Phase-field model for multicomponent alloy solidification

Cha, Pil-Ryung; Yeon, Dong-Hee; Yoon, Jong-Kyu

doi:10.1016/j.jcrysgro.2004.10.002

Cited by 37 publications

(18 citation statements)

References 33 publications

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“…The first term on RHS is the energy penalty for the interface, and the last two terms calculate the free energy of the liquid/solid mixture in the interface region.The phase field mobility M / can be calculated by Eq. [24] [26] …”

Section: Formulationmentioning

confidence: 99%

Multiscale Modeling of Transport Phenomena and Dendritic Growth in Laser Cladding Processes

Tan

Wen

Bailey

et al. 2011

Metall Mater Trans B

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A multiscale model is developed in this article to investigate the transport phenomena and dendrite growth in the diode-laser-cladding process. A transient model with an improved levelset method is built to simulate the heat/mass transport and the dynamic evolution of the molten pool surface on the macroscale. A novel model integrating the cellular automata (CA) and phase field (PF) methods is used to simulate the dendritic growth of multicomponent alloys in the mushy zone. The multiscale model is validated against the experiments, and the predicted geometry of clad tracks and the predicted dendrite arm spacing of microstructure match reasonably well with the experimental results. The effects of the processing parameters on the track geometry and microstructure are also investigated.

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Section: Formulationmentioning

confidence: 99%

Multiscale Modeling of Transport Phenomena and Dendritic Growth in Laser Cladding Processes

Tan

Wen

Bailey

et al. 2011

Metall Mater Trans B

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“…In this study, a model for multicomponent dendritic solidification is employed which is based on the work by Cha et al The model equations are the following ones:

\frac{1}{M} \dot{φ} = \nabla (ϵ^{2} \nabla φ) - \partial_{x} (ϵ ϵ^{'} φ_{y}) + \partial_{y} (ϵ ϵ^{'} φ_{x}) - f_{φ}

{\overset{c}{true}}_{k} = \nabla \sum_{j = 1}^{n - 1} \sum_{i = 1}^{n - 1} M_{k i} f_{c_{i} c_{j}} \nabla c_{j} + \nabla \sum_{i = 1}^{n - 1} M_{k i} f_{c_{i} φ} \nabla φ

Equation describes the evolution in space and time of the phase‐field variable ( φ ). f is the free‐energy density, which is designed to ensure local chemical equilibrium at the solid–liquid interface.…”

Section: Model and Simulation Proceduresmentioning

confidence: 99%

“…on the evolution of the microstructure during solidification under conditions of diffusion control, [10][11][12][13][14] to study the influence of elastic/plastic effects on liquid-solid and solid-solid phase transformations [15][16][17] and to investigate the interactions between convection and microstructure evolution during solidification. [18,19] In this study, a model for multicomponent dendritic solidification is employed which is based on the work by Cha et al [20] The model equations are the following ones:…”

Section: Model and Simulation Proceduresmentioning

confidence: 99%

Phase‐Field Modeling of the Dendrite Growth Morphology with Influence of Solid–Liquid Interface Effects

Rezende

Senk

Hüttenmeister

2014

steel research int.

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High manganese steels are able to deform by the TRIP effect, TWIP effect and microbanding formation. These steels are quite promising materials for mechanical construction, once they show an unusual combination of high ductility and high tensile strength. The casting of these steels represents a technological challenge, because they are extremely prone to macro-and microsegregation. Segregation, on its turn, may locally impair the desired mechanical properties. Simulations by the phase-field method may be utilized to investigate microstructure formation and the development of microsegregation patterns during solidification. Nevertheless, performing reliable microstructure simulations is only possible when reliable values for the solid-liquid interface energy are available. Through utilization of the sessile-drop method, first measurements of the interface energy in the Fe-Mn-C alloy system were performed. By utilizing the obtained values for the interface energy as an input, phase-field simulations were run aiming at investigating both the effect of the value for the interface energy and of the steel composition on the dendrite morphology.

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“…The equilibrium state in the PF interface region is defined following the basic assumption in the Kim-Kim-Suzuki model [30] and can be formulated for ternary alloys as shown in Eq. (18) [31]. …”

Section: Phase Fieldmentioning

confidence: 99%

Numerical Modeling of Transport Phenomena and Dendritic Growth in Laser Spot Conduction Welding of 304 Stainless Steel

Tan

Bailey

Shin

2012

Journal of Manufacturing Science and Engineering

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A multiscale model is developed to investigate the heat/mass transport and dendrite growth in laser spot conduction welding. A macroscale transient model of heat transport and fluid flow is built to study the evolution of temperature and velocity field of the molten pool. The molten pool shape is calculated and matches well with the experimental result. On the microscale level, the dendritic grvwth of 304 stainless steel is simulated by a novel model that has coupled the cellular automata (CA) and phase field (PF) methods. The epitaxial growth is accurately identified by defining both the gr-ain density and dendrite arm density at the fusion line. By applying the macroscale thermal history onto the microscale calculation domain, the microstructure evolution of the entire molten pool is simulated. The predicted micr-ostructure achieves a good quantitative agreement with the experimental results.

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Phase-field model for multicomponent alloy solidification

Cited by 37 publications

References 33 publications

Multiscale Modeling of Transport Phenomena and Dendritic Growth in Laser Cladding Processes

Multiscale Modeling of Transport Phenomena and Dendritic Growth in Laser Cladding Processes

Phase‐Field Modeling of the Dendrite Growth Morphology with Influence of Solid–Liquid Interface Effects

Numerical Modeling of Transport Phenomena and Dendritic Growth in Laser Spot Conduction Welding of 304 Stainless Steel

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