Phase-field models for eutectic solidification

JOM ◽  
2004 ◽  
Vol 56 (4) ◽  
pp. 34-39 ◽  
Author(s):  
Daniel Lewis ◽  
James Warren ◽  
William Boettinger ◽  
Tamás Pusztai ◽  
László Gránásy
Keyword(s):  
Phase Field ◽  
Eutectic Solidification ◽  
Phase Field Models

PHASE-FIELD MODELING OF ELASTIC EFFECTS IN EUTECTIC GROWTH WITH MISFIT STRESSES

2012 ◽  
Vol 04 (01) ◽  
pp. 1250024
Author(s):  
ZOHREH EBRAHIMI ◽  
JOAO REZENDEH
Keyword(s):  
Phase Field ◽  
Elastic Energy ◽  
Field Model ◽  
Phase Field Model ◽  
Solidification Process ◽  
Eutectic Growth ◽  
Point Of View ◽  
Eutectic Solidification ◽  
Elastic Model ◽  
Sharp Interface Model

Elastic interactions, arising from a difference of lattice spacing between two coherent phases in eutectic alloys with misfit stresses, can have an influence on microstructural pattern formation of eutectic colonies during solidification process. From a thermodynamic point of view the elastic energy contributes to the free energy of the phases and modifies their mutual stability. Therefore, the elastic stresses will have an effect on stability of lamellae, lamellae spacing and growth modes. In this paper, a phase-field model is employed to investigate the influence of elastic misfits in eutectic growth. The model reduces to the traditional sharp-interface model in a thin-interface limit, where the microscopic interface width is small but finite. An elastic model is designed, based on linear microelasticity theory, to incorporate the elastic energy in the phase-field model. Theoretical and numerical approaches, required to model elastic effects, are formulated and the stress distributions in eutectic solidification structures are evaluated. The two-dimensional simulations are performed for directed eutectic growth and the simulation results for different values of the misfit stresses are illustrated.

scholarly journals Spectral Approximation of Fractional PDEs in Image Processing and Phase Field Modeling

2017 ◽  
Vol 17 (4) ◽  
pp. 661-678 ◽  
Author(s):  
Harbir Antil ◽  
Sören Bartels
Keyword(s):  
Image Processing ◽  
Phase Field ◽  
Differential Operators ◽  
Mathematical Tool ◽  
Phase Field Models ◽  
Field Modeling ◽  
Regularity Properties ◽  
Fractional Pdes ◽  
Fractional Differential ◽  
Fractional Differential Operators

AbstractFractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets and sharp transitions across interfaces are of interest. The numerical solution of corresponding model problems via a spectral method is analyzed. Its efficiency and features of the model problems are illustrated by numerical experiments.

scholarly journals Minimization and Eulerian Formulation of Differential Geormetry Based Nonpolar Multiscale Solvation Models

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Zhan Chen
Keyword(s):  
Phase Field ◽  
Phase Field Model ◽  
Lagrangian Formulation ◽  
Global Minimizer ◽  
Solvation Model ◽  
Phase Field Models ◽  
Eulerian Formulation ◽  
Solvation Models ◽  
Similarity And Difference ◽  
Nonpolar Solvation

AbstractIn this work, the existence of a global minimizer for the previous Lagrangian formulation of nonpolar solvation model proposed in [1] has been proved. One of the proofs involves a construction of a phase field model that converges to the Lagrangian formulation. Moreover, an Eulerian formulation of nonpolar solvation model is proposed and implemented under a similar parameterization scheme to that in [1]. By doing so, the connection, similarity and difference between the Eulerian formulation and its Lagrangian counterpart can be analyzed. It turns out that both of them have a great potential in solvation prediction for nonpolar molecules, while their decompositions of attractive and repulsive parts are different. That indicates a distinction between phase field models of solvation and our Eulerian formulation.

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