Computation of dendrites using a phase field model

Wheeler, A. A.; Murray, Bruce T.; Schaefer, Robert

doi:10.1016/0167-2789(93)90242-s

Cited by 391 publications

(241 citation statements)

References 20 publications

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“…Dendritic growth analysis is popular in phase field studies and there are lots of application examples for pure materials like those featured in Kobayashi (1993) and Andersson (2002), as well as phase-field models for solidification of binary alloys as, e.g., the works of McFadden et al (1993) and Wheeler et al (1993), and ternary alloys, like in the paper by Lee and Suzuki (1999).…”

Section: Phase-field Simulation Of Dendritic Solidificationmentioning

confidence: 99%

Numerical simulation of the solidification of pure melt by a phase-field model using an adaptive computation domain

Ferreira¹,

Ferreira²,

Assis³

2011

J. Braz. Soc. Mech. Sci. & Eng.

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Section: Phase-field Simulation Of Dendritic Solidificationmentioning

confidence: 99%

Numerical simulation of the solidification of pure melt by a phase-field model using an adaptive computation domain

Ferreira¹,

Ferreira²,

Assis³

2011

J. Braz. Soc. Mech. Sci. & Eng.

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“…Therefore, the phase-field model has been applied to simulation of a variety of microstructural evolution processes during the solidifications in many systems. More specifically, for example the single phase solidification for pure substance and binary alloy systems, [96][97][98] and the solidification process for multicomponent and multiphase alloy systems. [99][100][101][102][103][104][105][106][107] The important works on the phase-field modeling and their applications can be found in several review articles.…”

Section: Phase-field Modeling (Microscopic-scale)mentioning

confidence: 99%

Methodological Progress for Computer Simulation of Solidification and Casting

Nakajima

Zhang²,

Oikawa

et al. 2010

ISIJ Int.

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The dramatic progress made over the last 10 to 15 years in the field of "computer simulation of solidification and casting" is greatly due to the supports by academic as well as industrial research. The driving force behind this undertaking was the promise of predictive capabilities that will allow process and material developments. Here, the recent works on modeling were summarized, for the macrosegregation in the macroscale simulation, and the Cellular Automaton, the solidification path combined with the microsegregation, the phase-field model in the meso-scale and micro-scale simulation.

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“…This manifests itself mathematically by the underlying presence of variational derivatives and diffusion parameters. To illustrate this, given a single phase formulation of the free energy, F = Ω f (φ, ∇φ, c, T ) d 3 x, in a domain Ω for the thermal-solutal (T, c) solidification of a metal, where φ ∈ [0, 1] indicates bulk melt or bulk solid at the extremes, the dynamical equations are typically given in variational form for the phase variable [2] …”

Section: Introductionmentioning

confidence: 99%

Thermo-Solutal Modelling of Microstructure Formation during Multiphase Alloy Solidification - a New Approach

Bollada

Mullis

Jimack

2014

MSF

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Abstract. This paper shows how to move from a specification of free energy for the solidification of a binary alloy to the dynamical equations using the elegance of a dissipative bracket analogous to the Poisson bracket of Hamiltonian mechanics. A key new result is the derivation of the temperature equation for single-phase thermal-solutal models, which contains generalisations and extra terms which challenge standard models. We also present, for the first time, the temperature equation for thermal multi-phase field models. There are two main ingredients: one, the specification of the free energy in terms of the time and space dependent field variables: n-phases φ i , a concentration variable c, and temperature T ; two, the specification of the dissipative bracket in terms of these variables, their gradients and a set of diffusion parameters, which may themselves depend on the field variables. The paper explains the method within this context and demonstrates its thermodynamic admissibility.

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Computation of dendrites using a phase field model

Cited by 391 publications

References 20 publications

Numerical simulation of the solidification of pure melt by a phase-field model using an adaptive computation domain

Numerical simulation of the solidification of pure melt by a phase-field model using an adaptive computation domain

Methodological Progress for Computer Simulation of Solidification and Casting

Thermo-Solutal Modelling of Microstructure Formation during Multiphase Alloy Solidification - a New Approach

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