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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
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 OSTI2025

Understanding coarsening of a post-corrosion microstructure in a molten salt by combining phase-field modeling and in situ tomography

Alloys corroding in molten salt have been observed to form bicontinuous, nanoporous microstructures via dealloying, which subsequently undergo coarsening due to facile transport in high-temperature conditions. In this work, we describe a methodology to elucidate the underlying transport mechanisms during coarsening of a bicontinuous microstructure via quantitative comparisons between phase-field simulations and four-dimensional in situ experiments, in this case X-ray nanotomography of the coarsening of a dealloyed 80 wt% Ni-20 wt% Cr microwire in molten KCl-MgCl 2 at 800°C. We conduct phase-field simulations initialized from experimental data to model coarsening via three different transport mechanisms: surface diffusion, solid bulk diffusion, and liquid bulk diffusion. These simulations reproduce key features of the experiment, such as the densification of the outer layer of the dealloyed wire and the reduction in radius over time. We quantitatively compare different microstructural characteristics between the simulations and experiment and extract temporal scaling factors that optimally match the time scales of the simulations to that of the experiment. This allows us to evaluate morphological similarity between the simulations and experiment and relate the experimental coarsening kinetics to fundamental material properties. We find that surface diffusion is most likely to be the dominant coarsening mechanism, and its kinetics imply a surface diffusivity of D S = 8.9 x 10 -20 m 3 /s, which is within the range of reported values for Ni-vacuum interfaces at 800°C. However, the difference between the experiment and the surface diffusion simulation increases substantially at late times, suggesting that other mechanisms, such as the dissolution of residual Cr, may be at play.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A probabilistic-phase field model for the fracture of brittle materials

Abstract We develop a computational method to determine the failure probability of brittle materials under general mechanical loading conditions. The method is a combination of two parts: (1) numerical simulations of materials with multiple cracks using phase field theory, where the complete fracture process is viewed as ‘damage percolation’ along critical paths or clusters of cracks, rather than the traditional weak-link failure mechanism of Weibull, and (2) an extension of the Batdorf statistical theory of fracture to finite domains, where it is implemented within the finite element framework. The results of phase-field simulations at the ‘percolation threshold’ are used as failure data in the Batdorf theory to determine the overall probability of failure. The input to this approach is the size distribution of cracks in a pristine material. An example is shown, where alumina samples that were previously tested by Abe and coworkers (Abeet al2003J. Am. Ceram. Soc.861019–21) in four-point loading are compared to the results of our numerical simulations. The approach developed here has the advantage of being extendable to more complex thermomechanical loading.

Materials Science↗
DOE OSTI2024

Phase Field Modeling of Pressure Induced Densification in Solid Electrolytes

Adoption of dense and homogeneous solid electrolytes can possibly mitigate the propagation of lithium dendrites and enable lithium metal anodes. Application of external pressure helps to minimize the sintering temperature in oxide ceramics and can potentially densify softer sulfide electrolytes even under room temperature conditions. Here, a previously developed phase field-based computational scheme for predicting the high-temperature sintering-induced densification of oxide ceramic solid electrolytes is extended in the present context to capture the influence of external pressure for densifying solid electrolytes. Two different bulk deformation mechanisms, namely, "reorganization" and "creep deformation," are dominant under external pressure, which is different from the surface and grain-boundary diffusion-induced densification of solid electrolytes that occurs during high temperature sintering. External pressure also increases the points of contact between the particles, which further enhances the propensity of diffusion-induced sintering process. Results obtained from simulations indicate that densification under external pressure is independent of the solid electrolyte particle morphology. Finally, a phase map is generated between applied pressure and temperature for achieving complete densification of oxide ceramics, which can possibly guide the synthesis of thin and dense solid electrolyte separators.

25 ENERGY STORAGE↗
DOE OSTI2023

Phase field modeling of shearing processes of a dual-lobed γ"|γ'|γ" coprecipitate

The Ni-based superalloy IN718 is one of the most widely used commercial alloy in the aerospace industry since its development in 1960s. The excellent mechanical properties have been attributed in a great deal to strengthening by coherent γ' and γ" precipitates. The deformation mechanisms of these two phases have been well studied individually. Recent experimental characterization has shown coprecipitates of these two phases in a variety of morphologies and it was argued that these coprecipitates may lead to improved strengthening as compared to their monolithic counterparts. However, the deformation mechanisms of these coprecipitates are still not well understood. In this study, we performed microscopic phase field simulations, with generalized-stacking-fault (GSF) energy surfaces from ab initio calculations as inputs, to systematically study the shearing processes of a periodical array of dual-lobed coprecipitates as well as monolithic precipitates. We found that the coupling between the γ' and γ" phases in the coprecipitates forces dislocations to take high energy shearing pathways in both phases that would not occur if they were in monolithic forms. The coupling also creates stacking fault configurations in the coprecipitates that require high stress to form. Thus, the presence of coprecipitates in general should increase the resistance to dislocation shearing and lead to higher strength levels. Various fault configurations observed during the shearing process are documented as a reference for future comparison with experimental observations. The link between stacking fault shearing and microtwinning is also discussed. Here, the mechanisms analyzed in this study deepens our understanding of coprecipitation effects on alloy strength and may form a cornerstone for multi-precipitate strengthened alloy design strategies.

36 MATERIALS SCIENCE↗
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.↗
DOE OSTI2024

Phase-Field Model Incorporating Large Inelastic Strain with Application to the Oxidation of High-Temperature Coating Systems

Structural metallic and ceramic materials at high temperatures often suffer from creep, fatigue and oxidation, which typically involves local large inelastic strain. The large strain is usually approached by Lagrangian-description-based finite deformation theory. Here we develop an efficient, Eulerian-description-based, Incremental Realization of Inelastic Deformation (IRID) algorithm to deal with large inelastic strain with small elastic strain. We apply this algorithm to simulate high temperature oxidation with severe volume expansion using a phase-field approach. The oxidation and deformation of bond coat can lead to spallation and failure of the thermal barrier coatings (TBC) and environmental barrier coatings (EBC), which is a critical concern in design of these coatings. We simulate the growth of thermally grown oxide (TGO) in these coating systems, with phase transformations and microstructure evolution incorporated. The simulation results are compared with relevant experimental reports in the literature.

Cheng, Tianle↗
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 OSTI2020

Structure and Dynamics of Domains in Ferroelectric Nanostructures – Phase-Field Modeling (Final Technical Report)

Domain pattern formation is one of the most common phenomena in nature and is a topic of immense interest in many fields ranging from materials science and physics to chemistry and biology. This DOE sponsored research project explored the basic science concerning the thermodynamic stability of mesoscale polarization domain patterns and their temporal evolution mechanisms during formation and subsequent switching in ferroelectric nanostructures and heterostructures. The project employed the computational phase-field method in combination of microelasticity and electrostatic theories. The research was carried out in close collaboration with a number of experimental groups who used High Resolution Transmission Electron Microscopy (HRTEM), in situ TEM with Scanning Probe Microscopy (SPM), or Piezoresponse Force Microscopy (PFM) to characterize the domain structures and dynamics of ferroelectric thin films and heterostructures and who grow high-quality ferroelectric and multiferroic thin films using advanced growth techniques such as Molecular Beam Epitaxy (MBE), Pulsed Laser Deposition (PLLD), and sputtering. The research efforts of the project help establish the phase-field method as the most powerful method for understanding and predicting domain structures in ferroelectric thin films and nanostructures. The findings of the project led to the basic understanding of stability and switching mechanisms of ferroelectric domains under different mechanical boundary conditions and under either homogeneous capacitor configurations or local fields using metallic probes as electrodes and the emergence of charged domain walls during domain switching. The project predicted the spatial length scales, temperature ranges, and electromechanical conditions for different polar states in heterostructures and guided the discovery of both transient and stable novel polarization states containing vortex lattices in oxide superlattices. The project resulted in 134 journal publications and 6 PhD theses with all the PhD graduates currently working in either academia or industry within the United States. The basic understanding on the stability of mesoscale polar states and pattern evolution achieved by the project improved our ability to control and engineer properties of ferroelectric thin films and heterostructures for potential applications in nanoscale electronic devices.

36 MATERIALS SCIENCE↗