scholarly journals A Phase Field Model of the Solidification Process of Alloys and Numerical Simulations

1999 ◽  
Vol 63 (7) ◽  
pp. 912-916 ◽  
Author(s):  
Kazushige Sakai
Keyword(s):  
Numerical Simulations ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Solidification Process

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.

Numerical simulations of the phase separation properties for the thermal aged CDSS with Phase Field Model

2011 ◽  
Vol 241 (7) ◽  
pp. 2378-2385 ◽  
Author(s):  
Fei Xue ◽  
Zhao-Xi Wang ◽  
Guo-Dong Zhang ◽  
Bao-Ping Qu ◽  
Hui-Ji Shi ◽  
...  
Keyword(s):  
Phase Separation ◽  
Numerical Simulations ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model

Study for Step Instabilities Induced by ES Barrier

2005 ◽  
Vol 475-479 ◽  
pp. 3181-3184
Author(s):  
Jin You Kim ◽  
Dong Hee Yeon ◽  
Pil Ryung Cha ◽  
Jong Kyu Yoon
Keyword(s):  
Numerical Simulations ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Time Dependent ◽  
Vicinal Surface ◽  
Step Flow ◽  
Collective Motions ◽  
Step Dynamics ◽  
Step Flow Growth

A phase field model for step dynamics on vicinal surface is presented. Using this model, time dependent, collective motions of steps were investigated. Through numerical simulations, morphological step instabilities induced by ES barrier were analyzed, and it is shown that this model could interpret various phenomena during step flow growth such as step bunching and meandering.

Phase Field Dynamic Modelling of Shape Memory Alloys Based on Isogeometric Analysis

2012 ◽  
Vol 78 ◽  
pp. 63-68 ◽  
Author(s):  
Rakesh Dhote ◽  
Hector Gomez ◽  
Roderick Melnik ◽  
Jean Zu
Keyword(s):  
Shape Memory Alloys ◽  
Numerical Simulations ◽  
Shape Memory ◽  
Microstructure Evolution ◽  
Phase Field ◽  
Isogeometric Analysis ◽  
Field Model ◽  
Phase Field Model ◽  
Higher Order ◽  
Martensitic Phase Transformations

Shape Memory Alloys (SMAs) exhibit complex behaviors as a result of their constituent phases and microstructure evolution. In this paper, we focus on the numerical simulations of microstructure evolution in SMAs using a phase-field model for the two dimensional square-to-rectangular martensitic phase transformations. The phase-field model, based on the Ginzburg-Landau theory, has strong non-linearity, thermo-mechanical coupling, and higher-order differential terms and presents substantial challenges for numerical simulations. The isogeometric analysis, developed in this paper using the rich NURBS basis functions, offers several advantages in solving such complex problems with higher-order partial differential equations as the problem at hand. To our best knowledge, we report here for the first time the use of the new method in the study of microstructure evolution in SMAs. The numerical experiments of microstructure evolution have been carried out on the FePd SMA specimen. The results are in good agreement with those previously reported in the literature.

A Γ-convergence result for fluid-filled fracture propagation

2020 ◽  
Vol 54 (3) ◽  
pp. 1003-1023
Author(s):  
Annika Bach ◽  
Liesel Sommer
Keyword(s):  
Asymptotic Analysis ◽  
Numerical Simulations ◽  
Discontinuous Galerkin ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Fracture Propagation ◽  
Convergence Result ◽  
Elastic Media ◽  
Γ Convergence

In this paper we provide a rigorous asymptotic analysis of a phase-field model used to simulate pressure-driven fracture propagation in poro-elastic media. More precisely, assuming a given pressure p ∈ W 1,∞ (Ω) we show that functionals of the form $$ E(\vec{u})={\int }_{\mathrm{\Omega }} e(\vec{u}):\mathbb{C}e(\vec{u})+p\nabla \cdot \vec{u}+\left\langle \nabla p,\vec{u}\right\rangle\enspace \mathrm{d}x+{\mathcal{H}}^{n-1}({J}_{\vec{u}}),\enspace \vec{u}\in \mathrm{G}{SBD}(\mathrm{\Omega })\cap {L}^1(\mathrm{\Omega };{\mathbb{R}}^n) $$ can be approximated in terms of Γ-convergence by a sequence of phase-field functionals, which are suitable for numerical simulations. The Γ-convergence result is complemented by a numerical example where the phase-field model is implemented using a Discontinuous Galerkin Discretization.

Interfacial Energy Anisotropy Affecting Dendrite Growth of Magnesium Alloy

2015 ◽  
Vol 1088 ◽  
pp. 238-241
Author(s):  
Xun Feng Yuan ◽  
Yan Yang
Keyword(s):  
Magnesium Alloy ◽  
Numerical Simulations ◽  
Phase Field ◽  
Interfacial Energy ◽  
Field Model ◽  
Phase Field Model ◽  
Dendrite Growth ◽  
Secondary Branch ◽  
Energy Anisotropy ◽  
Interfacial Energy Anisotropy

Numerical simulations based on a new regularized phase field model were presented, simulating the solidification of magnesium alloy. The effects of weak and strong interfacial energy anisotropy on the dendrite growth are studied. The results indicate that with weak interfacial energy anisotropy, the entire dendrite displays six-fold symmetry and no secondary branch appeared. Under strong interfacial energy anisotropy conditions, corners form on both the main stem and the tips of the side branches of the dendrites, the entire facet dendrite displays six-fold symmetry. As the solidification time increases, the tip temperature and velocity of the dendrite and facet dendrite finally tend to stable values. The stable velocity of the facet dendrite is 0.4 at ε6 is 0.05 and this velocity is twice that observed (0.2) at ε6 is 0.005.

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