Finite Element Simulations of 3D Zener Pinning


Article Preview

An original model, based on a variational formulation for boundary motion by viscous drag, is developed to simulate single grain boundary motion and its interaction with particles. The equations are solved by a 3D finite element method to obtain the instantaneous velocity at each triangular element on the boundary surface, before, during and after contact with one or more particles. After validation by comparison with some simple, analytical and numerical cases, it is adapted to model curvature driven grain growth. For single phase material, the single grain boundary model closely matches the grain coarsening kinetics of a 3D multi boundary vertex model. In the presence of spherical incoherent particles the growth rate slows down to give a growth exponent of 2.5. When the boundary is anchored there is a significantly higher density, by a factor of 4, of particles on the boundary than the density predicted by the classic Zener analysis, and many particles exert less than this Zener drag force. As a result the Zener drag is increased by a factor of about 2.2. The limiting grain radius is compared with some experimental results.



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




G. Couturier et al., "Finite Element Simulations of 3D Zener Pinning", Materials Science Forum, Vols. 467-470, pp. 1009-1018, 2004

Online since:

October 2004




[1] C. S. Smith: Trans. Am. Inst. Min. Engrs. Vol. 175 (1948), p.15.

[2] P.A. Manohar, M. Ferry and T. Chandra: ISIJ International Vol. 38 (1998), p.913.

[3] M.P. Anderson, D.J. Srolovitz, G.S. Grest and P.S. Sahni: Acta metall. Vol. 32 (1984), p.783.

[4] D.J. Srolovitz, M.P. Anderson, G.S. Grest and P.S. Sahni: Acta metall. Vol. 32 (1984), p.1429.

[5] A. Olguín, M. Ortíz and C.H. Wörner: Phil. Mag. B Vol. 81 (2001), p.731.

[6] M. Miodownik, E.A. Holm and G.N. Hassold: Scripta mater. Vol. 42 (2000), p.1173.

[7] S.P. Riege, C.V. Thompson and H.J. Frost: Grain Growth in Polycristalline Materials III. The Minerals, Metals & Materials Society, 1998. p.295.

[8] D. Weygand, Y. Bréchet and J. Lépinoux : Acta mater. Vol 47 (1999), p.961.

[9] G. Couturier, C. Maurice and R. Fortunier : Phil. Mag. Vol 83 (2003), p.3387.

[10] K. Kawasaki, T. Nagai and K. Nakashima: Phil. Mag. B Vol. 60 (1989), p.399.

[11] K. Fuchizaki, T. Kusaba and K. Kawasaki: Phil. Mag. B Vol 71 (1995), p.333.

[12] G. Couturier : PhD dissertation (2003), Ecole des Mines de Saint-Etienne, France.

[13] B. N. Kim and T. Kishi: Acta mater. Vol. 47 (1999), p.2293.

[14] G. Couturier, R. Fortunier and C. Maurice, Proc. 21st Riso International Symposium on Materials Science, 2000, p.303.

[15] G. Couturier, R. Doherty, C. Maurice and R. Fortunier, submitted to Acta Materialia.

[16] D. Weygand PhD dissertation (1998), ENSEEG, Institut National Polytechnique de Grenoble, France.

[17] P. Hellman and M. Hillert: Scandinavian Journal of Metallurgy Vol 4 (1975), p.211.