Abstract
A Cahn-Hilliard phase-field—elasticity model was used to study the effect of compositional strain on the diffusive interface thickness and on the solid state phase transformations in binary alloys. Compositional strain was introduced using the Vegard’s law. Mixed order finite element analyses and analytical solutions of an infinite diffusion couple with a flat interface were used to track the phase-field interface morphology. Both analytical and numerical calculations showed a substantial rate-increasing effect of compositional strain on the interface thickness, especially for low energy barrier values. Compositional strain was found to cause substantial patterning of single precipitates during their evolution in a parent matrix and significantly change the equilibrium size of the precipitates. Results show a considerable influence of compositional strain on the coarsening kinetics of coherent precipitates.
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References
L.Q. Chen, Phase-Field Models for Microstructure Evolution, Annu. Rev. Mater. Res., 2002, 32, p 113-140
N. Moelans, B. Blanpain, and P. Wollants, An Introduction to Phase-Field Modeling of Microstructure Evolution, Calphad, 2008, 32(2), p 268-294
B. Echebarria, R. Folch, A. Karma, and M. Plapp, Quantitative Phase-Field Model of Alloy Solidification, Phys. Rev. E, 2004, 70(6), p 061604
S. Torabi, J. Lowengrub, A. Voigt, and S. Wise, A New Phase-Field Model for Strongly Anisotropic Systems, Proc. R. Soc. A, 2009, 465, p 1337-1359
M. Selzer, B. Nestler, and D. Danilov, Influence of the Phase Diagram on the Diffuse Interface Thickness and on the Microstructure Formation in a Phase-Field Model for Binary Alloy, Math. Comput. Simul., 2010, 80(7), p 1428-1437
J.W. Cahn and J.E. Hilliard, Free Energy of a Nonuniform System. I. Interfacial Free Energy, J. Chem. Phys., 1958, 28, p 258-267
J.W. Cahn, On Spinodal Decomposition, Acta Metall., 1961, 9, p 795-801
A.G. Khachaturyan, Theory of Structural Transformations in Solids, Wiley, New York, 1983
F.C. Larche and J.W. Cahn, Thermochemical Equilibrium of Multiphase Solids Under Stress, Acta Metall. Mater., 1978, 26, p 1579-1589
F.C. Larche and J.W. Cahn, Phase Changes in a Thin Plate with Non-Local Self-Stress Effects, Acta Metall. Mater., 1992, 40, p 947-955
P.H. Leo, J.S. Lowengrub, and H.J. Hou, A Diffuse Interface Model for Microstructural Evolution in Elastically Stressed Solids, Acta Mater., 1998, 46(6), p 2113-2130
L.Q. Chen, Y. Wang, and A.G. Khachaturyan, Transformation-Induced Elastic Strain Effect on Precipitation Kinetics of Ordered Intermetallics, Philos. Mag. Lett., 1991, 64(5), p 241-251
J.W. Cahn and R. Kobayashi, Exponentially Rapid Coarsening and Buckling in Coherently Self-Stressed Thin Plates, Acta Metall. Mater., 1995, 43, p 931-944
D.Y. Li and L.Q. Chen, Computer Simulation of Morphological Evolution and Rafting of γ′ Particles in Ni-based Superalloys Under Applied Stresses, Scripta Mater., 1997, 37(9), p 1271-1277
P.-R. Cha, D.-H. Yeon, and S.-H. Chung, Phase-Field Study for the Splitting Mechanism of Coherent Misfitting Precipitates in Anisotropic Elastic Media, Scripta Mater., 2005, 52(12), p 1241-1245
D.-H. Yeon, P.-R. Cha, J.-H. Kim, M. Grant, and J.-K. Yoon, A Phase Field Model for Phase Transformation in an Elastically Stressed Binary Alloy, Model. Simul. Mater. Sci. Eng., 2005, 13, p 299-319
H. El Kadiri, M.F. Horstemeyer, and D.J. Bammann, A Theory for Stress-Driven Interfacial Damage Upon Cationic-Selective Oxidation of Alloys, J. Mech. Phys. Solids, 2008, 56, p 3392-3415
A.R. Denton and N.W. Ashcroft, Vegards’s Law, Phys. Rev. A, 1991, 43, p 3161-3164
F.C. Larche and J.W. Cahn, A Linear Theory of Thermochemical Equilibrium of Solids Under Stress, Acta Metall., 1973, 21, p 1051-1063
M. Asle Zaeem and S.Dj. Mesarovic, Finite Element Method for Conserved Phase Fields: Stress-Mediated Diffusional Phase Transformation, J. Comp. Phys., 2010, 229(24), p 9135-9149
M. Asle Zaeem and S.Dj. Mesarovic, Investigation of Phase Transformation in Thin Film Using Finite Element Method, Solid State Phenom., 2009, 150, p 29-41
M. Asle Zaeem and S.Dj. Mesarovic, Morphological Instabilities in Thin Films: Evolution Maps, Comput. Mater. Sci., 2011, 50(3), p 1030-1036
W.C. Johnson, On the Growth of an Intermediate Phase in Coherently Stressed Thin Plates, Acta Mater., 2000, 48, p 1021-1032
W. Ostwald, On the Supposed Isomerism of Red and Yellow Mercury Oxide and the Surface Tension of Solid Substances, Z. Phys. Chem., 1900, 34, p 495-503
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Asle Zaeem, M., El Kadiri, H., Mesarovic, S.D. et al. Effect of the Compositional Strain on the Diffusive Interface Thickness and on the Phase Transformation in a Phase-Field Model for Binary Alloys. J. Phase Equilib. Diffus. 32, 302–308 (2011). https://doi.org/10.1007/s11669-011-9905-y
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DOI: https://doi.org/10.1007/s11669-011-9905-y