Three-dimensional phase-field simulations of coarsening kinetics of γ′ particles in binary Ni–Al alloys

Zhu, Jianxin; Wang, T.; Ardell, A.J.; Zhou, S. Kevin; Liu, Zhe; Chen, Lei

doi:10.1016/j.actamat.2004.02.032

Cited by 217 publications

(90 citation statements)

References 36 publications

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“…According to our data analysis the coarsening exponent m in the case without the elastic interaction is near 2.0, while it is equal to 3.6 in the case when the elastic interaction is taken into account. Notably, in most of experiments and other simulations on superalloys the obtained coarsening exponent is around 3 [1,8,9,16]. It is evident that our simulation times are significantly lower than the typical experiment time.…”

Section: Coarsening Exponentmentioning

confidence: 87%

“…7 with a comparison to various known distributions [2,9,16]. Figure 7 corresponds to simulation with and without the elastic contribution at t = 50 s. The results demonstrate that starting from initially narrow distribution the γ PSD evolves towards the Lifshitz, Slyozov and Wagner's (LSW) model [6,7] …”

Section: Particle Size Distributionmentioning

confidence: 99%

“…Thus in order to analyse the coarsening kinetics of γ -γ microstructure it is important to consider the simulations in 3D with relatively high number of γ precipitates for good statistics. However there are very few published 3D phase-field simulation results of γ precipitation [16,17] and other work concern the morphological evolution of γ particles [3]. One could also find very few attempts involving stochastic methods such as Monte Carlo approach but on relatively small-scale simulation [18,19].…”

Section: Simulation Setupmentioning

confidence: 99%

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Large scale 3-D phase-field simulation of coarsening in Ni-base superalloys

Rajendran

Shchyglo²,

Steinbach³

2014

MATEC Web of Conferences

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Abstract. In this study we present a large scale numerical simulation of γ -γ microstructure evolution in Nibase superalloy using the multi-phase field method in three dimensions. We numerically simulated precipitation hardening heat treatment cycles. Large scale three dimensional simulations are necessary in order to get sufficient statistics for predicting the morphological evolution, average γ precipitate size, precipitates size distribution over time and ripening exponent for a given temperature and composition. A detailed analysis of obtained result is presented emphasising the effect of elastic interaction on the coarsening kinetics in Ni-base superalloy. The study is performed using the phase-field modelling library "OpenPhase" which is based on a multi-phase field multi-component model.

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Section: Coarsening Exponentmentioning

confidence: 87%

Section: Particle Size Distributionmentioning

confidence: 99%

Section: Simulation Setupmentioning

confidence: 99%

See 1 more Smart Citation

Large scale 3-D phase-field simulation of coarsening in Ni-base superalloys

Rajendran

Shchyglo²,

Steinbach³

2014

MATEC Web of Conferences

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“…A similar dynamic evolution model has also been used to predict equilibrium shapes in 3Ds in Reference 28. Apart from the determination of equilibrium shapes, the diffuse-interface methods have also been used for the study of growth and coarsening of multi-particle systems, [27,[29][30][31][32][33][34] instabilities, [35] and rafting. [36][37][38][39][40][41] In all the above studies, the central focus of investigation has been the study of equilibrium shapes of precipitates where the anisotropy exists only in the elastic energy.…”

Section: Introductionmentioning

confidence: 99%

Phase-Field Modeling of Equilibrium Precipitate Shapes Under the Influence of Coherency Stresses

Bhadak

Sankarasubramanian

Choudhury

2018

Metall Mater Trans A

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Coherency misfit stresses and their related anisotropies are known to influence the equilibrium shapes of precipitates. Additionally, mechanical properties of the alloys are also dependent on the shapes of the precipitates. Therefore, in order to investigate the mechanical response of a material which undergoes precipitation during heat treatment, it is important to derive the range of precipitate shapes that evolve. In this regard, several studies have been conducted in the past using sharp-interface approaches where the influence of elastic energy anisotropy on the precipitate shapes has been investigated. In this paper, we propose a diffuse interface approach which allows us to minimize grid-anisotropy-related issues applicable to sharp-interface methods. In this context, we introduce a novel phase-field method where we minimize the functional consisting of the elastic and surface energy contributions while preserving the precipitate volume. Using this technique, we reproduce the shape bifurcation diagrams for the cases of pure dilatational misfit that have been studied previously using sharp-interface methods and then extend them to include interfacial energy anisotropy with different anisotropy strengths which has not been a part of previous sharp-interface models. While we restrict ourselves to cubic anisotropies in both elastic and interfacial energies in this study, the model is generic enough to handle any combination of anisotropies in both the bulk and interfacial terms. Further, we have examined the influence of asymmetry in dilatational misfit strains along with interfacial energy anisotropy on precipitate morphologies.

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“…[1][2][3][4] The phase-field model describes a microstructure using a set of conserved or non-conserved field variables. The microstructure evolution can be simulated by a set of equations governing the evolution of the fields under the condition of achieving the minimum of the total free energy of the system.…”

Section: Introductionmentioning

confidence: 99%

Phase-Field Simulation of the Effect of Elastic Inhomogeneity on Microstructure Evolution in Ni-Based Superalloys

et al. 2009

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Phase-field simulation is performed to examine the effect of elastic inhomogeneity between the and 0 phases on microstructure evolution of the 0 phase in Ni-based superalloys. For solving the elastic equilibrium equation numerically in the elastically inhomogeneous system, an iterative approach is used. In this simulation, both elastic anisotropy and shear modulus are varied independently based on the elastic constants of a practical Ni-based superalloy. Four different types of anti-phase domains in the 0 phase are also considered in this simulation. The variation of elastic anisotropy affected significantly the manner of both morphology of the 0 phase and distribution function of the 0 particle size, whereas the variation of shear modulus did not affect them.

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Three-dimensional phase-field simulations of coarsening kinetics of γ′ particles in binary Ni–Al alloys

Cited by 217 publications

References 36 publications

Large scale 3-D phase-field simulation of coarsening in Ni-base superalloys

Large scale 3-D phase-field simulation of coarsening in Ni-base superalloys

Phase-Field Modeling of Equilibrium Precipitate Shapes Under the Influence of Coherency Stresses

Phase-Field Simulation of the Effect of Elastic Inhomogeneity on Microstructure Evolution in Ni-Based Superalloys

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