A method for coupling the phase-field model based on a grand-potential formalism to thermodynamic databases

Choudhury, Abhik; Kellner, Michael; Nestler, Britta

doi:10.1016/j.cossms.2015.03.003

Cited by 61 publications

(25 citation statements)

References 22 publications

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“…To incorporate this thermodynamic information into the different phase-field models, based on the Allen-Cahn or Cahn-Hilliard model, several approaches have been established [2][3][4][5][6][7][8][9][10][11][12]. During the simulations, an obvious approach is the direct access to the information from the databases.…”

Section: Introductionmentioning

confidence: 99%

“…The advantages of the parabolically approximated functions are their lightweight computations and the proper representation of the thermodynamic information. In recent years, different binary [3,5,[14][15][16] and ternary [5,[17][18][19][20][21] alloys have therefore been modeled with parabolically approximated functions. A further advantage of this approach is that these functions are suitable for the application in free-energy-based [8,22] as well as in grand-potential-based phase-field models [23,24].…”

Section: Introductionmentioning

confidence: 99%

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Data workflow to incorporate thermodynamic energies from Calphad databases into grand-potential-based phase-field models

et al. 2021

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In order to approximate Gibbs energy functions, a semi-automated framework is introduced for binary and ternary material systems, using Calphad databases. To generate Gibbs energy formulations by means of second-order polynomials, the framework includes a precise approach. Furthermore, an optional extensional step enables the modeling of systems in which a direct generation leads to the unsatisfactory results in the representation of the thermodynamics. Furthermore, an optional extensional step enables the modeling of systems, in which a direct generation leads to the unsatisfactory results, when representing the thermodynamics. Within this extension, the commonly generated functions are modified to satisfy the equilibrium conditions in the observed material systems, leading to a better correlation with thermodynamic databases. The generated Gibbs energy formulations are verified by recalculating the equilibrium concentrations of the phases and rebuilding the phase diagrams in the considered concentration and temperature ranges, prior to the simulation studies. For all comparisons, a close match is achieved between the results and the Calphad databases. As practical examples of the method, phase-field simulation studies for the directional solidification of the binary – and the ternary – eutectic systems are performed. Good agreements between the simulation results and the reported theoretical and experimental studies from literature are found, which indicates the applicability of the presented approaches. Graphical Abstract

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Data workflow to incorporate thermodynamic energies from Calphad databases into grand-potential-based phase-field models

et al. 2021

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“…We first determine the exponents for coarsening without elastic effects in Ni-9.6 wt%Al denoted as NiAl(NE) and a multi-component superalloy denoted as CMSX4(NE). [20] does not hold for Ni-base superalloys due to their largely anisotropic microstructures, the influence of elastic effects on coarsening kinetics was clearly highlighted. The exponents are almost equal to the exponent derived in Equation 15 for the case of coarsening without elastic effects.…”

Section: Simulation Of Coarsening Law In Elastically Stressed Ni-basementioning

confidence: 99%

Phase‐Field Study of Anisotropic γ′‐Coarsening Kinetics in Ni‐Base Superalloys with Varying Re and Ru Contents

et al. 2015

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The coarsening kinetics of g 0 -precipitates in single crystalline Ni-based superalloys is studied using phase-field simulations. At first, we discuss interdiffusion-limited g 0 -coarsening in technologically relevant superalloys with the explicit inclusion of up to nine chemical components. The simulations show that an additional influence from the coherency strain leads to a substantially faster coarseningevolution compared to the predictions from the LSW-theory. Second, we perform a virtual experiment to determine the influence of varying rhenium (Re) and ruthenium (Ru) additions on the temporal evolution of the g-g 0 microstructure under thermo-mechanical loads. We observe that a change in the Re content strongly alters the coarsening kinetics. On the contrary, it is found that Ru variations have no significant effect on the coarsening kinetics.

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“…To maintain a certain level of consistency, whenever a chemical potential of unit J/mol appears, it is written with a tilde, otherwise the unit J/m 3 does apply. Following [13,78], the chemical potentials should be treated more as chemical potential differences (so-called diffusion potentials), according to the definition above. Therefore, we writeμ i ≡μ ind i −μ ind K , whereμ ind i represents the true individual chemical potential of the component i.…”

Section: A Grand-potential Modelmentioning

confidence: 99%

Multiphase-field model for surface diffusion and attachment kinetics in the grand-potential framework

et al. 2021

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Grand-potential based multiphase-field model is extended to include surface diffusion. Diffusion is elevated in the interface through a scalar degenerate term. In contrast to the classical Cahn-Hilliard-based formulations, the present model circumvents the related difficulties in restricting diffusion solely to the interface by combining two second-order equations, an Allen-Cahn-type equation for the phase field supplemented with an obstacletype potential and a conservative diffusion equation for the chemical potential or composition evolution. The sharp interface limiting behavior of the model is deduced by means of asymptotic analysis. A combination of surface diffusion and finite attachment kinetics is retrieved as the governing law. Infinite attachment kinetics can be achieved through a minor modification of the model, and with a slight change in the interpretation, the same model handles the cases of pure substances and alloys. Relations between model parameters and physical properties are obtained which allow one to quantitatively interpret simulation results. An extensive study of thermal grooving is conducted to validate the model based on existing theories. The results show good agreement with the theoretical sharp-interface solutions. The obviation of fourth-order derivatives and the usage of the obstacle potential make the model computationally cost-effective.

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A method for coupling the phase-field model based on a grand-potential formalism to thermodynamic databases

Cited by 61 publications

References 22 publications

Data workflow to incorporate thermodynamic energies from Calphad databases into grand-potential-based phase-field models

Data workflow to incorporate thermodynamic energies from Calphad databases into grand-potential-based phase-field models

Phase‐Field Study of Anisotropic γ′‐Coarsening Kinetics in Ni‐Base Superalloys with Varying Re and Ru Contents

Multiphase-field model for surface diffusion and attachment kinetics in the grand-potential framework

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