scholarly journals Quantitative Shape-Classification of Misfitting Precipitates during Cubic to Tetragonal Transformations: Phase-Field Simulations and Experiments

Materials ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1373
Author(s):  
Yueh-Yu Lin ◽  
Felix Schleifer ◽  
Markus Holzinger ◽  
Na Ta ◽  
Birgit Skrotzki ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Phase Field ◽  
Phase Field Model ◽  
Invariant Moments ◽  
Plane Normal ◽  
Plane Shape ◽  
Formation And Evolution ◽  
The Given ◽  
Good Agreement

The effectiveness of the mechanism of precipitation strengthening in metallic alloys depends on the shapes of the precipitates. Two different material systems are considered: tetragonal γ′′ precipitates in Ni-based alloys and tetragonal θ′ precipitates in Al-Cu-alloys. The shape formation and evolution of the tetragonally misfitting precipitates was investigated by means of experiments and phase-field simulations. We employed the method of invariant moments for the consistent shape quantification of precipitates obtained from the simulation as well as those obtained from the experiment. Two well-defined shape-quantities are proposed: (i) a generalized measure for the particles aspect ratio and (ii) the normalized λ2, as a measure for shape deviations from an ideal ellipse of the given aspect ratio. Considering the size dependence of the aspect ratio of γ′′ precipitates, we find good agreement between the simulation results and the experiment. Further, the precipitates’ in-plane shape is defined as the central 2D cut through the 3D particle in a plane normal to the tetragonal c-axes of the precipitate. The experimentally observed in-plane shapes of γ′′-precipitates can be quantitatively reproduced by the phase-field model.

Phase Field Model for Influence of Edge Dislocation on Precipitation

2011 ◽  
Vol 415-417 ◽  
pp. 1482-1485
Author(s):  
Chuang Gao Huang ◽  
Ying Jun Gao ◽  
Li Lin Huang ◽  
Jun Long Tian
Keyword(s):  
Edge Dislocation ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Field Method ◽  
Phase Field Method ◽  
Second Phase ◽  
Free Energy Function ◽  
Phase Nucleation ◽  
Good Agreement

The second phase nucleation and precipitation around the edge dislocation are studied using phase-field method. A new free energy function is established. The simulation results are in good agreement with that of theory of dislocation and theory of non-uniform nucleation.

Microstructure evolution in multilayer c-TiAlN/TiN coatings during spinodal decomposition — A phase-field study

2016 ◽  
Vol 01 (01) ◽  
pp. 1650002 ◽  
Author(s):  
Jingjing Zhou ◽  
Lijun Zhang ◽  
Li Chen ◽  
Hong Wu ◽  
Yong Du
Keyword(s):  
Spinodal Decomposition ◽  
Microstructure Evolution ◽  
Phase Field ◽  
Phase Field Model ◽  
Dislocation Motion ◽  
Combined Model ◽  
Modulation Period ◽  
Tin Coatings ◽  
Good Agreement ◽  
Modulation Ratio

By means of the combined model, i.e., the phase-field model with finite interface dissipation in combination with the modified Cahn–Hilliard model, together with the materials parameters comprehensively verified in monolithic c-TiAlN coatings, the microstructure evolution in multilayer c-Ti[Formula: see text]Al[Formula: see text]N/TiN coatings annealed at [Formula: see text]C was quantitatively simulated by directly comparing with the experimental data. The sharp interface between c-TiN and c-Ti[Formula: see text]Al[Formula: see text]N layers in the as-deposited state was found to change into a diffuse one, which can act as highly effective obstacles against dislocation motion. Moreover, the simulations indicate that the spinodal decomposition occurs in the Ti[Formula: see text]Al[Formula: see text]N layer and the decomposed layer becomes thinner, which is in good agreement with the experimental observation. In addition, the effect of modulation period and modulation ratio on microstructure evolution in c-Ti[Formula: see text]Al[Formula: see text]N/TiN coating was further studied. The relatively smaller modulation period can generate more layers in the real scale of coatings, which can help to strengthen the coatings due to refinement of grains and restriction of dislocations. As for the modulation ratio, when the value decreases from 5:1 to 1:1, Ti atoms in the decomposed layer disappear faster. A further extension into a larger-sized simulation was also performed.

A Phase-Field Model for Rapid Solidification with Non-Equilibrium Solute Diffusion

2015 ◽  
Vol 817 ◽  
pp. 14-20
Author(s):  
Hai Feng Wang ◽  
Cun Lai ◽  
Xiao Zhang ◽  
Kuang Wang ◽  
Feng Liu
Keyword(s):  
Rapid Solidification ◽  
Phase Field ◽  
Growth Velocity ◽  
Field Model ◽  
Phase Field Model ◽  
Solute Diffusion ◽  
Current Phase ◽  
Diffusion Velocity ◽  
Good Agreement ◽  
Non Equilibrium

Since the growth velocity can be comparable with or even larger than the solute diffusion velocity in the bulk phases, modeling of rapid solidification with non-equilibrium solute diffusion becomes quite an important topic. In this paper, an effective mobility approach was proposed to derive the current phase field model (PFM). In contrast with the previous PFMs that were derived by the so-called kinetic energy approach, diffusionless solidification happens not only in the bulk phases but also inside the interface when the growth velocity is equal to the solute diffusion velocity in liquid. A good agreement between the model predictions and experimental results is obtained for rapid solidification of Si-9at.%As alloy.

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.

CO2 fracturing using the phase field approach for the brittle fracture

2021 ◽  
Author(s):  
Mostafa Mollaali ◽  
Vahid Ziaei-Rad ◽  
Yongxing Shen
Keyword(s):  
Analytical Solutions ◽  
Phase Field ◽  
Field Model ◽  
Isothermal Condition ◽  
Phase Field Model ◽  
Fracture Initiation ◽  
State Equation ◽  
Fracture Path ◽  
Field Approach ◽  
Good Agreement

<p>To simulate CO<sub>2</sub> fracturing under an isothermal condition, we propose a phase field model. We take advantage of the ability of the phase field approach to predict fracture initiation and branching, as well as to avoid tracking the fracture path. We model the CO<sub>2</sub> as a compressible fluid by modifying Darcy's law. In particular, we assume that the permeability is correlated to the value of the phase field by the exponential function. The dependence of the CO<sub>2</sub> density as a function of the pressure is captured by the Span-Wagner state equation. The computed pressure breakdown values show good agreement with analytical solutions and experimental results.</p>

Modelling Static Recrystallisation Textures Using a Coupled Crystal Plasticity-Phase Field Technique

2011 ◽  
Vol 702-703 ◽  
pp. 663-666
Author(s):  
Yong Jun Lan ◽  
C. Pinna
Keyword(s):  
Crystal Plasticity ◽  
Phase Field ◽  
Boundary Energy ◽  
Phase Field Model ◽  
Stored Energy ◽  
Crystal Plasticity Finite Element ◽  
Bcc Metals ◽  
Nucleation Sites ◽  
Experimental Rolling ◽  
Good Agreement

An integrated crystal plasticity-phase field model has been developed to simulate the static recrystallisation textures of both Face-Centred Cubic (FCC) and Body-Centred Cubic (BCC) metals. Nucleation sites are determined using the Orientation Dependent Recovery (ODR) theory. Both the interface mobility and the grain boundary energy are set to be dependent on mis-orientation angles in the simulations. A pre-deformed microstructure without a particular texture is generated using a Monte Carlo simulation. Plane strain compression textures before recrystallisation are predicted by a Crystal Plasticity Finite Element (CPFE) model showing a good agreement with the typical experimental rolling textures. It is shown that the typical recrystallisation textures for FCC and BCC metals can be simulated correctly using a Phase Field (PF) method by choosing appropriate critical values for the nucleation criterion. A comparison between the two different nucleation criteria based on the ODR theory or the stored energy is also presented.

A Phase-Field Fracture Model of Ferroelectric Materials Under Electro-Mechanical Loading

2011 ◽  
Author(s):  
Amir Abdollahi ◽  
Irene Arias
Keyword(s):  
Phase Field ◽  
Phase Field Model ◽  
Ferroelectric Materials ◽  
Crack Face ◽  
Fracture Evolution ◽  
Main Challenge ◽  
Crack Interactions ◽  
Formation And Evolution ◽  
Crack Faces ◽  
Field Approaches

A phase-field model is proposed for the coupled simulation of microstructure and fracture evolution in ferroelectric materials. The model is based on energetic phase-field approaches for brittle fracture and ferroelectric domain formation and evolution. The variational nature of these approaches makes their coupling very natural. However the main challenge is to encode the electro-mechanical conditions of the sharp crack faces into the phase-field framework since the crack in this model is smeared and represented by an internal layer. We develope the model for different crack face boundary conditions. Simulations show the microstructure induced by the presence of the crack. Interactions between the microstructure and the crack are investigated under different electro-mechanical loadings.

scholarly journals Multiphase Phase-Field Lattice Boltzmann Method for Simulation of Soluble Surfactants

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1019
Author(s):  
Ehsan Kian Far ◽  
Mohsen Gorakifard ◽  
Ehsan Fattahi
Keyword(s):  
Interfacial Tension ◽  
Lattice Boltzmann Method ◽  
Phase Field ◽  
Lattice Boltzmann ◽  
Phase Field Model ◽  
Multiphase System ◽  
Model Parameters ◽  
Oil Water ◽  
Boltzmann Method ◽  
The Given

This paper proposes a phase-field model for the lattice Boltzmann method which has discretized symmetrical directions of velocities in a cartesian grid, to simulate the soluble surfactant in a Multicomponent multiphase system. Despite other existing phase-field models following Langmuir relation, the interfacial tension can be calculated analytically in this proposed model. Parameters playing roles in the models and controlling the surfactant’s strength and interaction with other phases are obtained directly from a given initial interfacial tension and bulk surfactant. Consequently, there is no further need for trial-and-error simulations, and a real system, e.g., oil-water-surfactant, can be simulated with given initial parameters. The model is validated with the analytical result for a planar oil–water-surfactant system. Furthermore, the method for reobtaining numerical interfacial tension for five different cases is tested and compared with the given initial values for an oil droplet surrounded by water and surfactant. The results show that the obtained interfacial tension from the method is in good agreement with the given initial interfacial tension. Furthermore, the spurious velocity of the model is calculated and seen that the magnitude of spurious velocities is proportional to interfacial tension.

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