Phase Field Model For Simulation Research Articles

Phase field study on the grain size dependent electrical resistivity-strain response in superelastic nanocrystalline NiTi alloys

The superelastic NiTi alloy's electrical resistivity exhibits significant variations in response to deformation, making it a highly attractive material for sensing applications. However, there exists a lack of comprehensive knowledge of the effects of grain size (GS) on the electrical properties of NiTi alloy. To address this gap, a novel electro-mechanical coupled phase field simulation model is developed, with crucial parameters determined through experimental investigations. The results demonstrate a notable change in the relationship between electrical resistivity and strain, transitioning from a quasi-linear pattern to a piecewise nonlinear one as the GS increases. The observed modification is found to be primarily influenced by the martensitic transformation, characterized by a transition from a uniform mode to a localized mode. As the GS increases, there is an initial drop in the total change of electrical resistivity at peak strain, followed by a subsequent stabilization. This is because the GS, through the stress and the degree of phase transformation, exerts two opposing effects on the variation of electrical resistivity. Furthermore, the combined influence of hysteresis and hysteresis in the martensite fraction contributes to a consistent decrease in resistivity hysteresis as the GS diminishes. This study improves the understanding of how GS affects NiTi alloy's electrical resistivity-strain response and lays the foundation for future sensing performance regulation, expanding its multi-functionality as an intelligent material.

A conservative second order phase field model for simulation of N-phase flows

We present a novel N-phase extension to the second-order conservative phase field method, first introduced by Chiu and Lin [1]. The proposed N-phase model is in conservative form and is symmetric with respect to the phases while satisfying volume conservation. The model is reduction consistent, meaning that in the absence of M phases, the equations reduce to the equations for an N−M-phase flow. This eliminates the possibility of fictitious phases appearing. For coupling to momentum transport, we extend the two-phase mass-momentum consistent model to N-phase flows. By adopting second-order central spatial schemes, the boundedness properties of the two-phase model are inherited by the N-phase model, and the coupled mass-momentum consistent N-phase flow solver inherits the conservation properties of its two-phase version, resulting in the first N-phase flow method that analytically and discretely conserves mass, momentum and kinetic energy (in the absence of capillary and viscous effects). A novel surface tension model is proposed for modeling surface tension forces in N-phase flows. The phase field model allows for variable interface thicknesses between different phase pairs. This endows the model with the property of attaining correct equilibirum configurations at triple junction points. Specifically, we analytically demonstrate that by using interfacial thicknesses that are inversely proportional with the pairwise surface tension, the coupled system achieves steady state at the correct configuration. Using several canonical and practical numerical tests, we demonstrate the accuracy of the phase field equation, the surface tension model, and the fully coupled N-phase flow solver.

Concentration-driving pinning effect in lead-free Mn-substituted BCZT ferroelectric ceramics

Domain wall motion in ferroelectrics, closely related to electric characteristics and amenable to tuning through doping, remains incompletely understood, particularly with regard to the pinning defect in the (Ba0.85Ca0.15)(Zr0.1Ti0.9)O3 (BCZT) system, which has attracted significant interest. Here, we investigate the defect dipole-assisted pinning effect in Mn-substituted BCZT (abbreviated as BCZT-xMn) ceramics with Mn concentrations ranging from x = 0 to 0.04. As x increases, we observe a gradual decrease in the maximum permittivity, accompanied by a leftward shift in temperature, leading to a diffuse phase transition. Analysis of the dielectric spectrum reveals a consistent trend in the activation energy within a specific concentration range, suggesting the incorporation of oxygen vacancies to maintain electric neutrality. The resulting oxygen vacancies, combined with Mn dopants, form defect dipoles Mn4++e′− VO⋅⋅ −Mn4++e′, attaining sufficient concentration at x = 0.02, and enabling precise establishment of the pinning effect. This phenomenon is extensively documented by the observation of pinched polarization-electric field loops and double current peaks in the current-electric field curves, visually corroborated by experimental data and a 3D phase-field simulation model. Consequently, this study not only elucidates the concentration-driven pinning effect in the BCZT system but also provides valuable insights into doping effects in other lead-free ferroelectrics.

Generation mechanism and motion behavior of sliver defect in single crystal Ni-based superalloy

Sliver is a common but easily neglected defect in single crystal Ni-based superalloy castings. To date, there is still no unified viewpoint on its formation mechanism and generation causes. In this work, the orientation discontinuity and motion behavior of sliver defects were studied through experiments and numerical simulations. The ultrathin wedge-shaped specimen containing the grain boundary of the sliver and the matrix was prepared at the initial position of the sliver defect for the observation of equal thickness fringes. The discontinuity of equal thickness fringes on both sides of the grain boundary was observed through a transmission electron microscope, which directly confirms the abrupt change in the orientation between the sliver and matrix from the nanoscale. The crystal lattices at the smooth area and the bulging area of the grain boundary were found to have unusually different arrangements. The irregular lattice arrangement at the bulging area shows that the grain boundary has experienced high-stress deformation. Statistical results of sliver orientation deviation with a further composition analysis show the micro protuberance of the mold shell has a noticeable inductive effect on the sliver generation. Furthermore, a self-developed three-dimensional phase-field simulation model coupled with the spatial topology algorithm is established to simulate the orientation deflection behavior and orientation deviation threshold of fractured dendrites. The simulation results indicated that there is an upper limit of the cross-section solid fraction at the fracture position for the motion of the fractured dendrites. When the cross-section solid fraction at the fracture position is higher than this upper limit, it will be difficult to produce large deviation slivers due to the structural limitation of surrounding dendrites. This upper limit does not change with the solidification temperature gradient.

Effect of ultrasonic excitation on the process of L-PBFAM

Abstract Laser-Powder bed fusion additive manufacturing (L-PBFAM) is a layer-by-layer metal manufacturing technique that allows unlimited freedom of design with no increase in manufacturing complexity. Currently, parts made through L-PBFAM need to be heat treated and annealed to prevent residual stress, anisotropy, low ductility, and low fatigue life inherent to the process. This paper demonstrates that the adoption ultrasonic excitation to the L-PBFAM process is able to alleviate some of the aforementioned problems. To determine the effects of ultrasonic excitation on the solidification process and microstructure formation, a phase field simulation model incorporating the effect of ultrasonic cavitation in the melt pool was created. Finite Element Method simulation in ANSYS was used to determine the initial macro thermal condition of the melt pool, while the phase field was used to simulate the nucleation and grain growth within the melt pool under ultrasonic excitation based on thermodynamic theory. Robust Design of Experiment (DOE), guided by insights on the L-PBFAM process, was conducted to determine the contributions of different process parameters on the grain size and configuration. The simulated grain structure showed close correlation to optical micrographs of fabricated 304 L Stainless Steel L-PBFAM samples. The ultrasonic excitation is shown to have a significant effect on the microstructure and the cooling rate of the melt pool is found to be the key process optimization parameter affecting the grain morphology.

Influence of crystallographic orientation of epitaxial solidification on the initial instability during the solidification of welding pool

To predict onset of the initial instability with different crystallographic orientation of epitaxial solidification during the solidification of welding pool, coupled equations were conducted to describe the transient conditions of the crystal growth near the fusion line. The equations were coupled to a quantitative phase field model and a dynamic analytical model base on the time dependent instability analysis to simulate the growth processes of the epitaxial solidification with different tilting growth angles between the preferred crystallographic orientation and the temperature gradient direction. The linear growth result of initial average spacing obtained by the phase field simulation model and the analytical model are in good agreement with that in experiment result. It shows that the greater the tilting growth angles, the better the stability of the planar interface, and the larger the critical time of onset of initial planar instability. The initial average spacing generally increases with increasing the tilting growth angle, however, due to the transient conditions in welding pool and the randomness of the amplification mechanism in linear instability, the initial average spacing is seemingly irrelevant to the tilting growth angle of the epitaxial solidification.

Flexible Multiferroic Bulk Heterojunction with Giant Magnetoelectric Coupling via van der Waals Epitaxy.

Magnetoelectric nanocomposites have been a topic of intense research due to their profound potential in the applications of electronic devices based on spintronic technology. Nevertheless, in spite of significant progress made in the growth of high-quality nanocomposite thin films, the substrate clamping effect still remains a major hurdle in realizing the ultimate magnetoelectric coupling. To overcome this obstacle, an alternative strategy of fabricating a self-assembled ferroelectric-ferrimagnetic bulk heterojunction on a flexible muscovite via van der Waals epitaxy is adopted. In this study, we investigated the magnetoelectric coupling in a self-assembled BiFeO3 (BFO)-CoFe2O4 (CFO) bulk heterojunction epitaxially grown on a flexible muscovite substrate. The obtained heterojunction is composed of vertically aligned multiferroic BFO nanopillars embedded in a ferrimagnetic CFO matrix. Moreover, due to the weak interaction between the flexible substrate and bulk heterojunction, the interface is incoherent and, hence, the substrate clamping effect is greatly reduced. The phase-field simulation model also complements our results. The magnetic and electrical characterizations highlight the improvement in magnetoelectric coupling of the BFO-CFO bulk heterojunction. A magnetoelectric coupling coefficient of 74 mV/cm·Oe of this bulk heterojunction is larger than the magnetoelectric coefficient reported earlier on flexible substrates. Therefore, this study delivers a viable route of fabricating a remarkable magnetoelectric heterojunction and yet flexible electronic devices that are robust against extreme conditions with optimized performance.

Phase-field simulations of pore migration and morphology change in thermal gradients

Here we present a phase-field simulation model that captures the thermal-gradient-driven migration of pores in oxide fuel associated with fuel restructuring. The model utilizes a Cahn-Hilliard equation supplemented with an advection term to describe the vapor transport of fuel material through the pore interior due to gradients in vapor pressure. Simulations demonstrate that the model not only predicts pore migration towards the centerline of the fuel, but also a concurrent change in pore shape during migration from an initially isotropic morphology to either a lenticular morphology or a prolate morphology depending on the vapor transport conditions. This model is a necessary first step to conducting accurate simulations of the microscopic changes that occur during the complicated process of oxide fuel restructuring.

이방성 결정립 계면에너지의 2차원 결정립 성장에 미치는 효과에 대한 컴퓨터 모사

결정립 성장은 여러 가지 재료의 성질에 미치는 큰 영향으로 재료공학에서 매우 중요하다. 그래서 본 연구에서는 PC에서 대규모 상장 모델을 사용하여 이방성 결정립 계면에너지의 2차원 결정립 성장에 미치는 효과를 조사하였다. 컴퓨터 모사에서는 <TEX>$2000{\times}2000$</TEX>의 그리드 시스템과 약 7300개의 초기 결정립 개수가 사용되었다. 결정립계 에너지의 이방성의 비, <TEX>${\sigma}_{max}/{\sigma}_{min}$</TEX>는 1부터 3까지 변경되었다. 이방성이 증가함에 따라 결정립 성장 지수, n은 2.05에서 2.37로 증가하였다. 결정립 크기의 분포는 등방성인 경우에는 중앙에 평탄한 영역을 보였으나 이방성의 경우에는 중앙의 평탄한 영역이 사라지고 매우 느리게 사라지는 작은 결정립에 기인하여 작은 결정립 크기의 분포가 약간 증가하였다. 마지막으로 모사된 결정립 미세구조가 이방성에 따라 비교, 분석되었다. The grain growth is very important because of its great influence on the various materials properties. Therefore, in this study, the effects of anisotropic grain boundary energy on grain growth in 2-D have been investigated with a large scale phase field simulation model on PC. A <TEX>$2000{\times}2000$</TEX> grid system and the initial number of grains of about 73,000 were used in the computer simulation. The anisotropic ratio of grain boundary energy, <TEX>${\sigma}_{max}/{\sigma}_{min}$</TEX>, has been varied from 1 to 3. As the anisotropy increased, the grain growth exponent, n, increased from 2.05 to 2.37. The grain size distribution showed a central plateau in the isotropic case, and was changed into no central plateau and the increasing population of very small grains in the anisotropic case, resulting from slowly disappearing grains. Finally, simulated microstructures were compared according to anisotropy.

Phase Field Simulations of Hysteresis and Butterfly Loops in Ferroelectrics Subjected to Electro‐Mechanical Coupled Loading

Two‐dimensional computer simulations of ferroelectric polarization switching have been performed using the phase field simulation model developed by employing the time‐dependent Ginsburg–Landau equations. The bulk‐free energy, polarization gradient energy, long‐range dipole–dipole electrostatic interactions, and elastic energy were taken into account in the above‐mentioned simulations. The influences of electric–mechanical coupled loading on the hysteresis and butterfly loops were studied. The results showed that the coupled electro‐mechanical loading could change both the coercive field of ferroelectric materials and the symmetry of hysteresis and butterfly loops.

Semisharp Phase Field Method for Quantitative Phase Change Simulations

The standard phase field model for simulation of phase change requires an asymptotic analysis in a vanishing interface width, in order to connect the model parameters to the sharp interface parameters, which has hampered the quantitative usefulness of the method. In this Letter the method is simplified to the point that the relevant reduced problem can be solved analytically, allowing the sharp and phase field parameters to be identified, in principle, without restrictions on the model parameters. The scheme is tested for standard cases of two-dimensional solidification, showing excellent agreement with sharp interface kinetics.