Phase field study of precipitate rafting under a uniaxial stress

Gururajan, M. P.; Abinandanan, T.A.

doi:10.1016/j.actamat.2007.05.021

Cited by 86 publications

(61 citation statements)

References 45 publications

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“…14, is solved using an iterative Fourier spectral technique with periodic boundary conditions (described in detail in Gururajan and Abinandanan [13]; see also…”

Section: Formulationmentioning

confidence: 99%

Phase field study of precipitate growth: Effect of misfit strain and interface curvature

2009

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We have studied diffusion controlled growth of an isolated, misfitting precipitate in a supersaturated matrix using a phase field model. Treating our simulations as computer experiments, we have critically compared our simulation results with those from Zener-Frank and Laraia-Johnson theories for the growth of non-misfitting and misfitting precipitates, respectively. The agreement between simulations and the ZF theory is very good for 1D systems. In 2D systems with interfacial curvature, we still get good agreement between simulations and both ZF and LJ theories, but only for large supersaturations. At small supersaturations, the growth coefficient from our simulations does converge towards that from theory, but a large gap does remain when the simulations end due to overlap of diffusion fields. An interesting finding from the simulations is the less complete realization of the Gibbs-Thomson effect during growth, particularly in more supersaturated alloys. Thus, even at the same precipitate size, the curvature effects are less severe in more supersaturated alloys.

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“…14, is solved using an iterative Fourier spectral technique with periodic boundary conditions (described in detail in Gururajan and Abinandanan [13]; see also…”

Section: Formulationmentioning

confidence: 99%

Phase field study of precipitate growth: Effect of misfit strain and interface curvature

2009

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“…There have been some models of the phase-field method for simulating microstructure evolutions in Ni-Al alloys. [12][13][14] Also, there are a few reports about the simulation of the rafting phenomena, 15) but a comprehensive simulation from the formation to the collapse of the rafted structure has not been reported as long as we know.…”

Section: )mentioning

confidence: 99%

“…These field variables vary spatially ðrÞ and temporally ðtÞ. Usually, alloy composition, cðr; tÞ, is used as a field variable, [12][13][14][15] but in this study, f ðr; tÞ is used instead of cðr; tÞ, because f ðr; tÞ is suitable to treat the multi-component system when the phase field method is applied to the practical Ni-based alloys. The temporal evolution of the field variables is given by solving the following Cahn …”

Section: Calculation Modelmentioning

confidence: 99%

Phase-Field Simulation on the Formation and Collapse Processes of the Rafted Structure in Ni-Based Superalloys

et al. 2008

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In Ni-based superalloys, the rafted structure is known to form in the early stage of creep and to get into wavy morphology in the final stage of creep at elevated temperatures. This rafting phenomenon is essentially related to the anisotropic relaxation of the lattice misfit between the and 0 phases due to the creep strain under the external stress. In this study, in order to simulate comprehensively from the formation to collapse processes of the rafted structure by the phase-field method, a new idea that the anisotropy increases with simulation time is employed in the calculation of the elastic strain energy in alloy. This idea corresponds to the phenomenon that creep strain increases with creep time. The results are in good agreement with the microstructural change observed in practical Ni-based alloys.

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“…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. The coupled influence of both the interfacial energy and elastic anisotropies on the equilibrium morphologies is performed using the boundary integral method by Leo et al [42] In a study by Greenwood et al, [43] the authors have developed a phase-field model of microstructural evolution, where they study the morphological evolution of solid-state dendrites as function of anisotropies in both surface as well as 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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Phase field study of precipitate rafting under a uniaxial stress

Cited by 86 publications

References 45 publications

Phase field study of precipitate growth: Effect of misfit strain and interface curvature

Phase field study of precipitate growth: Effect of misfit strain and interface curvature

Phase-Field Simulation on the Formation and Collapse Processes of the Rafted Structure in Ni-Based Superalloys

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

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