Evaluation of microsegregation during dendritic solidification of a binary alloy using phase field method and analytical models

Subject Areas : journal of New Materials

هادی براتی ¹ , محمدرضا ابوطالبی ² , سعید شبستری ³

1 - کارشناس ارشد دانشکده مهندسی مواد و متالورژی دانشگاه علم و صنعت تهران
2 - استاد دانشکده مهندسی مواد و متالورژی دانشگاه علم و صنعت تهران
3 - استاد دانشکده مهندسی مواد و متالورژی دانشگاه علم و صنعت تهران

Received: 2015-12-30 Accepted : 2015-12-30 Published : 2010-09-23

Keywords: Simulation, microsegregation, dendritic solidification, phase field method,

Abstract :

In this research microsegregation in the dendritic directional solidification has been investigated using phase field simulation and some of analytical models. Comparison of the numerical and analytical results showed that in the investigation conditions, the analytical equations overestimated the phase field simulation results. It is found under both back diffusion and no back diffusion conditions. In a range of the solid fraction numerical and analytical results were comparable and difference between them was increased by increasing of the solid fraction. 

References:

1- V. R. Voller, "A semi-analytical model of microsegregation in a binary alloy", Journal of Crystal Growth, 197, 1999, 325-332.

2- J. Li, J. Wang, and G. Yang, "Investigation into microsegregation during solidification of a binary alloy by phase-field simulations", Journal of Crystal Growth, 311, 2009, 1217-1222.

3- T. W. Clyne and W. Kurz, "Solute Redistribution during Solidification with Rapid Solid State Diffusion", Metallurgical transactions. A, Physical metallurgy and materials science, 12 A, 1981, 965-971.

4- I. Ohnaka, "Mathematical Analysis of Solute Redistribution during Solidification with Diffusion in Solid Phase", Transactions of the Iron and Steel Institute of Japan, 26, 1986, 1045-1051.

5- Q. Du and A. Jacot, "A two-dimensional microsegregation model for the description of microstructure formation during solidification in multicomponent alloys: Formulation and behaviour of the model", Acta Materialia, 53, 2005, 3479-3493.

6- Q. Du, D. G. Eskin, A. Jacot, and L. Katgerman, "Two-dimensional modelling and experimental study on microsegregation during solidification of an Al-Cu binary alloy", Acta Materialia, 55, 2007, 1523-1532.

7- A. Karma and W. J. Rappel, "Phase-field method for computationally efficient modeling of solidification with arbitrary interface kinetics", Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 53, 1996, R3017-R3020.

8- A. Karma and W. J. Rappel, "Numerical simulation of three-dimensional dendritic growth", Physical Review Letters, 77, 1996, 4050-4053.

9- I. Loginova, G. Amberg, and J. Agren, "Phase-field simulations of non-isothermal binary alloy solidification", Acta Materialia, 49, 2001, 573-581.

10- J. A. Warren and W. J. Boettinger, "Prediction of dendritic growth and microsegregation patterns in a binary alloy using the phase-field method", Acta Metallurgica Et Materialia, 43, 1995, 689-703.

11- J. C. Ramirez and C. Beckermann, "Examination of binary alloy free dendritic growth theories with a phase-field model", Acta Materialia, 53, 2005, 1721-1736.

12- J. C. Ramirez, C. Beckermann, A. Karma, and H. J. Diepers, "Phase-field modeling of binary alloy solidification with coupled heat and solute diffusion", Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 69, 2004, 051607.

13- A. Karma, "Phase-Field Formulation for Quantitative Modeling of Alloy Solidification", Physical Review Letters, 87, 2001, 115701.

14- C. W. Lan and C. J. Shih, "Phase field simulation of non-isothermal free dendritic growth of a binary alloy in a forced flow", Journal of Crystal Growth, 264, 2004, 472-482.

15- B. Giovanola and W. Kurz, "Modeling of microsegregation under rapid solidification conditions", Metallurgical Transactions A, 21, 1990, 260-263.

16- V. R. Voller and C. Beckermann, "A unified model of microsegregation and coarsening", Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 30, 1999, 2183-2189.

17- A. Mortensen, "On the influence of coarsening on microsegregation", Metallurgical Transactions A, 20, 1989, 247-253.