scholarly journals Variational formulation and numerical accuracy of a quantitative phase-field model for binary alloy solidification with two-sided diffusion

2016 ◽  
Vol 93 (1) ◽  
Author(s):  
Munekazu Ohno ◽  
Tomohiro Takaki ◽  
Yasushi Shibuta
Keyword(s):  
Binary Alloy ◽  
Phase Field ◽  
Variational Formulation ◽  
Field Model ◽  
Phase Field Model ◽  
Numerical Accuracy ◽  
Alloy Solidification ◽  
Quantitative Phase

scholarly journals A Phase Field Model for Binary Alloy Solidification with Boundary Interface Intersection

2016 ◽  
Vol 8 ◽  
pp. 9-18
Author(s):  
Jie Liao
Keyword(s):  
Binary Alloy ◽  
Phase Field ◽  
Field Model ◽  
Contact Region ◽  
Contact Point ◽  
Boundary Surface ◽  
Phase Field Model ◽  
Diffuse Interface ◽  
Interface Problem ◽  
Alloy Solidification

A phase field model for binary alloy solidification with boundary interface intersection is developed. In the phase field model, the heat and solute conservation equations are appropriately modified to account for the presence of heat and solute rejection inside the diffuse interface, and a relaxation boundary condition for the phase field variable is introduced to balance the interface energy and boundary surface energy in the multiphase contact region. The thin interface asymptotic analysis is applied on the phase field model to yield the free interface problem with dynamic contact point condition.

scholarly journals Quantitative phase-field model of alloy solidification

2004 ◽  
Vol 70 (6) ◽  
Author(s):  
Blas Echebarria ◽  
Roger Folch ◽  
Alain Karma ◽  
Mathis Plapp
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Alloy Solidification ◽  
Quantitative Phase

On the Fully Implicit Solution of a Phase-Field Model for Binary Alloy Solidification in Three Dimensions

2012 ◽  
Vol 4 (06) ◽  
pp. 665-684 ◽  
Author(s):  
Christopher E. Goodyer ◽  
Peter K. Jimack ◽  
Andrew M. Mullis ◽  
Hongbiao Dong ◽  
Yu Xie
Keyword(s):  
Binary Alloy ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Second Order ◽  
Three Dimensions ◽  
Computational Techniques ◽  
Time Step ◽  
Alloy Solidification ◽  
Fully Implicit

AbstractA fully implicit numerical method, based upon a combination of adaptively refined hierarchical meshes and geometric multigrid, is presented for the simulation of binary alloy solidification in three space dimensions. The computational techniques are presented for a particular mathematical model, based upon the phase-field approach, however their applicability is of greater generality than for the specific phase-field model used here. In particular, an implicit second order time discretization is combined with the use of second order spatial differences to yield a large nonlinear system of algebraic equations as each time step. It is demonstrated that these equations may be solved reliably and efficiently through the use of a nonlinear multigrid scheme for locally refined grids. In effect this paper presents an extension of earlier research in two space dimensions (J. Comput. Phys., 225 (2007), pp. 1271-1287) to fully three-dimensional problems. This extension is validated against earlier two-dimensional results and against some of the limited results available in three dimensions, obtained using an explicit scheme. The efficiency of the implicit approach and the multigrid solver are then demonstrated and some sample computational results for the simulation of the growth of dendrite structures are presented.

A phase field model for phase transformation in an elastically stressed binary alloy

2005 ◽  
Vol 13 (3) ◽  
pp. 299-319 ◽  
Author(s):  
Dong-Hee Yeon ◽  
Pil-Ryung Cha ◽  
Ji-Hee Kim ◽  
Martin Grant ◽  
Jong-Kyu Yoon
Keyword(s):  
Phase Transformation ◽  
Binary Alloy ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model

Study on Microstructural Evolution of Binary Alloy Crystal Growth in Directional Solidification Process

2013 ◽  
Vol 470 ◽  
pp. 100-103
Author(s):  
Dong Sheng Chen ◽  
Ming Chen ◽  
Rui Chang Wang
Keyword(s):  
Crystal Growth ◽  
Directional Solidification ◽  
Binary Alloy ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Pure Substance ◽  
Columnar Dendrite

PFM (phase field method) was employed to study microstructure evolution, and considering the effect of solute concentration to the undercooling, we developed a phase field model for binary alloy on the basis of pure substance model. In the paper, the temperature field and solute field were coupled together in the phase field model to calculate the crystal growth of magnesium alloy in directional solidification. The simulation results showed a non-planar crystal growth of planar to cellular to columnar dendrite, the comparison of different dendrite patterns were carried out in the numerical simulation, and with the increasing of the anisotropy, the second dendrite arms became more developed.

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