Sharp Phase Field Method.
TL;DR: A new formulation of phase field modeling is presented, which is intrinsically discrete, in which the interfaces are resolved with essentially one grid point with no pinning on the grid and an accurate rotational invariance, improving drastically the numerical capabilities of the method.
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Abstract: Phase field modeling offers an extremely general framework to predict microstructural evolutions in complex systems. However, its computational implementation requires a discretization scheme with a grid spacing small enough to preserve the continuous character of the theory. We present here a new formulation, which is intrinsically discrete, in which the interfaces are resolved with essentially one grid point with no pinning on the grid and an accurate rotational invariance, improving drastically the numerical capabilities of the method. We show that interfacial kinetic properties are reproduced with a high accuracy. Finally, we apply the model to a situation where conserved and nonconserved fields are coupled.
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Citations
Phase-field modeling of microstructure evolution: Recent applications, perspectives and challenges
TL;DR: The state-of-the-art in phase-field modeling of microstructure evolution has been reviewed in this paper , where the focus is placed on recent applications of phase field simulations of solid-state microstructures.
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Phase-field modeling of γ/γ″ microstructure formation in Ni-based superalloys with high γ″ volume fraction
TL;DR: In this article, a phase-field model was used to investigate various influencing factors that determine the equilibrium shapes of Ni-based superalloy IN718 precipitates, minimizing the sum of the total elastic and interfacial energy.
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Modeling and simulation of microstructure in metallic systems based on multi-physics approaches
Jaber Rezaei Mianroodi,Pratheek Shanthraj,Chuanlai Liu,Samad Vakili,Sharan Roongta,Nima H. Siboni,Nathan Perchikov,Yang Bai,Bob Svendsen,Franz Roters,Dierk Raabe,Martin Diehl +11 more
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References
Free Energy of a Nonuniform System. I. Interfacial Free Energy
John W. Cahn,John E. Hilliard +1 more
TL;DR: In this article, it was shown that the thickness of the interface increases with increasing temperature and becomes infinite at the critical temperature Tc, and that at a temperature T just below Tc the interfacial free energy σ is proportional to (T c −T) 3 2.
10.4K
Phase-Field Models for Microstructure Evolution
TL;DR: The phase-field method has recently emerged as a powerful computational approach to modeling and predicting mesoscale morphological and microstructure evolution in materials as discussed by the authors, which is able to predict the evolution of arbitrary morphologies and complex microstructures without explicitly tracking the positions of interfaces.
Quantitative phase-field model of alloy solidification.
TL;DR: A phase-field model that can accurately simulate microstructural pattern formation for low-speed directional solidification of a dilute binary alloy is presented, and the addition of a phenomenological "antitrapping" solute current in the mass conservation relation is achieved.
782
Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. I. Theoretical approach.
TL;DR: The conditions on the interface thickness are discussed in detail to control the accuracy and convergence of the phase-field model to the limiting Hele-Shaw dynamics, and the convergence appears to be slower for high viscosity contrasts.