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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Phase-field modeling of stored-energy-driven grain growth with intra-granular variation in dislocation density

Abstract We present a phase-field (PF) model to simulate the microstructure evolution occurring in polycrystalline materials with a variation in the intra-granular dislocation density. The model accounts for two mechanisms that lead to the grain boundary migration: the driving force due to capillarity and that due to the stored energy arising from a spatially varying dislocation density. In addition to the order parameters that distinguish regions occupied by different grains, we introduce dislocation density fields that describe spatial variation of the dislocation density. We assume that the dislocation density decays as a function of the distance the grain boundary has migrated. To demonstrate and parameterize the model, we simulate microstructure evolution in two dimensions, for which the initial microstructure is based on real-time experimental data. Additionally, we applied the model to study the effect of a cyclic heat treatment (CHT) on the microstructure evolution. Specifically, we simulated stored-energy-driven grain growth during three thermal cycles, as well as grain growth without stored energy that serves as a baseline for comparison. We showed that the microstructure evolution proceeded much faster when the stored energy was considered. A non-self-similar evolution was observed in this case, while a nearly self-similar evolution was found when the microstructure evolution is driven solely by capillarity. These results suggest a possible mechanism for the initiation of abnormal grain growth during CHT. Finally, we demonstrate an integrated experimental-computational workflow that utilizes the experimental measurements to inform the PF model and its parameterization, which provides a foundation for the development of future simulation tools capable of quantitative prediction of microstructure evolution during non-isothermal heat treatment.

Materials Science↗
DOE OSTI2024

Crack opening calculation in phase-field modeling of fluid-filled fracture: A robust and efficient strain-based method

The phase-field method has become popular for the numerical modeling of fluid-filled fractures, thanks to its ability to represent complex fracture geometry without algorithms. However, the algorithm-free representation of fracture geometry poses a significant challenge in calculating the crack opening (aperture) of phase-field fracture, which governs the fracture permeability and hence the overall hydromechanical behavior. Although several approaches have been devised to compute the crack opening of phase-field fracture, they require a sophisticated algorithm for post-processing the phase-field values or an additional parameter sensitive to the element size and alignment. Here, we develop a novel method for calculating the crack opening of fluid-filled phase-field fracture, which enables one to obtain the crack opening without additional algorithms or parameters. Here we transform the displacement-jump-based kinematics of a fracture into a continuous strain-based version, insert it into a force balance equation on the fracture, and apply the phase-field approximation. Through this procedure, we obtain a simple equation for the crack opening which can be calculated with quantities at individual material points. We verify the proposed method with analytical and numerical solutions obtained based on discrete representations of fractures, demonstrating its capability to calculate the crack opening regardless of the element size or alignment.

58 GEOSCIENCES↗
DOE OSTI2025

Inference of phase field fracture models

The phase field approach to modeling fracture uses a diffuse damage field to represent cracks. This representation mollifies singularities that arise in computations with sharp interface models and some of the resultant difficulties in the mathematical and numerical treatment of fracture. Phase field fracture models have proven effective at representing crack propagation, branching, and merging. Specific formulations, beginning with brittle fracture, have also been shown to converge to classical solutions. Extensions to cover the range of material failure, including ductile and cohesive fracture, lead to an array of possible models. There exists a large body of literature focusing on this class of models and on the impact of model form on the predicted crack evolution. However, there have not been systematic studies into how optimal models may be chosen. Here, we take a first step in this direction by developing formal methods for identification of the best parsimonious model of phase field fracture given full-field data on the damage and deformation fields. We consider some of the main models that have been used for the degradation of elastic response due to damage and its propagation. Our approach builds upon Variational System Identification (VSI), a weak form variant of the Sparse Identification of Nonlinear Dynamics (SINDy). Furthermore, in this first communication we focus on synthetically generated data but we also consider central issues associated with the use of experimental full-field data, such as data sparsity and noise.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Phase Field Modeling of Near-Wellbore Hydraulic Fracture Nucleation and Propagation

The goal of Task 2 of the project titled "Closing the loop between in situ stress complexity and EGS fracture complexity" is to model fracture nucleation and propagation in the near wellbore region and, in combination with the experimental study conducted as part of Task 4, investigate the relationship between the in situ stress and the near-wellbore fracture patterns. To this end, We have identified phase field as a promising modeling approach to model the nucleation and propagation process in the near wellbore region. In phase field, fractures are represented by a diffuse variable, i.e the damage. Compared to approaches that model fractures as sharp interfaces, phase field does not require any re-meshing or element insertion algorithm, which makes the treatment of complex fracture geometries straightforward, even with simple meshes.

15 GEOTHERMAL ENERGY↗
DOE OSTI2023

A phase-field model for hydraulic fracture nucleation and propagation in porous media

Many geo-engineering applications, for example, enhanced geothermal systems, rely on hydraulic fracturing to enhance the permeability of natural formations and allow for sufficient fluid circulation. Over the past few decades, the phase-field method has grown in popularity as a valid approach to modeling hydraulic fracturing because of the ease of handling complex fracture propagation geometries. However, existing phase-field methods cannot appropriately capture nucleation of hydraulic fractures because their formulations are solely energy-based and do not explicitly take into account the strength of the material. Thus, in this work, we propose a novel phase-field formulation for hydraulic fracturing with the main goal of modeling fracture nucleation in porous media, for example, rocks. Built on the variational formulation of previous phase-field methods, the proposed model incorporates the material strength envelope for hydraulic fracture nucleation through two important steps: (i) an external driving force term, included in the damage evolution equation, that accounts for the material strength; (ii) a properly designed damage function that defines the fluid pressure contribution on the crack driving force. In conclusion, the comparison of numerical results for two-dimensional test cases with existing analytical solutions demonstrates that the proposed phase-field model can accurately model both nucleation and propagation of hydraulic fractures. Additionally, we present the simulation of hydraulic fracturing in a three-dimensional domain with various stress conditions to demonstrate the applicability of the method to realistic scenarios.

15 GEOTHERMAL ENERGY↗
DOE OSTI2021

Precipitate growth kinetics under inhomogeneous concentration fields using a phase-field model

We investigate precipitation dynamics in the presence of a local solute gradient using phase-field simulations. During the homogenization heat treatment of the solidified Inconel 718 alloy, high Nb concentration within the Laves phases or at the core of the secondary arms results in Nb diffusion into the γ matrix. The volume fraction and spatial distribution of precipitation during subsequent annealing can be controlled by tailoring the Nb concentration gradient in the matrix during homogenization. We use a surrogate Ni-Fe-Nb alloy for Inconel 718 to explore the growth dynamics of δ precipitates related to the local Nb concentration levels. The simulations indicate that in the presence of a Nb concentration gradient the growth rate of δ precipitates is higher than in a matrix of uniform average Nb concentration. The higher growth rate is a result of the higher local thermodynamic driving force at the interface between the solute-rich matrix and the δ interface. Here, we propose a phenomenological model to describe the diffusion-controlled growth kinetics of the δ phase under a solute concentration gradient.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Investigation of the discontinuous precipitation of U-Nb alloys via thermodynamic analysis and phase-field modeling

U-Nb’s discontinuous precipitation, $\gamma^{bcc}_{matrix}$, $\alpha^{orth}_{cellular}$, $\gamma\prime^{bcc}_{cellular}$, is intriguing in the sense that it allows formation and growth of the metastable $\gamma\prime$ phase during the course of its occurrence. Previous attempts to explain the thermodynamic origin of U-Nb’s discontinuous precipitation hypothesized that the energy of $\alpha$ forms an intermediate common tangent with the first potential of the double-well energy of $\gamma$ at the $\gamma\prime$ composition. In this work, we examine different possible mechanisms by which the discontinuous precipitation product in the U-Nb system can be stabilized. We put forward a mechanism by which the bulk free energy of the $\gamma$ can develop a non-monotonic dependency with composition. Additionally we posit that local contributions due to lattice mismatch between the $\alpha$ and $\gamma$ phases may be responsible for the generation of metastable states that may stabilized by thermodynamics as well as by kinetics. Our work suggests that local misfit strain tends to play a crucial role in the growth of the discontinuous precipitation product. Depending on the magnitude of strain developed at the $\alpha$/$\gamma\prime$ interfaces, either an increasing $\gamma\prime$ composition or a random distribution of $\gamma\prime$ compositions around the equiatomic value with respect to increasing temperature could be expected. Moreover, we show how it is possible to stabilize the discontinuous precipitation front through highly anisotropic and fast interface diffusion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Calibrating a finite-strain phase-field model of fracture for bonded granular materials with uncertainty quantification

To study the mechanical behavior of mock high explosives, an experimental and simulation program was developed to calibrate, with quantified uncertainty, a material model of the bonded granular material Idoxuridine and nitroplasticized Estane-5703. This paper reports on the efficacy of such a framework as a generalizable methodology for calibrating material models against experimental data with uncertainty quantification. Additionally, this paper studies the effect of two manufacturing temperatures and three initial granular configurations on the unconfined compressive behavior of the resulting bonded granular materials. In each of these cases, the same calibration framework was used; in that, hundreds of high-fidelity direct numerical simulations using a new, graphics processing unit-enabled, high-performance finite element method software, Ratel, were run to calibrate a finite-strain phase-field fracture model against experimental data. It was found that manufacturing temperature influenced the elastic response of the mock high explosives, with higher temperatures yielding a stiffer response. By contrast, it was found that the initial configuration of the grains had a negligible impact on the overall behavior of the mock high explosives though it remains possible that local damage accumulation within the specimens could be altered by the initial configurations. Overall, the calibration framework was successful at creating well-calibrated models, showing its usefulness as an engineering and scientific tool.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Integral boundary conditions in phase field models

Modeling the chemical, electric and thermal transport as well as phase transitions and the accompanying mesoscale microstructure evolution within a material in an electronic device setting involves the solution of partial differential equations often with integral boundary conditions. Employing the familiar Poisson equation describing the electric potential evolution in a material exhibiting insulator to metal transitions, we exploit a special property of such an integral boundary condition, and we properly formulate the variational problem and establish its well-posedness. Next, we compare our method with the commonly-used Lagrange multiplier method that can also handle such boundary conditions. Numerical experiments demonstrate that our new method achieves optimal convergence rate in contrast to the conventional Lagrange multiplier method. Furthermore, the linear system derived from our method is symmetric positive definite, and can be efficiently solved by Conjugate Gradient method with algebraic multigrid preconditioning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Phase-field modeling of radiation-induced composition redistribution: An application to additively manufactured austenitic Fe–Cr–Ni

Multicomponent alloys undergoing irradiation damage develop radiation-induced composition redistribution at point defect sinks such as grain boundaries (GBs) and dislocations. Such redistribution results in undesired changes to their mechanical behavior and corrosion resistance. Additively manufactured alloys proposed for future nuclear applications are expected to demonstrate a distinct response to irradiation owing to their unique microstructure with as-solidified dislocation density and chemical microsegregation. To capture the composition redistribution in such systems, we develop a mesoscale model with coupled evolution of atomic and point defect components in the presence of dislocation density, dislocation heterogeneity, and thermodynamic interactions at the GB. The model is parameterized for an FCC Fe–Cr–Ni alloy as a representative system for austenitic stainless steels, and simulations are performed in 1D and 2D as a function of irradiation temperature, dose, dislocation density, and grain size. Radiation-induced segregation (RIS) characterized by Cr depletion and Ni enrichment is predicted at both the GB and the dislocation cell wall, with RIS being lower in magnitude but wider at the cell wall. Strongly biased absorption of self-interstitials by dislocations is found to suppress Ni enrichment but slightly enhance Cr depletion under certain conditions. Thermodynamic segregation at the GB is predicted to be narrower and opposite in sign to RIS for both Cr and Ni. Importantly, non-monotonic segregation is found to occur when both thermodynamic and RIS mechanisms are considered, providing a novel physical interpretation of experimental observations. The model is expected to serve as a key tool in accelerated qualification of irradiated materials.

additively manufactured microstructure↗
DOE OSTI2025

Cross slip of extended dislocations in face-centered cubic metals through phase-field modeling

Cross slip is a dislocation mechanism that significantly impacts the mechanical behavior of engineering alloys. Here, in this work, we advance a 3D phase-field dislocation dynamics (PFDD) mesoscale technique to simulate cross slip across a broad range of face-centered cubic (FCC) metals. The formulation incorporates elastic anisotropy, an FCC numerical grid, and a high-fidelity representation of the entire γ -surface from density functional theory for eight FCC metals and no adjustable parameters or rules. The relaxed core structures under zero stress for all metals are predicted to extend in plane. The analytical model for stacking fault width agrees well with the PFDD result under the assumption of elastic isotropy but overestimates it under elastic anisotropy, when the degree of anisotropy is large. The dynamic simulations are designed to elucidate the material parameters that influence the propensity for cross slip. Whether cross slip occurs under a non-Schmid stress or to bypass a hard obstacle, the critical stress to cross slip scales strongly with the anisotropic energy coefficient for a screw dislocation.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Simulation and analysis of small angle scattering (SAS) patterns of Ni-based superalloy microstructures generated by a phase-field model

This paper investigates the relationship between microstructural features and small-angle scattering (SAS) patterns in Ni-based superalloys using a combined phase-field and SAS simulation approach coupled with microstructure analyses. The simulated SAS patterns accurately capture key experimental observations previously reported in the literature, including the time-dependent transition from circular to square-shaped precipitates and the development of anisotropic SAS patterns. Importantly, our analysis reveals the correlations between characteristic length scales extracted from SAS profiles and microstructural descriptors, such as precipitate size and inter-precipitate distance. These findings provide a comprehensive understanding of the link between SAS profiles and microstructure evolution in Ni-based superalloys, offering valuable insights for materials characterization and design.

Microstructure↗
DOE OSTI2025

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

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

36 MATERIALS SCIENCE↗
DOE OSTI2021

Phase-field modeling of the interactions between an edge dislocation and an array of obstacles

Obstacles, such as voids and precipitates, are prevalent in crystalline materials. They strengthen crystals by serving as barriers to dislocation glide. Here in this work, we develop a phase-field dislocation dynamics (PFDD) technique for investigating the interactions between dislocations and second-phase obstacles, which can be either voids or precipitates. The PFDD technique is constructed to account for elastic heterogeneity, elastic anisotropy, dissociation of the dislocation, and dislocation transmission across bicrystalline interfaces. Within the framework, we present a model for “pseudo-voids”, which are voids shearable by dislocations, in contrast to unphysical, unshearable voids in conventional phase-field dislocation formulations. We employ the PFDD technique to investigate the in-plane interactions between an edge dislocation and an array of nano-scale obstacles with different spacings. In this application, the interactions take place in glide planes of either a face-centered cubic (FCC) Cu or a body-centered cubic (BCC) Nb matrix, while the precipitates have a Cu 1-x Nb x composition, with x varying from 0.1 to 0.9. Our atomistic simulations find that the alloy precipitates can have an FCC, an amorphous, or a BCC phase, depending on the compositional ratio between Cu and Nb, i.e., value of x. Among all types of obstacles, the critical stresses for dislocation bypass are the highest for unshearable amorphous precipitates, followed by shearable crystalline precipitates, and then the pseudo-voids.

42 ENGINEERING↗
DOE OSTI2023

Phase-field modeling of dislocation–interstitial interactions

The mechanical behavior of body-centered cubic (BCC) materials can be dramatically affected by the presence of interstitial solute atoms. Here we present a new phase-field dislocation dynamics formulation to include the diffusion of interstitials. Short-range interactions are accounted for by a concentration-dependent lattice energy, and long-range interactions are accounted for by modifications to the elastic energy. The interstitial diffusion law introduces gradients that require methods for minimizing Gibbs oscillations, which is done via a modified Green’s function. The formulation is general to any solute-solvent system and is applied here to Nb-O as a model system, whose interstitial parameters are obtained from ab initio calculations. The effect of O on the core structures of Nb edge and screw dislocations is calculated. The diffusion of O to form interstitial atmospheres around dislocation cores is simulated, as well as the critical stresses required for dislocations to break away or cross slip from these atmospheres. Future applications of the method to simulate complex interstitial embrittlement mechanisms are discussed.

36 MATERIALS SCIENCE↗