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DOE OSTI2025

Coupled phase field damage and crystal plasticity analysis of intragranular fracture: The role of crystallographic orientation and voids

Damage evolution in engineering metal alloys at the grain scale exhibits significant microstructural heterogeneity and anisotropy. These heterogeneities create local hotspots for stress and strain localization, leading to void nucleation. Crystal orientation influences the active slip systems around voids, affecting lattice rotation and potentially forming discontinuities. At low triaxiality, voids may change shape due to lower stress, rotation, elongation, and coalescence. At high triaxiality, the correlation between crystal orientation and void growth rate becomes stronger, resembling the behavior observed in isolated single crystals. Therefore, understanding the effects of crystal orientation, heterogeneous strain, and defect evolution is crucial for single crystal fracture characterization. Here, in this work, a coupled phase-field damage (PFD) and crystal plasticity (CP) model is implemented within a finite element framework to analyze crystal deformation and failure. The CP method employs a dislocation density-based constitutive model, while intragranular failure is modeled using an anisotropic PFD method. The PFD model considers both the stored energy due to elastic stretching and the energy release due to defect formation and crack formation. A single crystal Al2219 with an intracrystalline spherical void is chosen to analyze fracture. The study finds that fracture propagation is strongly correlated with crystal orientations. This coupled CP-PFD model provides accurate failure prediction in crystalline materials by incorporating the effects of crystal orientations and existing voids. This study demonstrates how the local microstructure and defects influence plastic deformation and failure mechanisms in metal alloys.

Aluminum alloy↗

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 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

High-magnetic-field phases in U 1-x Th x Te 2

At temperatures T much lower than its superconducting critical temperature T c = 2.1 K, the heavy fermion superconductor UTe 2 has a unique phase diagram of magnetic field H vs. φ and θ, angles H is tilted from the b-axis toward the a- and c-axes, respectively, of its orthorhombic unit cell. The phase diagram contains three distinct superconducting phases: SC1 in which φ and θ extend from 0 to 90° and H ≤ ~15 T; SC 2 for φ ≤ ~7°, θ ≤ ~4° and ~15 T ≤ H ≤ H m = ~35 T, the onset of the magnetic field polarized (FP) phase, and SC FP which resides entirely within the FP phase in a pocket of superconductivity extending from θ ≈ 20° to 40° and from ~40 T to above 60 T. We studied the evolution of the H vs. θ phase diagram for Th concentrations 0.005 ≤ x ≤ 0.047 in the U 1-x Th x Te 2 system at ~0.6 K. Within this range of x values, SC 1 extends over 0 ≤ θ ≤ 90° and H ≤ ~10 T for x = 0.047, while SC 2 is suppressed. The SC FP and FP phases are unaffected to x = 0.02 but are completely suppressed in the region x = 0.025 to 0.047 where the residual resistance ratio RRR ~3 indicates a significant amount of disorder. In conclusion, these results complement recent studies of nonsuperconducting disordered UTe 2 single crystals in which the SC 1 and SC 2 phases are absent, but the FP and so-called “orphan” SC FP phases are retained.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Accelerating phase field simulations through a hybrid adaptive Fourier neural operator with U-net backbone

Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For one such process as liquid-metal dealloying (LMD), phase field models have been developed to understand the mechanisms leading to complex morphologies. However, the LMD governing equations in these models often involve coupled non-linear partial differential equations (PDE), which are challenging to solve numerically. In particular, numerical stiffness in the PDEs requires an extremely refined time step size (on the order of 10 -12 s or smaller). This computational bottleneck is especially problematic when running LMD simulation until a late time horizon is required. This motivates the development of surrogate models capable of leaping forward in time, by skipping several consecutive time steps at-once. In this paper, we propose a U-shaped adaptive Fourier neural operator (U-AFNO), a machine learning (ML) based model inspired by recent advances in neural operator learning. U-AFNO employs U-Nets for extracting and reconstructing local features within the physical fields, and passes the latent space through a vision transformer (ViT) implemented in the Fourier space (AFNO). We use U-AFNOs to learn the dynamics of mapping the field at a current time step into a later time step. We also identify global quantities of interest (QoI) describing the corrosion process (e.g., the deformation of the liquid-metal interface, lost metal, etc.) and show that our proposed U-AFNO model is able to accurately predict the field dynamics, in spite of the chaotic nature of LMD. Most notably, our model reproduces the key microstructure statistics and QoIs with a level of accuracy on par with the high-fidelity numerical solver, while achieving a significant 11, 200 × speed-up on a high-resolution grid when comparing the computational expense per time step. Finally, we also investigate the opportunity of using hybrid simulations, in which we alternate forward leaps in time using the U-AFNO with high-fidelity time stepping. We demonstrate that while advantageous for some surrogate model design choices, our proposed U-AFNO model in fully auto-regressive settings consistently outperforms hybrid schemes.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Phase Field Modeling of Chemical Reaction Related Damage Evolution in Environmental Barrier Coatings

The advent of next-generation engines necessitates materials capable of withstanding temperatures beyond the reach of current superalloys. SiC-based ceramic matrix composites, augmented with environmental barrier coatings (EBCs), present a promising materials solution. Given the active search for effective and durable EBCs, there is a pressing need for modeling tools to understand and predict damage evolution in these materials to help accelerate their development. This study introduces a phase-field model (PFM) designed to simulate the thermally grown oxides (TGO) and phase transformation in the degradation and failure of EBCs. The model accounts for the severe volume expansion due to oxidation, alongside phase transformations and porosity evolution during thermal cycling, offering a comprehensive view of the damage processes. Simulation results are validated against experimental findings reported in the literature, establishing the model's potential as a significant tool for understanding and improving the resilience of EBCs in cyclic oxidative environments.

fast-diffusion path↗

DOE OSTI2026

Phase-field approach to cellular blebbing

Bulges in the plasma membrane of cells known as blebs can form spontaneously in a wide range of biological processes, but what controls their shape and stability remains incompletely understood. Here, to address this we introduce a dual phase-field model with coupled order parameters representing the cell cortex and plasma membrane that can quantitatively model blebbing in three dimensions. Simulations and sharp-interface analyses reveal that, depending on whether blebbing occurs by detachment of the plasma membrane or rupture of the actin cortex, blebs can form discontinuously through a saddle-node bifurcation or continuously with increasing cortical tension. The model predictions are in good quantitative agreement with existing experimental data for laser-induced cortex rupture.

Biological and medical sciences↗

DOE OSTI2024

Pressure–Temperature–Magnetic Field Phase Diagram of Multiferroic (NH 4 ) 2 FeCl 5 ·H 2 O

We combined synchrotron-based infrared absorbance and Raman scattering spectroscopies with diamond anvil cell techniques and a symmetry analysis to explore the properties of multiferroic (NH 4 ) 2 FeCl 5 ·H 2 O under extreme pressure–temperature conditions. Compression-induced splitting of the Fe–Cl stretching, Cl–Fe–Cl and Cl–Fe–O bending, and NH 4 + librational modes defines two structural phase transitions, and a group–subgroup analysis reveals space group sequences that vary depending upon proximity to the unexpectedly wide order–disorder transition. Here, we bring these findings together with prior high-field work to develop the pressure–temperature–magnetic field phase diagram uncovering competing polar, chiral, and magnetic phases in this system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1999

Laser Interferometer Space Antenna (LISA) Far Field Phase Pattern

The Laser Interferometry Space Antenna (LISA) for the detection of Gravitational Waves is a very long baseline interferometer that will measure the changes in the distance of a five million kilometer arm to pico meter accuracies. Knowledge of the phase deviations from a spherical wave and what causes these deviations are needed considerations in (as a minimum) the design of the telescope and in determining pointing requirements. Here we present the far field phase deviations from a spherical wave for given Zernike aberrations and obscurations of the exit pupil.

Waluschka, Eugene↗

NASA NTRS1999

Laser Interferometer Space Antenna (LISA) Far Field Phase Patterns

The Laser Interferometer Space Antenna (LISA) for the detection of Gravitational Waves is a very long baseline interferometer, which will measure the changes in the distance of a five million kilometer arm to picometer accuracies. Knowledge of the phase deviations from a spherical wave and what causes these deviations are needed considerations in (as a minimum) the design of the telescope and in determining pointing requirements. Here we will present the far field phase deviations from a spherical wave for given Zernike aberrations of the exit pupil and discuss how these results affect the choice of a telescope design.

Waluschka, Eugene↗

DOE OSTI2024

Phase-Field Modeling of Thermally-Grown Oxide and the Induced Damage Evolution in Environmental Barrier Coatings

The advent of next-generation hydrogen-based engines necessitates materials capable of withstanding temperatures beyond the reach of current superalloys. SiC-based ceramic matrix composites, augmented with environmental barrier coatings (EBCs), present a promising materials solution. Given the active search for effective and durable EBCs, there is a pressing need for modeling tools to understand and predict damage evolution in these materials to help accelerate their development. This study introduces a phase-field model (PFM) designed to simulate the critical role of thermally grown oxides (TGO) in the degradation and failure of EBCs. The model accounts for the severe volume expansion due to oxidation, alongside phase transformations and microstructural evolution during thermal cycling, offering a comprehensive view of the damage processes. Simulation results are validated against experimental findings reported in the literature, establishing the model's potential as a significant tool for understanding and improving the resilience of EBCs in cyclic oxidative environments.

Cheng, Tianle↗

NASA NTRS2001

Phase Field Modeling of Microstructure Development in Microgravity

This newly funded project seeks to extend our NASA-sponsored project on modeling of dendritic microstructures to facilitate collaboration between our research group and those of other NASA investigators. In our ongoing program, we have applied advanced computational techniques to study microstructural evolution in dendritic solidification, for both pure isolated dendrites and directionally solidified alloys. This work has enabled us to compute dendritic microstructures using both realistic material parameters and experimentally relevant processing conditions, thus allowing for the first time direct comparison of phase field computations with laboratory observations. This work has been well received by the materials science and physics communities, and has led to several opportunities for collaboration with scientists working on experimental investigations of pattern selection and segregation in solidification. While we have been able to pursue these collaborations to a limited extent, with some important findings, this project focuses specifically on those collaborations. We have two target collaborations: with Prof. Glicksman's group working on the Isothermal Dendritic Growth Experiment (IDGE), and with Prof. Poirier's group studying directional solidification in Pb-Sb alloys. These two space experiments match well with our two thrusts in modeling, one for pure materials, as in the IDGE, and the other directional solidification. Such collaboration will benefit all of the research groups involved, and will provide for rapid dissemination of the results of our work where it will have significant impact.

Dantzig, Jonathan A.↗

NASA NTRSDate not supplied

Evolution of Dendritic Extended 3D Patterns during Directional Solidification: Microgravity Experiments in DECLIC-DSI onboard ISS and Phase-field Modeling

To characterize the dynamical formation of three-dimensional (3D) arrays of dendrites under diffusive growth conditions, in situ monitoring of a series of experiments on a transparent succinonitrile – 0.46 wt% camphor model alloy was carried out under low gravity in the DECLIC Directional Solidification Insert onboard the International Space Station. These experiments offer continuous interface observation and enable the construction of space-time evolution maps of dendrite location and primary spacing during directional solidification. We present the evolution of dendritic extended 3D patterns for a large range of parameters displaying different levels of side branching in both experiments and phase-field simulations. The combined and separate effects of macroscopic interface curvature and crystal mis-orientation are evidenced and detailed. In addition, the aligned dendritic array caused by the invasion of dendrites formed at the edge of the crucible border is investigated.

Kaihua Ji↗

DOE OSTI2025

Phase-field predictions of the influence of cooling rates during AM on the Evolution of Microstructures in Nickel-Based Single Crystal Superalloys

Additive manufacturing of single crystals made of Ni-based superalloys offers major cost savings for gas turbine engines with the inclusion of internal cooling channels. However, the lack of understanding of the effect of transient thermal conditions on solidification grain structure during additive manufacturing hinders the potential for process control to maintain the single crystal quality. The use of high-fidelity simulations through high performance computing to predict the evolution of the solidification microstructure will enhance the abilities to tailor the microstructures through process optimization. Phase field simulations are used to determine the effect local thermal conditions and defects on the stability of the solidification morphology, specifically with respect to the onset of columnar-to-equiaxed transition that results in the loss of the single crystal. The results are expected to be instrumental for developing future surrogate models to speed up the integration of design and manufacturing of turbine blades under the harsh in-service conditions.

36 MATERIALS SCIENCE↗

NASA NTRSDate not supplied

Characterization of Dendritic Spatially Extended 3D Patterns in Directional Solidification: Microgravity Experiments in DECLIC-DSI onboard ISS and 3D Phase-field Simulations

To clarify and characterize the fundamental physical mechanisms active in the dynamical formation of three-dimensional (3D) arrays of dendrites under diffusive growth conditions, in situ monitoring of series of experiments on transparent model alloy succinonitrile – 0.46 wt% camphor was carried out under low gravity in the DECLIC Directional Solidification Insert onboard the International Space Station. These experiments offer the very unique opportunity to observe in situ and characterize the dynamics of the microstructure formation and evolution in extended 3D patterns under microgravity environment. The analyses of the dendritic patterns for a broad range of growth velocities displaying different levels of sidebranching will be presented. Especially, the time evolution of primary spacing, in case of solidifications at constant pulling rate as well as for experiments with pulling rate jump, will be compared to 3D phase-field simulations, and the results will be discussed in terms of stable spacing range.

Kaihua Ji↗

NASA NTRSDate not supplied

Characterization of Dendritic Spatially Extended 3D Patterns in Directional Solidification: Microgravity Experiments in DECLIC-DSI Onboard ISS and 3D Phase-field Simulations

Kaihua Ji↗

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↗

NASA NTRS2002

Phase-Field Methods for Structure Evolution in Sheared Multiphase Systems

A homogeneous disordered phase separates into ordered structures when quenched into a broken-symmetry phase. The competition of broken-symmetry phases to select an equilibrium state may be studied in terms of coarse-grained order parameters described by a suitable Landau free-energy function. A network of equilibrium-phase domains develops on quenching and coarsens with time with a topology that may be controlled by shear. We use three-dimensional simulations, in which time-dependent models for conserved-order parameters coupled to Navier-Stokes fluid models are solved, to investigate the evolution of such domains, e.g. spinodal decompositions of polymeric materials under shear. The numerical problems are formidable because of the strong nonlinearities inherent in the coupled model, and these are amongst the first 3D calculations undertaken. In linear shear fields we find stable nanostrings, also recently seen in experiments. The affinity of the ordered phases to boundaries plays a role in the form of the structures that develop, with stacked plate-like phase distributions emerging under certain conditions. Such methods appear quite promising for design and analysis of multiphase and complex fluid formulations. The behavior of foams in such conditions is of particular interest in microgravity environments. Additional information can be found in the original extended abstract.

Badalassi, Vittorio↗