Phase Field Model of Grain Growth Using Quaternions

Abstract:

The microstructure of a material determines its mechanical properties. Since microstructure can be tailored by thermo-mechanical processing of the metal, it is important to understand how the microstructure evolves under thermo-mechanical processing. We have constructed a phase field formalism to study recrystallization and grain growth in polycrystalline material. A unique feature of our model is that the Euler Angles (φ₁,φ,φ₂), obtained from Electron Back Scattered Diffraction (EBSD) data of a polycrystalline sample can be taken as an input to our model. In our model, the grain orientations at discrete grid points are represented by a non-conserved vector field, namely a quaternion. The free energy used for the evolution of the local orientations contains bulk energy for various preferred grain types and grain boundary energy. The grain orientations evolve in time following a Langevin dynamics. So far we have established that the rate of grain growth follows the usual L ~ t^1/2 scaling law when the grain boundary energy is independent of the misorientation angle between neighboring grains. Work on other aspects of this model is in progress.

• Periodical: Materials Science Forum (Volumes 715-716)
• Pages: 776-781
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.715-716.776
• Online since: April 2012
• Authors: Santidan Biswas, Indradev Samajdar, Arunansu Haldar, Anirban Sain
• Keywords: Grain Growth, Phase Field Model, Quaternions

References

[1] F. J. Humphreys and M. Hatherly: Recrystallization and related annealing phenomena (Pergamon Press, Oxford, 1996).

[2] V. Randle and O. Engler: Introduction to Texture Analysis: Macrotexture, Microtexture and Orientation Mapping (Taylor and Francis, London, 2003).

DOI: 10.1201/9781482287479

[3] F. J. Humphreys, Materials Science Forum: Vol. 107 (2004), p.467.

[4] L.Q. Chen, Annu. Rev. Mater. Res. Vol. 32 (2002), p.113.

[5] A. Mallick and S. Vedantam, Computational Materials Science, Vol. 46 (2009), p.21.

[6] I.M. McKenna, M.P. Gururajan, P.W. Voorhees, Journal of Materials Science Vol. 44 (2009), p.2206.

[7] T. Pusztai, G. Bortel, and L. Gr´an´asy, Europhys. Lett. Vol. 71 (2005), p.131.

[8] R. Kobayashi and J.A. Warren, Physica A Vol. 356 (2005), p.127.

[9] M.R. Dorr et al, J. Comput. Phys., Vol. 229 (2010), p.626.

[10] C. G. Bac et al , Phys. Rev. E. Vol. 63 (2001), p.42701.

[11] N. V. Priezjev and R. A. Pelcovits, Phys. Rev. E. Vol. 66 (2002), p.51705.