Incorporating the CALPHAD sublattice approach of ordering into the phase-field model with finite interface dissipation

Zhang, Lijun; Stratmann, Matthias; Du, Yong; Sundman, Bo; Steinbach, Ingo

doi:10.1016/j.actamat.2014.11.037

Cited by 90 publications

(54 citation statements)

References 41 publications

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“…The proposed approximation method is advantageous over other techniques of incorporating CALPHAD-based free energy expressions into phase field simulations because it is both simple to implement and addresses the issues in using these free energies. One alternative method, linking the phase field software directly to a thermodynamic database [26,50,51], requires an interface to database software, potentially costly software licensing, and additional computational expense to query the database at each mesh point and each time step. Another alternative method, polynomial approximation of the free energy expressions [35, 52--55, 76], requires more effort than the proposed method.…”

Section: Resultsmentioning

confidence: 99%

“…Previously proposed methods of incorporating CALPHAD-based free energies into phase field models include direct coupling to a thermodynamic database [26,50,51] or polynomial approximations of the free energies [35, 52--55]. However, direct coupling may incur substantial computational expense by querying external software at each mesh point for every simulation step, and it may necessitate the use of commercial software, which may require costly licensing fees.…”

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confidence: 99%

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General method for incorporating CALPHAD free energies of mixing into phase field models: Application to the α-zirconium/δ-hydride system

Jokisaari

Thornton

2015

Calphad

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This paper presents a general method of incorporating CALPHAD-based free energies into a phase field model. While CALPHAD-based free energy descriptions provide realistic energetics of alloys, their formulations may pose numerical difficulties for phase field simulations. Specifically, the free energies of mixing for different phases may not necessarily be defined over the same concentration ranges, and their derivatives may exhibit highly nonlinear behavior. The method presented approximates the free energies of mixing using piecewise functions to eliminate the aforementioned characteristics while largely retaining the free energy values and the first and second derivative information, which affect the thermodynamic and kinetic behavior of the system. The method is verified by planar interface simulations of the α-zirconium/δ-hydride system. The phase fractions and compositions obtained from the phase field simulations are compared to the values calculated from the common tangent construction on the original free energies. The results indicate a high degree of accuracy. CALPHAD; phase field model; finite element; zirconium; zirconium hydride 1. Introduction Quantitative microstructural modeling of phase transformations such as solidification

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Section: Resultsmentioning

confidence: 99%

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confidence: 99%

General method for incorporating CALPHAD free energies of mixing into phase field models: Application to the α-zirconium/δ-hydride system

Jokisaari

Thornton

2015

Calphad

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“…This grand potential formulation, which has also been extended to rapid solidification [34], appears to be a promising candidate to handle alloys with arbitrary phase diagrams, with the potential to be coupled with CalPhaD calculations (see e.g. [42,18,45,163]). …”

Section: Multi-phase and Multicomponent Systemsmentioning

confidence: 99%

Atomistic to continuum modeling of solidification microstructures

Karma

Tourret

2016

Current Opinion in Solid State and Materials Science

106

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a b s t r a c tWe summarize recent advances in modeling of solidification microstructures using computational methods that bridge atomistic to continuum scales. We first discuss progress in atomistic modeling of equilibrium and non-equilibrium solid-liquid interface properties influencing microstructure formation, as well as interface coalescence phenomena influencing the late stages of solidification. The latter is relevant in the context of hot tearing reviewed in the article by M. Rappaz in this issue. We then discuss progress to model microstructures on a continuum scale using phase-field methods. We focus on selected examples in which modeling of 3D cellular and dendritic microstructures has been directly linked to experimental observations. Finally, we discuss a recently introduced coarse-grained dendritic needle network approach to simulate the formation of well-developed dendritic microstructures. This approach reliably bridges the well-separated scales traditionally simulated by phase-field and grain structure models, hence opening new avenues for quantitative modeling of complex intra-and inter-grain dynamical interactions on a grain scale.Published by Elsevier Ltd.

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“…While the thermodynamic data were compiled for phases using the sublattice model [ 29 ], a relation was found between sublattice occupancies and the phase composition in mole fractions for the ferritic phase and the cementite, which made more complex extensions to the phase field model and further algorithms unnecessary [ 30 ].…”

Section: Thermodynamics and Diffusionmentioning

confidence: 99%

Microstructure Design of Tempered Martensite by Atomistically Informed Full-Field Simulation: From Quenching to Fracture

Borukhovich

Stratmann

et al. 2016

Materials

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Martensitic steels form a material class with a versatile range of properties that can be selected by varying the processing chain. In order to study and design the desired processing with the minimal experimental effort, modeling tools are required. In this work, a full processing cycle from quenching over tempering to mechanical testing is simulated with a single modeling framework that combines the features of the phase-field method and a coupled chemo-mechanical approach. In order to perform the mechanical testing, the mechanical part is extended to the large deformations case and coupled to crystal plasticity and a linear damage model. The quenching process is governed by the austenite-martensite transformation. In the tempering step, carbon segregation to the grain boundaries and the resulting cementite formation occur. During mechanical testing, the obtained material sample undergoes a large deformation that leads to local failure. The initial formation of the damage zones is observed to happen next to the carbides, while the final damage morphology follows the martensite microstructure. This multi-scale approach can be applied to design optimal microstructures dependent on processing and materials composition.

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Incorporating the CALPHAD sublattice approach of ordering into the phase-field model with finite interface dissipation

Cited by 90 publications

References 41 publications

General method for incorporating CALPHAD free energies of mixing into phase field models: Application to the α-zirconium/δ-hydride system

General method for incorporating CALPHAD free energies of mixing into phase field models: Application to the α-zirconium/δ-hydride system

Atomistic to continuum modeling of solidification microstructures

Microstructure Design of Tempered Martensite by Atomistically Informed Full-Field Simulation: From Quenching to Fracture

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