An existence and uniqueness result for a phase-field model of diffusion-induced grain-boundary motion

2001 ◽  
Vol 131 (6) ◽  
pp. 1323-1344 ◽  
Author(s):  
Klaus Deckelnick ◽  
Charles M. Elliott
Keyword(s):  
Grain Boundary ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Uniqueness Result ◽  
Degenerate Diffusion ◽  
Boundary Motion ◽  
Regularization Technique ◽  
Additional Regularity ◽  
Grain Boundary Motion

We consider a phase-field model for diffusion-induced grain boundary motion. The model couples a parabolic variational inequality to a degenerate diffusion equation. Using a regularization technique, we prove an existence theorem for the resulting system. We also obtain a uniqueness result, provided the solution has some additional regularity.

A phase-field model for diffusion-induced grain-boundary motion

1997 ◽  
Vol 45 (10) ◽  
pp. 4397-4413 ◽  
Author(s):  
J.W. Cahn ◽  
P. Fife ◽  
O. Penrose
Keyword(s):  
Grain Boundary ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Boundary Motion ◽  
Grain Boundary Motion

scholarly journals A phase-field model of grain boundary motion

2008 ◽  
Vol 53 (5) ◽  
pp. 433-454 ◽  
Author(s):  
Akio Ito ◽  
Nobuyuki Kenmochi ◽  
Noriaki Yamazaki
Keyword(s):  
Grain Boundary ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Boundary Motion ◽  
Grain Boundary Motion

Stress- and diffusion-induced interface motion: Modelling and numerical simulations

2007 ◽  
Vol 18 (6) ◽  
pp. 631-657 ◽  
Author(s):  
HARALD GARCKE ◽  
ROBERT NÜRNBERG ◽  
VANESSA STYLES
Keyword(s):  
Grain Boundary ◽  
Numerical Simulations ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Boundary Motion ◽  
Interface Motion ◽  
Stress Effects ◽  
Grain Boundary Motion ◽  
And Diffusion

We propose a phase field model for stress and diffusion-induced interface motion. This model, in particular, can be used to describe diffusion-induced grain boundary motion and generalizes a model of Cahn, Fife and Penrose as it more accurately incorporates stress effects. In this paper we will demonstrate that the model can also be used to describe other stress-driven interface motion. As an example, interface motion resulting from interactions of interfaces with dislocations is studied.

scholarly journals A phase field model of grain boundary migration and grain rotation under elasto–plastic anisotropies

2019 ◽  
Vol 178-179 ◽  
pp. 1-18 ◽  
Author(s):  
Jakub Mikula ◽  
Shailendra P. Joshi ◽  
Tong-Earn Tay ◽  
Rajeev Ahluwalia ◽  
Siu Sin Quek
Keyword(s):  
Grain Boundary ◽  
Phase Field ◽  
Field Model ◽  
Boundary Migration ◽  
Phase Field Model ◽  
Grain Boundary Migration ◽  
Grain Rotation

Phase-field Model for Diffusional Phase Transformations in Elastically Inhomogeneous Polycrystals

2011 ◽  
Vol 172-174 ◽  
pp. 1084-1089 ◽  
Author(s):  
Tae Wook Heo ◽  
Saswata Bhattacharyya ◽  
Long Qing Chen
Keyword(s):  
Grain Boundary ◽  
Phase Field ◽  
Field Model ◽  
Boundary Segregation ◽  
Phase Field Model ◽  
Transformation Process ◽  
Second Phase ◽  
Perturbation Scheme ◽  
Local Pressure ◽  
Second Phase Particles

A phase-field model is described for predicting the diffusional phase transformation process in elastically inhomogeneous polycrystals. The elastic interactions are incorporated by solving the mechanical equilibrium equation using the Fourier-spectral iterative-perturbation scheme taking into account elastic modulus inhomogeneity. A number of examples are presented, including grain boundary segregation, precipitation of second-phase particles in a polycrystal, and interaction between segregation at a grain boundary and coherent precipitates inside grains. It is shown that the local pressure distribution due to coherent precipitates leads to highly inhomogeneous solute distribution along grain boundaries.

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