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Results for “Grain microstructure evolution”

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DOE OSTI2021

A duality-based coupling of Cosserat crystal plasticity and phase field theories for modeling grain refinement

High-rate deformation processes of metals entail intense grain refinement and special attention needs to be paid to capture the evolution of microstructure. In this article, a new formulation for coupling Cosserat crystal plasticity and phase field is developed. A common approach is to penalize kinematic incompatibility between lattice orientation and displacement-based elastic rotation. However, this can lead to significant solution sensitivity to the penalty parameter, resulting in low accuracy and convergence rates. To address these issues, a duality-based formulation is developed which directly imposes the rotational kinematic compatibility. A weak inf-sup-based skew-symmetric stress projection is introduced to suppress instabilities present in the dual formulation. An additional least squares stabilization is introduced to suppress the spurious lattice rotation with a suitable parameter range derived analytically and validated numerically. The required high-order continuity is attained by the reproducing kernel approximation. It is observed that equal order displacement-rotation-phase field approximations are stable, which allows efficient employment of the same set of shape functions for all independent variables. The proposed formulation is shown to yield superior accuracy and convergence with marginal parameter sensitivity compared to the penalty-based approach and successfully captures the dominant rotational recrystallization mechanism including block dislocation structures and grain boundary migration.

42 ENGINEERING↗

DOE OSTI2020

Microstructure evolution during binder jet additive manufacturing of H13 tool steel

H13 is one of the most used tool steels for both hot and cold work tooling applications. Binder jet additive manufacturing offers the potential to deposit complex tools at scale due to larger powder bed sizes and faster deposition rates. However, to date there is no published literature on the sintering of H13 to full densification. Here, we discuss the pressureless sintering of binder jet AM H13 steel to full densification via supersolidus liquid phase sintering (SLPS) while presenting appropriate process windows (1360 °C – 1380 °C) for densification without distortion. The process windows have been rationalized based on thermodynamic calculations of liquid volume fractions with temperature. We show that higher binder saturation results in higher carbon retention and subsequently early liquid formation that can initiate the sintering process at lower temperatures. We report abnormal grain growth during sintering and found that the solidification phase transformations play a critical role on microstructural evolution and must be considered to accurately model the kinetics of SLPS.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Phase-field modeling of aging-induced microstructure evolution in pentaerythritol tetranitrate thin films and ramifications for shock initiation

Aging of energetic materials may change performance and affect their safety and reliability, but the relationship between microstructure changes induced by aging and consequent performance changes has not been fully established. This work presents results of phase-field method simulations used to model microstructure evolution of vapor-deposited pentaerythritol tetranitrate (PETN) thin films. Simulated aging is shown to induce grain coarsening and substantial changes of the configuration of porosity in the film: Specifically, we show that porosity tends to concentrate in large pores to a greater degree in aged films, a state that is arrived at by closure or consolidation of small pores. To evaluate the performance of the as-deposited and aged films, we perform two-dimensional hydrocode flyer-film impact simulations that incorporate the phase-field output microstructures directly, permitting us to connect features therein to changes in reactivity, a key metric of energy output for shock initiation. The results demonstrate that declining sensitivity obtained for the simulated aged films can be correlated with the loss of fine-structured pores relatively early in the aging process, while long-term microstructure evolution that gradually alters the shape of large, branching pores is less impactful. Finally, we discuss commonalities and discrepancies between our simulation results and high-throughput initiation experiments on shock initiation of aged PETN thin films.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A generalizable machine learning-assisted fast Fourier transform algorithm to simulate the large strain phenomena in polycrystalline materials

Machine learning methods have shown initial promise in constitutive modeling for single crystals or homogenized polycrystals, delivering notable computational efficiency. However, existing machine learning-based constitutive models often lack generalizability, limiting their application across diverse boundary value problems. This study introduces a thermodynamics-informed artificial neural network model to accelerate rate-tangent crystal plasticity fast Fourier transform simulations for cross-scale deformation behaviors of polycrystals under complex loading. Our model integrates microstructural variability and local interactions effectively. To address local effects in each grain, we employ K-means clustering to group Gauss points within the microstructure into clusters assumed to be in similar mechanical states. This approach, based on self-clustering analysis, extends model scope from macroscopic stress response to the granular level, capturing mechanical responses and orientation evolution across grains. This reduces the number of nonlinear problems to solve, with cluster responses propagated throughout each group. The thermodynamics-based artificial neural network-extracted features are further processed using local material state clusters to account for history-dependent deformation and evolving microstructures. Additionally, representative volume element simulations with rate-tangent crystal plasticity fast Fourier transform provide reliable datasets for model training. The proposed model demonstrates high efficiency, accuracy, self-consistency, and enhanced generalizability in predicting strain–stress responses and orientation evolution at both individual grain and aggregate scales under complex loading conditions, such as biaxial tension and arbitrary loading scenarios.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Characterization of fusion welded ceramics in the SiC-ZrB 2 -ZrC system

Various SiC-ZrB 2 -ZrC ceramics were joined by fusion welding to determine the maximum silicon carbide content that could be joined. Commercial powders were hot pressed, machined, and preheated to 1450 °C before joining with a tungsten inert gas welding torch at 160–200 A. Resulting welds were cross-sectioned and analyzed to determine which compositions were weldable and to characterize microstructural evolution in welded samples. As compositions approached the ternary eutectic, the welds had smaller SiC grains and exhibited better weldability. Penetration depth of welds was controlled by a combination of current input and welding speed. Here, the ternary eutectic in the system was found at 36.9 ± 1.3 vol% SiC, 42.7 ± 1.5 vol% ZrB 2 , and 20.4 ± 1.9 vol% ZrC and its melting temperature was 2330 ± 23 °C. A ternary phase diagram for the SiC-ZrB 2 -ZrC was constructed and proposed via microstructural analysis of arc melted pellets on binary joins between each binary eutectic and the ternary eutectic in the system.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Mechanical response and microstructure evolution from multiaxial stress relaxation in textured zircaloy nuclear cladding

Modern energy markets provide motivation for nuclear reactors to increase operational flexibility and load following capacity of existing reactor designs. The operational power changes result in fuel pellet expansion and contraction resulting in pellet-cladding mechanical interaction (PCMI) and high cladding stresses that are strongly related to stressed corrosion cracking (SCC) which can lead to fuel rod failure. This work aims to quantify the stress fields in cladding with a focus on multiaxial stress relaxation response from an imposed strain and the resulting microstructure changes in textured zircaloy claddings. Stress relaxation tests resulting in multiaxial stress fields are performed to measure the material response of Zircaloy-4 nuclear cladding. Multiple experiments using samples from the same piece of cladding are performed so samples with the same processing history may be removed at strategic points throughout mechanical testing for microstructure characterization. The microstructure evolution is analyzed with mechanical response to evaluate the static recovery impact on crystallographic texture and grain morphology. Experiments are performed at Idaho National Laboratory using an experimental device capable of applying internal pressure and independent axial load to commercial nuclear cladding at elevated temperatures with stress- or strain-controlled experimental capability. X-ray diffraction and electron backscatter diffraction are used for microstructure analysis. Rheological models are used to visualize the multiaxial stress-strain relationships and isolate elastic, plastic, and viscoplastic material properties for analysis.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Coupling Thermomechanical Processing and Alloy Design to Improve Textures in Mg-Zn-Ca Sheet Alloys

Abstract The effect of Ca and Zn additions on the microstructure and texture evolution during thermomechanical processing of Mg-Zn-Ca sheet alloys was systematically investigated and quantified. Plane strain compression testing in a Gleeble thermomechanical simulator was used to physically simulate a 10-pass rolling schedule, while allowing for careful control and monitoring of the processing parameters. Textures in the as-deformed ternary alloy samples demonstrate a weak maximum basal intensity and spreading in the transverse direction. Increasing the Zn content to 3.2 wt.% in the ternary alloys resulted in samples that exhibited weak textures in the as-deformed state. Importantly, static recrystallization (SRX) during post-deformation annealing of these alloys promoted a desirable annular texture, with the c -axis tipped from the normal direction and a lower basal texture intensity. The evolution in texture during SRX is associated with as-deformed microstructures with broad grain orientation spreads and a low degree of recrystallization.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Shear localization in metallic materials at high strain rates

Three factors govern adiabatic shear localization: strain hardening (or softening), strain-rate hardening, and thermal softening. It is typically associated with large shear strains (>1), high strain rates (10 3 –10 7 s –1 ), and high temperatures (40–100% of melting point), all of which happen within narrow regions with widths of about 1–200 μm. It is often an undesirable phenomenon, leading to failure, but there are situations where it is desirable, e. g., the generation of machining chips. Here, we review the development of both theoretical and experimental achievements, from the initiation of shear bands to their propagation with emphasis on three aspects: novel experimental techniques, novel materials, and nano/microstructural effects. The principal characteristics of adiabatic shear bands in metallic materials at the nano- and micro-scale are described. Bands that were formerly identified as transformed actually consist of nanocrystalline/ultrafine grains. These grains result from the breakup of the microstructure by a rotational recrystallization process. The evolution of the microstructure inside shear bands and their interactions for hcp, bcc, and fcc alloys, high-entropy alloys, nanocrystalline alloys, and metallic glasses are analyzed mechanistically. In conclusion, the gaps in the field and opportunities for future research are identified. Modern experimental characterization and computational techniques enable a more profound and predictive understanding of adiabatic shear localization and its avoidance in advanced materials.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Unraveling Thermodynamic and Kinetic Contributions to the Stability of Doped Nanocrystalline Alloys using Nanometallic Multilayers

Abstract Targeted doping of grain boundaries is widely pursued as a pathway for combating thermal instabilities in nanocrystalline metals. However, certain dopants predicted to produce grain‐boundary‐segregated nanocrystalline configurations instead form small nanoprecipitates at elevated temperatures that act to kinetically inhibit grain growth. Here, thermodynamic modeling is implemented to select the Mo–Au system for exploring the interplay between thermodynamic and kinetic contributions to nanostructure stability. Using nanoscale multilayers and in situ transmission electron microscopy thermal aging, evolving segregation states and the corresponding phase transitions are mapped with temperature. The microstructure is shown to evolve through a transformation at lower homologous temperatures (<600 °C) where solute atoms cluster and segregate to the grain boundaries, consistent with predictions from thermodynamic models. An increase in temperature to 800 °C is accompanied by coarsening of the grain structure via grain boundary migration but with multiple pinning events uncovered between migrating segments of the grain boundary and local solute clustering. Direct comparison between the thermodynamic predictions and experimental observations of microstructure evolution thus demonstrates a transition from thermodynamically preferred to kinetically inhibited nanocrystalline stability and provides a general framework for decoupling contributions to complex stability transitions while simultaneously targeting a dominant thermal stability regime.

25 ENERGY STORAGE↗

DOE OSTI2026

Coupling Microstructural Evolution Simulations to Material Property Degradation Predictions for Plasma-Facing Materials

Reliable material performance is required for plasma-facing material (PFM) candidates. Previous research has shown that plasma and neutron radiation exposure induces microstructural changes in PFMs; changes in thermal and electrical conductivities and in material hardening and embrittlement were also observed after neutron irradiation. These material property changes will negatively impact the performance of the PFMs in a fusion reactor. Despite the well-known connection between material microstructure, properties, and performance, there is a need for validated modeling capabilities connecting PFM property degradation with microstructural evolution under fusion-relevant conditions. We are developing a simulation capability to couple plasma-induced microstructural evolution to material property degradation. Our approach relies on deliberate mapping between individual simulation models and experimental characterization for validation. The open-source Multiphysics Object-Oriented Simulation Environment (MOOSE) software was used for this simulation capability development. A MOOSE phase-field model was coupled with the cluster dynamics code, Xolotl, to predict microstructural evolution. Microstructure characterization techniques, including scanning electron microscopy (SEM), transmission electron microscopy (TEM), and laser scanning confocal microscopy (LSCM) are used to validate these microstructural evolution simulations. Calculation of thermal and electrical conductivities with first principles simulations was performed for bulk material and for grain boundaries; these results are used within MOOSE models to calculate effective thermal and electrical conductivities as a function of grain characteristics. Thermoreflectance and four-probe techniques were employed to measure the thermal and electrical conductivities, respectively. A MOOSE crystal plasticity model was adapted to predict microstructure-sensitive deformation behavior, and X-ray diffraction (XRD) was used to collect bulk dislocation density data for validation. After individual simulation validation, these models are coupled to predict material property changes resulting from plasma exposure. We focused here on an experimental design to emphasize the separate effects of moderate thermal loads and plasma exposure using tungsten. Annealing of tungsten was performed under a protective environment for temperatures ranging from 500 C to 1500 C. The plasma exposure was completed in the Tritium Plasma Experiment at Idaho National Laboratory under a deuterium flux of 1e22 D/m^2-s. This incremental approach is employed to build confidence in the modeling capability: separate-effects tests ensure that the models capture key mechanisms from single environmental conditions before predicting PFM property degradation under combined loads. We will show our early results from coupling these simulation models to predict PFM property changes from microstructural evolution. Comparisons of the simulation results with preliminary validation data will be discussed.

36 - MATERIALS SCIENCE↗

DOE OSTI2026

Connect microstructure evolution to property degradation with validated simulation

Reliable material performance is required for plasma-facing material (PFM) candidates. Previous research has shown that plasma and neutron radiation exposure induces microstructural changes in PFMs; changes in thermal and electrical conductivities and in material hardening and embrittlement were also observed after neutron irradiation. These material property changes will negatively impact the performance of the PFMs in a fusion reactor. Despite the well-known connection between material microstructure, properties, and performance, there is a need for validated modeling capabilities connecting PFM property degradation with microstructural evolution under fusion-relevant conditions. We are developing a simulation capability to couple plasma-induced microstructural evolution to material property degradation. Our approach relies on deliberate mapping between individual simulation models and experimental characterization for validation. The open-source Multiphysics Object-Oriented Simulation Environment (MOOSE) software was used for this simulation capability development. A MOOSE phase-field model was coupled with the cluster dynamics code, Xolotl, to predict microstructural evolution. Microstructure characterization techniques, including scanning electron microscopy (SEM), transmission electron microscopy (TEM), and laser scanning confocal microscopy (LSCM) are used to validate these microstructural evolution simulations. Calculation of thermal and electrical conductivities with first principles simulations was performed for bulk material and for grain boundaries; these results are used within MOOSE models to calculate effective thermal and electrical conductivities as a function of grain characteristics. Thermoreflectance and four-probe techniques were employed to measure the thermal and electrical conductivities, respectively. A MOOSE crystal plasticity model was adapted to predict microstructure-sensitive deformation behavior, and X-ray diffraction (XRD) was used to collect bulk dislocation density data for validation. After individual simulation validation, these models are coupled to predict material property changes resulting from plasma exposure. We focused here on an experimental design to emphasize the separate effects of moderate thermal loads and plasma exposure using tungsten. Annealing of tungsten was performed under a protective environment for temperatures ranging from 500$^o$C to 1500$^o$C. The plasma exposure was completed in the Tritium Plasma Experiment at Idaho National Laboratory under a deuterium flux of 1e22 $\frac{D}{m^2s}$. This incremental approach is employed to build confidence in the modeling capability: separate-effects tests ensure that the models capture key mechanisms from single environmental conditions before predicting PFM property degradation under combined loads. We will show our early results from coupling these simulation models to predict PFM property changes from microstructural evolution. Comparisons of the simulation results with preliminary validation data will be discussed.

36 - MATERIALS SCIENCE↗

DOE OSTI2023

Computational modeling of grain boundary segregation: A review

Nearly all metals, alloys, ceramics, and their associated composites are polycrystalline in nature, with grain boundaries that separate well-defined crystalline regions that influence materials properties. In all but the most pure elemental systems, intentional solutes or impurities are present and can segregate to, or less commonly away from, the grain boundaries, in turn influencing boundary behavior, their stability, and associated materials properties. In some cases, grain-boundary segregation can also trigger “phase-like” structural transitions that dramatically alter the essential nature of the boundary. With the development of advanced electron microscopy techniques, researchers can directly observe grain-boundary structures and segregation with atomic precision. Despite such spatial resolution, the underlying mechanisms governing grain-boundary segregation remain difficult to characterize. As a result, computational modeling techniques such as density functional theory, molecular dynamics, mesoscale phase-field, continuum defect theory, and others are important complementary tools to experimental observations for studying grain-boundary segregation behavior. In conclusion, these computational methods offer the ability to explore the underlying formation mechanisms of grain-boundary segregation, elucidate complex segregation behavior, and provide insights into solutions to effectively controlling microstructure.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Defect cluster and nonequilibrium gas bubble associated growth in irradiated UMo fuels – a cluster dynamics and phase field model

Irradiation examination shows that gas bubble swelling kinetics is much faster after irradiation-induced recrystallization than that prior recrystallization in UMo fuels. It implies that gas bubbles in coarse grains and small recrystallized grains have different growth behavior. In this work, a phase-field model of gas bubble evolution integrating microstructure dependent cluster dynamics has been developed, for the first time, to study the gas bubble swelling behavior in the recrystallization zone of UMo fuels. Generation, diffusion, reaction, sink, emission and clustering of vacancies and interstitials are described by the cluster dynamics model while a phase-field model is used to describe the evolution of non-equilibrium gas bubbles including nucleation and growth. With the coupled model, the effect of defect generation rate, clustering rate, interstitial emission and sink rates on grain boundaries on the gas bubble evolution are systematically simulated. A set of model parameters (defect generation rate, clustering rate, interstitial emission and sink rates) is determined by comparing measured and simulated gas bubble swelling kinetics. The results demonstrate that interstitial clustering is one of the important physical mechanisms which results in a fast gas bubble swelling kinetics in the recrystallization zone. The developed model can also be extended to study the associated growth of defect and second phase precipitates often observed in irradiated materials.

Hu, Shenyang↗

DOE OSTI2022

Mass transport in a highly immiscible alloy on extended shear deformation

Forced mixing to a single phase or supersaturated solid solution (SSS) and its prerequisite microstructure evolution in immiscible systems has been a focus of research for both fundamental science and a variety of applications. Controlling the formation of SSS by shear deformation assisted processing could enable a material design beyond conventional equilibrium microstructure in immiscible systems. Here, a highly immiscible (mixing enthalpy of ~ 20 kJ·mol -1 ) Cu-50 at. % Cr binary alloy was employed to investigate the microstructure evolution and localized tendencies of SSS during severe shear deformation. The present results demonstrate distinctive microstructure refinement process in each phase and how they lead to localized SSS as a function of shear strain. Preferential dynamic recrystallization occurs in the softer Cu phase due to strain localization, leading to substantial grain refinement. The refinement of Cr phase in the top-most layer, however, is enabled by the progressive evolution of grain lamination, splitting, and fragmentation as a function of shear strain. The eventual SSS is found to be strongly dependent on the local environments that affect the dislocation activity, including the level of microstructure refinement, the interfacial orientation relationship, hardness difference, and supposed stability of oxidation. Ab initio simulations comfirm that it is more favorable to oxidize Cr than Cu at incoherent Cu/Cr interfaces which then limits the mass transport on an incoherent boundary. Our results shed light on the underpinning mechanism for non-equilibrium mass transport in immiscible systems upon severe deformation that can be applicable to a variety of processing techniques aimed at producing immiscible alloys with superior mechanical properties.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Microstructural evolution in Cu-Nb processed via friction consolidation

Immiscible alloys, whether in well-mixed or layered forms, are of increasing interest based on their novel structural and functional properties, such as enhanced thermal stability against grain growth or radiation-induced defect trapping at the interfaces. To address the need for new approaches to tailor microstructures, the microstructural development of an immiscible Cu-Nb alloy processed via friction consolidation of elemental powders is investigated. Friction consolidation is a solid-phase processing technique that imparts severe plastic strain into a deforming volume resulting in elevated temperatures below the melting temperature of the alloy. Two distinct processing pathways were chosen to understand the effect of thermomechanical conditions on the final microstructure. The microstructure was characterized using scanning electron microscopy, scanning transmission electron microscopy, and X-ray diffraction techniques. Path 1 exhibited larger strain, strain rate, and temperature as compared with path 2. In path 1, agglomerated Nb particles were present in the recrystallized ultrafine-grained Cu matrix, while in path 2 extremely fine and dispersed Nb particles were present in a highly deformed Cu matrix. In both pathways, supersaturation of Cu in Nb lattices was noted, but not vice-versa. The asymmetry in mixing is explained based on deformation-based, thermodynamic and kinetic factors. These findings provide a pathway for creation of novel tailored microstructures and improved properties in any number of binary immiscible alloy systems.

Cu-Nb alloys, Microstructural refinement, Friction↗

DOE OSTI2025

Characterization of Recrystallized Grains During Static Recrystallization of Hot-Compressed Mg–Zn–Ca Alloys Using In Situ Far-Field High-Energy Diffraction Microscopy

In this study, we explored the effect of Zn content on the static recrystallization of three 80 pct hot-compressed alloys, Mg–0.5Zn–0.1Ca wt pct (ZX050), Mg–1Zn–0.1Ca wt pct (ZX10), and Mg–3.2Zn–0.1Ca wt pct (ZX30), using far-field high-energy microscopy (ff-HEDM). Individual recrystallized grains were tracked and their 3D centroid, relative volume, and grain-averaged crystallographic orientation were measured during annealing. These measurements were used to compare the recrystallization kinetics and texture evolution of recrystallized grains in ZX alloys as a function of the Zn content. Fully recrystallized microstructures were observed for the ZX30 and the ZX10 alloys after annealing at 230 °C and 330 °C, respectively. In contrast, only a partially recrystallized microstructure for the ZX050 alloy was observed after > 1 hour of annealing at 430 °C. The resistance to recrystallization with decreasing Zn content was also confirmed by detecting faster growth rates of recrystallized grains in the ZX10 and ZX30 alloys, and slower growth rates in the ZX050 alloy. The significant recrystallization texture weakening of the ZX10 and ZX30 alloys and the development of a basal texture in the ZX05 alloy were described based on the orientation dependency of nucleation and growth of recrystallized grains. The analysis demonstrated that texture weakening was associated with increasing Zn content in Mg–Zn–Ca alloys.

Roumina, Reza [Univ. of Michigan, Ann Arbor, MI (U↗

DOE OSTI2025

The microscopic mechanisms of high temperature oxidation of Haynes 282

Nickel-based superalloy finds widespread applications in aerospace and extreme environments. They are known for their high temperature oxidation resistance under extended periods. However, the oxide formation and evolution which sets the stages for the later parabolic oxidation kinetics is not fully understood. This paper aims to provide new insights into the transient stage oxidation mechanism and kinetics of a typical Ni-based superalloy (Haynes 282). While tracking the chemical and microstructural evolution under micrometer scale at 800°C, we show that the oxide scale and its grain boundary species change significantly during the initial stages of oxidation and can have a profound impact on the oxidation kinetics. Cr 2 O 3 forms initially at the grain boundary along with minor amount of Al 2 O 3 . Then, the grain boundary region is enriched with copious amounts TiO 2 while Cr migrates away from the grain boundary. A noticeable change in the isothermal oxidation kinetics observed likely results from a mechanistic change from uniform surface oxidation to preferential outward diffusion of Ti 4+ ions through the grain boundary. Through first-principles calculations combined with energy dispersive spectroscopy, we confirmed the preferential outward diffusion of Ti 4+ ions as the diffusion barrier is lower for Ti than Cr along the grain boundaries. In conclusion, these findings highlight the critical role of early-stage grain boundary oxidation dynamics in dictating the long-term oxidation resistance of Ni-based superalloys and provide a foundation for future strategies to enhance their performance in extreme environments.

DFT↗

DOE OSTI2020

Three-dimensional phase field sintering simulations accounting for the rigid-body motion of individual grains

Sintering is a widely used powder processing technique in industrial applications. During sintering, atoms migrate to decrease the energy of the system via two main mechanisms: coarsening and densification, both of which lead to significant morphological variation of the sintered microstructure. When simulating sintering dynamics, the phase-field method has been broadly utilized because of its convenience in tracking morphology evolution. When a large number of grains is involved, it is common to use the same order parameter to describe multiple grains that are not in direct contact with one another (in order to reduce the computational memory demands). However, with this treatment it is difficult to handle the rigid-body motion of individual grains during densification. In this work, an implementation scheme is introduced to overcome the challenge of calculating individual particle motion based on existing equations. It uses a grouping algorithm and sets a cutoff radius on each grain for calculating the particle velocity during densification. This method allows for the incorporation of the densification mechanism, which has been commonly ignored in previous work, into phase-field sintering models in three-dimensional simulations with a large number of particles/grains. Moreover, through combination with the smoothed boundary method, material properties of sintered microstructures, such as the effective diffusivity and Young’s modulus, can be calculated during the sintering processes.

36 MATERIALS SCIENCE↗