Modeling Grain Structures of Some Carbon Steels using Voronoi Tesselation

O.O. Oluwole, A.L. Akinkunmi

Materials Science and Engineering Dept., Obafemi Awolowo Univ., Nigeria.
Mechanical Engineering Dept., Univ. of Ibadan, Nigeria.

DOI: 10.4236/jmmce.2011.103021                

Abstract

Modeled grain structures of normalized carbon steels using voronoi tessellation is reported in this work. Three stages of programming were used in modeling the microstructures. The first stage was iteration of the voronoi cells in order to obtain equivalent grain size with experimental specimens. In the second stage, the pearlite phase was introduced using the lever rule represented by a plot of random points. The third layer was modeled to reveal the grain boundaries of the carbon steels. The values of the grain sizes of modeled microstructures showed good agreement with experimental values. The study has shown that the microstructures can be modeled fairly accurately thus enabling a fairly quick export of geometric models on to some other finite element packages for analysis of stress-strain effect on microstructure and generally a stressmicrostructure response could be determined.

Keywords

microstructure -modeling, voronoi tessellation, carbon steels

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Reed-Hill, R.E., (1973) Physical Metallurgy Principles, 2nd ed., Van Nostrand
[2]	Makinamuhendisi (2008) ‘Low Carbon steel’ http://www.makinamuhendisi.com / mechanical / mechanical-engineering-archives/176-Low-Carbon-Steels-Mild-Steel.html
[3]	Key-to-steel (2008) Hardenable Carbon Steels http://www.key-tosteel. com/ViewArticle.asp?ID=90
[4]	Wikepedia(2008) ‘Carbon Steels’ http://en.wikipedia.org/wiki/Carbon_steel
[5]	JSTOR SIAM (1999 ) Generating Voronoi Tesselations’ JSTOR SIAM Review, 41( 4), 637-676.
[6]	Arwade, S. R., 2000, Probabilistic Models for Aluminum Microstructures and Intergranular Fracture Analysis, Masters Thesis, Cornell University.
[7]	Sinum (2006)Lloyd algorithm for computing CVTs. http://www.math.psu.edu/qdu/Res/Pre/dmj06sinum.pdf
[8]	JSTOR(2008)‘Centroidal voronoi tessellations’.
[9]	Qiang Du, Vance Faber and Max Gunzburger, (1999) Centroidal Voronoi Tessellations: Applications and Algorithms, Society for Industrial and Applied Mathematics.
[10]	Oluwole, O.O., D.T. Oloruntoba, and O. Awheme. (2008) "Effect of Zinc Plating of Low Carbon Steel on Corrosion Resistance in Cocoa Fluid Environment". Materials and Design, 29(6):1266-1274.
[11]	Singh.V (2005) ‘Physical Metallurgy’ Standard Publishers, New-Delhi,p.493-497
[12]	Higham.D.J and N.J. Higham (2000) Matlab Guide SIAM Philadelphia.
[13]	Mathwork (2004) Introduction: What is Matlab? Matlab Help File, Mathwork, Inc.USA