scholarly journals 3D Phase Field Modeling of Multi-Dendrites Evolution in Solidification and Validation by Synchrotron X-ray Tomography

Materials ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 520
Author(s):  
Shuo Wang ◽  
Zhipeng Guo ◽  
Jinwu Kang ◽  
Meishuai Zou ◽  
Xiaodong Li ◽  
...  
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Phase Field Model ◽  
Computationally Efficient ◽  
X Ray ◽  
Cu Alloy ◽  
Field Modeling ◽  
Micro Tomography

In this paper, the dynamics of multi-dendrite concurrent growth and coarsening of an Al-15 wt.% Cu alloy was studied using a highly computationally efficient 3D phase field model and real-time synchrotron X-ray micro-tomography. High fidelity multi-dendrite simulations were achieved and the results were compared directly with the time-evolved tomography datasets to quantify the relative importance of multi-dendritic growth and coarsening. Coarsening mechanisms under different solidification conditions were further elucidated. The dominant coarsening mechanisms change from small arm melting and interdendritic groove advancement to coalescence when the solid volume fraction approaches ~0.70. Both tomography experiments and phase field simulations indicated that multi-dendrite coarsening obeys the classical Lifshitz–Slyozov–Wagner theory Rn−R0n = kc(t−t0), but with a higher constant of n = 4.3.

Phase-field modeling of the coupled domain structure and dielectric breakdown evolution in a ferroelectric single crystal

2019 ◽  
Vol 21 (29) ◽  
pp. 16207-16212 ◽  
Author(s):  
Ziming Cai ◽  
Chaoqiong Zhu ◽  
Xiaohui Wang ◽  
Longtu Li
Keyword(s):  
Single Crystal ◽  
Domain Structure ◽  
Phase Field ◽  
Field Model ◽  
Dielectric Breakdown ◽  
Phase Field Model ◽  
Phase Field Modeling ◽  
Field Modeling ◽  
Ferroelectric Single Crystal

The coupled evolution of domain structure and dielectric breakdown is simulated via a phase-field model.

An Approach for Modeling Transformation Plasticity Using a Phase Field Model

2011 ◽  
Vol 320 ◽  
pp. 285-290 ◽  
Author(s):  
Takuya Uehara
Keyword(s):  
Thermal Expansion ◽  
Phase Transformation ◽  
Phase Field ◽  
Transformation Temperature ◽  
Field Model ◽  
Volume Fraction ◽  
Phase Field Model ◽  
Field Variable ◽  
Transformation Plasticity ◽  
Temperature Strain

In this paper, an approach for modeling transformation plasticity using a phase field model is presented. A conventional formula is utilized to represent the strain due to transformation plasticity as well as thermal expansion and transformation dilatation. A phase-field variable is introduced to express the state of phase in material instead of volume fraction, and numerical simulations under simplified conditions are demonstrated. As a result, the strain induced by phase transformation is suitably regenerated, and qualitatively appropriate temperature-strain curves are obtained. In addition, the effect of each parameter is investigated, and various dependencies, such as transformation temperature and stress, on the induced strain are demonstrated. It is then concluded that the results indicate the applicability of the presented model for practical use by adjusting the parameters.

2D Phase-Field Simulation of the Directional Solidification Process

2014 ◽  
Vol 704 ◽  
pp. 17-21 ◽  
Author(s):  
Alexandre Furtado Ferreira ◽  
José Adilson de Castro ◽  
Ivaldo Leão Ferreira
Keyword(s):  
Directional Solidification ◽  
Phase Field ◽  
Field Model ◽  
Solid Phase ◽  
Morphological Evolution ◽  
Phase Field Model ◽  
Columnar Dendrite ◽  
Liquid Region ◽  
Field Equations ◽  
Cu Alloy

The microstructure evolution during the directional solidification of Al-Cu alloy is simulated using a phase field model. The transformation from liquid to solid phase is a non-equilibrium process with three regions (liquid, solid and interface) involved. Phase field model is defined for each of the three regions. The evolution of each phase is calculated by a set of phase field equations, whereas the solute in those regions is calculated by a concentration equation. In this work, the phase field model which is generally valid for most kinds of transitions between phases, it is applied to the directional solidification problem. Numerical results for the morphological evolution of columnar dendrite in Al-Cu alloy are in agreement with experimental observations found in the literature. The growth velocity of the dendrite tip and the concentration profile in the solid, interface and liquid region were calculated.

scholarly journals Lattice Phase Field Model for Nanomaterials

Materials ◽  
2021 ◽  
Vol 14 (23) ◽  
pp. 7317
Author(s):  
Pingping Wu ◽  
Yongfeng Liang
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Lattice Parameter ◽  
Grid Spacing ◽  
Field Equations ◽  
Future Directions ◽  
Superlattice Structure ◽  
Field Modeling ◽  
Phase Field Equations

The lattice phase field model is developed to simulate microstructures of nanoscale materials. The grid spacing in simulation is rescaled and restricted to the lattice parameter of real materials. Two possible approaches are used to solve the phase field equations at the length scale of lattice parameter. Examples for lattice phase field modeling of complex nanostructures are presented to demonstrate the potential and capability of this model, including ferroelectric superlattice structure, ferromagnetic composites, and the grain growth process under stress. Advantages, disadvantages, and future directions with this phase field model are discussed briefly.

Phase Field Modeling for Grain Growth of Static Recrystallization of Deformed Alloys

2011 ◽  
Vol 399-401 ◽  
pp. 1785-1788
Author(s):  
Ying Jun Gao ◽  
Zhi Rong Luo
Keyword(s):  
Grain Growth ◽  
Phase Field ◽  
Field Model ◽  
Static Recrystallization ◽  
Phase Field Model ◽  
Free Energy Function ◽  
Phase Field Modeling ◽  
Field Modeling ◽  
Storage Energy ◽  
Good Agreement

A multi-state free energy function for deformation alloy with storage energy is proposed to simulate the microstructure evolution of static recrystallization with phase field model. The grain growth and grain size distribution during recrystallization are discussed. The simulation results are in good agreement with other theoretical or experimental results.

Phase Field Simulation of Solidified Multiple Grains

2012 ◽  
Vol 602-604 ◽  
pp. 1874-1877
Author(s):  
Hong Min Guo ◽  
Tao Wei ◽  
Xiang Jie Yang
Keyword(s):  
Latent Heat ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Dendrite Growth ◽  
Competitive Growth ◽  
Equiaxed Dendrite ◽  
Isothermal Conditions ◽  
Cu Alloy ◽  
Field Simulation

A phase-field model based on the Ginzburg-Landan theory and KKS model is used to simulate the dendrite growth of multiple grains for Al-Cu alloy. The influence of solidification latent heat and undercooling on the growth of equiaxed dendrite, solute distribution and temperature distribution were studied. The results show that the dendrite has well-developed and the competitive growth between grains more intense with the increasing of undercooling. The release of solidification latent heat restrain dendrite growth to a certain extent, which led to the less developed growth of dendrite solidified in non-isothermal conditions than that in isothermal conditions.

DESIGN OPTIMIZATION OF A FERROELECTRIC NANO-ACTUATOR USING PHASE-FIELD MODELING

2014 ◽  
Vol 1674 ◽  
Author(s):  
Ananya Renuka Balakrishna ◽  
John E. Huber
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Two Dimensional ◽  
Phase Field Modeling ◽  
Ferroelectric Crystal ◽  
Surface Conditions ◽  
Field Modeling ◽  
Working Principle ◽  
Ferroelectric Switching

ABSTRACTA ferroelectric crystal with charge-free surface conditions contains polarized domains which can form a flux closure with zero net polarization. In the presence of an external electric field, the flux closure in a two-dimensional continuum reorients its spontaneous polarization to align with the field. Based on this concept of ferroelectric switching coupled with mechanical straining, we demonstrate the working principle of a ferroelectric nano-actuator. The behavior of the actuator is explored under the action of electro-mechanical loading and its mechanism is simulated with a 2D phase-field model. The design of nano-actuator is modified to achieve greater actuation displacements by bending a thin device.

Phase-Field Modeling of Dendritic Solidification in Undercooled Droplets Processed by Electromagnetic Levitation

2006 ◽  
Vol 508 ◽  
pp. 431-436 ◽  
Author(s):  
Peter K. Galenko ◽  
Dieter M. Herlach ◽  
G. Phanikumar ◽  
O. Funke
Keyword(s):  
Phase Field ◽  
Dendritic Growth ◽  
Field Model ◽  
Phase Field Model ◽  
Electromagnetic Levitation ◽  
Dendritic Solidification ◽  
Field Modeling ◽  
Theoretical Predictions ◽  
Forced Convective Flow ◽  
Undercooled Melts

The results on modeling dendritic solidification from undercooled melts processed by the electromagnetic levitation technique are discussed. In order to model the details of formation of dendritic patterns we use a phase-field model of dendritic growth in a pure undercooled system with convection of the liquid phase. The predictions of the phase-field model are discussed referring to our latest high accuracy measurements of dendrite growth velocities in nickel samples. Special emphasis is given to the growth of dendrites at small and moderate undercoolings. At small undercoolings, the theoretical predictions deviate systematically from experimental data for solidification of nickel dendrites. It is shown that small amounts of impurities and forced convective flow can lead to an enhancement of the velocity of dendritic solidification at small undercoolings.

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