Results Of Phase-field Simulations Research Articles

A probabilistic-phase field model for the fracture of brittle materials

We develop a computational method to determine the failure probability of brittle materials under general mechanical loading conditions. The method is a combination of two parts: (1) numerical simulations of materials with multiple cracks using phase field theory, where the complete fracture process is viewed as ‘damage percolation’ along critical paths or clusters of cracks, rather than the traditional weak-link failure mechanism of Weibull, and (2) an extension of the Batdorf statistical theory of fracture to finite domains, where it is implemented within the finite element framework. The results of phase-field simulations at the ‘percolation threshold’ are used as failure data in the Batdorf theory to determine the overall probability of failure. The input to this approach is the size distribution of cracks in a pristine material. An example is shown, where alumina samples that were previously tested by Abe and coworkers (Abe et al 2003 J. Am. Ceram. Soc. 86 1019–21) in four-point loading are compared to the results of our numerical simulations. The approach developed here has the advantage of being extendable to more complex thermomechanical loading.

Poling above the Curie temperature driven large enhancement in piezoelectric performance of Mn doped PZT-based piezoceramics

The enhancement of piezoelectricity is usually in sacrifice of Curie temperature, which in turn limits its working temperature range. It is well known that there are some trade-off among the various performance parameters of most piezoelectric ceramics, and it is still difficult to achieve synergistic improvement in multiple parameters. Here, it is reported that the piezoelectric coefficient d33 of a 0.6 mol% Mn-doped Pb(Sb0.5Nb0.5)0.02Zr0.51Ti0.47O3 piezoelectric ceramics is increased to 436 pC N−1, and its electro-strain can reach 0.16% (d33* = 800 pm/V) at 2 kV mm− 1 by high-temperature poling, whose Curie temperature can still keep at 347 ℃. The features of "hard" piezoelectric ceramics such as low dielectric loss (tgδ = 0.23%) and high mechanical quality factor (Qm = 546) are also preserved. Through structural characterization, combined with the theoretical results of phase field simulation, it is shown that its excellent piezoelectric performance originates from the highly oriented domain structure and small domain size after high temperature poling. On the other hand, the valence state transition of Mn3+ ions during high-temperature poling increases the defect vacancies and lattice distortion in ceramics, which keeps the acceptor-doped characteristic of the ceramics.

Superior energy storage capacity of a Bi0.5Na0.5TiO3-based dielectric capacitor under moderate electric field by constructing multiscale polymorphic domains

The challenge of electronic components failing in service when exposed to ultra-high electric fields necessitates the development of dielectric capacitors with a higher energy storage density per electric field. Therefore, the development of dielectric capacitors with high energy storage density under moderate electric fields is of great importance. To address this issue, a polymorphic multiscale domain construction strategy has been proposed in this work. Guided by the results of phase field simulations, lead-free Bi0.5Na0.5TiO3-Sr0.7Bi0.2TiO3-La(Mg0.5Ti0.5)O3 ceramics have been prepared, which enable the coexistence of rhombohedral (R) + tetragonal (T) nanodomains and polar nanoregions (PNRs). This has resulted in a total energy density of 7.3 J·cm−3 and efficiency of 93% at 390 kV·cm−1 in the current system. Additionally, the energy storage potential (Wrec/Eb) of this ceramic is the highest in Bi0.5Na0.5TiO3-based systems among the latest research. Furthermore, the ceramic displays excellent thermal stability from − 50 to 200 ℃. This work provides a new approach to enhance the energy storage properties (ESPs) of dielectric ceramics under moderate electric fields.

Phase Field Study of Cr-Oxide Growth Kinetics in the Crofer 22 APU Alloy Supported by Wagner’s Theory

The Crofer 22 APU alloy is a frequently used metallic material to manufacture interconnects in solid oxide fuel cells. However, the formation and evaporation of Cr2O3 not only increases the electrical resistance but also leads to the Cr-related degradation over the service time. In order to investigate the growth kinetics of Cr-oxide, i.e., Cr2O3, the multi-phase field model coupled with reliable CALPHAD databases is employed. The phase field simulation results are benchmarked with the predictions of Wagner’s theory. Moreover, we evidence the influence of the temperature and Cr concentration on the ferritic matrix phase and the oxygen concentration at the Cr2O3/gas interface on the growth kinetics of Cr-oxide, paving the way for further investigations of Cr-related solid oxide fuel cell degradation processes.

Study on the mechanism of carbide precipitation by surface quenching treatment on GCr15 bearing rings based on the phase-field method

In this paper, the thermodynamics database describing Gibbs free energy of FCC phase and M23C6 phase based on Fe-Cr-C ternary alloy was coupled into phase field simulation, and the phase field model was developed on the mesoscopic scale which simulates precipitation, growth and coarsening of M23C6 carbides in FCC austenitic matrix by considering the elastic energy. As the boundary condition of imported phase field calculation, the heat treatment COSMAP software was applied to obtain the macro numerical simulation results of quenching. The phase composition, element distribution, and the evolution including the nucleation, growth and coarsening was simulated by phase field method for the M23C6 carbides in quenching process of GCr15 bearing ring. By means of comparison between the calculation results of phase field simulation and the morphology, quantity and distribution of carbides observed by SEM experiment, this paper present the mechanism on precipitation of micro M23C6 carbides influenced by quenching process parameters, and the experiment verifies the feasibility and accuracy of phase field simulation.

Achieving Ultrahigh Energy-Storage Density with Excellent Thermal Stability in Sr0.7Bi0.2TiO3-Based Relaxors via Polarization Behavior Modulation.

Dielectric capacitors possessing the inherent superiorities of high power density and ultrafast charge-discharge speed make their utilization in energy-storage devices extremely propitious, although the relatively low recoverable energy-storage density (Wrec) may impede their applications. In this work, unlike the mainstream approach of destroying long-range ferroelectric/antiferroelectric order and inducing relaxor properties to achieve a high Wrec value, we have selected end members with a high polarization gene to promote the polarization behavior of the typical relaxor Sr0.7Bi0.2TiO3. Therefore, an ultrahigh Wrec ∼ 8 J/cm3 and a superior efficiency (η) ∼ 91% are accomplished in the 0.98[0.56(Sr0.7Bi0.2)TiO3-0.44(Bi0.5Na0.5)TiO3]-0.02 Bi(Mg0.5Ti0.5)O3 sample. The achieved Wrec value is record high in Sr0.7Bi0.2TiO3-based systems as far as we know. The polarization-enhancement behavior can be explained by the phase field simulation results, phase content variance in X-ray diffraction Rietveld refinement, hardening trend in Raman spectroscopy, domain morphology, and local symmetry in transmission electron microscope analysis. Meanwhile, the ceramic possesses excellent thermal stability (ΔWrec < 12.7% and Δη < 10.4%, -50-200 °C), frequency (ΔWrec < 2.69% and Δη < 2.06%, 0.5-500 Hz), and fatigue-resistant stability (ΔWrec < 0.08% and Δη < 0.2%, up to 1 × 105 cycles). Accordingly, this work proposes a design idea to tailor the polarization behavior and energy-storage properties of typical relaxors.

New insights into the thermal aging mechanism of yttria stabilized zirconia: A phase field study

In this paper, a novel phase-field (PF) model is proposed to study the thermal aging mechanism of single crystalline t'-YSZ. The influences of the initial compositional content of yttria and the initial twin structure of the t' phase on the aging process are systematically discussed. The PF model can recover the modulated structure and nano/micro hybrid structure observed in experiments. The PF simulation results indicate that the initial compositional content of yttria is the most important influential factor of the thermal aging process. Besides that, the transformation strain, the initial twin structure and the anti-phase boundaries (APBs) of the t' phase can also have significant influences on the thermal aging kinetics. The typical spinodal region is more suitable to predict the thermal aging behavior of single domain YSZ. For multi-domain YSZ with initial twin structures and APBs, the spinodal region should be further divided into the kernel region and marginal region. In the kernel region, the thermal aging occurs by spinodal decomposition with the formation of a modulated structure, which is followed by merging and coarsening. In the marginal region and outside the spinodal region, the phase decomposition leads to a hybrid structure with coarse grained cubic phase and fine grained tetragonal phase, which exhibits the characteristics of nucleation and growth. The hybrid structure is consistent with previous experimental observations. It is revealed that the boundaries of the nano sized tetragonal grains evolve from the twin boundaries and APBs. The nucleation-growth mechanism should be properly understood when it is applied to illustrate the evolution process of the hybrid structure. The PF model and the new insights obtained in this study are helpful to understand the thermal aging mechanisms of t'-YSZ.

Enhancement of energy storage properties of Bi0.5Na0.5TiO3-based relaxor ferroelectric under moderate electric field

Dielectric capacitors, as one of the important electronic devices, are widely used in various fields. However, most ferroelectric capacitors with high energy storage density require excessively high electric fields. In this work, we have prepared 0.9(Bi0.5Na0.5)0.7Sr0.3TiO3-0.1 Bi(Mg2/3Nb1/3)O3 relaxor ferroelectric ceramics with different BaZrO3 doping levels. A high energy storage (Wr) of 4.07 J/cm3 and efficiency (η) of 91% are simultaneously obtained in 0.94[0.9(Bi0.5Na0.5)0.7Sr0.3TiO3-0.1 Bi(Mg2/3Nb1/3)O3]-0.06BaZrO3 ceramic under a medium electric field of 260 kV/cm. Additionally, the ceramic also exhibits excellent temperature and frequency stability. Furthermore, the phase field simulation is used to simulate the evolution of domain structure and hysteresis loops of the ceramics with different doping levels. The results of phase field simulation explicitly explain the influence of different relaxation degrees on energy storage density and efficiency of the ceramics. We believe that the ceramic prepared in this work is one of the most promising candidate materials for some miniaturized energy storage devices operating under low or medium electric fields.

Effect of Transient Thermal Conditions on Columnar-to-Equiaxed Transition during Laser Welding: A Phase-Field Study

The columnar-to-equiaxed transition (CET) is commonly observed in laser welds. It is able to prevent the growth of large columnar grains and consequently improve the mechanical properties of welded joints. In this paper, the CET behaviors at different locations in the laser weld of an Al–Mg alloy are observed experimentally and studied systematically. In order to describe the dynamic CET behaviors, an integrated phase-field (PF) model coupled with transient thermal conditions and a Gaussian heterogeneous nucleation model is developed. Investigations on columnar growth under steady conditions are performed first. In particular, the effects of thermal conditions, i.e., solidification rate and temperature gradient, on the constitutionally undercooled degree and region ahead of the solidification front are quantitatively studied. In a laser weld, it is found that the CET behaviors vary significantly along the thickness direction. Our PF simulation results indicate that the CET depends strongly on the locally transient thermal conditions in the fusion zone. The transient thermal conditions affect CET behaviors by dynamically adjusting the constitutionally undercooled degree and region during the solidification process. The predicted CET behaviors under transient conditions exhibit reasonably good agreements with corresponding experimental results.

Influence of Cooling Scenarios on the Evolution of Microstructures in Nickel-Based Single Crystal Superalloys

The reprecipitation and evolution of γ’ precipitates during various cooling approaches from supersolvus temperature are studied experimentally and via phase field simulation in nickel-based single crystal superalloys. The focus of this paper is to explore the influence of cooling methods on the evolution of the morphology and the distribution of γ’ precipitates. It is demonstrated that small and uniform spherical shape γ’ particles formed with air cooling method. When the average cooling rate decreases, the particle number decreases while the average matrix and precipitate channel widths increase. The shape of γ’ precipitates which changed from spherical to cubic and irregular characteristics due to the elastic interaction and elements diffusion are observed with the decrease of the average cooling rate. The phase field simulation results are in good agreement with the experimental results in this paper. The research is a benefit for the study of the rejuvenation heat treatment in re-service nickel-based superalloys.

Dewetting of Ni silicide thin film on Si substrate: In-situ experimental study and phase-field modeling

In this paper, the in-situ Scanning Electron Microscopy (in-situ SEM) technique and three-dimensional (3-D) phase-field simulation were combined to perform a comprehensive study on the kinetics and mechanisms of dewetting (or agglomeration) of a 30 nm NiSi films on Si(100) substrate at 600 °C. The evolution of texture during agglomeration of the polycrystalline NiSi thin film was also studied by ex-situ Electron BackScattered Diffraction (EBSD). The phase-field simulation results showed that abnormal grain growth plays an important role in the dewetting process of polycrystalline films, while the misorientations between the NiSi grains and the Si substrate are the main reason for the agglomeration of NiSi polycrystalline thin film on the monocrystal Si substrate. Moreover, 3-D phase-field simulations coupled with experimental information on misorientation distribution and initial grain size were also performed, and the simulated Ni silicide grain morphology is in good agreement with the in-situ SEM results during agglomeration. In order to slow down or to suppress the agglomeration, it is highly recommended to increase the volume fraction of low angle grains, and/or to decrease the misorientation between the NiSi grain and the Si substrate or between the NiSi grains.

Phase Field Modeling of Cubic to Tetragonal Transformation in YSZ and its Effect on Ionic Conductivity Degradation and Mechanical Damages

During the high-temperature operation of solid oxide fuel cells (SOFCs), the degradations of electrolyte material yttria-stabilized zirconia (YSZ) in both ionic conductivity and mechanical strength can be caused by the cubic to tetragonal phase transformation. In this work, microelasticity phase field model is built to simulate the YSZ phase transformation considering the effects of grain boundary and solid morphology. The YSZ skeleton in real SOFC anode is reconstructed using focused ion beam-scanning electron microscopy (FIB-SEM) dual-beam technique. The ionic conductivity degradation and the mechanical damages under external mechanical loads of brittle YSZ phase in anode are investigated based on the phase field simulation results. The simulation results may provide theoretical guidelines for improving the SOFC anode during fabrication.

A Multi-Scale Approach for Phase Field Modeling of Ultra-Hard Ceramic Composites.

Diamond-silicon carbide (SiC) polycrystalline composite blends are studied using a computational approach combining molecular dynamics (MD) simulations for obtaining grain boundary (GB) fracture properties and phase field mechanics for capturing polycrystalline deformation and failure. An authentic microstructure, reconstructed from experimental lattice diffraction data with locally refined discretization in GB regions, is used to probe effects of local heterogeneities on material response in phase field simulations. The nominal microstructure consists of larger diamond and SiC (cubic polytype) grains, a matrix of smaller diamond grains and nanocrystalline SiC, and GB layers encasing the larger grains. These layers may consist of nanocrystalline SiC, diamond, or graphite, where volume fractions of each phase are varied within physically reasonable limits in parametric studies. Distributions of fracture energies from MD tension simulations are used in the phase field energy functional for SiC-SiC and SiC-diamond interfaces, where grain boundary geometries are obtained from statistical analysis of lattice orientation data on the real microstructure. An elastic homogenization method is used to account for distributions of second-phase graphitic inclusions as well as initial voids too small to be resolved individually in the continuum field discretization. In phase field simulations, SiC single crystals may twin, and all phases may fracture. The results of MD calculations show mean strengths of diamond-SiC interfaces are much lower than those of SiC-SiC GBs. In phase field simulations, effects on peak aggregate stress and ductility from different GB fracture energy realizations with the same mean fracture energy and from different random microstructure orientations are modest. Results of phase field simulations show unconfined compressive strength is compromised by diamond-SiC GBs, graphitic layers, graphitic inclusions, and initial porosity. Explored ranges of porosity and graphite fraction are informed by physical observations and constrained by accuracy limits of elastic homogenization. Modest reductions in strength and energy absorption are witnessed for microstructures with 4% porosity or 4% graphite distributed uniformly among intergranular matrix regions. Further reductions are much more severe when porosity is increased to 8% relative to when graphite is increased to 8%.

Modelling grain growth with the generalized Kampmann-Wagner numerical model

The multi-phase Kampmann-Wagner Numerical (KWN) model, which had been successfully applied for modeling particle precipitation (i.e. Ostwald ripening), is extended toward grain growth modeling. The extensions consist of adopting grain topology- and size-dependent growth rate equation obtained from either the reported parameterization of phase field simulations results or theoretical analysis. Global volume conservation equation is imposed in the extended model to reflect the spacing filling constraints that grains do not overlap and no voids appear. The extended model has been applied to simulate ideal grain growth, grain growth with the initial states of lognormal/normal/Weibull distributions, bi-modal grain size distribution and arbitrary Voronoi tessellations, and the simulation results have been verified by Hillert's asymptotic solution and phase field simulation results. The extension has enabled the KWN approach applicable to model grain growth thus reducing the threshold for the establishment of an efficient Integrated Computational Materials Engineering modeling framework.

Phase-field model of deformation twin-grain boundary interactions in hexagonal systems

A phase-field model for describing dynamic interactions between deformation twins and grain boundaries in a hexagonal close packed (HCP) metal is established. It is applied to simulating the coupled evolution mechanisms of grains and twins in magnesium (Mg) by probing the transmission of {101¯2}deformation twins across grain boundaries. We analyze the effect of the strain relaxation near a grain boundary, which is related to the geometric compatibility arising from the misorientation angle between adjoining grains. Phase-field simulations demonstrate that twin transmission across a grain boundary into a neighboring grain leads to grain boundary migration towards the neighboring grain with a reduced grain boundary width. The preferred nucleation site of new twin variant in the neighboring grain is related to the elastic interaction energy distribution. These predicted transmission behaviors agree well with existing experimental observations and molecular dynamics simulations. By analyzing set of systematic phase-field simulation results, we establish a rotation-angle-related twin variant selection rule for analyzing the transmission of {101¯2}deformation twins across grain boundaries in Mg and its alloys.

Phase-Field Model of Deformation Twin - Grain Boundary Interactions in Polycrystalline Hexagonal Systems

A phase-field model for describing dynamic interactions between deformation twins and grain boundaries in a hexagonal close packed (HCP) metal is established. It is applied to simulating the coupled evolution mechanisms of grains and twins in magnesium (Mg) by probing the transmission of {101 2} deformation twins across grain boundaries. We analyze the effect of the strain relaxation near a grain boundary, which is related to the geometric compatibility arising from the misorientation angle between adjoining grains. Phase-field simulations demonstrate that twin transmission across a grain boundary into a neighboring grain leads to grain boundary migration towards the neighboring grain with a reduced grain boundary width. The preferred nucleation site of new twin variant in the neighboring grain is related to the elastic interaction energy distribution. These predicted transmission behaviors agree well with existing experimental observations and molecular dynamics simulations. By analyzing set of systematic phase-field simulation results, we establish a rotation-angle-related twin variant selection rule for analyzing the transmission of {101 2} deformation twins across grain boundaries in Mg and its alloys.

Phase-field model and its application in electrochemical energy storage materials

With the rapid progress of computer technology, computational research exhibits significant advantages in investigating microstructure evolution of material systems. As a computational research method of material dynamics, increasing attention has been paid to the phase-field model because of its avoidance of complicated interface tracking and convenience of dealing with applied fields. Theoretical framework of the phase-field model and three current phase-field models for multicomponent multiphase systems (the Carter, Steinbach, and Chen models) are introduced and reviewed in terms of interpretation of phase-field variables, way of coupling thermodynamic database, way of constructing the free energy density, and evolution equations. This review only focuses on the application of the phase-field model in electrochemical energy storage materials, and introduces its existing phase-field simulation results, which demonstrates that the phase-field model has tremendous potential in describing the microstructure evolution (anisotropic transport and phase separation, elastic and plastic deformation, crack propagation and fracture, dendrite growth, etc) and improving the performance of electrochemical energy storage materials. Finally, from two aspects of improving phase-field theory and extending application, future development trend and problems to be solved of phase-field simulations in electrochemical energy storage materials are discussed and looked ahead.

An improved phase field method by using statistical learning theory-based optimization algorithm for simulation of martensitic transformation in NiTi alloy

An improved phase field method by using statistical learning theory based optimization algorithm is developed for solving the phase field equations through building simple relationships between the key phase field variables and the phase evolution driving force, and using statistical analysis of mass computed data during phase field simulation. Phase field simulation results of growth of R phase and the B2–R phase transformation in a Ni-rich Ni50.5Ti49.5 alloy by using the proposed statistical strategy algorithm are compared with that using the conventional numerical algorithm, which demonstrates that with coupling the statistical learning theory, i.e., by means of the optimization algorithm, the credible simulated microstructure is obtained while maintaining high accuracy, and meanwhile the computational time has been significantly reduced.

A non-isothermal phase field study of the shape memory effect and pseudoelasticity of polycrystalline shape memory alloys

In this paper, a non-isothermal phase field (PF) model is proposed to investigate the shape memory effect (SME) and pseudoelasticity (PE) of polycrystalline shape memory alloys (SMAs) with consideration of the latent heat effect. The latent heat release and absorption accompanying the phase transformation processes are explicitly considered by coupling the phase field evolution with latent heat conduction. A modified Gibbs free energy function is proposed to accommodate the continuously varying temperature. It is shown that the SME and PE of polycrystalline SMAs under different ambient temperatures can be well characterized with the proposed PF model within a unified framework. The PF simulation results are in accordance with the previously reported experimental results. The influences of various factors such as the ambient temperature, grain size, crystal orientation, and latent heat effect on the phase transformation process and mechanical responses as well as the temperature evolution of SMAs are systematically discussed by conducting PF simulations. Some important implications for the devise of elastocaloric cooling devices are provided.

Ultrahigh discharge efficiency in multilayered polymer nanocomposites of high energy density

Poly(vinylidene fluoride) (PVDF)-based dielectric polymers are in great demand for the future electronic and electrical industry because of their high dielectric constants and energy density. However, some issues that limit their practical applications remain unsolved. One of the most urgent issues is their high dielectric loss and hence low efficiency. In this contribution, we proposed and demonstrate that substantially enhanced discharge efficiency of PVDF-based polymers nanocomposites could be achieved by simultaneously optimizing their topological-structure and phase composition. In the poly(vinylidene fluoride-co-hexafluoropropylene) (P(VDF-HFP))/poly(vinylidene fluoride-ter-trifluoroethylene-ter-chlorofluoroethylene) (P(VDF-TrFE-CFE)) multilayered nanocomposites fabricated by non-equilibrium process, an ultrahigh discharge efficiency of ~85% is achieved up to 600 MV/m, which is the highest discharge efficiency reported so far for any polar-polymer dielectric materials at such high electric field. By adjusting the quenching temperature, the phase-composition hence dielectric permittivity in the terpolymer layers could be tuned for suppressed ferroelectric loss. Results of phase-field simulations further reveal that local electric field is substantially weakened at the interfaces between the Co/Ter polymer layers, which will act as barriers to motion of charge carriers and give rise to much suppressed conduction loss and a remarkably enhanced breakdown strength. Synergy of the optimized topological-structure and phase-composition thus leads to a nanocomposite that exhibits an unprecedented high discharge efficiency of the multilayered nanocomposites that is comparable to the bench-mark biaxially oriented polypropylene (BOPP) at high electric field as well as a high discharge energy density that is over 10 times higher than that of BOPP.