A Flux-Corrected Phase-Field Method for Surface Diffusion

2017 ◽  
Vol 22 (2) ◽  
pp. 422-440 ◽  
Author(s):  
Yujie Zhang ◽  
Wenjing Ye
Keyword(s):  
Surface Diffusion ◽  
Phase Field ◽  
Field Method ◽  
Phase Field Method ◽  
Current Phase ◽  
Field Methods ◽  
Degenerate Mobility ◽  
Shrinkage Effect ◽  
Diffusion Motion ◽  
Phase Field Methods

AbstractPhase-field methods with a degenerate mobility have been widely used to simulate surface diffusion motion. However, apart from the motion induced by surface diffusion, adverse effects such as shrinkage, coarsening and false merging have been observed in the results obtained from the current phase-field methods, which largely affect the accuracy and numerical stability of these methods. In this paper, a flux-corrected phase-field method is proposed to improve the performance of phase-field methods for simulating surface diffusion. The three effects were numerically studied for the proposed method and compared with those observed in the two existing methods, the original phase-field method and the profile-corrected phase-field method. Results show that compared to the original phase-field method, the shrinkage effect in the profile-corrected phase-field method has been significantly reduced. However, coarsening and false merging effects still present and can be significant in some cases. The flux-corrected phase field performs the best in terms of eliminating the shrinkage and coarsening effects. The false merging effect still exists when the diffuse regions of different interfaces overlap with each other. But it has been much reduced as compared to that in the other two methods.

Coupled microstructural-compositional evolution informed by a thermodynamic database using the hybrid Potts-phase field model

2013 ◽  
Vol 1524 ◽  
Author(s):  
Jordan J. Cox ◽  
Eric R. Homer ◽  
Veena Tikare
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Field Methods ◽  
Energy Functionals ◽  
Compositional Evolution ◽  
Recent Developments ◽  
Phase Field Methods

ABSTRACTA recently introduced hybrid Potts-phase field method has demonstrated the ability to evolve microstructures in conjunction with compositional fields tied to different phases. In this approach, Monte Carlo Potts methods are used to evolve the microstructure while phase field methods are used to evolve the composition, and the two fields are coupled through free energy functionals. Recent developments of the model allow different multi-component alloy systems to be simulated by using thermodynamic databases and kinetic quantities to dictate the behavior. An example of the method using the aluminum-silicon binary system is demonstrated.

Phase field simulation of the void destabilization and splitting processes in interconnects under electromigration induced surface diffusion

2021 ◽  
Author(s):  
Zhangjiaming Zhang ◽  
Peizhen Huang
Keyword(s):  
Electric Field ◽  
Surface Diffusion ◽  
Phase Field ◽  
Numerical Solutions ◽  
Driving Forces ◽  
Morphological Evolution ◽  
Phase Field Model ◽  
Phase Field Method ◽  
Type I ◽  
Degenerate Mobility

Abstract Interconnect lines of integrated circuits inevitably exist micro-damage, such as voids, inclusions or cracks. Under the effect of different intrinsic physical mechanisms as well as external driving forces, the micro-damage will have different morphological evolution and even destabilize and split, which can affect the various properties of the interconnects. Based on the theory of diffusion interface of microstructure evolution in solid materials, a phase field model is established to simulate the morphological evolution of micro-damage in the interconnect line under electromigration-induced surface diffusion. Unlike the previously published work, the bulk free energy density and the degenerate mobility used in the model are both constructed by quartic double-well potential function. The applicability of the model for the morphological evolution of intracrystalline voids is proved by asymptotic analysis. The governing equation of the phase field method is solved by finite element method. And, the validity of the method is confirmed by the agreement of the numerical solutions with the theoretical solutions of a small circular void. The effects of the relative electric field intensity Χ, the linewidth h ∽ and the initial aspect ratio β on void evolution are discussed in detail. The results indicate that the intracrystalline voids drift in the direction of the electric field, and there is a destabilization critical value Χ cr . When Χ ≧Χ cr , there exist two splitting forms after destabilization for circular void, type I and type II, respectively. The value of Χ cr decreases as h ∽ decreases or β increases. The smaller h ∽ or the larger β is more prone to cause void destabilization. The effect of h ∽ or β on Χ cr is more significant as h ∽ or β is relatively small. In particular, when h ∽ or β is sufficiently large, there exists upper or lower limit for Χ cr , respectively.

Theoretical phase-field-method-based model of the γ phase dissolution of base metals in duplex stainless steels

2021 ◽  
Vol 26 ◽  
pp. 102150
Author(s):  
Dong-Cho Kim ◽  
Tomo Ogura ◽  
Ryosuke Hamada ◽  
Shotaro Yamashita ◽  
Kazuyoshi Saida
Keyword(s):  
Phase Field ◽  
Stainless Steels ◽  
Field Method ◽  
Duplex Stainless Steels ◽  
Phase Field Method ◽  
Base Metals ◽  
Phase Dissolution

scholarly journals Viscoelastic phase-field fracture using the framework of representative crack elements

2021 ◽  
Author(s):  
Bo Yin ◽  
Johannes Storm ◽  
Michael Kaliske
Keyword(s):  
Phase Field ◽  
Consistency Condition ◽  
Field Method ◽  
Anisotropic Elasticity ◽  
Phase Field Method ◽  
Internal Variables ◽  
Crack Model ◽  
Material Degradation ◽  
Discrete Crack ◽  
Deformation State

AbstractThe promising phase-field method has been intensively studied for crack approximation in brittle materials. The realistic representation of material degradation at a fully evolved crack is still one of the main challenges. Several energy split formulations have been postulated to describe the crack evolution physically. A recent approach based on the concept of representative crack elements (RCE) in Storm et al. (The concept of representative crack elements (RCE) for phase-field fracture: anisotropic elasticity and thermo-elasticity. Int J Numer Methods Eng 121:779–805, 2020) introduces a variational framework to derive the kinematically consistent material degradation. The realistic material degradation is further tested using the self-consistency condition, which is particularly compared to a discrete crack model. This work extends the brittle RCE phase-field modeling towards rate-dependent fracture evolution in a viscoelastic continuum. The novelty of this paper is taking internal variables due to viscoelasticity into account to determine the crack deformation state. Meanwhile, a transient extension from Storm et al. (The concept of representative crack elements (RCE) for phase-field fracture: anisotropic elasticity and thermo-elasticity. Int J Numer Methods Eng 121:779–805, 2020) is also considered. The model is derived thermodynamic-consistently and implemented into the FE framework. Several representative numerical examples are investigated, and consequently, the according findings and potential perspectives are discussed to close this paper.

Phase Field Model for Influence of Edge Dislocation on Precipitation

2011 ◽  
Vol 415-417 ◽  
pp. 1482-1485
Author(s):  
Chuang Gao Huang ◽  
Ying Jun Gao ◽  
Li Lin Huang ◽  
Jun Long Tian
Keyword(s):  
Edge Dislocation ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Second Phase ◽  
Free Energy Function ◽  
Phase Nucleation ◽  
Good Agreement

The second phase nucleation and precipitation around the edge dislocation are studied using phase-field method. A new free energy function is established. The simulation results are in good agreement with that of theory of dislocation and theory of non-uniform nucleation.

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