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DOE OSTI2022

MEUMAPPS (C++ Version)

Many materials, metal alloys in particular, have features on the on micrometer or nanometer scale that have a large impact on the properties of the material. These features are known as the microstructure of the material. Understanding why and how the microstructure forms in a material is of fundamental scientific interest as well as of significant technological interest. The capability to predict microstructure evolution in a material allows the intentional design of microstructures and hence the intentional design of material properties. The phase-field method is one of the leading methods for predicting microstructure evolution. One of the most significant problems for phase-field models is their computational expense. Even limited phase-field simulations can easily require thousands of CPU core-hours to complete, which significantly limits their use. This code provides both a general framework for creating scalable, GPU-accelerated phase-field model applications as well as several applications themselves. The code is capable of using hundreds of GPUs efficiently, which greatly reduces the time required to perform simulations. The code is written with an emphasis on performance portability, that is the ability for the code to run efficiently on a number of different computing architectures without modification of the source code. The performance portability of this code is primarily enabled through the use of two libraries, Kokkos (performance portable data structures and execution patterns) and heFFTe (performance portable distributed 3D fast Fourier transforms). The code consists of a core library, applications, and tests. The core library includes shared functionality between applications. This includes interfaces with fast Fourier transform (FFT) libraries such as heFFTe, data structures based on Kokkos, file input and output capabilities, and a solver for infinitesimal strain mechanical equilibrium problems. Five applications are included in the code. The flagship application is the MEUMAPPS-SS application, which implements the Kim-Kim-Suzuki phase-field model for precipitation for an arbitrary number of phases and components in a metal alloy. Five simpler applications are also included that solve the Eshelby inclusion problem, Allen-Cahn equation, the coupled Allen-Cahn and diffusion equations, and the Cahn-Hilliard equation. The code includes two applications to solve the Cahn-Hilliard equation, one with constant-step-size first-order time integration and the second with adaptive high-order time integration.

DeWitt, Stephen [Oak Ridge National Lab. (ORNL), O↗

DOE OSTI2024

Analytical model and dynamical phase-field simulation of terahertz transmission across ferroelectrics

Here, we theoretically investigate the steady-state transmission of continuous terahertz (THz) wave across a freestanding ferroelectric slab. Based on the Landau-Ginzburg-Devonshire theory of ferroelectrics and the coupled equations of motion for polarization and electromagnetic (EM) waves, we derive the analytical expressions of the frequency- and thickness-dependent dielectric susceptibility and transmission coefficient at the thin slab limit in the harmonic excitation regime. When the slab thickness is much smaller than the THz wavelength in the ferroelectric, the analytical predictions agree well with the numerical simulations from a dynamical phase-field model that incorporates the coupled dynamics of strain, polarization, and EM wave in multiphase systems. At larger thicknesses, the transmission is mainly determined by the frequency-dependent attenuation of THz waves in the ferroelectric and the formation of a standing polarization/THz wave. Our results advance the understanding of the interaction between THz wave and ferroelectrics and suggest the potential of exploiting ferroelectrics to achieve low-heat-dissipation, nonvolatile voltage modulation of THz transmission for high-data-rate wireless communication.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Comparison of excess free energy at an interface according to the applied interpolation scheme for elasticity: A phase-field method

Phase-field modeling is an effective simulation technique for modeling microstructure evolution of elastically anisotropic systems. To introduce the elastic energy contribution in a phase field model, an interpolation scheme is used to define the mechanical properties within the phases and across the continuous interface. Several existing interpolation schemes introduce a potential excess elastic energy at the interface, which undesirable effect on microstructure evolution needs to be evaluated. In this study, we focused on three interpolation schemes including Khachaturyan’ scheme (KHS), Voigt–Taylor’s scheme (VTS), and Steinbach–Apel’s scheme (SAS). Comparisons of these schemes’ performances were performed in three configuration types using the MOOSE (Multiphysics Object-Oriented Simulation Environment) framework: bi-crystal, isotropic particle-matrix and anisotropic particle-matrix. The contribution of excess elastic energy on the interface energy as a function of interface width and the computational time to steady-state were evaluated in these three configurations. SAS introduces the lowest excess elastic energy contribution and the VTS has the biggest contribution amongst the considered schemes. Moreover, when modeling precipitation in an anisotropic elastic material, the SAS approach seems to predict more physical convex shapes during growth, making it preferable to KHS and VTS. Finally, as currently implemented, SAS requires the largest computational time and KHS requires the smallest time to reach steady-state amongst the considered schemes.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Benchmark problems for the Mesoscale Multiphysics Phase Field Simulator (MEMPHIS)

This report details the current benchmark results to verify, validate and demonstrate the capabilities of the in-house multi-physics phase-field modeling framework Mesoscale Multiphysics Phase Field Simulator (MEMPHIS) developed at the Center for Integrated Nanotechnologies (CINT). MEMPHIS is a general phase-field capability to model various nanoscience and materials science phenomena related to microstructure evolution. MEMPHIS has been benchmarked against a suite of reported classical phase-field benchmark problems to verify and validate the correctness, accuracy and precision of the models and numerical methods currently implemented into the code.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

A phase-field diffraction model for thermo-hydro-mechanical propagating fractures

This paper introduces a novel diffraction based thermo-hydraulic–mechanical (THM) model for fracture propagation using a phase-field fracture (PFF) approach. The key innovation of the THM-PFF model lies in its integrated treatment of four solution variables—displacements, phase-field, pressure, and temperature—each governed by a combination of conservation of momentum (mechanics problem), a variational inequality (constrained minimization problem), mass conservation (pressure problem), and energy conservation (temperature problem). This leads to a new formulation of a coupled variational inequality system. A major advancement is the development of an extended fixed-stress algorithm, where displacements, phase-field, pressures, and temperatures are solved in a staggered sequence. An important aspect of this work is the global coupling of pressures and temperatures across the domain using diffraction systems, with diffraction coefficients defined by material parameters weighted by the diffusive phase-field variable. To ensure robust local mass conservation, we employ enriched Galerkin finite elements (EG) for both pressure and temperature diffraction equations. By enriching the continuous Galerkin basis functions with discontinuous piecewise constants, EG accurately represents solution and parameter discontinuities while preserving local mass and energy conservation—crucial aspects for THM problems and realistic behavior. Moreover, the use of a predictor–corrector local mesh adaptivity scheme is employed, allowing the model to handle small phase-field length-scale parameters while maintaining high numerical accuracy and reasonable computational cost. Furthermore, these new model and algorithmic developments represent significant advances in the field and have been substantiated through rigorous numerical tests.

Diffraction systems↗

DOE OSTI2022

Assessment of four strain energy decomposition methods for phase field fracture models using quasi-static and dynamic benchmark cases

Abstract Strain energy decomposition methods in phase field fracture models separate strain energy that contributes to fracture from that which does not. However, various decomposition methods have been proposed in the literature, and it can be difficult to determine an appropriate method for a given problem. The goal of this work is to facilitate the choice of strain decomposition method by assessing the performance of three existing methods (spectral decomposition of the stress or the strain and deviatoric decomposition of the strain) and one new method (deviatoric decomposition of the stress) with several benchmark problems. In each benchmark problem, we compare the performance of the four methods using both qualitative and quantitative metrics. In the first benchmark, we compare the predicted mechanical behavior of cracked material. We then use four quasi-static benchmark cases: a single edge notched tension test, a single edge notched shear test, a three-point bending test, and a L-shaped panel test. Finally, we use two dynamic benchmark cases: a dynamic tensile fracture test and a dynamic shear fracture test. All four methods perform well in tension, the two spectral methods perform better in compression and with mixed mode (though the stress spectral method performs the best), and all the methods show minor issues in at least one of the shear cases. In general, whether the strain or the stress is decomposed does not have a significant impact on the predicted behavior.

Zhang, Shuaifang↗

NASA NTRS1982

Analytical prediction of the interior noise for cylindrical models of aircraft fuselages for prescribed exterior noise fields. Phase 2: Models for sidewall trim, stiffened structures and cabin acoustics with floor partition

An airplane interior noise prediction model is developed to determine the important parameters associated with sound transmission into the interiors of airplanes, and to identify apropriate noise control methods. Models for stiffened structures, and cabin acoustics with floor partition are developed. Validation studies are undertaken using three test articles: a ring stringer stiffened cylinder, an unstiffened cylinder with floor partition, and ring stringer stiffened cylinder with floor partition and sidewall trim. The noise reductions of the three test articles are computed using the heoretical models and compared to measured values. A statistical analysis of the comparison data indicates that there is no bias in the predictions although a substantial random error exists so that a discrepancy of more than five or six dB can be expected for about one out of three predictions.

Pope, L. D.↗

DOE OSTI2021

Modeling discontinuous dynamic recrystallization containing second phase particles in magnesium alloys utilizing phase field method

Pre-existing second phase particles can induce particle stimulated nucleation (PSN) and pinning effect on grain boundaries during DRX process of magnesium alloys. The interaction among pinning effect, PSN mechanism and strain-induced grain boundary migration (SIBM) nucleation mechanism imposes challenge in quantitative study of microstructure evolution. A phase field model that describes discontinuous dynamic recrystallization process considering second phase particles (PF-DDRX-SP) which mainly distribute along grain boundaries is developed. The second phase order parameter with diffusion interface is introduced to the free energy function. With considering the pinning effect of second phase particles on grain boundaries, the grain boundary energy couples the interaction between second phase and grains. The effect of second phase on dislocation density evolution is considered in the model, and the PSN and SIBM mechanism are both executed by limiting the nucleation position to the grain boundary and the second phase interface. For the validation, the initial topology consistent with initial microstructure is applied to the simulation of DRX kinetics and flow behavior of AZ80 magnesium alloy, and great reliability and accuracy of developed model is indicated. Furthermore, through the model, the microstructure evolution with different particle size and with different volume fraction of round particle during DRX process were simulated. Finally, the results show that particles with higher dispersion reduce the number of DRX nuclei, which indicate that second phase particles suppress the nucleation at grain boundaries because of the pinning effect. More importantly, the proposed model could also quantitatively predict the relationships between the parameters of second phase particles and DRX behaviors, and enable to optimize the initial second phase structure in a uniform grain structure during thermomechanical process.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Multi-scale modeling of the electric field assisted sintering process

The electric field assisted sintering (EFAS) process involves tightly coupled physics that influence microstructural evolution in the particles being compacted. It is also an inherently multi-scale phenomenon, with the microstructure of the compact influencing the subsequent engineering-scale response of the sintering system. To improve understanding of how processing parameters influence microstructural evolution, we have developed a multi-scale modeling approach that couples a continuum-level model of the sintering system with a phase-field model for microstructural evolution of particles within the compact. The phase-field model couples the effect of chemical and electrical driving forces on microstructural evolution and includes the effect of charged defect segregation to surfaces and grain boundaries; this segregation leads to enhanced defect transport and heat generation at these interfaces in response to applied electric field. The effect of enhanced heat generation on particle neck growth and the influence of microstructural evolution on the engineering-scale model are demonstrated.

36 - MATERIALS SCIENCE↗

DOE OSTI2023

Multi-scale modeling of the electric field assisted sintering process

36 MATERIALS SCIENCE↗

DOE OSTI2021

A consistent and conservative model and its scheme for N -phase- M -component incompressible flows

Here, we propose a consistent and conservative model for multiphase and multicomponent incompressible flows, where there can be arbitrary numbers of phases and components. Each phase has a background fluid called the pure phase, each pair of phases is immiscible, and components are dissolvable in some specific phases. The model is developed based on the multiphase Phase-Field model including the contact angle boundary condition, the diffuse domain approach, and the analyses on the proposed consistency conditions for multiphase and multicomponent flows. The model conserves the mass of individual pure phases, the amount of each component in its dissolvable region, and thus the mass of the fluid mixture, and the momentum of the flow. It ensures that no fictitious phases or components can be generated and that the summation of the volume fractions from the Phase-Field model is unity everywhere so that there is no local void or overfilling. It satisfies a physical energy law and it is Galilean invariant. A corresponding numerical scheme is developed for the proposed model, whose formal accuracy is 2nd-order in both time and space. It is shown to be consistent and conservative and its solution is demonstrated to preserve the Galilean invariance and energy law. Numerical tests indicate that the proposed model and scheme are effective and robust to study various challenging multiphase and multicomponent flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

High Performance Circuit Pastes for Solid Oxide Fuel Cell Applications: Final Technical Report

Using a combination of in-plane electrical conductivity measurements, electrical contact resistance measurements, tensile fracture tests, double shear lap fracture tests, rapid thermal cycling adhesion tests, in situ wetting angle measurements, 3D X-ray tomography, reduction-oxidation (RedOx) cycling, scanning electron microscopy (SEM), energy dispersive x-ray spectroscopy (EDAX), Density Functional Theory (DFT) modeling, Molecular Dynamics (MD) modeling, and Phase Field modeling, this project determined that a new brazing technique developed by the PIs (specifically the use of nickel particles to direct the wetting and spreading of molten silver) could be used to produce well-adhered, >97% dense, electrically-conductive circuits, current collectors, and/or electrical contacts on a variety of ceramic and ceramic-coated substrates (specifically lanthanum strontium manganite, yttria stabilized zirconia, sapphire, Cr2O3-passivated stainless steel, and Al2O3-passivated stainless steel). Compared to other silver-based alternatives, Ag:Ni led to less manufacturing defects and was more tolerant of the extreme environments (isothermal high-temperature aging) and occasional abuse (rapid thermal cycling and RedOx cycling) encountered during Solid Oxide Fuel Cell and/or Solid Oxide Electrolysis Cell operation. Further, in some situations (such as when to produce Ag:Ni electrical contacts to Al2O3-protected stainless steel) the Ni particles also improved operation by acting as chemical getters that removed electrically-insulating, surface-segregating substrate impurities (i.e. by lowering the contact resistance with the underlying substrate).

36 MATERIALS SCIENCE↗

DOE OSTI2022

The effects of dose, dose rate, and irradiation type and their equivalence on radiation-induced segregation in binary alloy systems via phase-field simulations

Radiation-induced segregation is a phenomenon commonly observed in many alloys which consists of the redistribution of elements (solute or interstitial impurities) under irradiation. The onset and development of radiation-induced segregation can only occur when a sufficient flux of defects is sustained and defect sinks are present. Irradiation dose, dose rate, and particle types all affect defect flux. In this work, we employ a phase-field model to examine the effects of dose, dose rate, and type of incident particles on radiation-induced segregation behavior in a model binary alloy. The phase-field model takes into account the formation and evolution of point defects as well as defect clusters, the diffusion and clustering of alloy species, the presence of additional extrinsic defect sinks in the form of dislocations, and two different methods of radiation-damage insertion, which are intended to simulate either light-ion/electron irradiation via Frenkel pairs or heavy-ion irradiation in the form of cascades. Our results show a dose-rate and particle-type dependence on the amount of solute segregation. We show that the material systems exposed to higher dose rates are less subjected to solute segregation at equivalent doses. We also show that such dose-rate-dependence behavior is due to a delay of the incubation dose at which radiation-induced segregation effectively starts. Particle type and the presence of dislocations can accentuate this behavior. Our model predictions correlate with many experimental observations made over the years on radiation-induced segregation providing credence to the simulation results. The methodology presented in this study allows for a first-order prediction of the dose rate at which proxy irradiation experiments could be performed to approximate radiation-induced segregation behaviors seen in targeted irradiation conditions.

36 MATERIALS SCIENCE↗

DOE OSTI2020

A numerical-homogenization based phase-field fracture modeling of linear elastic heterogeneous porous media

Most porous media, such as geomaterials and biomaterials are highly heterogeneous in nature, and they contain large variations of microscopic pore structures, such as pore sizes, pore distribution, and pore shapes. The oscillation of microscopic structures is a substantial challenge in theoretical characterization and is usually ignored in continuous modeling. However, mechanical behavior of porous media such as deformation and failure, are essentially impacted by the microscopic heterogeneity which needs to be considered in modeling a porous media. Here, this research proposes a numerical modeling framework with a capability to investigate the effect of microscopic heterogeneity on the macroscopic fracture behavior in porous media by using a numerical homogenization technique, combined with the phase-field fracture modeling method. This numerical modeling strategy computes a homogenized elasticity tensor based on microscopic heterogeneous pore structures heterogenous porous domain by solving boundary value problems at microscopic domain. The strain energy and subsequent propagation of macroscopic fractures will be updated using homogenized stiffness information. Using this numerical scheme, the microscopic pore structure’s impact on the fracture behavior through the homogenized elastic tensor will be taken into account. This multiscale technique is benchmarked against classical problems. Finally, the results highlight the importance of the underlying pore structure and reveal that both fracture strength and propagation path can be influenced by the microscopic heterogeneity.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Dendrite Growth Morphology Modeling in Liquid and Solid Electrolytes

The main goal of this project is to develop a multi-scale modeling approach that connects micron-scale phase-field models and atomic-scale density functional theory (DFT)-based simulations via parameter- and relationship-passing in order to predict Li-metal dendrite morphology evolution, in both liquid and solid electrolytes. The key hypothesis of the DFT-informed phase-field multiscale modeling approach is that it can capture the electrochemical-mechanical driving forces and incorporate the roles of nano-meter-thin solid electrolyte interphase (SEI) in liquid electrolytes as well as of the microstructures of micro-meter-thick solid electrolytes (SEs) for all-solid-state batteries. In this project, we have formulated and implemented phase-field models to incorporate the electrochemical driving forces in liquid electrolytes and then incorporate mechanical driving forces to simulate dendrite growth in solid electrolytes with resolved microstructures. We have implemented two treatments for the SEI: an explicit model to include the microstructure of the SE or SEI in the phase field model and an implicit model to simulate the impact of nano-meter thick SEI in liquid electrolytes by varying the electrode/electrolyte interfacial properties. The key interfacial properties, including the electronic and ionic transport properties, the charge transfer reaction kinetics, and mechanical properties, were computed by DFT-based calculations. At the DFT-based model, one key advancement is to directly predict the charge transfer reaction kinetics at a complex Li/SEI/electrolyte interface by linking DFT with density functional tight binding (DFTB) calculations. As the main accomplishments, we have demonstrated two successful predictions in both solid electrolyte and liquid electrolyte based on this multiscale approach. The predicted intergranular Li dendrite growth in LLZO revealed the importance of trapped electrons at internal interfaces in the microstructure of LLZO. The predicted electroplating morphology of mossy Li and faceted Mg agreed well with experiments. The insights provided by the multiscale model and the model enabled electrolyte and SEI design will accelerate the development of Li-metal electrode for high energy density batteries, that meet DOE’s target on cell density (>350 Wh/kg) and cost below $100/kWhuse for EV applications.

25 ENERGY STORAGE↗

DOE OSTI2022

Solidification and grain formation in alloys: a 2D application of the grand-potential-based phase-field approach

Solidification is a significant step in the forming of crystalline structures during various manufacturing and material processing techniques. Solidification characteristics and the microstructures formed during the process dictate the properties and performance of the materials. Hence, understanding how the process conditions relate to various microstructure formations is paramount. In this work, a grand-potential-based multi-phase, multi-component, multi-order-parameter phase-field model is used to demonstrate the solidification of alloys in 2D. This model has several key advantages over other multi-phase models such as it decouples the bulk energy from the interfacial energy, removes the constraints for the phase concentration variable, and prevents spurious third-phase formation at the two phase interfaces. Here, the model is implemented in a finite-element-based phase-field modeling code. The role of various modeling parameters in governing the solidification rate and the shape of the solidified structure is evaluated. It is demonstrated that the process conditions such as temperature gradient, thermal diffusion, cooling rate, etc, influence the solidification characteristics by altering the level of undercooling. Furthermore, the capability of the model to capture directional solidification and polycrystalline structure formation exhibiting various grain shapes is illustrated. In both these cases, the process conditions have been related to the growth rate and associated shape of the dendritic structure. As a result, this work serves as a stepping stone towards resolving the larger problem of understanding the process–structure–property–performance correlation in solidified materials.

36 MATERIALS SCIENCE↗

DOE OSTI2021

BISON microstructure-based pulverization criterion in high burnup structure

To improve the economics of commercial nuclear power production, utilities are seeking to increase the allowable burnup limit of UO$_2$ fuel. One of the main factors that contributes to the current burnup limit of 62 GWd/MTU in commercial light water reactors (LWRs) is the risk of fine fragmentation or pulverization during a loss of coolant accident (LOCA). Pulverization primarily occurs at high burnups, especially when the high burnup structure (HBS) has formed. To allow the industry to pursue increased burnup and develop mitigation strategies, it is essential to have improved capability to predict the onset of pulverization. However, the mechanism of pulverization is not well understood, and the existing predictive capabilities implemented in the BISON fuel performance code are empirical in nature. In this report, mesoscale simulations are used to improve understanding of the formation mechanism of the HBS and how it responds during a LOCA transient, and inform development of a BISON pulverization criterion. A phase-field model was used to simulate the evolution of bubble pressure as a result of HBS formation. The simulations showed that gas atoms diffuse from grain interiors to the new grain boundaries created during HBS formation, and diffuse rapidly along these grain boundaries to reach existing bubbles. This causes an increase in bubble pressure in existing bubbles, leading to bubble growth during steady-state operation. To simulate the response of HBS bubbles to a LOCA transient, a newly developed phase-field model was used; in agreement with preliminary results from FY20, bubble size did not change significantly during the duration of the transient. A phase-field fracture model was used to study fragmentation patterns in the HBS, including using input from the phase-field model as initial conditions. Phase-field fracture simulations were used to determine a pulverization criterion for BISON. A function for the critical pressure for pulverization to occur was fit to data from the phase-field fracture simulations, and this function was implemented as a material property in BISON. For comparison, an analytical criterion for pulverization was developed and implemented within the same material property.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Thermo4PFM: Facilitating Phase-field simulations of alloys with thermodynamic driving forces

Phase-field modeling is a popular front-tracking approach used to model solidification. Its time-evolution equations are often coupled to alloy composition and/or thermal diffusion in high-resolution multiphysics approaches. Materials thermodynamic properties tabulated in CALPHAD databases can be used for phase-field modeling to parameterize bulk energies of alloys. In addition, they can be naturally integrated into models such as the Kim-Kim-Suzuki (KKS) model where driving forces depend on the differences between chemical potentials of co-existing phases. In that case, a small system of coupled nonlinear equations needs to be solved at every point in space where the phase-field order parameter is to be updated and evolved in time. Here we present Thermo4PFM, a solver for the KKS equations for binary and ternary alloys, with two or three phases, and parameterized with CALPHAD models. Thermo4PFM is open source, written in C++, and can take advantage of Graphics Processing Units (GPU) accelerators. Using OpenMP offload capabilities for C++ classes, an excellent performance is demonstrated on GPU using the LLVM compiler. CALPHAD data is read from simple JSON files using an open source parser from the boost library.

36 MATERIALS SCIENCE↗