Developed Random Tessellation for Modeling of Microstructure

Abstract:

The concept of random tessellation is extensively used in wide area of natural sciences, especially material sciences. In this paper a simple but complete explanation of the random tessellation and mathematical tools requirements is presented. Then introducing the algorithm and the program for display random tessellation diagram was written. This program, with high speed and simple algorithm for random tessellation has the ability to change the level of statistical parameters such as number, mean, variance of the area of the grain. The ability to model microstructures of metals and grains for mechanical application, such as estimation of mechanical properties and crack propagation model in microstructure scale is very important. Finally, the microstructure produced by this program show good fitness of random generation with real microstructure.

• Periodical: Key Engineering Materials (Volumes 488-489)
• Pages: 529-532
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.488-489.529
• Online since: September 2011
• Authors: Khalil Farhangdoost, S. Rahnama
• Keywords: Algorithm (GA), Grain, Image Processing, Microstructure, Random Tessellation

References

[1] Kh. Farhangdoost, S. Rahnama: A Comparison of Macroscopic Fracture Surface and Crack Growth Rate of Ti-6Al-4V, Advanced Materials Research Vols. 97-101 pp.687-690. (2010).

DOI: 10.4028/www.scientific.net/amr.97-101.687

[2] W. Yu, C. D. Wright, S. P. Banks, and E. J. Palmiere: Cellular automata method for simulating microstructure evolution, Iee Proceedings-Science Measurement and Technology, vol. 150, pp.211-213, (2003).

DOI: 10.1049/ip-smt:20030866

[3] G. Voronoi: Nouvelles Applications des Parameters Continus a la Theorie des Formes, Quadratiques, J. Reine Angew, Math, vol. 134, pp.198-287, (1908).

DOI: 10.1515/crll.1908.134.198

[4] W. A. Johnson and R. F. Mehl: Reaction Kinetics in Processes of Nucleation and Growth, Trans. Am. Inst. Min. Metall., vol. 135, pp.416-458, (1939).

[5] M. Castro, A. Sanchez, and F. Dominguez-Adame: Lattice model for kinetics and grain-size distribution in crystallization, Physical Review B, vol. 61, pp.6579-6586, (2000).

DOI: 10.1103/physrevb.61.6579

[6] Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf, Computational Geometry (2nd revised ed. ), Springer-Verlag, ISBN 3-540-65620-0 Section 7. 2: Computing the Voronoi Diagram: 151–160. (2000).

DOI: 10.1145/369836.571192

[7] Aurenhammer, F. Voronoi: Diagrams-A Survey of a Fundamental Geometric Data Structure, ACM Computing Surveys, vol. 23, no. 3, pages 345-405.

DOI: 10.1145/116873.116880