Phase field simulation of grain refinement in silver-based filler metal

Numerical simulation is one of the important auxiliary methods for studying materials-related problems. In this study, phase field simulation was employed to investigate the refinement behavior of BAg55CuZn-x B brazing alloys. Simulation and experimental studies were conducted for B contents ranging from 0 wt.% to 0.2 wt.%. The results demonstrated that the addition of 0.05 wt.% B in the brazing alloy leads to a significant refinement effect. As the B content increases, the grain size further reduces, and a refinement stagnation phenomenon occurs after exceeding 0.15 wt.%. The solidification process of brazing alloys with different B content was predicted by simulation, and the simulation results showed that with the increase of B content, the initial number of nucleation increased, and the radius of the dendrite tip decreased. The simulation results are in good agreement with the experimental findings, providing further evidence of the refining effect of the B element and the reliable predictive capability of the phase field model.

Multi-dimensional Simulation of Phase Change by a 0D-2D Model Coupling via Stefan Condition

Considering phase changes associated with a high-temperature molten material cooled down from the outside,this work presents an improvement of the modelling and the numerical simulation of such processes for an application pertaining to the safety of light water nuclear reactors.Postulating a core meltdown accident,the behaviour of the core melt(aka corium)into a steel vessel is of tremendous importance when evaluating the vessel integrity.Evaluating correctly the heat fluxes requires the numerical simulation of the interaction between the liquid material and its solid counterpart which forms during the solidification process,but also may melt back.To simulate this configuration,encoun-tered in various industrial applications,one considers a bi-phase model constituted by a liquid phase in contact and interaction with its solid phase.The liquid phase may solidify in presence of low energetic source,while the solid phase may melt due to an intense heat flux from the high-temperature liquid.In the frame of the in-house legacy code,several simplifying assumptions(0D multi-layer discretization,instantaneous heat transfer via a quadratic temperature profile in solids)are made for the modelling of such phase changes.In the present work,these shortcomings are illustrated and further overcome by solving a 2D heat conduction model in the solid by a mixed Raviart-Thomas finite element method coupled to the liquid phase due to heat and mass exchanges through Stefan condition.The liquid phase is modeled with a 0D multi-layer approach.The 0D-liquid and 2D-solid mod-els are coupled by a Stefan like phase change interface model.Several sanity checks are performed to assess the validity of the approach on 1D and 2D academical configurations for which exact or reference solutions are available.Then more advanced situations(genu-ine multi-dimensional phase changes and an"industrial-like scenario")are simulated to verify the appropriate behavior of the obtained coupled simulation scheme.

Unconventional phase field simulations of transforming materials with evolving microstructures

Transforming materials with evolving microstructures is one of the most important classes of smart materials that have many potential technological applications, and an unconventional phase field approach based on the characteristic functions of transforming variants has been developed to simulate the formation and evolution of their microstructures. This approach is advantageous in its explicit material symmetry and energy well structure, minimal number of ma- terial coefficients, and easiness in coupling multiple physical processes and order parameters, and has been applied successfully to study the microstructures and macroscopic prop- erties of shape memory alloys, ferroelectrics, ferromagnetic shape memory alloys, and multiferroic magnetoelectric crys- tals and films with increased complexity. In this topical re- view, the formulation of this unconventional phase field approach will be introduced in details, and its applications to various transforming materials will be discussed. Some ex- amples of specific microstructures will also be presented.

Phase field simulation of the 180°domain-switching process in PbTiO_3 single crystal under an antiparallel electric field

The process of 180°domain switching in PbTiO_3 single crystal under an antiparallel electric field was investigated by the three-dimensional phase field simulation,especially the effect of electric field on the type and duration of domain switching.It is found that the polarization reversal of domains takes place under an antiparallel electric field in PbTiO_3 single crystal.The results of the phase field simulation indicate that there is only 90°domain switching under a weak electric field.With the rise of the electric field,180°domain switching appears.If the electric field is strengthened further,90°domain switching disappears and the duration of domain switching is shortened.

Experiment and simulation on the pyrite removal from the recirculating load of pulverizer with a dilute phase gas-solid fluidized bed

In order to reduce the energy consumption and subsequent air pollution of coal-fired power station, based on the analysis to size and density distribution of particles from the recirculating load of the classifier of pulverizer, the separation experiment on sampling material from power plant with a dilute phase fluidized bed to remove pyrite and other minerals and numerical simulation on the separation process were done. The results show that the minimum fluidization velocity is 1.62 cm/s. Pyrite and other minerals in the material are separated. Ash of the upper and bottom layer material account for 33.34% and 73.42% respectively and sulfur content occupy 1.12% and 8.96% respectively. Scanning electron microscopy and spectroscopy tests show that sulfur in the bottom material exist in the form of pyrite. Numerical simulation on the flow field form of the dilute phase separation bed with gas-solid two phase and particle motion verifies the experimental results.

Three-Dimensional Phase Field Simulations of Hysteresis and Butterfly Loops by the Finite Volume Method

Three-dimensional simulations of ferroelectric hysteresis and butterfly loops are carried out based on solving the time dependent Ginzburg-Landau equations using a finite volume method. The influence of externally mechanical loadings with a tensile strain and a compressive strain on the hysteresis and butterfly loops is studied numerically. Different from the traditional finite element and finite difference methods, the finite volume method is applicable to simulate the ferroelectric phase transitions and properties of ferroelectric materials even for more realistic and physical problems.

Applied Strain Field on Microstructure Optimization of Ti-Al-Nb Alloy Computer Simulated by Phase Field Approach

The effects of applied tensile strain on the coherent α_2→O-phase transformation in Ti-Al-Nb alloys are explored bycomputer simulation using a phase-field method. The focus is on the influence of the applied strain direction onthe microstructure and volume fraction of the O-phase precipitates. It is found that altering applied strain directioncan modify microstructure of Ti-25Al-10～12Nb (at. pct) alloy during α_2→O-phase transformation effectively andfull laminate microstructure in the Ti-25Al-10Nb (at. pct) alloy can be realized by an applied strain only along thedirection 30°away from the α_2 phase <1010> in magnitude equivalent to the stress-free transformation strain. Thesimulation also shows that not only the magnitude of applied strain but also the applied strain direction influencesthe O-phase volume fraction and the effect of strain direction on the volume fraction is up to 25%.

Irradiation-induced void evolution in iron：A phase-field approach with atomistic derived parameters

A series of material parameters are derived from atomistic simulations and implemented into a phase field（PF） model to simulate void evolution in body-centered cubic（bcc） iron subjected to different irradiation doses at different temperatures.The simulation results show good agreement with experimental observations — the porosity as a function of temperature varies in a bell-shaped manner and the void density monotonically decreases with increasing temperatures; both porosity and void density increase with increasing irradiation dose at the same temperature. Analysis reveals that the evolution of void number and size is determined by the interplay among the production, diffusion and recombination of vacancy and interstitial.

APPLICATIONS OF PHYSICAL SIMULATION IN THE DEVELOPMENT OF HOT WORKING PROCESSES

Modelling has become a more and more valuable tool in the design, control and development of steel processing. Empirical regression equations, physically based approachs, artificial neural networks and hybrid models are being theied in computer modelling. In all cases, relevant data are necessary, which can be most economically obtained by physical simulation. Physical simulation with a Gleeble simulator has been used in a large number of tasks at the University of Oulu for ten years in cooperotion with the Finnish metals industry. Some examples of these will be described and discussed below, such as the optimization of the recrystallization controlled rolling process, the improvement of the hot strength model for the control of coiling tension and the optimization of continuous strip annealing schedules.Finally,brief remarks will be then on a couple of projects now under way.

Electrocaloric effect in ferroelectric materials:From phase field to first-principles based effective Hamiltonian modeling

Electrocaloric effect(ECE)of ferroelectrics has attracted considerable interest due to its potential application in environmentally friendly solid-state refrigeration.The discovery of giant ECE in ferroelectric thin films has greatly renewed the research activities and significantly stimulated experimental and theoretical investigations.In this review,the recent progress on the theoretical modeling of ECE in ferroelectric and antiferroelectric materials are introduced,which mainly focuses on the phase field modeling and first-principles based effective Hamiltonian method.We firstly provide the theoretical foundation and technique details for each method.Then a comprehensive review on the progress in the application of two methods and the strategies to tune the ECE are presented.Finally,we outline the practical procedure on the development of multi-scale computational method without experiemtal parameters for the screening of optimized electrocaloric materials.

Domain size and charge defects affecting the polarization switching of antiferroelectric domains

The switching behavior of antiferroelectric domain structures under the applied electric field is not fully understood.In this work,by using the phase field simulation,we have studied the polarization switching property of antiferroelectric domains.Our results indicate that the ferroelectric domains nucleate preferably at the boundaries of the antiferroelectric domains,and antiferroelectrics with larger initial domain sizes possess a higher coercive electric field as demonstrated by hysteresis loops.Moreover,we introduce charge defects into the sample and numerically investigate their influence.It is also shown that charge defects can induce local ferroelectric domains,which could suppress the saturation polarization and narrow the enclosed area of the hysteresis loop.Our results give insights into understanding the antiferroelectric phase transformation and optimizing the energy storage property in experiments.

Modeling of Ni_4Ti_3 precipitation during stress-free and stress-assisted aging of bi-crystalline NiTi shape memory alloys

The phase field method was applied to study the microstructure evolution of Ni4Ti3 precipitates during stress-free and stress-assisted aging of bi-crystalline NiTi shape memory alloys （SAMs） with two different initial Ni-contents of 51.5% and 52.5% （mole fraction）, respectively. The simulation results show that, during stress-free aging of the NiTi alloy with a low supersaturation of Ni （i.e., Ti-51.5%Ni）, the Ni4Ti3 precipitates exhibit a heterogeneous distribution with a high number density of particles at the grain boundary, leaving most of the grain interiors free of precipitates; while for the NiTi alloy with a high supersaturation of Ni （i.e., Ti-52.5%Ni）, the Ni4Ti3 precipitates show a homogeneous distribution across the entire simulation system. The stress-assisted aging can give rise to homogeneous distribution of the precipitates, regardless of the initial Ni-content; however, the distribution of variant type within the two grains is heterogeneous.

Laboratory simulation on acoustic well-logging with phased array transmitter

Two small scale acoustic phased arrays with 4 elements have been designed and assembled in the laboratory. Experiments have been carried out with them. It is found that both directivity and radiation lobe width of the phased array can be regulated by changing the time delay between the input signals on neighboring elements. Results measured are in good agreement with those calculated. By using the phased array as an acoustic transmitter and hydrophone as a receiver, small scale acoustic well-logging simulations have been carried out both on an aluminum modei well and on a concrete one. Experimental results show that, by increasing the time delay of the input signals on neighboring elements, the steered radiation angle of the phased array becomes larger and larger, and generation conditions of the refracted compressional wave and the refracted shear wave are reached successively, and the refracted compressional wave, the refracted shear wave and the Stoneley wave are strengthened, respec-tively. Therefore, by choosing element spacing of a phased array and acoustic wave frequency appropriately, the main radiation lobe of the phased array can be widened to cover the first critical angle of all kinds of formations, which makes it possible to apply phased array acoustic well-logging in any formation continuously without regulating directivity of the phased array.

GPU-accelerated phase field simulation of directional solidification

The phase field simulation has been actively studied as a powerful method to investigate the microstructural evolution during the solidification.However,it is a great challenge to perform the phase field simulation in large length and time scale.The developed graphics processing unit(GPU)calculation is used in the phase filed simulation,greatly accelerating the calculation efficiency.The results show that the computation with GPU is about 36 times faster than that with a single Central Processing Unit(CPU)core.It provides the feasibility of the GPU-accelerated phase field simulation on a desktop computer.The GPU-accelerated strategy will bring a new opportunity to the application of phase field simulation.

Measurement and correlation of solubility of trimethylolethane in different pure solvents and binary mixtures

The solubilities of trimethylolethane in butanol,methyl acetate,ethyl acetate as well as in mixed solvents of(methanol+ethyl acetate) and(ethanol+ethyl acetate) were measured with the gravimetric method in the temperature range from 283.15 K to 318.15 K under atmosphere pressure.The experiment results showed that the solubility of trimethylolethane increased with the temperature,or along with the concentration of methanol or ethanol in the solvents of(methanol+ethyl acetate) and(ethanol + ethyl acetate).In addition,the experiment values were correlated by the van't Hoff equation,Modi fied Apelblat Equation,λh Equation,CNIBS/R-K equation and Jouyban–Acree Model.The Modi fied Apelblat Equation provided the best fitting results of the solubility data of TME in the pure solvents while the CNIBS/R-K model showed the best estimation of the solubility in the binary solvent mixtures.Furthermore,the density functional theory(DFT) calculations showed that solubility in different solvents related to the strength of the interaction between the trimethylolethane and the solvent molecules.Finally,the standard molar enthalpy and molar entropy of trimethylolethane during the dissolving process was also calculated by Modi fied Apelblat equation in this work.

Phase field simulation of solidification under supergravity

In order to understand the influence of supergravity on the microstructure of materials,crystal nucleation,dendritic growth,and polycrystal solidification under supergravity are investigated by using the modified nucleation theory and phase field models.Firstly,supergravity is considered in the nucleation theory by using pressure-dependent Gibbs free energy.It is found that the critical radius decreases and the nucleation rate increases when supergravity rises.Secondly,anisotropic heat transport is proposed in the phase field model to investigate the influence of supergravity on dendritic growth.Phase field simulations show that supergravity promotes the secondary dendritic growth in the direction parallel to supergravity.Finally,a multiply phase field model with pressure-dependent interfacial energy is employed to simulate the polycrystalline solidification under supergravity.Due to the depth-dependent pressure by supergravity,crystal grains are significantly refined by high pressure.In addition,gradient distribution of grain size is obtained in the solidification morphology of polycrystalline,which is consistent with previous experimental observations.Results of this work suggest that supergravity can be used to tune the microstructures and properties of materials.

Influences of Marangoni effect on solidification of curved interfaces with constant curvature

The asymptotic method and phase field simulation are applied to study the influences of variation of the surface tension with temperature on the movements of solid-liquid interfaces in the solidification process of spherical and cylindrical nuclei, respectively. Results indicate that Marangoni effect will increase the critical nucleation radius, slow up the movement of interface. The tip speed of dendrite decreases linearly with Marangoni number for melt without convection. The results of phase field simulation are qualitatively in accord with that of asymptotic method.

Temperature-Dependence of Microstructure Evolution in a Ferroelectric Single Crystal with Conducting Crack

The different temperature-induced nonlinear behavior near a conducting crack tip in a ferroelectric single crystal is studied based on a phase field approach containing the time-dependent Ginzburg-Landau equation.Since domain switching in a crack tip plays an important role in the fracture behavior,by using three-dimensional nonlinear finite element method,the temperature-induced domain switching behavior of a ferroelectric single crystal is simulated under applied electrical and mechanical loads.The simulations show that increasing the temperature will enhance the crack propagation under a strong electric field,which results in switching-weakening.In particular,increasing the temperature from 300°C to 600°C will impede the crack propagation under combined mechanical and electric field loading,which results in switching-toughening.Salient features of the results are consistent with many experimental observations.

Simulation study of the superharmonic field generated from a phase array transducer

Ultrasound imaging is the most widely used noninvasive medical imaging modality. Its latest elite concept is Superharmonic Imaging which is the most talked-about future of medical diagnostic ultrasound. In this paper, the computational and analytical study for superharmonic field generation from phased array transducer of 16 × 16 elements is presented. For this, the model preferred, includes the calculation for diffraction effect in frequency domain and nonlinear effect in time domain. The attenuation is included along with the diffraction in frequency domain as well. The comparative analysis of superharmonic field is also carried out with simulated fundamental and second harmonic fields by the same model. Similarly, the comparison with the results from the literature is also reported.

An unconventional phase field modeling of domains formation and evolution in tetragonal ferroelectrics

Based on characteristic functions of variants, we developed an unconventional phase field modeling for investigating domains formation and evolution in tetragonal ferroelectrics. In order to develop this computational approach, we constructed the anisotropy energy of tetragonal variants, which is used instead of Landau-Devonshire potential in the conventional phase field method, resulting in that much fewer parameters are needed for simulations. This approach is advantageous in simulations of emerging ferroelectric materials. We employ it to study the formation and evolution of domains in tetragonal barium titanate single crystal, as well as the nonlinear behaviors under cyclical stress and electric field loading. A multi-rank laminated ferroelectric domain pattern, 90° domain switching accompanied by polarization rotation, and 180° domain switching accompanied by move of domain wall are predicted. It is found that the speed of 90° domain switching is slower than that of 180° domain switching, due to both polarization and transformation strain changed in 90° domain switching. It also suggests that large strain actuation can be generated in single crystal ferroelectrics via combined electromechanical loading inducing 90° domain switching. The good agreement between simulation results and experimental measurements is observed.