.

DOI: 10.1016/0921-5093(93)90407-6