• Title/Summary/Keyword: Phase-field model

### Phase Field Modeling of Graphitization in Ductile Cast Iron by Strip Casting(I);Modeling of Phases with Negligible Solubility (스트립캐스팅한 구상흑연주철 박판의 흑연화 과정에 대한 phase-field 모델링 (I);고용도가 없는 상의 모델링)

• Kim, Sung-Gyun;Ra, Hyung-Yong
• Journal of Korea Foundry Society
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• v.20 no.2
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• pp.129-140
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• 2000
• This study aims at the phase-field modeling of the phase transformation in graphitization of the cast iron. As the first step, we constructed a phase-field model including the phases with negligible solubility. Under the dilute regular solution approximation, a simplified version of the phase-field model was obtained, which can be used for the phase transformation related with the stoichiometric phases. The results from the numerical calculation of the phase-field model was in good agreement with the exact analytic solution. The compositional shift due to Gibbs-Thomson effect can be reproduced within 0.5% error in the numerical calculation. The interface velocity, whereas, in numerical calculation of phase-field model appeared to be 15% larger than that from the analytic solution. This error is due to the shift of the interface position in phase-field model from the position with ${\phi}=0.5$.

### THREE-DIMENSIONAL NUMERICAL SIMULATIONS OF A PHASE-FIELD MODEL FOR ANISOTROPIC INTERFACIAL ENERGY

• Kim, Jun-Seok
• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.453-464
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• 2007
• A computationally efficient numerical scheme is presented for the phase-field model of two-phase systems for anisotropic interfacial energy. The scheme is solved by using a nonlinear multigrid method. When the coefficient for the anisotropic interfacial energy is sufficiently high, the interface of the system shows corners or missing crystallographic orientations. Numerical simulations with high and low anisotropic coefficients show excellent agreement with exact equilibrium shapes. We also present spinodal decomposition, which shows the robustness of the pro-posed scheme.

### Study of Li-Ion Diffusion and Phase Transition in Cathode of Li-Ion Battery (리튬 이차전지의 양극 내부 이온 확산 및 상변화 특성 연구)

• Kim, Sooil;Kim, Dongchoul
• Transactions of the Korean Society of Mechanical Engineers B
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• v.37 no.7
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• pp.665-667
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• 2013
• Metal ions show various transitions in the cathode of a lithium-ion battery. The diffusion process of lithiumions and the phase transition in the cathode need to be thoroughly understood for the advanced design of an improved lithium-ion battery. Here, we employ a phase field model to simulate the diffusion of lithiumions and to study the phase transition in the cathode.

### Grain Growth and Texture Evolution of Mg: Phase Field Modeling (마그네슘의 결정립 성장과 집합조직: 상장모델 계산)

• Kim, Dong-Uk;Cha, Pil-Ryung
• Journal of Korean Powder Metallurgy Institute
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• v.18 no.2
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• pp.168-171
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• 2011
• We investigate grain growth behavior of poly-crystalline Mg sheet having strong basal fiber texture using phase field model for grain growth and micro-elasticity. Strong initial basal texture was maintained when external load was not imposed, but was weaken when external biaxial strain was imposed. Elastic interaction between elastic anisotropy of Mg grain and external load is the reason why texture evolution occurs.

### Numerical Calculation of Transformation Plasticity Using a FE Analysis Coupled with n Phase Field Model (상장모델과 유한요소법의 연계해석을 통한 변태소성 전산모사)

• Cho, Y.G.;Kim, J.Y.;Cha, P.R.;Lee, J.K.;Han, H.N.
• Proceedings of the Korean Society for Technology of Plasticity Conference
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• pp.318-321
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• 2009
• Transformation plasticity is that when a phase transformation of ferrous or non-ferrous alloys progresses even under an extremely small applied stress compared with a yield stress of the material, a permanent deformation occurs. One of widely accepted description for the transformation was proposed by Greenwood and Johnson [1]. Their description is based on an assumption that a weaker phase of an ideal plastic material could deform plastically to accommodate the externally applied stress and the internal stress caused by the volumetric change accompanying the phase transformation. In this study, an implicit finite element model was developed to simulate the deformation behavior of a low carbon steel during phase transformation. The finite element model was coupled with a phase field model, which could simulate the kinetics for ferrite to austenite transformation of the steel. The thermo-elasto-plastic constitutive equation for each phase was adopted to confirm the weaker phase yielding, which was proposed by Greenwood and Johnson [1]. From the simulation, the origin of the transformation plasticity was quantitatively discussed comparing with the other descriptions of it.

### Introduction to Crack Phase Field Model and Applications (균열상장 모델의 소개와 적용)

• Han, Dong-Seok
• Computational Structural Engineering
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• v.28 no.4
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• pp.25-29
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• 2015

### Multi-Scale Scheme Implemented on Phase-Field Model to Simulate Freezing in Turbulent Flow

• Xu Ying;McDonough J.M.;Tagavi K.A.
• 한국전산유체공학회:학술대회논문집
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• pp.368-371
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• 2006

### Design Optimization of Moving-Coil Type Linear Actuator Using Level Set Method and Phase-Field Model (레벨셋법과 페이즈 필드 모델을 이용한 가동코일형 리니어 액추에이터 최적설계)

• Lim, Sung-Hoon;Oh, Se-Ahn;Min, Seung-Jae;Hong, Jung-Pyo
• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.10
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• pp.1223-1228
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• 2011
• A moving-coil type linear actuator has been widely used in the system reciprocating short stroke because of its several advantages, such as the structural simplicity, low weight and a fast control response speed. This paper presents a design approach for improving the actuating performance with a clear expression of optimal configuration represented by a level set function. The optimization problem is formulated to minimize the variation of magnetic force at every moving displacement of the mover for fast and easy control. To consider the manufacturability of actuator, the concept of phase-field model is incorporated to control the complexity of structural boundaries. To verify the usefulness of the proposed method, the core design example of cylindrical linear actuator is performed.

### PHASE FIELD MODELING OF CRYSTAL GROWTH

• Sekerka, Robert F.
• Proceedings of the Korea Association of Crystal Growth Conference
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• pp.139-156
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• 1996
• The phase field model is becoming the model of choice for the theoretical study of the morphologies of crystals growth from the melt. This model provides an alternative approach to the solution of the classical (sharp interface) model of solidification by introducing a new variable, the phase field, Ø, to identify the phase. The variable Ø takes on constant values in the bulk phases and makes a continuous transition between these values over a thin transition layer that plays the role of the classically sharp interface. This results in Ø being governed by a new partial differential equation(in addition to the PDE's that govern the classical fields, such as temperature and composition) that guarantees (in the asymptotic limit of a suitably thin transition layer) that the appropriate boundary conditions at the crystal-melt interface are satisfied. Thus, one can proceed to solve coupled PDE's without the necessity of explicitly tracking the interface (free boundary) that would be necessary to solve the classical (sharp interface) model. Recent advances in supercomputing and algorithms now enable generation of interesting and valuable results that display most of the fundamental solidification phenomena and processes that are observed experimentally. These include morphological instability, solute trapping, cellular growth, dendritic growth (with anisotropic sidebranching, tip splitting, and coupling to periodic forcing), coarsening, recalescence, eutectic growth, faceting, and texture development. This talk will focus on the fundamental basis of the phase field model in terms of irreversible thermodynamics as well as it computational limitations and prognosis for future improvement. This work is supported by the National Science Foundation under grant DMR 9211276

### FAST AND AUTOMATIC INPAINTING OF BINARY IMAGES USING A PHASE-FIELD MODEL

• Jeong, Da-Rae;Li, Yibao;Lee, Hyun-Geun;Kim, Jun-Seok
• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.3
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• pp.225-236
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• 2009
• Image inpainting is the process of reconstructing lost or deteriorated parts of images using information from surrounding areas. We propose a computationally efficient and fast phase-field method which uses automatic switching parameter, adaptive time step, and automatic stopping of calculation. The algorithm is based on an energy functional. We demonstrate the performance of our new method and compare it with a previous method.