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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
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

A $C^1$-Conforming Arbitrary-Order Two-Dimensional Virtual Element Method for the Fourth-Order Phase-Field Equation

We present a two-dimensional conforming virtual element method for the fourth-order phase-field equation. Our proposed numerical approach to the solution of this high-order phase-field (HOPF) equation relies on the design of an arbitrary-order accurate, virtual element space with $C^1$ global regularity. Such regularity is guaranteed by taking the values of the virtual element functions and their full gradient at the mesh vertices as degrees of freedom. Attaining high-order accuracy requires also edge polynomial moments of the trace of the virtual element functions and their normal derivatives. In this work, we detail the scheme construction, and prove its convergence by deriving error estimates in different norms. A set of representative test cases allows us to assess the behavior of the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Grain boundary effects in high-temperature liquid-metal dealloying: a multi-phase field study

Abstract A multi-phase field model is employed to study the microstructural evolution of an alloy undergoing liquid dealloying, specifically considering the role of grain boundaries. A semi-implicit time-stepping algorithm using spectral methods is implemented, which enables simulating large 2D and 3D domains over long time scales while still maintaining a realistic interfacial thickness. Simulations reveal a mechanism of coupled grain–boundary migration to maintain equilibrium contact angles with the topologically complex solid–liquid interface, which locally accelerates diffusion-coupled growth of a liquid channel into the precursor. This mechanism asymmetrically disrupts the ligament connectivity of the dealloyed structure in qualitative agreement with published experimental observations. The grain boundary migration-assisted corrosion channels form even for precursors with small amounts of the dissolving alloy species, below the parting limit . The activation of this grain boundary dealloying mechanism depends strongly on grain boundary mobility.

36 MATERIALS SCIENCE↗
DOE OSTI2019

A phase field model for dislocations in hexagonal close packed crystals

In this work, an application of a phase field formulation suitable for modeling the motion of individual partial and full dislocations in hexagonal close packed (HCP) crystals is presented. The formulation incorporates periodic potentials for glide on the distinct HCP slip systems, which are informed here by density functional theory (DFT). The model is applied to simulate the dissociation process starting from an unstable perfect dislocation and ending at its final equilibrium structure for different slip planes and in different HCP metals. The structural characteristics that are predicted for these dislocations include the partial Burgers vectors, dissociation distances, core widths of the partials, and any asymmetries in these quantities. Mg is selected as one of the model materials since its dislocations are the most well studied and it is nearly elastically isotropic. For Mg, it is shown that the predictions for dissociation distances agree with those reported previously by atomic-scale calculations, including density functional theory, for dislocations on the basal < a >, prismatic < a >, and pyramidal type II slip systems. Furthermore, phase field model results are also presented for dislocations in Ti and Zr, which we find develop distinctively different equilibrium structures than Mg.

36 MATERIALS SCIENCE↗
DOE OSTI2018

An optimization‐based phase‐field method for continuous‐discontinuous crack propagation

Summary A new continuous‐discontinuous strategy for the computational modeling of crack propagation within the context of phase‐field models of fracture is presented. The method is designed to introduce and update a sharp crack surface within an evolving damage band and to enhance the kinematics of the finite element approximation accordingly. The proposed approach relies on three key elements. First, we propose the use of a crack length functional to provide a trigger for initiating a continuous to discontinuous transition. Next, the crack path identification is addressed by introducing the concept of an auxiliary damage field that varies with an extension of the sharp crack surface. The sharp crack surface is extended through an optimization algorithm, in which the difference between the auxiliary field and the actual damage field stemming from the phase‐field framework is minimized. Finally, a strong discontinuity is inserted in the wake of the diffuse crack tip with the extended finite element method, completing the continuous to discontinuous transition. Several benchmark problems in two‐dimensional quasi‐static fracture mechanics are presented to demonstrate the accuracy and robustness of the method.

Geelen, Rudy J. M.↗
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 OSTI2021

Tusas: A fully implicit parallel approach for coupled phase-field equations

In this study, we develop a fully-coupled, fully-implicit approach for phase-field modeling of solidification in metals and alloys. Predictive simulation of solidification in pure metals and metal alloys remains a significant challenge in the field of materials science, as microstructure formation during the solidification process plays a critical role in the properties and performance of the solid material. Our simulation approach consists of a finite element spatial discretization of the fully-coupled nonlinear system of partial differential equations at the microscale, which is treated implicitly in time with a preconditioned Jacobian-free Newton-Krylov method. The approach is algorithmically scalable as well as efficient due to an effective preconditioning strategy based on algebraic multigrid and block factorization. We implement this approach in the open-source Tusas framework, which is a general, flexible tool developed in C++ for solving coupled systems of nonlinear partial differential equations. The performance of our approach is analyzed in terms of algorithmic scalability and efficiency, while the computational performance of Tusas is presented in terms of parallel scalability and efficiency on emerging heterogeneous architectures. We demonstrate that modern algorithms, discretizations, and computational science, and heterogeneous hardware provide a robust route for predictive phase-field simulation of microstructure evolution during additive manufacturing.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

On the kinetics of dendritic sidebranching: A three dimensional phase field study

The underlying mechanism for dendritic sidebranching was studied using 3-D phase field modeling. Results showed that in 3-D the requirement of applying the random thermal noise to induce dendritic sidebranching (i.e., normally the case for 2-D phase field simulations) was fully relaxed. The stretching of the secondary or higher order arms occurred spontaneously and symmetrically as the growth of the dendrite. With periodic external perturbation and if the stimulating frequency was lower than a critical value, both tip velocity and sidebranching would get completely synchronized with the perturbation. Whereas if the perturbation frequency was higher than the critical value, rather than increasing, the sidebranching frequency would become stable and maintain at the same magnitude as that of the natural sidebranching, i.e., when no external perturbation was applied. It was shown that the underlying mechanism for sidebranching was deterministic rather than stochastic, and anisotropy tendency and curvature effect were shown to be the most important influence factors. Moreover, the difference of the anisotropy tendency would lead to an uneven distribution of curvature on the solid/liquid interface, i.e., formation of concave and convex geometries. The growth of these geometries would subsequently break the initial spherical structure of solid seed and lead to further sidebranching.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

A space-time adaptive finite element method with exponential time integrator for the phase field model of pitting corrosion

In this paper we propose a space-time adaptive finite element method for the phase field model of pitting corrosion, which is a parabolic partial differential equation system consisting of a phase variable and a concentration variable. A major challenge in solving this phase field model is that the problem is very stiff, which makes the time step size extremely small for standard temporal discretizations. Another difficulty is that a high spatial resolution is required to capture the steep gradients within the diffused interface, which results in very large number of degrees of freedom for uniform meshes. To overcome the stiffness of this model, we combine the Rosenbrock–Euler exponential integrator with Crank–Nicolson scheme for the temporal discretization. Moreover, by exploiting the fact that the speed of the corroding interface decreases with time, we derive an adaptive time stepping formula. For the spatial approximation, we propose a simple and efficient strategy to generate adaptive meshes that reduces the computational cost significantly. Thus, the proposed method utilizes local adaptivity and mesh refinement for efficient simulation of the corrosive dissolution over long times in heterogeneous media with complex microstructures. We also present an extensive set of numerical experiments in both two and three dimensional spaces to demonstrate efficiency and robustness of the proposed method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Understanding and control of Zener pinning via phase field and ensemble learning

Zener pinning refers to the dispersion of fine particles which influences grain size distribution via movement of grain boundaries in a polycrystalline material. Grain size distribution in polycrystals has a significant impact on their properties including physical, chemical, mechanical, and optical to name a few. We explore the use of Phase-field modeling and machine-learning techniques to understand and improve the control of grain size distribution via Zener pinning in polycrystalline materials. We develop a machine learning model that determines the relative importance of various parameters to exercise microstructure control via Zener pinning. Our workflow combines high-throughput phase-field simulations and machine learning to address the computational bottlenecks associated with large-scale simulations as well as identify features necessary for microstructure control in polycrystals. A random forest (RF) regression model was developed to predict grain sizes based on five Phase-field model parameters, achieving an average prediction error of 0.72 nm for the training data and 1.44 nm for the test data. The importance of the input parameters is analyzed using the SHapley Additive exPlanations (SHAP) approach which reveals that diffusivity, volume fraction, and particle diameter are the most important parameters in determining the final grain size. These findings will allow us to select the best second-phase particles, optimize grain size distributions and thus design microstructures with the desired properties. The developed method is a highly versatile and generalizable approach that can be used to assess the combined effects of individual features in the presence of multiple variables.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Creating physically-based three-dimensional microstructures: Bridging phase-field and crystal plasticity models.

In order to better incorporate microstructures in continuum scale models, we use a novel finite element (FE) meshing technique to generate three-dimensional polycrystalline aggregates from a phase field grain growth model of grain microstructures. The proposed meshing technique creates hexahedral FE meshes that capture smooth interfaces between adjacent grains. Three dimensional realizations of grain microstructures from the phase field model are used in crystal plasticity-finite element (CP-FE) simulations of polycrystalline a -iron. We show that the interface conformal meshes significantly reduce artificial stress localizations in voxelated meshes that exhibit the so-called "wedding cake" interfaces. This framework provides a direct link between two mesoscale models - phase field and crystal plasticity - and for the first time allows mechanics simulations of polycrystalline materials using three-dimensional hexahedral finite element meshes with realistic topological features.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Phase-field-based calculations of the disregistry fields of static extended dislocations in FCC metals

In the continuum context, the displacements of atoms induced by a dislocation can be approximated by a continuum disregistry field. In this paper, two phase-field (PF)-based approaches and their variants are employed to calculate the disregistry fields of static, extended dislocations of pure edge and pure screw character in two face-centred cubic metals: Au and Al, which have distinct stable stacking fault energy and elastic anisotropy. A new truncated Fourier series form is developed to approximate the generalised stacking fault energy (GSFE) surface, which shows significant improvement over the previously employed Fourier series form. By measuring the intrinsic stacking fault (ISF) width and partial dislocation core size in different ways, the PF-based disregistry fields are quantitatively compared against those predicted by molecular statics. In particular, two new measures for the ISF widths are proposed and shown to overcome drawbacks of the more commonly used standards in the literature. Our calculations also show that continuum formulation of the elastic energy and the GSFE for a homogeneous surface can successfully characterise the core structure. Finally, our comparisons highlight the significance of including the gradient energy in the free energy formulation when an accurate description of the dislocation core structure is desired.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Gradient flow based phase-field modeling using separable neural networks

Allen–Cahn equation is a reaction–diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen–Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space–time approach. To overcome these challenges, we propose solving the gradient flow of the Ginzburg–Landau free energy functional, which is equivalent to the Allen–Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen–Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space–time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulation and computational implementation, several case studies illustrate the applicability of the proposed method.

42 ENGINEERING↗
DOE OSTI2017

Phase field model of fluid-driven fracture in elastic media: Immersed-fracture formulation and validation with analytical solutions

Propagation of fluid-driven fractures plays an important role in natural and engineering processes, including transport of magma in the lithosphere, geologic sequestration of carbon dioxide, and oil and gas recovery from low-permeability formations, among many others. The simulation of fracture propagation poses a computational challenge as a result of the complex physics of fracture and the need to capture disparate length scales. Phase field models represent fractures as a diffuse interface and enjoy the advantage that fracture nucleation, propagation, branching, or twisting can be simulated without ad hoc computational strategies like remeshing or local enrichment of the solution space. Here we propose a new quasi-static phase field formulation for modeling fluid-driven fracturing in elastic media at small strains. The approach fully couples the fluid flow in the fracture (described via the Reynolds lubrication approximation) and the deformation of the surrounding medium. The flow is solved on a lower dimensionality mesh immersed in the elastic medium. This approach leads to accurate coupling of both physics. We assessed the performance of the model extensively by comparing results for the evolution of fracture length, aperture, and fracture fluid pressure against analytical solutions under different fracture propagation regimes. Thus, the excellent performance of the numerical model in all regimes builds confidence in the applicability of phase field approaches to simulate fluid-driven fracture.

58 GEOSCIENCES↗
DOE OSTI2019

A phase-field model for hydride formation in polycrystalline metals: Application to δ-hydride in zirconium alloys

We report a phase-field model for simulating metal hydride formation involving large volume expansion in single- and polycrystals. As an example, we consider δ-hydride formation in α-zirconium (Zr), which involves both displacive crystallographic structural change and hydrogen diffusion process. Thermodynamic Gibbs energy functions are extracted from the available thermodynamic database based on the sublattice model for the interstitial solid solutions. Solute-grain boundary interactions and inhomogeneous elasticity of polycrystals are taken into consideration within the context of diffuse-interface description. The stress-free transformation strains of multiple variants for hcp -Zr (α) to fcc -hydride (δ) transformation are derived based on the well-established orientation relationship between the α and δ phases as well as the corresponding temperature-dependent lattice parameters. In particular, to account for the large volume expansion, we introduced the mixed interfacial coherency concept between those phases—basal planes are coherent and prismatic planes are semi-coherent in computing the strain energy contribution to the thermodynamics. We analyzed the morphological characteristics of hydrides involving multiple structural variants and their interactions with grain boundaries. Moreover, our simulation study allows for the exploration of the possible hydride re-orientation mechanisms when precipitating under applied tensile load, taking into account the variation in the interfacial coherency between hydrides and matrix, their elastic interactions with the applied stress, as well as their morphology-dependent interactions with grain boundaries. Here, the phase-field model presented here is generally applicable to hydride formation in any binary metal–hydrogen systems.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Application of Phase Field Simulations to Fuel Behavior

The application of the phase filed method to simulate the formation and the stress induced re-orientation of zirconium hydride during dry storage of the spent fuel and clad assembly is discussed. The phase field technique is able to capture qualitatively the effect of external stress on the hydride orientation in Zr-H system. However, the modeling effort to-date is far from adequate and several issues remain to be addressed before the simulations can be used as a predictive tool for the behavior of the clad during long time dry storage.

elastic energy↗
DOE OSTI2023

Phase-Field Modeling of Materials Interfaces and Nanostructures

Nanostructured materials offer unique properties for a wide range of energy applications. Among various known processing methods, liquid metal dealloying (LMD)—the selective dissolution of a base alloy element into a metallic melt—has emerged as a powerful technique to produce a new class of nano-/meso-scale open porous and bicontinuous composite structures with ultra-high interfacial area. LMD has recently been complemented by the advent of vapor phase dealloying (VPD), a novel technique that exploits the selective evaporation of one element from a parent alloy containing elements with very different vapor pressures, thereby enabling to fabricate open nanoporous structures of various elements from less-noble metals to inorganic elements regardless of their chemical activity without requiring high LMD temperatures and chemical etching. Together LMD and VPD have greatly expanded the scope of dealloying techniques, limited by traditional electrochemical means to noble metals, and boosted the design of new functional and structural materials that combine a wide variety of elements. Topologically-connected open porous structures with ultra-high surface area allow mass transport within the structure while preserving structural integrity, enabling them to serve as catalysts, fuel cells, supercapacitors, or high-capacity battery materials. Bicontinuous composite structures in turn can display high strength and high ductility or superior radiation-damage resistance due to the ultra-high interface area between interpenetrating solid phases. This research program makes use of state-of-the-art computational methods to understand at a basic level the self-organizing dealloying process with main focus on dealloying kinetics and interfacial pattern formation at the dealloying front controlling initial structure size, topology, and phase compositions. Phase-field simulation studies of LMD focus on solid solutions, line compounds, and intermetallic systems that can form ternary composites by nucleation and growth of a new phase. Studies of VPD employ phase-field modeling and a hybrid method combining a kinetic Monte Carlo (KMC) model of evaporation and surface diffusion with molecular dynamics for vapor-phase transport inside nanopores. Simulations explore mechanisms of interface- and diffusion-controlled dealloying kinetics, both observed in VPD but not fundamentally understood. In addition, our newly developed multi-physics phase-field approach of large-volume-change phase transformations is being used to model novel 3D anode geometries based on dealloyed nanoporous structures including novel sandwiched graphene/Si/silica for highrate Li ion battery. Those studies are aimed at elucidating geometric design principles that improve mechanical stability. We expect this research to enhance the capability to tailor nano-/mesoscale structures for a wide range of energy-related materials applications and to yield further advances in computational methodologies that benefit a broad materials research community.

77 NANOSCIENCE AND NANOTECHNOLOGY↗