Phase Field Method Simulation of Dendrite Crystal Growth of Metal Nickel Based on Fractal Theory

2012 ◽  
Vol 190-191 ◽  
pp. 522-527
Author(s):  
Zhi Yi Ruan ◽  
Sheng Da Zeng ◽  
Li Xin Lin ◽  
Lu Rong Wu
Keyword(s):  
Crystal Growth ◽  
Growth Model ◽  
Phase Field ◽  
Field Model ◽  
Fractal Theory ◽  
Phase Field Model ◽  
Crystal Nucleation ◽  
Pure Substance ◽  
Simulation Results ◽  
Matlab Programming

Using fractal theory simulation of dendrite crystal DLA growth model of pure substance, the undercooling during solidification process of crystal nucleation is simulated; and then in the crystal nuclei are formed on the basis of a pure substance, the phase field model and combined with the finite difference method further differentiation simulation of dendrite crystal growth. According to MATLAB programming, the simulation results obtained by field and temperature field can be seen in the DLA growth, growth model with random premise, for the same kind of material simulated dendrite crystal have both similarities and differences exist. Then, we can get the conclusion, through fractal growth of DLA model with phase field model of dendrite nucleation, growth process is carried out the simulation results, a simple by phase field model is more accord with the dendrite crystal in the experiment.

Study on Microstructural Evolution of Binary Alloy Crystal Growth in Directional Solidification Process

2013 ◽  
Vol 470 ◽  
pp. 100-103
Author(s):  
Dong Sheng Chen ◽  
Ming Chen ◽  
Rui Chang Wang
Keyword(s):  
Crystal Growth ◽  
Directional Solidification ◽  
Binary Alloy ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Pure Substance ◽  
Columnar Dendrite

PFM (phase field method) was employed to study microstructure evolution, and considering the effect of solute concentration to the undercooling, we developed a phase field model for binary alloy on the basis of pure substance model. In the paper, the temperature field and solute field were coupled together in the phase field model to calculate the crystal growth of magnesium alloy in directional solidification. The simulation results showed a non-planar crystal growth of planar to cellular to columnar dendrite, the comparison of different dendrite patterns were carried out in the numerical simulation, and with the increasing of the anisotropy, the second dendrite arms became more developed.

scholarly journals A regularized phase-field model for faceting in a kinetically controlled crystal growth

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200227
Author(s):  
T. Philippe ◽  
H. Henry ◽  
M. Plapp
Keyword(s):  
Crystal Growth ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Sharp Interface ◽  
Diffuse Interface ◽  
Interface Problem ◽  
Kinetically Controlled ◽  
Interface Theory ◽  
Coarsening Dynamics

At equilibrium, the shape of a strongly anisotropic crystal exhibits corners when for some orientations the surface stiffness is negative. In the sharp-interface problem, the surface free energy is traditionally augmented with a curvature-dependent term in order to round the corners and regularize the dynamic equations that describe the motion of such interfaces. In this paper, we adopt a diffuse interface description and present a phase-field model for strongly anisotropic crystals that is regularized using an approximation of the Willmore energy. The Allen–Cahn equation is employed to model kinetically controlled crystal growth. Using the method of matched asymptotic expansions, it is shown that the model converges to the sharp-interface theory proposed by Herring. Then, the stress tensor is used to derive the force acting on the diffuse interface and to examine the properties of a corner at equilibrium. Finally, the coarsening dynamics of the faceting instability during growth is investigated. Phase-field simulations reveal the existence of a parabolic regime, with the mean facet length evolving in t , with t the time, as predicted by the sharp-interface theory. A specific coarsening mechanism is observed: a hill disappears as the two neighbouring valleys merge.

The Twinning Modes of B2-B19′ Martensitic Transformation in NiTi Alloys - A Phase Field Study

2011 ◽  
Vol 399-401 ◽  
pp. 1768-1772 ◽  
Author(s):  
Chang Bo Ke ◽  
Shan Shan Cao ◽  
Xiao Ma ◽  
Xin Ping Zhang
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Three Dimensional ◽  
Phase Field Model ◽  
Elastic Interaction ◽  
Type I ◽  
Good Precision ◽  
Niti Alloys ◽  
Twinning Plane ◽  
Simulation Results

A three-dimensional phase field model applicable for the B2-B19′ martensitic phase transformation of NiTi alloys was developed to predict the twinning modes in the B2-B19′ transition. The phase field simulation results showed that by taking into account the transformation induced elastic strain, the martensite variants were self-accommodated and sheared along the specific interface in the entire transition stage for reducing the elastic energy, whether the formed interface between the variants belongs to twinning plane could be determined by calculating the minimum value of long range elastic interaction energy, Bpq. Through comparison with the existing analytical solutions, it is demonstrated that the phase field model can be used to predict the type I twinning modes in the B2-B19′ phase transition with good precision.

Introduction to Phase-Field Model and Its Applications in the Fields of Crystal Growth and Planetary Science

2010 ◽  
Author(s):  
Hitoshi Miura ◽  
Etsuro Yokoyama ◽  
Katsuo Tsukamoto ◽  
W. Wang ◽  
Katsuo Tsukamoto ◽  
...  
Keyword(s):  
Crystal Growth ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Planetary Science

Phase-Field Simulation of Interface Effect during Grain Nucleation

2012 ◽  
Vol 490-495 ◽  
pp. 3339-3343
Author(s):  
Fei Huo ◽  
Ji Wei Zhao
Keyword(s):  
Grain Growth ◽  
Phase Field ◽  
Field Model ◽  
Landau Theory ◽  
Phase Field Model ◽  
Ginzburg Landau ◽  
Euler Formula ◽  
Topological Theory ◽  
Field Simulation ◽  
Simulation Results

In this paper, a phase field model based on Ginzburg-Landau theory is used to analyze the topological phenomena during grain growth. The simulation results show that two topological transformations exist during the grain growth—Neighbor Switching and Grain Annihilation; and we have found different kinds of topological events during the disappearance of a grain: direct vanishing of trilateral grain and pentagonal grain, as well as neighbor switching，which are right with classical topological theory and Euler formula. The simulation results are similar with experiments.

Effect of Restored Energy Items in Recrystallization Simulation of AZ31 Magnesium Alloy

2021 ◽  
Vol 1035 ◽  
pp. 827-832
Author(s):  
Jin Lin Xiong ◽  
Yan Wu ◽  
Qiang Luo ◽  
Ji Bing Chen ◽  
Wei Dong Cheng
Keyword(s):  
Magnesium Alloy ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Mg Alloy ◽  
Az31 Magnesium Alloy ◽  
Impact Factors ◽  
Az31 Mg Alloy ◽  
Simulation Results ◽  
The Impact

The effect of restored energy items in recrystallization simulation of AZ31 Mg alloy was studied with multi-order phase field model, and the impact factors during the recrystallization were discussed by changing the parameters of the restored energy item. The simulation results showed that the greater the restored energy, the greater the number of the recrystallized grains.

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