Mesoscale Simulation of Grain Growth


Article Preview

Simulation is becoming an increasingly important tool, not only in materials science in a general way, but in the study of grain growth in particular. Here we exhibit a consistent variational approach to the mesoscale simulation of large systems of grain boundaries subject to Mullins Equation of curvature driven growth. Simulations must be accurate and at a scale large enough to have statistical significance. Moreover, they must be sufficiently flexible to use very general energies and mobilities. We introduce this theory and its discretization as a dissipative system in two and three dimensions. The approach has several interesting features. It consists in solving very large systems of nonlinear evolution equations with nonlinear boundary conditions at triple points or on triple lines. Critical events, the disappearance of grains and and the disappearance or exhange of edges, must be accomodated. The data structure is curves in two dimensions and surfaces in three dimensions. We discuss some consequences and challenges, including some ideas about coarse graining the simulation.



Materials Science Forum (Volumes 467-470)

Edited by:

B. Bacroix, J.H. Driver, R. Le Gall, Cl. Maurice, R. Penelle, H. Réglé and L. Tabourot




D. Kinderlehrer et al., "Mesoscale Simulation of Grain Growth", Materials Science Forum, Vols. 467-470, pp. 1057-1062, 2004

Online since:

October 2004




[1] D. Raabe, F. Roters, F. Barlat, and L. -Q. Chen: Continuum scale simulations of engineering materials: fundamentals-microstructures-process applications, Wiley-VCH Verlag (2004).


[2] D. Kinderlehrer, I. Livshits, G.S. Rohrer, S. Ta'asan and P. Yu: these proceedings.

[3] D. Kinderlehrer and C. Liu: Math. Models and Meth. Appl. Math. Vol. 11 (2001) 713.

[4] D. Kinderlehrer, J. Lee, I. Livshits, and S. Ta'asan: in ref.

[1] .

[5] A. Kuprat: SIAM J. Sci. Comp. Vol. 22 (2000) 535.

[6] D. Kinderlehrer, I. Livshits, and S. Ta'asan: submitted.

[7] S.A. Hilgenfeldt, A. Kraynik, S. Koehler and H. Stone: PRL Vol. 86 (2001) 2685.

[8] M. Glicksman: to appear.

[9] D.M. Saylor, J. Fridy, B.S. El-Dasher, K. -Y. Jung, and A.D. Rollett: Metallurgical & Materials Transactions, in press (2004).

[10] K. Barmak et al., Proc MRS (2004), to appear.