Solute trapping in directional solidification at high speed: A one-dimensional study with the phase-field model

1997 ◽  
Vol 56 (3) ◽  
pp. 3717-3720 ◽  
Author(s):  
M. Conti
Keyword(s):  
Directional Solidification ◽  
Phase Field ◽  
High Speed ◽  
Field Model ◽  
Phase Field Model ◽  
Solute Trapping ◽  
One Dimensional

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.

One-dimensional phase-field model for binary alloys

2000 ◽  
Vol 212 (3-4) ◽  
pp. 574-583 ◽  
Author(s):  
D.I. Popov ◽  
L.L. Regel ◽  
W.R. Wilcox
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Binary Alloys ◽  
Phase Field Model ◽  
One Dimensional

Solute trapping and solute drag in a phase-field model of rapid solidification

1998 ◽  
Vol 58 (3) ◽  
pp. 3436-3450 ◽  
Author(s):  
N. A. Ahmad ◽  
A. A. Wheeler ◽  
W. J. Boettinger ◽  
G. B. McFadden
Keyword(s):  
Rapid Solidification ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Solute Drag ◽  
Solute Trapping

Linear stability analysis and metastable solutions for a phase-field model

1999 ◽  
Vol 129 (3) ◽  
pp. 571-600 ◽  
Author(s):  
A. Jiménez-Casas ◽  
A. Rodríguez-Bernal
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Phase Field ◽  
Field Model ◽  
Equilibrium Points ◽  
Phase Field Model ◽  
One Dimensional ◽  
Stability And Instability ◽  
The One

We study the linear stability of equilibrium points of a semilinear phase-field model, giving criteria for stability and instability. In the one-dimensional case, we study the distribution of equilibria and also prove the existence of metastable solutions that evolve very slowly in time.

Phase field model for electrically induced damage using microforce theory

2021 ◽  
pp. 108128652110520
Author(s):  
Elizaveta Zipunova ◽  
Evgeny Savenkov
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Order Term ◽  
Phase Field Model ◽  
Special Problem ◽  
Three Dimensions ◽  
Electric Permittivity ◽  
One Dimensional ◽  
Codimension Two ◽  
Problem Setting

In this paper, we present a consistent derivation of the phase field model for electrically induced damage. The derivation is based on Gurtin’s microstress and microforce theory and the Coleman–Noll procedure. The resulting model accounts for Ohmic currents, includes charge conservation law and allows for finite electric permittivity and conductivity distribution in the medium. Special attention is devoted to the case when the damaged region is a codimension-two object, i.e., a curve in three dimensions. It is shown that in this case the free energy of the model necessarily includes a high-order term, which ensures the well-posedness of the problem. A special problem setting is proposed to account for the prescribed charge distribution. Local features of the phase field distribution are illustrated with one-dimensional axisymmetric numerical experiments.

2D Phase-Field Simulation of the Directional Solidification Process

2014 ◽  
Vol 704 ◽  
pp. 17-21 ◽  
Author(s):  
Alexandre Furtado Ferreira ◽  
José Adilson de Castro ◽  
Ivaldo Leão Ferreira
Keyword(s):  
Directional Solidification ◽  
Phase Field ◽  
Field Model ◽  
Solid Phase ◽  
Morphological Evolution ◽  
Phase Field Model ◽  
Columnar Dendrite ◽  
Liquid Region ◽  
Field Equations ◽  
Cu Alloy

The microstructure evolution during the directional solidification of Al-Cu alloy is simulated using a phase field model. The transformation from liquid to solid phase is a non-equilibrium process with three regions (liquid, solid and interface) involved. Phase field model is defined for each of the three regions. The evolution of each phase is calculated by a set of phase field equations, whereas the solute in those regions is calculated by a concentration equation. In this work, the phase field model which is generally valid for most kinds of transitions between phases, it is applied to the directional solidification problem. Numerical results for the morphological evolution of columnar dendrite in Al-Cu alloy are in agreement with experimental observations found in the literature. The growth velocity of the dendrite tip and the concentration profile in the solid, interface and liquid region were calculated.

Phase Field Modeling of Solute Trapping in a Al-Sn Alloy during Rapid Solidification

2014 ◽  
Vol 794-796 ◽  
pp. 740-745 ◽  
Author(s):  
Xiong Yang ◽  
Li Jun Zhang ◽  
Yong Du
Keyword(s):  
Rapid Solidification ◽  
Phase Field ◽  
Field Model ◽  
Kinetic Equations ◽  
Phase Field Model ◽  
Interface Velocity ◽  
Interface Energy ◽  
Phase Field Simulation ◽  
Solute Trapping ◽  
Field Simulation

During rapid solidification, interfaces are often driven far from equilibrium and the "solute trapping" phenomenon is usually observed. Very recently, a phase field model with finite interface dissipation, in which separate kinetic equations are assigned to each phase concentration instead of an equilibrium partitioning condition, has been newly developed. By introducing the so-called interface permeability, the phase field model with finite interface dissipation can nicely describe solute trapping during solidification in the length scale of micrometer. This model was then applied to perform a phase field simulation in a Al-Sn alloy (Al-0.2 at.% Sn) during rapid solidification. A simplified linear phase diagram was constructed for providing the reliable driving force and potential information. The other thermophysical parameters, such as interface energy and diffusivities, were directly taken from the literature. As for the interface mobility, it was estimated via a kinetic relationship in the present work. According to the present phase field simulation, the interface velocity increases as temperature decreases, resulting in the enhancement of solute trapping. Moreover, the simulated solute segregation coefficients in Al-0.2 at.% Sn can nicely reproduce the experimental data.

Sign in / Sign up

Export Citation Format

Share Document