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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A phase-field model for void and gas bubble superlattice formation in irradiated solids

A phase-field model to simulate the formation of both void and gas bubble superlattices is derived from a grand potential functional, assuming 1D diffusion of self-interstitial atoms. The model is capable of accounting for superlattice formation by either a nucleation and growth or spinodal decomposition mechanism; in this work, we focus on the nucleation and growth mechanism, using a discrete nucleation approach in the phase-field model. In simulations of void formation, short aligned rows of voids were initially formed, followed by growth in the size of the aligned rows, and finally leading to superlattice formation, consistent with experimental observations. Void superlattice spacing as a function of model parameters was quantified. Increased nucleation rates led to smaller superlattice spacing, while increased vacancy diffusivity led to larger superlattice spacing. In simulations of gas bubble superlattice formation, superlattice spacing decreased with increasing gas atom flux, consistent with experimental observations. Here, simulations with increasing ratio of gas atom flux to vacancy-interstitial pair production led to increased superlattice spacing, which is inconsistent with experimental observations at high gas atom flux rates; this discrepancy is attributed to the fact that the model does not account for bound gas atom-vacancy pairs that may dominate at high gas flux rates.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Causality-respecting adaptive refinement for PINNs: enabling precise interface evolution in phase field modeling

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp moving boundaries with complex initial morphologies, remains a challenge. Here, this study introduces an approach combining residual-based adaptive refinement (RBAR) with causality-informed training to enhance the performance of PINNs in solving spatio-temporal PDEs. Our method employs a three-step iterative process: initial causality-based training, RBAR-guided domain refinement, and subsequent causality training on the refined mesh. Applied to the Allen-Cahn equation, a widely-used model in phase field simulations, our approach demonstrates significant improvements in solution accuracy and computational efficiency over traditional PINNs. Notably, we observe an ‘overshoot and relocate’ phenomenon in dynamic cases with complex morphologies, showcasing the method’s adaptive error correction capabilities. This synergistic interaction between RBAR and causality training enables accurate capture of interface evolution, even in challenging scenarios where traditional PINNs fail. Our framework not only resolves the limitations of uniform refinement strategies but also provides a generalizable methodology for solving a broad range of spatio-temporal PDEs. The enhanced performance of the RBAR–causality combined framework demonstrates its strong potential for advancing PINN-based modeling of physical systems characterized by complex, evolving interfaces.

Allen-Cahn equations↗
DOE OSTI2021

Phase-field model of precipitation processes with coherency loss

A phase-field model is proposed to simulate coherency loss coupled with microstructure evolution. A special field variable is employed to describe the degree of coherency loss of each particle and its evolution is governed by a Ginzburg-Landau type kinetic equation. For the sake of computational efficiency, a flood-fill algorithm is introduced that can drastically reduce the required number of field variables, which allows the model to efficiently simulate a large number of particles sufficient for characterizing their statistical features during Ostwald ripening. The model can incorporate size dependence of coherency loss, metastability of coherent particles, and effectively incorporate the underlying mechanisms of coherency loss by introducing a so-called differential energy criterion. The model is applied to simulate coarsening of Al 3 Sc precipitates in aluminum alloy and comprehensively compared with experiments. Our results clearly show how the particle size distribution is changed during coherency loss and affects the coarsening rate.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A Phase-Field Model for In-Space Manufacturing of Binary Alloys

The integrity of the final printed components is mostly dictated by the adhesion between the particles and phases that form upon solidification, which is a major problem in printing metallic parts using available In-Space Manufacturing (ISM) technologies based on the Fused Deposition Modeling (FDM) methodology. Understanding the melting/solidification process helps increase particle adherence and allows to produce components with greater mechanical integrity. We developed a phase-field model of solidification for binary alloys. The phase-field approach is unique in capturing the microstructure with computationally tractable costs. The developed phase-field model of solidification of binary alloys satisfies the stability conditions at all temperatures. The suggested model is tuned for Ni-Cu alloy feedstocks. We derived the Ginzburg-Landau equations governing the phase transformation kinetics and solved them analytically for the dilute solution. We calculated the concentration profile as a function of interface velocity for a one-dimensional steady-state diffuse interface neglecting elasticity and obtained the partition coefficient, k, as a function of interface velocity. Numerical simulations for the diluted solution are used to study the interface velocity as a function of undercooling for the classic sharp interface model, partitionless solidification, and thin interface.

36 MATERIALS SCIENCE↗
DOE OSTI2020

The effects of introducing elasticity using different interpolation schemes to the grand potential phase field model

Introducing elastic energy in the phase field method has been shown to influence interfacial energy, depending on the elastic interpolation scheme. This study investigates the impact of the elastic energy when using a grand potential-based phase field method, comparing the result of Khachaturyan’s strain interpolation scheme (KHS) and Voight-Taylor’s elastic energy interpolation scheme (VTS). The KHS model leads to a decrease in the interfacial energy, while the VTS model leads to an increase. The change in interfacial energy is greater with the VTS model than the KHS model, which suggests that the KHS model is more appropriate to limit the artificial impact of the elastic energy on the interfacial energy. When the contribution at the interface is not negligible, it is shown that both the microstructure evolution kinetics and the equilibrium microstructure can be influenced by the choice of the elastic scheme being used. In addition, this paper shows that the grand potential model might not be appropriate when the system requires the introduction of a composition-dependent term in the elastic energy contribution. This limitation is due to the need for an explicit and invertible relation between the total potential and the composition.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Attaining regularization length insensitivity in phase-field models of ductile failure

In this work, a cohesive phase-field model of ductile fracture in a finite-deformation setting is presented. The model is based on a free-energy function in which both elastic and plastic work contributions are coupled to damage. Using a strictly variational framework, the field evolution equations, damage kinetics, and flow rule are jointly derived from a scalar least-action principle. Particular emphasis is placed on the use of a rational function for the stress degradation that maintains a fixed effective strength with decreasing regularization length. The model is employed to examine crack growth in pure mode-I problems through the generation of crack growth resistance (J-R) curves. In contrast to alternative models, the current formulation gives rise to J-R curves that are insensitive to the regularization length. Numerical evidence suggests convergence of local fields with respect to diminishing regularization length as well.

42 ENGINEERING↗
DOE OSTI2023

Visualizing Uranium Crystallization from Melt: Experiment-Informed Phase Field Modeling and Machine Learning

The focus of this project was to observe and simulate the solidification of uranium metal at the crystallographic level from its molten state. Melting experiments were conducted at two different scales to observe microstructural evolution using either a laboratory-scale induction furnace (hundreds of grams of metal) or a microscope heating stage (hundreds of milligrams of metal), respectively. Experimental parameters and characterization data were then used to inform a phase field model of gamma-U crystal growth as dendrites with or without secondary phase impurities in the form of uranium carbide particles. Finally, training datasets were generated by the phase field model as inputs to a neural network, developed with the aim of providing a faster, cheaper surrogate model for microstructural simulations within a given parameter space. Progress is reported herein for each of these task areas. Ultimately, 1) an optical microscope heating stage capability has been stood-up for uranium metal solidification studies, 2) a phase field model was advanced to simulate multiple uranium grains growing in the presence of carbide impurity particles and 3) a neural network was constructed and optimized to predict the microstructure features of individually growing uranium crystals.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Implementing contact angle boundary conditions for second-order Phase-Field models of wall-bounded multiphase flows

In the present work, a general formulation is proposed to implement the contact angle boundary conditions for the second-order Phase-Field models, which is applicable to N-phase (N ≥ 2) moving contact line problems. To remedy the issue of mass change due to the contact angle boundary condition, a source term or Lagrange multiplier is added to the original second-order Phase-Field models, which is determined by the consistent and conservative volume distribution algorithm so that the summation of the order parameters and the consistency of reduction are not influenced. To physically couple the proposed formulation to the hydrodynamics, especially for large-density-ratio problems, the consistent formulation is employed. The reduction-consistent conservative Allen-Cahn models are chosen as examples to illustrate the application of the proposed formulation. The numerical scheme that preserves the consistency and conservation of the proposed formulation is employed to demonstrate its effectiveness. Results produced by the proposed formulation are in good agreement with the exact and/or asymptotic solutions. The proposed method captures complex dynamics of moving contact line problems having large density ratios.

97 MATHEMATICS AND COMPUTING↗
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↗