scholarly journals Phase-field model of precipitation processes with coherency loss

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Tian-Le Cheng ◽  
You-Hai Wen
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Ostwald Ripening ◽  
Phase Field Model ◽  
Energy Criterion ◽  
Field Variable ◽  
Ginzburg Landau ◽  
Underlying Mechanisms ◽  
Flood Fill ◽  
Coherency Loss

AbstractA phase-field model is proposed to simulate coherency loss coupled with microstructure evolution. A special field variable is employed to describe the degree of coherency loss of each particle and its evolution is governed by a Ginzburg-Landau type kinetic equation. For the sake of computational efficiency, a flood-fill algorithm is introduced that can drastically reduce the required number of field variables, which allows the model to efficiently simulate a large number of particles sufficient for characterizing their statistical features during Ostwald ripening. The model can incorporate size dependence of coherency loss, metastability of coherent particles, and effectively incorporate the underlying mechanisms of coherency loss by introducing a so-called differential energy criterion. The model is applied to simulate coarsening of Al3Sc precipitates in aluminum alloy and comprehensively compared with experiments. Our results clearly show how the particle size distribution is changed during coherency loss and affects the coarsening rate.

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.

Ostwald Ripening Analysis Using Phase-Field Model

2001 ◽  
Vol 42 (11) ◽  
pp. 2410-2414 ◽  
Author(s):  
Machiko Ode ◽  
Toshio Suzuki ◽  
Seong Gyoon Kim ◽  
Won Tae Kim
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Ostwald Ripening ◽  
Phase Field Model

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.

A nonlocal phase-field model of Ginzburg–Landau–Korteweg fluids

2014 ◽  
Vol 27 (3) ◽  
pp. 367-378 ◽  
Author(s):  
V. A. Cimmelli ◽  
F. Oliveri ◽  
A. R. Pace
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Ginzburg Landau

A phase field model of the premelting of grain boundaries in pure materials

2000 ◽  
Vol 652 ◽  
Author(s):  
Alexander E. Lobkovsky ◽  
James A. Warren
Keyword(s):  
Grain Boundaries ◽  
Phase Field ◽  
Field Model ◽  
Solid Phase ◽  
Phase Field Model ◽  
Field Variable ◽  
High Angle ◽  
Unified Framework ◽  
Crystalline Orientation ◽  
Solid Liquid

ABSTRACTWe present a phase field model of solidification which includes the effects of the crystalline orientation in the solid phase. This model describes grain boundaries as well as solid-liquid boundaries within a unified framework. With an appropriate choice of coupling of the phase field variable to the gradient of the crystalline orientation variable in the free energy, we find that high angle boundaries undergo a premelting transition. As the melting temperature is approached from below, low angle grain boundaries remain narrow. The width of the liquid layer at high angle grain boundaries diverges logarithmically.

Phase Field Simulation of Ferroelectric Single Crystals

Aerospace ◽  
2005 ◽  
Author(s):  
T. Liu ◽  
C. S. Lynch
Keyword(s):  
Phase Field ◽  
Wall Motion ◽  
Field Model ◽  
Landau Equation ◽  
Phase Field Model ◽  
Domain Wall Motion ◽  
Ferroelectric Materials ◽  
Time Dependent ◽  
Ginzburg Landau ◽  
Domain Structures

Ferroelectric materials exhibit spontaneous polarization and domain structures below the Curie temperature. In this study a cubic to tetragonal phase transformation and the evolution of domain structures in ferroelectric crystals are simulated by using the time-dependent Ginzburg-Landau equation. The effects of electric boundary conditions on the formation of domain patterns and field induced polarization switching are discussed. The phase field model is used to simulate the formation of domain structures, domain wall motion and the macroscopic response of ferroelectric materials under external fields.

On a SAV-MAC scheme for the Cahn–Hilliard–Navier–Stokes phase-field model and its error analysis for the corresponding Cahn–Hilliard–Stokes case

2020 ◽  
Vol 30 (12) ◽  
pp. 2263-2297
Author(s):  
Xiaoli Li ◽  
Jie Shen
Keyword(s):  
Error Analysis ◽  
Phase Field ◽  
Field Model ◽  
Chemical Potential ◽  
Phase Field Model ◽  
Auxiliary Variable ◽  
Field Variable ◽  
Second Order ◽  
Navier Stokes ◽  
Order Error

We construct a numerical scheme based on the scalar auxiliary variable (SAV) approach in time and the MAC discretization in space for the Cahn–Hilliard–Navier–Stokes phase- field model, prove its energy stability, and carry out error analysis for the corresponding Cahn–Hilliard–Stokes model only. The scheme is linear, second-order, unconditionally energy stable and can be implemented very efficiently. We establish second-order error estimates both in time and space for phase-field variable, chemical potential, velocity and pressure in different discrete norms for the Cahn–Hilliard–Stokes phase-field model. We also provide numerical experiments to verify our theoretical results and demonstrate the robustness and accuracy of our scheme.

Domain Structures and Phase Diagram in 2D Ferroelectrics Under Applied Biaxial Strains - Phase Field Simulations and Thermodynamic Calculations

2005 ◽  
Vol 881 ◽  
Author(s):  
Jie Wang ◽  
Yulan Li ◽  
Long-Qing Chen ◽  
Tong-Yi Zhang
Keyword(s):  
Phase Diagram ◽  
Phase Field ◽  
Field Model ◽  
Landau Equation ◽  
Phase Field Model ◽  
Ginzburg Landau ◽  
Elastic Interactions ◽  
Domain Structures ◽  
Domain State ◽  
Different Temperatures

Absract:The microscopic domain structures in 2D ferroelectrics under applied biaxial strains are investigated using a phase field model based on the time-dependent Ginzburg-Landau equation that takes both long-range electric and -elastic interactions into account. The stable polarization patterns are simulated at different temperatures and applied inequiaxial strains. The results show that the ferroelectrics transfer from multi-domain state to single-domain state when temperature surpasses a critical value. On the other hand, the macroscopic equilibrium polarization states are also studied through a nonlinear thermodynamic theory. The corresponding transition from a1, a2 state (p1 ≠ 0, P2 ≠ 0) to a1 state (p1 ≠0, P2 = 0) or a2 state (p2 ≠ 0, P2 = 0) is also found from the “strain-straintemperature” phase diagram, which is constructed by minimizing Helmholtz free energy.

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