Phase-field Study Research Articles

Analysis of Tilted Columnar Dendrites at Grain Boundaries During Wire and Laser Additive Manufacturing: a Phase-Field Study

Analysis of Tilted Columnar Dendrites at Grain Boundaries During Wire and Laser Additive Manufacturing: a Phase-Field Study

A phase-field study on the hydrogen-induced pitting corrosion with solid–solid phase transformation in [formula omitted]-Uranium

Hydrogen-induced pitting corrosion of uranium is a common phenomenon, which damages the integrity and durability of this widely and expensive nuclear material. Its numerical simulation is still a challenge due to many complex mechanisms, especially solid–solid phase transformation and mechanical interaction, leading to the anisotropic growth of hydride and inducing some bulges on the surface of the uranium matrix. We apply a phase-field model to simulate hydrogen-induced pitting corrosion in α-uranium (α-U) at 673 K. In the model, the elastic strain energy is introduced to approximate the mechanical interaction between the matrix and hydride, and the free boundary condition based on the finite element method is adopted to describe the surface bulges. In our simulation, the elliptical pit morphology and its kinetics are consistent with experiment results. An analysis of displacements and stresses inside the materials reveals that the surface bulge is caused by the compression of the matrix and the dilation of the hydride. Moreover, the compressive and tensile stress concentrations are observed around the edge and top of surface bulge respectively. This phenomenon is due to the dilation and growth of hydride on the matrix. Our study provides important simulating evidence and physical interpretations for the growth of pit morphology and failure of α-U materials. This work also shows the potential of the phase-field model in the simulation of hydrogen-induced pitting corrosion.

Phase-field numerical study on the dynamic process of thermocapillary patterning.

It is well known that surface tension is dependent on temperature, and thus a nonuniform temperature may cause thermocapillary flow which is referred to as the Marangoni effect. For a thin liquid-air film confined between a flat hot plate and a topographical cold template, it undergoes deformation due to thermocapillary flow. This phenomenon is termed as thermocapillary patterning, and has been used to fabricate micro- and nanostructure in polymer films. In most cases, the obtained structure conforms to the template; i.e., it can be considered as a replication technique. In this paper, we developed a two-phase flow numerical model based on the phase field to study the dynamic process of thermocapillary patterning. As a remeshing-free method, the phase field enables the incorporation of thermal field and multiphase flow with free surface deformation. The numerical model was employed to study the dynamic process of thermocapillary patterning. Meanwhile, the effects of some parameters, e.g., temperature, geometry parameters, and contact angle, were also investigated.

Investigation of fracture in porous materials: a phase-field fracture study informed by ReaxFF

Investigation of fracture in porous materials: a phase-field fracture study informed by ReaxFF

Temperature dependence of kinetics pathway of γ′ precipitation in Co-Al-W superalloys: A phase-field study

The expeditious development of novel Co-based superalloys depends on achieving a compressive understanding of the kinetics path way of γ′ precipitates. This paper investigates the temperature dependence of evolution processing and mechanism of γ′ phase in a model Co-9.5Al-9W (at%) alloy using phase-field method. The simulated microstructures during aging at 700, 800 and 900 ℃ show that spherical γ′ quickly changes to cuboidal aged at 900 ℃ while transforms into irregular interconnected morphology at low temperature, which is consistent well with experimental observations. By characterizing the long-range parameters, this irregular γ′ is attributed to the coalescence of adjacent precipitates with the same domain, primarily driven by the decrease of interfacial energy. The temporal evolution of average size of the γ′ precipitates suggests classical Lifshitz-Slyozov-Wagner coarsening at the three temperatures, and the coarsening rate constants K are determined. The temperature dependence of K is clarified by analyzing the thermodynamic driving force and chemical mobility. Additionally, the effects of particle inter-distance, shape and size on γ′ evolution are discussed from the perspective of diffusion potential.

Effect of interface anisotropy on tilted growth of eutectics: A phase field study

Interfacial energy anisotropy plays an important role in tilted growth of eutectics. However, previous studies mainly focused on the solid–solid interface energy anisotropy, and whether the solid–liquid interface energy anisotropy can significantly affect the tilted growth of eutectics still remains unclear. In this study, a multi-phase field model is employed to investigate both the effect of solid–liquid interfacial energy anisotropy and the effect of solid–solid interfacial energy anisotropy on tilted growth of eutectics. The findings reveal that both the solid–liquid interfacial energy anisotropy and the solid–solid interfacial energy anisotropy can induce the tilted growth of eutectics. The results also demonstrate that when the rotation angle is within a range of 30°–60°, the growth of tilted eutectics is governed jointly by the solid–solid interfacial energy anisotropy and the solid–liquid interfacial energy anisotropy; otherwise, it is mainly controlled by the solid–solid interfacial energy anisotropy. Further analysis shows that the unequal pinning angle at triple point caused by the adjustment of the force balance results in different solute-diffusion rates on both sides of triple point. This will further induce an asymmetrical concentration distribution along the pulling direction near the solid–liquid interface and the tilted growth of eutectics. Our findings not only shed light on the formation mechanism of tilted eutectics but also provide theoretical guidance for controlling the microstructure evolution during eutectic solidification.

Manipulation of charged domain walls in geometric improper ferroelectric thin films: A phase-field study

Using phase-field simulations, we show how interfaces acting on the geometric-improper ferroelectric polarization of hexagonal manganite and ferrite thin films can be used to control the formation of charged domain walls. We modify the Landau expansion of the free energy valid in bulk to emulate interface effects known from previous cross-sectional experiments, and we verify our model by comparing our results with images obtained in these experiments. We then show how the interface affects the orientation of ferroelectric domain walls in the fully three-dimensional case. Furthermore, we demonstrate that interface effects combined with an external electric field enable us to specifically choose the dominant domain-wall type (head-to-head, tail-to-tail, or neutral). We also find that an electric field can stabilize a novel domain-wall type which only emerges in the improper ferroelectric order but not in the primary structural distortion. Since the domain walls have a conductivity that is different from the interior of the domains, the influence of the interfaces of a thin film on the type and distribution of the walls gives us the possibility to control the transport properties of a material by appropriate thin-film engineering.

The effect of voids on boundary migration during recrystallization in additive manufactured samples—a phase field study

Experimental results show that voids inside additive manufactured (i.e. 3D printed) materials are unavoidable. As such samples are often post-printing annealed, it is thus of interest to understand how voids affect boundary migration. In this work, phase field simulations of recrystallization are carried out for systems containing voids and typical inhomogeneous microstructures. The simulation results show that the voids significantly affect the shape of the boundary and its migration kinetics during recrystallization. The location of the voids in relation to the inhomogeneous deformation microstructure is furthermore found to affect local boundary migration. The results are not only of importance for optimizing annealing of printed samples, but also for understanding local boundary migration in particle containing alloys.

Modification of Precipitate Coarsening Kinetics by Intragranular Nanoparticles—A Phase Field Study

Precipitate coarsening is a major mechanism responsible for the degradation in mechanical properties of many precipitation-hardened alloys at high temperatures. With recent developments in processing of nanocomposite materials, a substantial volume fraction of inert second phase ceramic nanoparticles can be introduced into the grain interiors of polycrystalline materials. These intragranular nanoparticles can have synergistic effects of impeding dislocation motion and interacting with coarsening precipitates to modify the coarsening rate. In this work, the precipitate coarsening behavior of an alloy in the presence of intragranular inert nanoparticles was studied using the phase field method. Two key measurements of coarsening kinetics, precipitate size distribution and coarsening rate, were found to be affected by the volume fraction and the size of nanoparticles. Two novel mechanisms related to geometric constraints imposed by inter-nanoparticle distance and the blockage of solute diffusion path by nanoparticle–matrix interfaces were proposed to explain the observed changes in precipitate coarsening kinetics. The simulation results in general suggest that the use of small nanoparticles with large number density is effective in slowing down the coarsening kinetics.

Factors that control stability, variability, and reliability issues of endurance cycle in ReRAM devices: A phase field study

The morphological evolution of the conducting filament (CF) predominantly controls the electric response of the resistive random access memory (ReRAM) devices. However, the parameters—in terms of the material and the processing—which control the growth of such CF are plenty. Extending the phase field technique for ReRAM systems presented by Roy and Cha [J. Appl. Phys. 128, 205102 (2020)], we could successfully model the complete SET (to attain low resistance state) and RESET (to attain high resistance state) processes due to the application of sweeping voltage. The key parameters that influence the stability of the multi-cycle I-V response or the endurance behavior are identified. The computational findings of the presented model ReRAM system are practical in correlating the multi-parametric influence with the stability, variability, and reliability of the endurance cycle that affect the device performance and also lead to the device failure. We believe that our computational approach of connecting the morphological changes of the CF with the electrical response has the potential to further understand and optimize the performance of the ReRAM devices.

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.

Influence of elasticity on the morphology of fcc-Cu precipitates in Fe-Cu alloys. A phase-field study

Cu-rich precipitation ensures high strength and satisfactory ductility of steels at low carbon content. Although in an over-aged state, it leads to the degradation of mechanical properties. It is of prime importance for nuclear reactor vessel steels, which are exposed to extreme conditions at elevated temperature for a long time. The precipitates at this state have an fcc structure and possess a characteristic elongated morphology. The invariant-line model was mostly used to explain the morphology of fcc-Cu precipitates in the bcc-Fe matrix, although it has several limitations. It idealizes morphology and does not consider the elastic properties of both precipitate and matrix. Also, this method does not reveal the influence of the eigenstrains on kinetics and the formation of the nanostructure. Besides, the influence of the applied stress on the precipitation process can’t be revealed with this method.With this in mind, we developed a phase-field model to investigate the formation of the elongated morphology of fcc-Cu precipitates in the bcc-Fe matrix. The effect of diffuse interface and discretization on the behavior of solution was verified with a sharp-interface model and invariant-line prediction. It was found that simulated precipitates agree qualitatively with available experimental data. The role of a minimal mismatch line on the morphology formation was verified. Also, it was shown that the anisotropy of elastic properties has a minor effect on morphology formation. The applied stress with different magnitudes and directions has a minor effect on the morphology of precipitates. Nevertheless, it results in variant selection due to the difference in interaction energy. The bifurcation diagram of interaction of two precipitates was constructed. The equilibrium configurations reveal that elasticity enhances the kinetics of the reaction and that there is a twin-like configuration, which enhances the accommodation of shear-like eigenstrain and reduces the elastic interaction energy.

Dendrite remelting during arc oscillation welding of magnesium alloys: a phase-field study

Dendrite remelting during arc oscillation welding of magnesium alloys: a phase-field study

Co-Based superalloy morphology evolution: A phase field study based on experimental thermodynamic and kinetic data

Cobalt-based superalloys with two phase γ/γ′ microstructures offer great promise as candidates for next-generation high-temperature alloys for applications, such as turbine blades. It is essential to understand the thermodynamic and kinetic factors that influence the microstructural evolution of these alloys in order to optimize the alloy compositions and processing steps with a goal to improve their coarsening, creep and rafting behavior. We are using a continuum phase field approach to study the diffusion process and to predict the equilibrium shapes of Co-Al-W γ′ precipitates. In order to obtain quantitatively predictive capabilities, we extract chemical free energies for the γ/γ′ phases based on CALculation of PHAse Diagrams (CALPHAD) thermodynamic data and diffusion mobilities for Co alloys based on CALPHAD kinetic data. We also use experimental or first-principles data for other quantities, such as misfit strain and interface information, for the parameterization of our model. A particular focus of our study is to understand how different energy balances, misfit strain and kinetics affect the coarsening and rafting behavior of γ′ precipitates, and the sensitivity of the final precipitate shape to materials parameters. We find that the equilibrium shape of the precipitate results from a delicate competition between chemical, interfacial, and elastic energies, and it is very sensitive to changes in model parameters. We examine how modeling input parameters affect the equilibrium shape of precipitates and relate these parameters to experimentally available values.

Late stage coarsening kinetics induced by a phase-dependent mobility: A phase field study of FeCr in the spinodal regime

An efficient algorithm is presented in this work to compute the late stage coarsening kinetics within the phase-field framework. Microstructures resulting from off-critical quenches over large time periods have been simulated in the FeCr system, which exhibits substantial variations in atomic mobilities between the Fe-matrix and Cr-rich precipitates. To understand the impact of such a phase-dependent mobility on the microstructure, 2D simulations have been performed in the spinodal regime using a constant, symmetric, and phase-dependent mobility. Detailed analyses of these simulations highlight the fact that the more realistic situation where atomic mobility is non-uniform induces a competition between coalescence and coarsening of precipitates. We use these simulations to shed light upon previously published numerical and experimental results.

Formation of radiator structures in quartz veins - Phase-field modeling of multi-crack sealing

The present work showcases a comprehensive phase-field study on the formation of multi-crack-seal veins in quartz microstructures. The microstructure simulation framework Pace3D incorporates the modeling of both fracturing and sealing in polycrystalline rock systems, where crystallographic anisotropies, crack resistances and growth velocities of different facets are included in the energy density contributions. In a two grain system we exemplary show the formation of three different archetypes of radiators which are observed in natural quartz veins. We extend the phase-field studies to a polycrystalline host rock and investigate therein the effects of fracture aperture, presence of accessory minerals, and oblique opening trajectories with refracturing of fully and partially sealed veins on the occurring vein crystal morphology. Our results show that the shape of the forming grain boundaries depends on the crystal orientation of the participating grains, the location of a fracture through the crystals, and the sealing state. Evolution of more pronounced radiator structures are found in simulation studies with increasing aperture. A broad spectrum of crystal structures which are frequently observed in natural quartz vein microstructures is reproduced in simulations using the combined crack-seal phase-field model.

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.

Phase field study of grain boundary migration and preferential growth in non-magnetic materials under magnetic field

This work reports a phase field model to enable a profound insight into the grain boundary (GB) migration of non-magnetic materials based on Bi bicrystals under a magnetic field. Simulation results on GB migration velocity agree well with the experimental results, and the velocity increases linearly with the square of the magnetic strength. It is also found that GB migration direction is affected by the magnetic field direction, and grain with c-axis parallel to the magnetic field direction grows preferentially at the expense of the grain with c-axis perpendicular to the magnetic field direction. It is revealed that the preferential grain growth is induced by the difference in magnetic free energy density of the grains with different orientations.

Stability of phase boundary between L12-Ni3Al phases: A phase field study

The evolution and stability of phase boundaries (PBs) between L12-Ni3Al phases in Ni75Al11V14 alloy aged at 1050k was studied using the microscopic equation phase-field method (MPFM). Four types of L12 PBs were found through atomic configuration, migration and occupation probability (OP). The evolution of metastable PBs and formation of stable PBs were tracked and explored, the effect of coherent elastic strain energy on the evolution and stability of PBs is also investigated by coupling the micro elastic theory with MPFM. In addition, the formation enthalpy, interface energy and electron distribution function of PBs are calculated by FP method, and the stability of PBs is further quantitatively predicted from the perspective of thermodynamic energy and gaining or losing electrons. FP calculation results are consistent with MPFM prediction, and the essence of the transition and stability of PBs is revealed based on the atomic migration dynamics, interface evolution morphology and thermodynamic energy. This is an effective method to further explore the formation and structure of PBs and design high stability PBs.

Heat transfer enhancement of two-phase droplet flow in microtube: a phase-field simulation study

Heat transfer enhancement of two-phase droplet flow in microtube: a phase-field simulation study