Two-dimensional phase-field study of competitive grain growth during directional solidification of polycrystalline binary alloy

Takaki, Tomohiro; Ohno, Munekazu; Shibuta, Yasushi; Sakane, Shinji; Shimokawabe, Takashi; Aoki, Takayuki

doi:10.1016/j.jcrysgro.2016.01.036

Cited by 83 publications

(44 citation statements)

References 25 publications

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“…However, recent advances in high-performance computing techniques have enabled large-scale phase-field simulations of the competitive growth of a bunch of dendrites [21][22][23]43,44]. Furthermore, molecular dynamics (MD) simulations have contributed to the estimation of the interfacial properties required for quantitative phase-field simulations [45,46] and large-scale MD simulations are now closing the gap in the knowledge between the microstructural and atomistic scales [47,48].…”

Section: Discussionmentioning

confidence: 99%

“…The simulation results of quantitative models rapidly converge to unique values (the solutions of the free-boundary problem) with decreasing W , indicating good numerical performance [11,14]. Quantitative phase-field models are increasingly utilized in studies on the formation processes of solidification microstructures [18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 90%

“…In addition, to reduce the computational cost, the growth of the solid in the x direction was simulated by moving the computational box in the x direction along with the growth front of the solid. The simulation was accelerated by using a TESLA K40 graphics processing unit (GPU) [21][22][23]. Figure 2 shows the results of the convergence test.…”

Section: And Q CI Is Given Asmentioning

confidence: 99%

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Variational formulation of a quantitative phase-field model for nonisothermal solidification in a multicomponent alloy

2017

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A variational formulation of a quantitative phase-field model is presented for nonisothermal solidification in a multicomponent alloy with two-sided asymmetric diffusion. The essential ingredient of this formulation is that the diffusion fluxes for conserved variables in both the liquid and solid are separately derived from functional derivatives of the total entropy and then these fluxes are related to each other on the basis of the local equilibrium conditions. In the present formulation, the cross-coupling terms between the phase-field and conserved variables naturally arise in the phase-field equation and diffusion equations, one of which corresponds to the antitrapping current, the phenomenological correction term in early nonvariational models. In addition, this formulation results in diffusivities of tensor form inside the interface. Asymptotic analysis demonstrates that this model can exactly reproduce the free-boundary problem in the thin-interface limit. The present model is widely applicable because approximations and simplifications are not formally introduced into the bulk's free energy densities and because off-diagonal elements of the diffusivity matrix are explicitly taken into account. Furthermore, we propose a nonvariational form of the present model to achieve high numerical performance. A numerical test of the nonvariational model is carried out for nonisothermal solidification in a binary alloy. It shows fast convergence of the results with decreasing interface thickness.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 90%

Section: And Q CI Is Given Asmentioning

confidence: 99%

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Variational formulation of a quantitative phase-field model for nonisothermal solidification in a multicomponent alloy

2017

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“…However, although it entails simple calculations, it loses numerous detailed facets in the data. Takaki and Ohno et al [33,34] simulated competition growth and the mutual influence of 2-D dendrites in a binary alloy under directional solidification by applying PFM and a parallel numerical computation method. Tourret et al [35] studied competitive growth of 2-D dendrites in a binary alloy during directional solidification by adopting PFM.…”

Section: * LI Fengmentioning

confidence: 99%

Phase-field numerical simulation of three-dimensional competitive growth of dendrites in a binary alloy

et al. 2018

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A s an important simulation method, the phasefield method (PFM), which enables researchers to directly simulate the formation of microstructures, is an efficient tool for studying the structure of complex solidification interfaces. PFM can couple nucleation and growth models and influencing factors of nucleation and growth process with the basic heat transfer equation to carry out accurate microscopic numerical simulation. In Abstract:The normal vector of migration direction in the solid-liquid interface of dendrites was used to describe the phase-field governing equation. By using the three angles formed by the normal vector for the migration direction of the dendritic growth interface and the coordinate axes of the simulation region, the authors expressed the interfacial anisotropy equation, and built a phase-field model for the competitive growth of multiple grains. Taking a Al-2%mole-Cu binary alloy as an example, the competitive growth of multiple grains during isothermal solidification was simulated by applying parallel computing techniques. In addition, the phase field simulation results were verified by the experimental method. The simulation results show that the competitive growth of equiaxed dendrite is divided into two types: the first occurs during the process of competitive growth, the tips of primary dendrite on different grains taking part in the competition stop growing in their optimal growth direction; the second also occurs during competitive growth, the tips of primary dendrite which participate in the competition on different grains never stop growing in their optimal growth direction. The dendritic morphologies of the first competition growth type are divided into two types. Primary dendrites of grains taking part in the competition stop growing in their optimal growth direction and the competition plane enlarges when neither one wins the competition. However, when one wins the competition, the primary dendrites of grains with superiority go through the blocking grains and continue to grow in their optimal growth direction. The primary dendrites of inferior grains stop growing in their optimal growth direction and then instead grow in those areas without obstacles. The dendritic morphology of the second competition-growth type is shown to be the deformation of primary dendrites, which are mainly represented as the deflection and bending observed from different views. Compared with the metallographic picture, the simulation results can show the morphology of the competitive growth in all directions, so this simulation method can better characterize the competitive growth process. this way, the quantitative relationship of the effect of primary process parameters on the microstructure during material forming processes can be obtained. As an open model, the phase-field model can be coupled with various external fields such as temperature, dissolution, gravity, and fluid fields, and can effectively combine the microscale with the macroscale. With the development of the phase-field model and im...

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“…11,12) This unusual overgrowth is frequently observed in 2D polycrystal grain competitive growth. 14) Grain selection in three-dimensional (3D) space is much more complicated than that in 2D space. 15,16) Unlike the 2D case, the interaction between FO and UO dendrites in the 3D case is not necessarily face-to-face, and there is a nonuniplanar GB, where the FO and UO dendrites are in a twist-ing relation, in addition to the converging and diverging GBs.…”

Section: Introductionmentioning

confidence: 99%

Large-scale Phase-field Studies of Three-dimensional Dendrite Competitive Growth at the Converging Grain Boundary during Directional Solidification of a Bicrystal Binary Alloy

et al. 2016

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Large-scale phase-field studies of three-dimensional (3D) dendrite competitive growth at the converging grain boundary (GB) of a bicrystal binary alloy were carried out using the GPU-rich supercomputer TSUBAME 2.5 at Tokyo Institute of Technology. First, a series of thin-sample simulations were performed to investigate the effects of thin-sample thickness, unfavorably oriented (UO) grain inclination angle, and dendrite arrangement on an unusual overgrowth phenomenon whereby the favorably oriented (FO) grain is overgrown by the UO grain. It was concluded that the unusual overgrowth easily occurs as the thickness of the thin sample and the UO grain inclination angle decrease. It was also concluded that the interaction between FO and UO dendrites at the converging GB depends on the dendrite arrangement for relatively large dendrite spacing. Next, realistic large-scale simulations whereby multiple dendrites interact at the converging GB were performed. Unusual overgrowth was also observed in such large-scale simulations, and this phenomenon easily occurred at smaller UO dendrite inclination angles. Furthermore, it was also concluded that the FO and UO dendrites rearrange toward a space-to-face interaction. Because the interaction between FO and UO dendrites differs according to the location on the GB, a zigzag GB was formed, especially at small UO grain inclination angles.

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Two-dimensional phase-field study of competitive grain growth during directional solidification of polycrystalline binary alloy

Cited by 83 publications

References 25 publications

Variational formulation of a quantitative phase-field model for nonisothermal solidification in a multicomponent alloy

Variational formulation of a quantitative phase-field model for nonisothermal solidification in a multicomponent alloy

Phase-field numerical simulation of three-dimensional competitive growth of dendrites in a binary alloy

Large-scale Phase-field Studies of Three-dimensional Dendrite Competitive Growth at the Converging Grain Boundary during Directional Solidification of a Bicrystal Binary Alloy

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