Araştırma Makalesi
Yıl 2021,
Sayı: 36, 11 - 17, 30.09.2021
Öz
Kaynakça
- V. P. Menushenkov, M. V. Gorshenkov, I. V. Shchetinin, A. G. Savchenko, E. S. Savchenko, D. G. Zhukov, Evolution of the Microstructure and Magnetic Properties of As-Cast and Melt Spun Fe2NiAl Alloy During Aging, Journal of Magnetism and Magnetic Materials 390 (2015) 40-49.
- H. R. Sistla, J. W. Newkirk, F. F. Liou, Effect of Al/Ni ratio, Heat Treatment on Phase Transformations and Microstructure of AlxFeCoCrNi2 x (x=0.3, 1) High Entropy Alloys, Materials Design 81 (2015) 113-121.
- M. Javanbakht, V. I. Levitas, Interaction between Phase Transformations and Dislocations at the Nanoscale. Part 2: Phase Field Simulation Examples, Journal of the Mechanics and Physics of Solids 82 (2015) 164-185.
- P. Steinmetz, Y. C. Yabansu, J. Hötzer, M. Jainta, B. Nestler, S. R. Kalidindi, Analytics for Microstructure Datasets Produced by Phase-Field Simulations, Acta Materialia 103 (2016) 192-203.
- J. Kundin, L. Mushongera, H. Emmerich, Phase-Field Modeling of Microstructure Formation During Rapid Solidification in Inconel 718 superalloy, Acta Materialia 95 (2015) 343-356.
- J. W. Cahn, J. E. Hilliard, Free Energy of a Nonuniform System. I. Interfacial Free Energy, The Journal of Chemical Physics 28 (1958) 258-267.
- J. W. Cahn, Free Energy of a Nonuniform System. II. Thermodynamic Basis, The Journal of Chemical Physics 30 (1959) 1121-1124.
- X. Zhang, G. Shen, C. W. Li, J. F. Gu, Analysis of Interface Migration and Isothermal Martensite Formation for Quenching and Partitioning Process in a Low-Carbon Steel by Phase Field Modeling, Modelling and Simulation in Materials Science and Engineering 27(7) (2019) 075011.
- P. P. Moskvin, S. I. Skurativskyi, O. P. Kravchenko, G. V. Skyba, H. V. Shapovalov, Spinodal Decomposition and Composition Modulation Effect at the Low-Temperature Synthesis of Ax3B1-x3C5 Semiconductor Solid Solutions, Journal of Crystal Growth, 510 (2019) 40-46.
- N. Kuwahara, H. Sato, K. Kubota, Kinetics of Spinodal Decomposition in a Polymer Mixture, Physical Review E 47 (1993) 1132-1138.
- D. Jeong, S. Lee, Y. Choi, J. Kim, Energy-Minimizing Wavelengths of Equilibrium States for Diblock Copolymers in the Hex-Cylinder Phase, Current Applied Physics 15 (2015) 799-804.
- Y. F. Wang, Z. H. Xiao, S. Q. Shi, Xe Gas Bubbles Evolution in UO2 Fuels-A Phase Field Simulation, Scientia Sinica: Physica, Mechanica et Astronomica 49 (2019) 11.
- A. L. Bertozzi, S. Esedoglu, A. Gillette, Inpainting of Binary Images Using the Cahn-Hilliard Equation, IEEE Transactions on Image Processing 16 (2007) 285-291.
- A. Vorobev, T. Lyubimova, Vibrational Convection in a Heterogeneous Binary Mixture. Part 1. Time-Averaged Equations, Journal of Fluid Mechanics 870 (2019) 543-562.
- E. V. Radkevich, E. A. Lukashev, O. A. Vasil'eva, Hydrodynamic Instabilities and Nonequilibrium Phase Transitions, Doklady Mathematics 99 (2019) 308-312.
- O. Wodo, B. Ganapathysubramanian, Computationally Efficient Solution to the Cahn-Hilliard Equation: Adaptive Implicit Time Schemes, Mesh Sensitivity Analysis and the 3D Isoperimetric Problem, Journal of Computational Physics 230 (2011) 6037-6060.
- C. Liu, F. Frank, B. M. Rivière, Numerical Error Analysis for Nonsymmetric Interior Penalty Discontinuous Galerkin Method of Cahn-Hilliard Equation, Numerical Methods for Partial Differential Equations 35 (2019) 1509-1537.
- M. Dehghan, V. Mohammadi, The Numerical Solution of Cahn-Hilliard (CH) Equation in One, Two and Three-Dimensions via Globally Radial Basis Functions (GRBFs) and RBFs-Differential Quadrature (RBFs-DQ) Methods, Engineering Analysis with Boundary Elements 51 (2015) 74-100.
- A. M. S. Mahdy, N. A. H. Mukhtar, Numerical Solution of Cahn-Hiliard Equation, International Journal of Applied Engineering Research 13 (2018) 3150-3156.
- D. Lu, M. S. Osman, M. M. A. Khater, R. A. M. Attia, D. Baleanu, Analytical and Numerical Simulations for the Kinetics of Phase Separation in Iron (Fe-Cr-X (X=Mo,Cu)) based on Ternary Alloys, Physica A: Statistical Mechanics and its Applications 537 (2020) 122634.
- A. Yokuş, An Expansion Method for Finding Traveling Wave Solutions to Nonlinear Pdes, Istanbul Commerce University Journal of Science 14 (2015) 65-81.
- H. Durur, A. Yokuş, Hyperbolic Traveling Wave Solutions for Sawada Kotera Equation Using (1/G')-Expansion Method, Afyon Kocatepe University Journal of Sciences and Engineering 19 (2019) 615-619.
- A. Yokuş, H. Durur, Complex Hyperbolic Traveling Wave Solutions of Kuramoto-Sivashinsky Equation Using (1/G') Expansion Method for Nonlinear Dynamic Theory, Journal of Balikesir University Institute of Science and Technology 21 (2019) 590-599.
Analytical Approximation for Cahn-Hillard Phase-Field Model for Spinodal Decomposition of a Binary System
Öz
Phase transformations which lead to dramatical property change are very important for engineering materials. Phase-field methods are one of the most successful and practical methods for modelling phase transformations in materials. The Cahn-Hillard phase-field model is among the most promising phase-field models. The most successful aspect of the model is that it can predict spinodal decomposition (which is essential to determining the microstructure of an alloy) in a binary system. It is used in both materials science and many other fields, such as polymer science, astrophysics, and computer science. In this study, the Cahn-Hillard phase-field model is evaluated by an analytical approach using the (1/G')-expansion method. The solutions obtained are tested for certain thermodynamic conditions, and their accuracy of predicting the spidonal decomposition of a binary system is confirmed.
Anahtar Kelimeler
Cahn-Hillard phase field model spidonal decomposition (1/G’)-expansion method
Kaynakça
- V. P. Menushenkov, M. V. Gorshenkov, I. V. Shchetinin, A. G. Savchenko, E. S. Savchenko, D. G. Zhukov, Evolution of the Microstructure and Magnetic Properties of As-Cast and Melt Spun Fe2NiAl Alloy During Aging, Journal of Magnetism and Magnetic Materials 390 (2015) 40-49.
- H. R. Sistla, J. W. Newkirk, F. F. Liou, Effect of Al/Ni ratio, Heat Treatment on Phase Transformations and Microstructure of AlxFeCoCrNi2 x (x=0.3, 1) High Entropy Alloys, Materials Design 81 (2015) 113-121.
- M. Javanbakht, V. I. Levitas, Interaction between Phase Transformations and Dislocations at the Nanoscale. Part 2: Phase Field Simulation Examples, Journal of the Mechanics and Physics of Solids 82 (2015) 164-185.
- P. Steinmetz, Y. C. Yabansu, J. Hötzer, M. Jainta, B. Nestler, S. R. Kalidindi, Analytics for Microstructure Datasets Produced by Phase-Field Simulations, Acta Materialia 103 (2016) 192-203.
- J. Kundin, L. Mushongera, H. Emmerich, Phase-Field Modeling of Microstructure Formation During Rapid Solidification in Inconel 718 superalloy, Acta Materialia 95 (2015) 343-356.
- J. W. Cahn, J. E. Hilliard, Free Energy of a Nonuniform System. I. Interfacial Free Energy, The Journal of Chemical Physics 28 (1958) 258-267.
- J. W. Cahn, Free Energy of a Nonuniform System. II. Thermodynamic Basis, The Journal of Chemical Physics 30 (1959) 1121-1124.
- X. Zhang, G. Shen, C. W. Li, J. F. Gu, Analysis of Interface Migration and Isothermal Martensite Formation for Quenching and Partitioning Process in a Low-Carbon Steel by Phase Field Modeling, Modelling and Simulation in Materials Science and Engineering 27(7) (2019) 075011.
- P. P. Moskvin, S. I. Skurativskyi, O. P. Kravchenko, G. V. Skyba, H. V. Shapovalov, Spinodal Decomposition and Composition Modulation Effect at the Low-Temperature Synthesis of Ax3B1-x3C5 Semiconductor Solid Solutions, Journal of Crystal Growth, 510 (2019) 40-46.
- N. Kuwahara, H. Sato, K. Kubota, Kinetics of Spinodal Decomposition in a Polymer Mixture, Physical Review E 47 (1993) 1132-1138.
- D. Jeong, S. Lee, Y. Choi, J. Kim, Energy-Minimizing Wavelengths of Equilibrium States for Diblock Copolymers in the Hex-Cylinder Phase, Current Applied Physics 15 (2015) 799-804.
- Y. F. Wang, Z. H. Xiao, S. Q. Shi, Xe Gas Bubbles Evolution in UO2 Fuels-A Phase Field Simulation, Scientia Sinica: Physica, Mechanica et Astronomica 49 (2019) 11.
- A. L. Bertozzi, S. Esedoglu, A. Gillette, Inpainting of Binary Images Using the Cahn-Hilliard Equation, IEEE Transactions on Image Processing 16 (2007) 285-291.
- A. Vorobev, T. Lyubimova, Vibrational Convection in a Heterogeneous Binary Mixture. Part 1. Time-Averaged Equations, Journal of Fluid Mechanics 870 (2019) 543-562.
- E. V. Radkevich, E. A. Lukashev, O. A. Vasil'eva, Hydrodynamic Instabilities and Nonequilibrium Phase Transitions, Doklady Mathematics 99 (2019) 308-312.
- O. Wodo, B. Ganapathysubramanian, Computationally Efficient Solution to the Cahn-Hilliard Equation: Adaptive Implicit Time Schemes, Mesh Sensitivity Analysis and the 3D Isoperimetric Problem, Journal of Computational Physics 230 (2011) 6037-6060.
- C. Liu, F. Frank, B. M. Rivière, Numerical Error Analysis for Nonsymmetric Interior Penalty Discontinuous Galerkin Method of Cahn-Hilliard Equation, Numerical Methods for Partial Differential Equations 35 (2019) 1509-1537.
- M. Dehghan, V. Mohammadi, The Numerical Solution of Cahn-Hilliard (CH) Equation in One, Two and Three-Dimensions via Globally Radial Basis Functions (GRBFs) and RBFs-Differential Quadrature (RBFs-DQ) Methods, Engineering Analysis with Boundary Elements 51 (2015) 74-100.
- A. M. S. Mahdy, N. A. H. Mukhtar, Numerical Solution of Cahn-Hiliard Equation, International Journal of Applied Engineering Research 13 (2018) 3150-3156.
- D. Lu, M. S. Osman, M. M. A. Khater, R. A. M. Attia, D. Baleanu, Analytical and Numerical Simulations for the Kinetics of Phase Separation in Iron (Fe-Cr-X (X=Mo,Cu)) based on Ternary Alloys, Physica A: Statistical Mechanics and its Applications 537 (2020) 122634.
- A. Yokuş, An Expansion Method for Finding Traveling Wave Solutions to Nonlinear Pdes, Istanbul Commerce University Journal of Science 14 (2015) 65-81.
- H. Durur, A. Yokuş, Hyperbolic Traveling Wave Solutions for Sawada Kotera Equation Using (1/G')-Expansion Method, Afyon Kocatepe University Journal of Sciences and Engineering 19 (2019) 615-619.
- A. Yokuş, H. Durur, Complex Hyperbolic Traveling Wave Solutions of Kuramoto-Sivashinsky Equation Using (1/G') Expansion Method for Nonlinear Dynamic Theory, Journal of Balikesir University Institute of Science and Technology 21 (2019) 590-599.
Toplam 23 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Uygulamalı Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Eylül 2021 |
| Gönderilme Tarihi | 2 Ekim 2020 |
| Yayımlandığı Sayı | Yıl 2021 Sayı: 36 |
Kaynak Göster
- Makale Dosyaları
|