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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Phase-Field Modeling of Mechanical Damages in Ceramic Matrix Composites

Developed a phase-field model for mechanical damages in CMCs, which incorporates the CMC microstructures, matrix cracking, fiber breakage, and interfacial sliding. Two types of mechanisms, fiber bridging and fiber pull-out, are considered. The obtained simulation results agree with experimental observations and an analytical solution. Simulation results suggest that the performance of CMCs would be enhanced with thicker fibers, longer fibers, and higher fiber density. Opposite trends of interfacial sliding resistances are suggested for the two types of situations. In reality, a mixture of the two situations may exist, and then an intermediate interfacial sliding resistance may be optimal.

Xue, Fei↗
DOE OSTI2020

On the elastocaloric effect in CuAlBe shape memory alloys: A quantitative phase-field modeling approach

We report the reversible stress-induced phase transformation in shape memory alloys (SMAs) is a dissipative process during which heat is absorbed or released. The inherent temperature variations inside the material has an elastocaloric effect (eCE) with appealing applications in solid-state cooling technology such as compact and efficient on-board refrigeration system for eletronic devices. In this manuscript, we conduct the first study of eCE of CuAlBe SMAs utilizing phase-field modeling. For an applied stress of 500 MPa, the results for polycrystalline Cu-Al11-2Be (at. %) show a minimum adiabatic unloading temperature change of -10 K over a pseudoelastic window of 40 K. In the absence of plastic deformation, the material demonstrates good reproducibility of the eCE over a few loading–unloading cycles. The presence of plastic deformation is found to cause functional fatigue that deteriorates the cooling capacity; however, the coefficient of performance only decreases from 9.04 to 8.03, which is still a very good value. These results place CuAlBe as a frontrunner SMA for solid-state cooling compared to the expensive NiTi.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Phase-field modeling of rate-dependent fluid-driven fracture initiation and propagation

The rate-dependent behavior associated with deformation and fracturing of materials, such as natural rocks, poses significant challenges for modeling. In addition to the complications of the viscoelastic response, the speed of fracture propagation reflects micromechanical mechanisms in the fracture process zone(FPZ). In order to represent these complicated behaviors, a thermodynamically consistent, rate-dependent fracture model is required. Based on rigorous thermodynamic principles, we derive a rate-dependent phase-field mechanical model coupled with single-phase fluid flow in both the matrix and the fracture. The model is guaranteed to satisfy energy conservation during fracture propagation. Here, the system of equations is solved using the introduced solution procedure and a novel preconditioner that accounts for the complex fluid-structure interaction. The proposed phase-field model is tested against several benchmark problems on solid-fluid coupling, fluid-driven fracture propagation and rate-dependent viscoelastic deformation. The model serves as a strong basis for investigating rate-dependent fracturing experiments and for making predictions of material behaviors under new conditions.

42 ENGINEERING↗
DOE OSTI2023

Phase-field modeling of solid-state metathesis reactions with the charge neutrality constraint

In this work, we present a phase-field model that captures the evolution of ionic concentrations and phase fractions during solid-state metathesis (SSM) reactions where diffusion limits the rate of transformation. The evolution of the mole fraction of each ion is obtained via governing equations that describe the reduction of a free energy, which includes an energy landscape with local minima located at compositions corresponding to stable products. We utilized two Lagrange multipliers to impose constraints of electroneutrality as well as on the sum of mole fractions, which were then eliminated to derive set of two partial differential equations that describe the dynamics of the mole fraction evolution. From these governing equations, the expressions for effective mobilities for the cations and the anions were obtained. We first study the effect of mobilities of ions on the reaction kinetics, using a simple model considering the ions with an identical absolute value of charge numbers. The simulation results show that the overall characteristic mobility, defined as the sum of the two effective ionic mobilities, provides an excellent measure of the rate at which reaction progresses and that the ratio of the effective mobilities of the anions and the cations signifies the manner by which the reaction progresses. We then generalize the model to consider ions with different charge numbers and tuned the mobility of ions based on their diffusion coefficients reported in the literature and experimental data from a thin-film experiment for the synthesis of FeS 2 to demonstrate the capability of the model to predict the phase evolution during SSM reactions. In particular, the simulation predicts nonplanar phase evolution, which is recently observed in thin-film reactions for the synthesis of FeS 2 via transmission electron microscopy. The approach can serve as a basis for models for phase transformations in other multiphase ionic mixtures, such as in all-solid-state batteries and in ionic liquids.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Towards inverse microstructure-centered materials design using generative phase-field modeling and deep variational autoencoders

The field of Integrated Computational Materials Engineering (ICME) combines a broad range of methods to study materials’ responses over a spectrum of length scales. A relatively unexplored aspect of microstructure-sensitive materials design is uncertainty propagation and quantification (UP/UQ) of materials’ microstructure, as well as establishing process-structure–property (PSP) relationships for inverse material design. In this study, an efficient UP technique built on the idea of changing probability measures and a deep generative unsupervised representative machine learning method for microstructure-based design of thermal conductivity of materials is proposed. Probability measures are used to represent microstructure space, and Wasserstein metrics are used to test the efficiency of the UP method. By using deep Variational AutoEncoder (VAE), we identify the correlations between the material/process parameters and the thermal conductivity of heterogeneous dual-phase microstructures. Through high-throughput screening, UP, and the deep-generative VAE method, PSP relationships that are too complex can be revealed by exploiting the materials’ design space with an emphasis on microstructures. As a last point, we demonstrate generative machine learning serves as a useful tool for inverse microstructure-centered materials design, and we demonstrate this by examining the inverse design of thermal conductivity in nano-structured materials. Here, the results reveal the effects of morphology, volume fraction, characteristic length scale, and the individual thermal diffusivity of phases on the thermal conductivity of dual-phase alloys. Our findings emphasize the advantages of high-throughput phase-field modeling and generative deep learning for linking PSP and inverse microstructure-centered materials design.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Mesoscale simulations of High Burnup Fuel Fragmentation: Applying phase-field modeling to understand high burnup fuel fragmentation during loss of coolant accident conditions

During a loss-of-coolant accident (LOCA) in a nuclear power plant, a rapid increase in temperature is experienced in the fuel. In commercial light water reactors (LWRs), the high burnup structure (HBS) forms in regions of the UO 2 fuel where local burnup is high, characterized by smaller grain sizes and large, overpressurized bubbles. During a LOCA transient, fuel in the HBS region is susceptible to fine fragmentation, where the fuel breaks up into micron-size fragments (sometimes referred to as pulverization). To better understand the mechanisms behind this phenomenon, mesoscale computational modeling using the Idaho National Laboratory code Marmot has been employed to simulate the process of HBS formation and response to a LOCA transient. The process of complete and partial HBS formation was demonstrated in prototypical LWR conditions. The simulated HBS microstructures from these simulations were passed to a phase-field model of fracture. To provide a more direct comparison with experiments, a set of experiments conducted by Studsvik on fine fragmentation/pulverization during LOCA conditions was simulated using the BISON fuel performance code. The temperature profiles from the BISON simulations were passed to a phase-field model to determine the gas bubble pressure as a function of time. These pressure histories were used in a phase-field model of fracture to determine under what conditions and in which types of bubbles fine fragmentation was likely to occur.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Phase Field Modeling of Crystallographic Corrosion Pits

The modeling of corrosion to understand and predict corrosion behavior is a topical issue. Here, a 3D phase field model is developed to simulate the pit morphology, primarily focusing on crystallographic pits. A crystallographic function is employed to incorporate different corrosion rates for different crystallographic planes. The model is benchmarked and validated against an analytical solution for a simple case. 3D crystallographic pits in a single crystal are simulated and the effect of substrate orientation on the pit morphology is studied. The crystallographic pit morphology changes significantly with the substrate orientation and these morphologies have a symmetry consistent with the substrate orientation. This first 3D phase field model of crystallographic pits will help in predicting the intricate shapes of pits, thereby, pushing the frontiers of pitting corrosion modeling.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A comparative study of two numerical approaches for solving Kim–Kim–Suzuki phase-field models

Among the standard multi-phase multi-component phase-field (PF) methods, the Kim–Kim–Suzuki (KKS) method has the advantage of decoupling interfacial energy from bulk energy and solving concentration as the conserved variable. There are two approaches to numerically solving a KKS method: the global solution approach (GSA) solves all variables in a global system simultaneously, and the local solution approach (LSA) solves phase concentrations locally using a Newton solver. This work compares the performance of LSA and GSA for solving four KKS models of increasing complexity with the finite element method using the MOOSE framework. The solution accuracy, degrees of freedom (DOFs), memory usage, and computational efficiency are compared. We find that GSA and LSA generate similar solutions, with a maximum difference of only 0.34%. For each model, LSA has a lower number of DOFs, utilizes less memory, and less wall time. Additionally, the savings of memory and wall time in LSA increase with increasing mesh density of the same model and are more pronounced in models with higher dimensionality and more nodes. However, GSA is easier to implement in existing codes and can better solve highly nonlinear systems by utilizing sophisticated solvers.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Phase-field model of freeze casting

Directional solidification of water-based solutions has emerged as a versatile technique for templating hierarchical porous materials. However, the underlying mechanisms of pattern formation remain incompletely understood. In this work, we present a detailed derivation and analysis of a quantitative phase-field model for simulating this nonequilibrium process. The phase-field model extends the thin-interface formulation of dilute binary alloy solidification with antitrapping to incorporate the highly anisotropic energetic and kinetic properties of the partially faceted ice-water interface. This interface is faceted in the basal plane normal to the ⟨0001⟩ directions and atomically rough in other directions within the basal plane. On the basal plane, the model reproduces a linear or nonlinear relationship between the interface growth rate and the kinetic undercooling that can be linked to experimental measurements. In both cases, spontaneous parity breaking of the solidification front is observed when the preferred growth direction is aligned with the temperature gradient. This phenomenon leads to the formation of partially faceted ice lamellae that drift laterally in one of the ⟨0001⟩ directions. Here, we demonstrate that the drifting velocity of the ice lamellae is controlled by the kinetics on the basal plane and converges as the thickness of the diffuse solid-liquid interface decreases. Furthermore, we examine the effect of the form of the kinetic anisotropy, which is chosen here such that the inverse of the kinetic coefficient varies linearly from a finite value in the ⟨0001⟩ directions to zero in all other directions within the basal plane, consistent with the assumption that the interface grows in local thermodynamic equilibrium in this plane. Our results indicate that the drifting velocity of ice lamellae is not affected by the slope of this linear relation, and the radius and undercooling at the tip of an ice lamella converge at relatively small slope values. Consequently, the phase-field simulations remain quantitative with computationally tractable choices of both the interface thickness and the slope assumed in the form of the kinetic anisotropy.

Materials science↗
DOE OSTI2020

PRISMS-PF: A general framework for phase-field modeling with a matrix-free finite element method

Abstract A new phase-field modeling framework with an emphasis on performance, flexibility, and ease of use is presented. Foremost among the strategies employed to fulfill these objectives are the use of a matrix-free finite element method and a modular, application-centric code structure. This approach is implemented in the new open-source PRISMS-PF framework. Its performance is enabled by the combination of a matrix-free variant of the finite element method with adaptive mesh refinement, explicit time integration, and multilevel parallelism. Benchmark testing with a particle growth problem shows PRISMS-PF with adaptive mesh refinement and higher-order elements to be up to 12 times faster than a finite difference code employing a second-order-accurate spatial discretization and first-order-accurate explicit time integration. Furthermore, for a two-dimensional solidification benchmark problem, the performance of PRISMS-PF meets or exceeds that of phase-field frameworks that focus on implicit/semi-implicit time stepping, even though the benchmark problem’s small computational size reduces the scalability advantage of explicit time-integration schemes. PRISMS-PF supports an arbitrary number of coupled governing equations. The code structure simplifies the modification of these governing equations by separating their definition from the implementation of the numerical methods used to solve them. As part of its modular design, the framework includes functionality for nucleation and polycrystalline systems available in any application to further broaden the phenomena that can be used to study. The versatility of this approach is demonstrated with examples from several common types of phase-field simulations, including coarsening subsequent to spinodal decomposition, solidification, precipitation, grain growth, and corrosion.

36 MATERIALS SCIENCE↗
DOE OSTI2016

UO 2 Grain Growth: Developing Phase Field Models for Pore Dragging, Solute Dragging and Anisotropic Grain Boundary Energies

A detailed phase field model for the effect of pore drag on grain growth kinetics was implemented in MARMOT. The model takes into consideration both the curvature-driven grain boundary motion and pore migration by surface diffusion. As such, the model accounts for the interaction between pore and grain boundary kinetics, which tends to retard the grain growth process. Our 2D and 3D simulations demonstrate that the model capture all possible pore-grain boundary interactions proposed in theoretical models. For high enough surface mobility, the pores move along with the migrating boundary as a quasi-rigid-body, albeit hindering its migration rate compared to the pore-free case. For less mobile pores, the migrating boundary can separate from the pores. For the pore-controlled grain growth kinetics, the model predicts a strong dependence of the growth rate on the number of pores, pore size, and surface diffusivity in agreement with theroretical models. An evolution equation for the grain size that includes these parameters was derived and showed to agree well with numerical solution. It shows a smooth transition from boundary-controlled kinetics to pore-controlled kinetics as the surface diffusivity decreases or the number of pores or their size increases. This equation can be utilized in BISON to give accurate estimate for the grain size evolution. This will be accomplished in the near future. The effect of solute drag and anisotropy of grain boundary on grain growth will be investigated in future studies.

36 MATERIALS SCIENCE↗
DOE OSTI2016

An energy-stable time-integrator for phase-field models

Here, we introduce a provably energy-stable time-integration method for general classes of phase-field models with polynomial potentials. We demonstrate how Taylor series expansions of the nonlinear terms present in the partial differential equations of these models can lead to expressions that guarantee energy-stability implicitly, which are second-order accurate in time. The spatial discretization relies on a mixed finite element formulation and isogeometric analysis. We also propose an adaptive time-stepping discretization that relies on a first-order backward approximation to give an error-estimator. This error estimator is accurate, robust, and does not require the computation of extra solutions to estimate the error. This methodology can be applied to any second-order accurate time-integration scheme. We present numerical examples in two and three spatial dimensions, which confirm the stability and robustness of the method. The implementation of the numerical schemes is done in PetIGA, a high-performance isogeometric analysis framework.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A phase-field model for quasi-dynamic nucleation, growth, and propagation of rate-and-state faults

Despite its critical role in the study of earthquake processes, numerical simulation of the entire stages of fault rupture remains a formidable task. The main challenges in simulating a fault rupture process include the complex evolution of fault geometry, frictional contact, and off-fault damage over a wide range of spatial and temporal scales. Here, in this paper, we develop a phase-field model for quasi-dynamic fault nucleation, growth, and propagation, which features two standout advantages: (i) it does not require any sophisticated algorithms to represent fault geometry and its evolution; and (ii) it allows for modeling fault nucleation, propagation, and off-fault damage processes with a single formulation. Built on a recently developed phase-field framework for shear fractures with frictional contact, the proposed formulation incorporates rate- and state-dependent friction, radiation damping, and their impacts on fault mechanics and off-fault damage. We show that the numerical results of the phase-field model are consistent with those obtained from well-verified approaches that model the fault as a surface of discontinuity, without suffering from the mesh convergence issue in the existing continuous approaches to fault rupture (e.g., the stress glut method). Further, through numerical examples of fault propagation in various settings, we demonstrate that the phase-field approach may open new opportunities for investigating complex earthquake processes that have remained overly challenging for the existing numerical methods.

58 GEOSCIENCES↗
DOE OSTI2024

Ni coarsening under humid atmosphere in the electrode of solid oxide cells: A combined study of density-functional theory and phase-field modeling

Ni coarsening in solid oxide cell (SOC) electrodes is known to be significantly faster under a humid atmosphere. The underlying mechanisms, though, have not been fully understood. In this work, we examine the surface diffusion of Ni(OH) x by a combination of density-functional theory and phase-field modeling. Here, density-functional theory is used to evaluate the adsorption and diffusion of the Ni(OH) x species on Ni (111) surface, and the results are used to obtain the effective surface diffusivity of Ni versus steam and hydrogen gas partial pressures. This diffusivity is used as an input for a phase-field model to investigate the Ni coarsening in SOC electrodes. It is found that Ni(OH) x formed through chemical reaction cannot accelerate coarsening unless an extremely high steam to hydrogen ratio is reached. However, if Ni(OH) x is formed through electrochemical reactions near triple phase boundaries (TPBs), surface diffusion of Ni(OH) x may cause faster Ni coarsening in fuel cell mode under a large overpotential. Specifically, surface diffusion of Ni(OH) may be comparable to or faster than that of Ni under an overpotential that is large but still possible under fuel cell operating conditions.

25 ENERGY STORAGE↗
DOE OSTI2020

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

Here, a phase-field model for describing dynamic interactions between deformation twins and grain boundaries in a hexagonal close packed (HCP) metal is established. It is applied to simulating the coupled evolution mechanisms of grains and twins in magnesium (Mg) by probing the transmission of $\{10\bar{1}2\}$ deformation twins across grain boundaries. We analyze the effect of the strain relaxation near a grain boundary, which is related to the geometric compatibility arising from the misorientation angle between adjoining grains. Phase-field simulations demonstrate that twin transmission across a grain boundary into a neighboring grain leads to grain boundary migration towards the neighboring grain with a reduced grain boundary width. The preferred nucleation site of new twin variant in the neighboring grain is related to the elastic interaction energy distribution. These predicted transmission behaviors agree well with existing experimental observations and molecular dynamics simulations. By analyzing set of systematic phase-field simulation results, we establish a rotation-angle-related twin variant selection rule for analyzing the transmission of $\{10\bar{1}2\}$ deformation twins across grain boundaries in Mg and its alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Gas Bubble Evolution in Polycrystalline UMo Fuels Under Elastic-Plastic Deformation: A Phase-Field Model With Crystal-Plasticity

In monolithic UMo fuels, the interaction between the Al cladding and large gas bubble volumetric swelling causes both elastic-plastic and creep deformation. In this work, a phase-field model of gas bubble evolution in polycrystalline UMo under elastic-plastic deformation was developed for studying the dynamic interaction between evolving gas bubble/voids and deformation. A crystal plasticity model, which assumes that the plastic strain rate is proportional to resolved shear stresses of dislocation slip systems on their slip planes, was used to describe plastic deformation in polycrystalline UMo. Xe diffusion and gas bubble evolution are driven by the minimization of chemical and deformation energies in the phase-field model, while evolving gas bubble structure was used to update the mechanical properties in the crystal plasticity model. With the developed model, we simulated the effect of gas bubble structures (different volume fractions and internal gas pressures) on stress-strain curves and the effect of local stresses on gas bubble evolution. The results show that 1) the effective Young’s modulus and yield stress decrease with the increase of gas bubble volume fraction; 2) the hardening coefficient increases with the increase of gas bubble volume fraction, especially for gas bubbles with higher internal pressure; and 3) the pressure dependence of Xe thermodynamic and kinetic properties in addition to the local stress state determine gas bubble growth or shrinkage. The simulated results can serve as a guide to improve material property models for macroscale fuel performance modeling.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Phase-field modeling of grain-boundary premelting using obstacle potentials

We investigate the multiorder parameter phase field model of Steinbach and Pezzolla [Physica D 134, 385 (1999)] concerning its ability to describe grain boundary premelting. For a single order parameter situation solid-melt interfaces are always attractive, which allows us to have (unstable) equilibrium solid-melt-solid coexistence above the bulk melting point. The temperature-dependent melt layer thickness and the disjoining potential, which describe the interface interaction, are affected by the choice of the thermal coupling function and the measure to define the amount of the liquid phase. Due to the strictly finite interface thickness the interaction range also is finite. For a multiorder parameter model we find either purely attractive or purely repulsive finite-ranged interactions. Lastly, the premelting transition is then directly linked to the ratio of the grain boundary and solid-melt interfacial energy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Effective parameterization of phase-field models of fission gas bubble growth

Fission gas bubbles are one of the most important microstructural features of ceramic nuclear fuels. As gas bubbles grow and interconnect, they allow release of gases, with important consequences for fuel performance. Phase-field modeling has been increasingly used to simulate the evolution of fission gas bubble microstructural because of its capability to capture complex microstructural features. However, computational performance limitations have made it difficult to simulate all the defects present in fuels during operation. For this reason, phase-field models have often simulated only vacancies and used multiple approaches to include the effect of vacancy-interstitial recombination and sinks in a simplified way. Here, we compare some of the most prevalent approaches, including source-only and source/sink. The kinetics of bubble growth using these approaches are analyzed analytically, and simulations with these approaches are compared to a full vacancy-interstitial model.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗