Abstract
When a polycrystalline material is held at elevated temperature, the boundaries between individual crystallites, or grains, can migrate, thus permitting some grains to grow at the expense of others. Planar sections taken through such a specimen reveal that the net result of this phenomenon of grain growth is a steady increase in the average grain size and, in many cases, the evolution toward a grain size distribution manifesting a characteristic shape independent of the state prior to annealing. Recognizing the tremendous importance of microstructure to the properties of polycrystalline samples, materials scientists have long struggled to develop a fundamental understanding of the microstructural evolution that occurs during materials processing. In general, this is an extraordinarily difficult task, given the structural variety of the various elements of microstructure, the topological complexities associated with their spatial arrangement and the range of length scales that they span. Even for single-phase samples containing no other defects besides grain boundaries, experimental and theoretical efforts have met with surprisingly limited success, with observations deviating significantly from the predictions of the best analytic models. Consequently, researchers are turning increasingly to computational methods for modeling microstructural evolution. Perhaps the most impressive evidence for the power of the computational approach is found in its application to single-phase grain growth, for which several successful simulation algorithms have been developed, including Monte Carlo Potts and cellular automata models (both discussed elsewhere in this chapter), and phase-field, front-tracking and vertex approaches.
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References
H.V. Atkinson, “Theories of normal grain growth in pure single phase systems”, Acta Metall., 36, 469–491, 1988.
F.J. Humphreys and M. Hatherly, Recrystallization and Related Annealing Phenomena, Pergamon Press, Oxford, 1996.
C.V. Thompson, “Grain growth and evolution of other cellular structures”, Solid State Phys., 55, 269–314, 2001.
C.E. Krill III and L.-Q. Chen, “Computer simulation of 3-D grain growth using a phase-field model”, Acta Mater., 50, 3057–3073, 2002.
J.E. Burke and D. Turnbull, “Recrystallization and grain growth”, Prog. Metal Phys., 3, 220–292, 1952.
M. Hillert, “On the theory of normal and abnormal grain growth”, Acta Metall., 13, 227–238, 1965.
H.J. Frost and C.V. Thompson, “Computer simulation of grain growth”, Curr. Op. Solid State Mater. Sci., 1, 361–368, 1996.
M.A. Miodownik, “A review of microstructural computer models used to simulate grain growth and recrystallisation in aluminium alloys”, J. Light Metals, 2, 125–135, 2002.
L.-Q. Chen, “Phase-field models for microstructure evolution”, Ann. Rev. Mater. Res., 32, 113–140, 2002.
L.-Q. Chen and W. Yang, “Computer simulation of the domain dynamics of a quenched system with a large number of nonconserved order parameters: The grain growth kinetics”, Phys. Rev. B, 50, 15752–15756, 1994.
I. Steinbach, F. Pezzolla, B. Nestler, M. Seeßelberg, R. Prieler, G.J. Schmitz, and J.L.L. Rezende, “A phase field concept for multiphase systems”, Physica D, 94, 135–147, 1996.
R. Kobayashi, J.A. Warren, and W.C. Carter, “A continuum model of grain boundaries”, Physica D, 140, 141–150, 2000.
D. Moldovan, D. Wolf, and S.R. Phillpot, “Theory of diffusion-accommodated grain rotation in columnar polycrystalline micro structures”, Acta Mater., 49, 3521–3532, 2001.
R. Kobayashi, J.A. Warren, and W.C. Carter, “Vector-valued phase field model for crystallization and grain boundary formation”, Physica D, 119, 415–423, 1998.
M.T. Lusk, “A phase-field paradigm for grain growth and recrystallization”, Proc. R. Soc. London A, 455, 677–700, 1999.
J.A. Warren, R. Kobayashi, A.E. Lobkovsky, and W.C. Carter, “Extending phase field models of solidification to polycrystalline materials”, Acta Mater., 51, 6035–6058, 2003.
S.M. Allen and J.W. Cahn, “A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening”, Acta Metall., 27, 1085–1095, 1979.
D. Fan, and L.-Q. Chen, “Computer simulation of grain growth using a continuum field model”, Acta Mater., 45, 611–622, 1997.
D. Fan, L.-Q. Chen, and S.P. Chen, “Effect of grain boundary width on grain growth in a diffuse-interface field model”, Mater. Sci. Eng. A, A238, 78–84, 1997.
L.-Q. Chen and J. Shen, “Applications of semi-implicit Fourier-spectral method to phase field equations”, Comput. Phys. Commun., 108, 147–158, 1998.
G. Gottstein and L.S. Shvindlerman, Grain Boundary Migration in Metals: Thermodynamics, Kinetics, Applications, CRC Press, Boca Raton, FL, 1999.
D. Wolf and K.L. Merkle, “Correlation between the structure and energy of grain boundaries in metals”, In: D. Wolf and S. Yip (eds.), Materials Interfaces: AtomicLevel Structure and Properties, Chapter 3, pp. 87–150, Chapman & Hall, London, 1992.
A. Kazaryan, Y. Wang, S.A. Dregia, and B.R. Patton, “Generalized phase-field model for computer simulation of grain growth in anisotropic systems”, Phys. Rev. 5,61, 14275–14278, 2000.
A. Kazaryan, Y. Wang, S.A. Dregia, and B.R. Patton, “Grain growth in anisotropic systems: comparison of effects of energy and mobility”, Acta Mater., 50, 2491–2502, 2002.
M. Upmanyu, G.N. Hassold, A. Kazaryan, E.A. Holm, Y. Wang, B. Patton, and DJ. Srolovitz, “Boundary mobility and energy anisotropy effects on microstructural evolution during grain growth”, Interface Sci., 10, 201–216, 2002.
D. Fan and L.-Q. Chen, “Topological evolution during coupled grain growth and Ostwald ripening in volume-conserved 2-D two-phase polycrystals”, Acta Mater., 45, 4145–4154, 1997.
V. Tikare, E.A. Holm, D. Fan, and L.-Q. Chen, “Comparison of phase-field and Potts models for coarsening processes”, Acta Mater., 47, 363–371, 1999.
C. Maurice, “Numerical modelling of grain growth: Current status”, In: G. Gottstein, and D.A. Molodov (eds.), Recrystallization and Grain Growth, Vol. 1, pp. 123–134, Springer-Verlag, Berlin, 2001.
K.M. Döbrich, C. Rau, and C.E. Krill III, “Quantitative characterization of the threedimensional microstructure of polycrystalline Al-Sn using x-ray microtomography”, Metall. Mater. Trans. A, 35A, 1953–1961, 2004.
H. Hu, “Grain growth in zone-refined iron”, Can. Metall. Q., 13, 275–286, 1974.
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Krill, C.E. (2005). Phase-Field Modeling of Grain Growth. In: Yip, S. (eds) Handbook of Materials Modeling. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-3286-8_112
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DOI: https://doi.org/10.1007/978-1-4020-3286-8_112
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