Existence of solutions to a phase-field model for the isothermal solidification process of a binary alloy

Elastic interactions, arising from a difference of lattice spacing between two coherent phases in eutectic alloys with misfit stresses, can have an influence on microstructural pattern formation of eutectic colonies during solidification process. From a thermodynamic point of view the elastic energy contributes to the free energy of the phases and modifies their mutual stability. Therefore, the elastic stresses will have an effect on stability of lamellae, lamellae spacing and growth modes. In this paper, a phase-field model is employed to investigate the influence of elastic misfits in eutectic growth. The model reduces to the traditional sharp-interface model in a thin-interface limit, where the microscopic interface width is small but finite. An elastic model is designed, based on linear microelasticity theory, to incorporate the elastic energy in the phase-field model. Theoretical and numerical approaches, required to model elastic effects, are formulated and the stress distributions in eutectic solidification structures are evaluated. The two-dimensional simulations are performed for directed eutectic growth and the simulation results for different values of the misfit stresses are illustrated.

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An adaptive, fully implicit multigrid phase-field model for the quantitative simulation of non-isothermal binary alloy solidification

Acta Materialia ◽

10.1016/j.actamat.2008.05.029 ◽

2008 ◽

Vol 56 (17) ◽

pp. 4559-4569 ◽

Cited By ~ 44

Author(s):

J. Rosam ◽

P.K. Jimack ◽

A.M. Mullis

Keyword(s):

Binary Alloy ◽

Phase Field ◽

Field Model ◽

Phase Field Model ◽

Alloy Solidification ◽

Fully Implicit

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Existence of solutions to an anisotropic phase-field model

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.405 ◽

2003 ◽

Vol 26 (13) ◽

pp. 1137-1160 ◽

Cited By ~ 7

Author(s):

Erik Burman ◽

Jacques Rappaz

Keyword(s):

Phase Field ◽

Field Model ◽

Existence Of Solutions ◽

Phase Field Model ◽

Anisotropic Phase

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A phase field model for phase transformation in an elastically stressed binary alloy

Modelling and Simulation in Materials Science and Engineering ◽

10.1088/0965-0393/13/3/001 ◽

2005 ◽

Vol 13 (3) ◽

pp. 299-319 ◽

Cited By ~ 9

Author(s):

Dong-Hee Yeon ◽

Pil-Ryung Cha ◽

Ji-Hee Kim ◽

Martin Grant ◽

Jong-Kyu Yoon

Keyword(s):

Phase Transformation ◽

Binary Alloy ◽

Phase Field ◽

Field Model ◽

Phase Field Model

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Study on Microstructural Evolution of Binary Alloy Crystal Growth in Directional Solidification Process

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.470.100 ◽

2013 ◽

Vol 470 ◽

pp. 100-103

Author(s):

Dong Sheng Chen ◽

Ming Chen ◽

Rui Chang Wang

Keyword(s):

Crystal Growth ◽

Directional Solidification ◽

Binary Alloy ◽

Phase Field ◽

Field Model ◽

Phase Field Model ◽

Field Method ◽

Phase Field Method ◽

Pure Substance ◽

Columnar Dendrite

PFM (phase field method) was employed to study microstructure evolution, and considering the effect of solute concentration to the undercooling, we developed a phase field model for binary alloy on the basis of pure substance model. In the paper, the temperature field and solute field were coupled together in the phase field model to calculate the crystal growth of magnesium alloy in directional solidification. The simulation results showed a non-planar crystal growth of planar to cellular to columnar dendrite, the comparison of different dendrite patterns were carried out in the numerical simulation, and with the increasing of the anisotropy, the second dendrite arms became more developed.

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