Phase Field Simulation of the Pure Material Dendrite Growth in a Forced Flow

2012 ◽  
Vol 571 ◽  
pp. 3-7
Author(s):  
Jing Liu ◽  
Ying Shuo Wang
Keyword(s):  
Phase Field ◽  
Vertical Direction ◽  
Field Method ◽  
Dendritic Morphology ◽  
Forced Flow ◽  
Phase Field Method ◽  
Pure Material ◽  
Phase Field Models ◽  
Field Simulation ◽  
Control Equation

The phase field method is effective in simulating the formation of solidification microstructure. Based on the phase field models of coupling flow field and noise field proposed by Tong and Beckermann, using finite difference method to solve control equation, apartly simulating the dendritic morphology under the condition of convection or none convection, and drawing the following conclusions after comparing the results: in the side, the dendrite will no longer be symmetrical under the condition of countercurrent and downstream, the dendrite tip grows faster with countercurrent than that of the latter, while the dendrite grows almost naturally in the vertical direction of convection.

A Hyperbolic Phase-Field Approach for Solidification With Supercooling

1999 ◽  
Author(s):  
Yuqi Chen ◽  
James M. McDonough ◽  
Kaveh A. Tagavi
Keyword(s):  
Phase Field ◽  
Supercooled Liquid ◽  
Field Method ◽  
Phase Field Method ◽  
Uniform Mesh ◽  
Phase Variable ◽  
Field Equations ◽  
Pure Material ◽  
Melt Temperature ◽  
Phase Field Equations

Abstract This report concerns the solidification of a “supercooled” liquid, whose temperature is initially below the equilibrium melt temperature, Tm of the solid. A new approach, the phase-field method, will be applied for this Stefan problem with supercooling, which simulates the solidification process of a pure material into a supercooled liquid in a spherical region. The advantage of the phase-field method is that it bypasses explicitly tracking the freezing front. In this approach the solid-liquid interface is treated as diffuse, and a dynamic equation for the phase variable is introduced in addition to the equation for heat flow. Thus, there are two coupled partial differential equations for temperature and phase field. In the reported study, an implicit numerical scheme using finite-difference techniques on a uniform mesh is employed to solve both Fourier phase-field equations and non-Fourier (known as damped wave or telegraph) phase-field equations. The latter gurantees a finite speed of propagation for the solidification front. Both Fourier (parabolic) and non-Fourier (hyperbolic) Stefan problems with supercooling are satisfactorily simulated and their solutions compared in the present work.

An Approximate Model of the Process of Non-Dendritic Morphology Formation in Solidification of Binary Melt under Stirring

2019 ◽  
Vol 22 (4) ◽  
pp. 367-374
Author(s):  
Yu. A. Lebedinsky ◽  
A. M. Branovitsky ◽  
V. A. Dement'ev
Keyword(s):  
Crystal Growth ◽  
Phase Field ◽  
Approximate Model ◽  
Solute Concentration ◽  
Field Method ◽  
Dendritic Morphology ◽  
Phase Field Method ◽  
Primary Crystal ◽  
Initial Concentration

The primary crystal growth in a binary melt is modeled on the base of the phase field method with approximate consideration of melt stirring. Changes in the second component (solute) concentration near a solidification area during stirring are considered as a main reason of modification of dendritic morphology of crystals. An effect of stirring is approximately simulated as forced changes in the solute concentration by either resetting to initial concentration, or averaging concentration. Dendritic morphology is shown to change to rosette and then to globular one depending on space parameters of forced changes.

scholarly journals Simulation of the Microstructural Evolution of Pure Material and Alloys in an Undercooled Melts via Phase-field Method and Adaptive Computational Domain

2015 ◽  
Vol 18 (3) ◽  
pp. 644-653 ◽  
Author(s):  
Alexandre Furtado Ferreira ◽  
Ivaldo Leão Ferreira ◽  
Janaan Pereira da Cunha ◽  
Ingrid Meirelles Salvino
Keyword(s):  
Microstructural Evolution ◽  
Phase Field ◽  
Field Method ◽  
Phase Field Method ◽  
Computational Domain ◽  
Pure Material ◽  
Undercooled Melts

Investigation of Spinodal Decomposition in Fe-Cr Alloys: CALPHAD Modeling and Phase Field Simulation

2011 ◽  
Vol 172-174 ◽  
pp. 1060-1065 ◽  
Author(s):  
Wei Xiong ◽  
Klara Asp Grönhagen ◽  
John Ågren ◽  
Malin Selleby ◽  
Joakim Odqvist ◽  
...  
Keyword(s):  
Spinodal Decomposition ◽  
Phase Field ◽  
Accurate Determination ◽  
Enthalpy Of Mixing ◽  
Field Method ◽  
Phase Field Method ◽  
Phase Field Simulation ◽  
Mobility Data ◽  
Field Simulation ◽  
Calphad Modeling

This work is dedicated to simulate the spinodal decomposition of Fe-Cr bcc (body centered cubic) alloys using the phase field method coupled with CALPHAD modeling. Thermodynamic descriptions have been revised after a comprehensive review of information on the Fe-Cr system. The present work demonstrates that it is impossible to reconcile the ab initio enthalpy of mixing at the ground state with the experimental one at 1529 K using the state-of-the-art CALPHAD models. While the phase field simulation results show typical microstructure of spinodal decomposition, large differences have been found on kinetics among experimental results and simulations using different thermodynamic inputs. It was found that magnetism plays a key role on the description of Gibbs energy and mobility which are the inputs to phase field simulation. This work calls for an accurate determination of the atomic mobility data at low temperatures.

Phase-Field Modeling of Morphological Change of Ferrite during Decomposition of Austenite in Fe-C Alloy

2007 ◽  
Vol 345-346 ◽  
pp. 935-938
Author(s):  
A. Yamanaka ◽  
Tomohiro Takaki ◽  
Yoshihiro Tomita
Keyword(s):  
Morphological Change ◽  
Phase Field ◽  
Numerical Approach ◽  
Field Method ◽  
Homogenization Method ◽  
Ferrite Phase ◽  
Phase Field Method ◽  
Element Analysis ◽  
Phase Field Simulation ◽  
Field Simulation

The integrated simulation model for microstructural design of Fe-C alloy using the phase-field method and the homogenization method is proposed. First, the phase-field simulation is performed to simulate the morphological change of the grain boundary ferrite to Widmanstätten ferrite. Then, in order to clarify the effects of the morphology of the ferrite phase on the micro- and macroscopic mechanical properties, the finite element analysis based on the homogenization method is conducted with the representative volume element obtained from the phase-field simulation. This numerical approach provides a powerful tool to investigate systematically the micro and macroscopic mechanical behavior with the morphological change of the ferrite phase in the Fe-C alloy.

1015 Dendritic Growth Simulations under Forced Flow by Phase-Field Method

2010 ◽  
Vol 2010.85 (0) ◽  
pp. _10-15_
Author(s):  
Hiroko KASHIMA ◽  
Tomohiro TAKAKI ◽  
Tomohiro FUKUI ◽  
Koji MORINISHI
Keyword(s):  
Phase Field ◽  
Dendritic Growth ◽  
Field Method ◽  
Forced Flow ◽  
Phase Field Method

Phase Field Simulation of Rafting Behavior of γ`Phase in Nickel Base Superalloy

2008 ◽  
Vol 33-37 ◽  
pp. 471-476 ◽  
Author(s):  
Akiyuki Takahashi ◽  
Yutaka Kobayashi ◽  
Masanori Kikuchi
Keyword(s):  
Network Model ◽  
Phase Field ◽  
Lattice Misfit ◽  
Field Method ◽  
Phase Field Method ◽  
Dislocation Network ◽  
Nickel Base Superalloy ◽  
Interfacial Dislocation ◽  
Phase Field Simulation ◽  
Field Simulation

This paper describes phase field simulations of the rafting behavior of γ’ phase with a simple interfacial dislocation network model. The interfacial dislocation network model accounts for the effect of the network on the lattice misfit between γ and γ’ phases and the subsequent rafting behavior. The model is implemented into the phase field simulation to see the dependence of the rafting behavior of γ’ phases on the interfacial dislocation network. Without the dislocation network model, the amount of the rafting was negligibly small. On the other hand, with the dislocation network model, the γ’ phases shows a large amount of rafting, which is in good agreement with the results of the experimental observations. Therefore, the combination of the phase field method and the simple interfacial dislocation network model developed in this work is appropriate for the simulation of the rafting of γ’ phases.

scholarly journals Review of γ’ Rafting Behavior in Nickel-Based Superalloys: Crystal Plasticity and Phase-Field Simulation

Crystals ◽  
2020 ◽  
Vol 10 (12) ◽  
pp. 1095
Author(s):  
Zhiyuan Yu ◽  
Xinmei Wang ◽  
Fuqian Yang ◽  
Zhufeng Yue ◽  
James C. M. Li
Keyword(s):  
Single Crystal ◽  
Crystal Plasticity ◽  
Microstructure Evolution ◽  
Phase Field ◽  
Field Method ◽  
Plasticity Theory ◽  
Phase Field Method ◽  
Field Simulation ◽  
Crystal Plasticity Theory ◽  
Excellent Tool

Rafting is an important phenomenon of the microstructure evolution in nickel-based single crystal superalloys at elevated temperature. Understanding the rafting mechanism and its effect on the microstructure evolution is of great importance in determining the structural stability and applications of the single crystal superalloys. Phase-field method, which is an excellent tool to analyze the microstructure evolution at mesoscale, has been gradually used to investigate the rafting behavior. In this work, we review the crystal plasticity theory and phase-field method and discuss the application of the crystal plasticity theory and phase-field method in the analysis of the creep deformation and microstructure evolution of the single crystal superalloys.

scholarly journals Fracture Propagation in Brazilian Discs with Multiple Pre-existing Notches by Using a Phase Field Method

2018 ◽  
Author(s):  
Shuwei Zhou
Keyword(s):  
Crack Propagation ◽  
Phase Field ◽  
Peak Load ◽  
Vertical Direction ◽  
Field Method ◽  
Phase Field Method ◽  
Phase Field Modeling ◽  
Direct Tension ◽  
Field Modeling ◽  
Splitting Test

The crack propagation in the Brazilian discs with multiple pre-existing notches is investigated by using a phase field method. The phase field modeling is verified by applying a direct tension test and an indirect splitting test on a Brazilian specimen with no pre-existing notches where the simulated results are in good agreement with previous numerical and experimental results. The influence of the notch number and spacing on the crack propagation in the Brazilian discs with multiple vertically and horizontally arranged notches is studied. Outer cracks initiate from the notch tips and propagate at a small angle with the vertical direction, finally coalescing with the ends of the discs. The strength of the specimen decreases as the notches increases. The Brazilian discs with horizontally arranged pre-existing notches only have outer cracks when the notch number is 1, 3, and 5 and have both outer and inner cracks for two and four notches. The peak load of the Brazilian discs with horizontally arranged notches increases as the notch spacing increases. The final crack patterns obtained by the phase field modeling are consistent with those by previous numerical simulations and experimental tests.

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