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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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All sourcesNASA NTRSDOE OSTI
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 OSTI2018

Liquidus temperature in the spinel primary phase field: A comparison between optical and crystal fraction methods

Liquidus temperature (TL) was measured for simulated high-level waste borosilicate glasses covering a Hanford composition region, using an optical method and a crystal-fraction extrapolation method with X-ray diffraction data from isothermal heat treatments. The 38 glasses encompassed a one-component-at-a-time variation of a 16-component matrix. The TL values ranged from 1006°C to 1603°C. First-order polynomial models were fitted to data to obtain coefficients in terms of the effect of 1 mass% component addition on the TL: TL-increasing oxides Cr2O3 (264°C), “Others” (minor components, 163°C), oxides of noble metals (137°C), NiO (91°C), Al2O3 and Fe2O3 (~19–21°C); TL-decreasing oxides K2O (-26°C), Na2O (-41°C), and Li2O (-68°C); oxides of little effect MnO, P2O5, ZrO2, F, Bi2O3, SiO2, B2O3, and CaO (9 to -12°C). Also presented are temperatures (T1%) at which glasses contain 1 vol% of spinel as these values are considered relevant to the Hanford Tank Waste Treatment and Immobilization Plant. The measured and estimated values are compared and contrasted and the effect of TL and T1% on glass formulation is discussed.

crystal fraction↗
DOE OSTI2016

Atomic density functional and diagram of structures in the phase field crystal model

The phase field crystal model provides a continual description of the atomic density over the diffusion time of reactions. We consider a homogeneous structure (liquid) and a perfect periodic crystal, which are constructed from the one-mode approximation of the phase field crystal model. A diagram of 2D structures is constructed from the analytic solutions of the model using atomic density functionals. The diagram predicts equilibrium atomic configurations for transitions from the metastable state and includes the domains of existence of homogeneous, triangular, and striped structures corresponding to a liquid, a body-centered cubic crystal, and a longitudinal cross section of cylindrical tubes. The method developed here is employed for constructing the diagram for the homogeneous liquid phase and the body-centered iron lattice. The expression for the free energy is derived analytically from density functional theory. The specific features of approximating the phase field crystal model are compared with the approximations and conclusions of the weak crystallization and 2D melting theories.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

3D Ferroelectric Phase Field Simulations of Polycrystalline Multi‐Phase Hafnia and Zirconia Based Ultra‐Thin Films

Abstract HfO 2 – and ZrO 2 –based ferroelectric thin films have emerged as promising candidates for the gate oxides of next‐generation electronic devices. Recent work has experimentally demonstrated that a tetragonal/orthorhombic (t/o‐) phase mixture with partially in‐plane polarization can lead to negative capacitance (NC) stabilization. However, there is a discrepancy between experiments and the theoretical understanding of domain formation and domain wall motion in these multi‐phase, polycrystalline materials. Furthermore, the effect of anisotropic domain wall coupling on NC has not been studied so far. Here, 3D phase field simulations of HfO 2 – and ZrO 2 –based mixed‐phase ultra‐thin films on silicon are applied to understand the necessary and beneficial conditions for NC stabilization. It is found that smaller ferroelectric grains and a larger angle of the polar axis with respect to the out‐of‐plane direction enhances the NC effect. Furthermore, it is shown that theoretically predicted negative domain wall coupling even along only one axis prevents NC stabilization. Therefore, it is concluded that topological domain walls play a critical role in experimentally observed NC phenomena in HfO 2 – and ZrO 2 –based ferroelectrics.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2015

A parallel domain decomposition-based implicit method for the Cahn–Hilliard–Cook phase-field equation in 3D

We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn–Hilliard–Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton–Krylov–Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracy (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A phase-field model for non-isothermal phase transformation and plasticity in polycrystalline yttria-stabilized tetragonal zirconia

Here we propose an elastoplastic phase-field (PF) model to investigate the mechanics of tetragonal-to-monoclinic phase transformation (TMPT) and elastoplastic deformation of polycrystalline yttria-stabilized tetragonal zirconia (YSTZ). A Landau polynomial with non-vanishing chemical energy at the equilibrium temperature is introduced to account for the actual formation energies of the phases. The effects of different grain orientations, latent heat, and temperature on TMPT and deformation mechanisms are considered. The suppressive transformation effects of the grain boundaries (GBs) is modeled using an inhomogeneous kinetic coefficient in the bulk and GBs. The simulation results for single crystals demonstrate the capability of the model to reproduce the orientation-dependent compressive deformation of YSTZ similar to atomistic simulations and micropillar experiments. The single crystal with [100] crystallographic orientation along the loading direction (SC[100]) displays both TMPT and plasticity, SC[101] experiences only phase transformation, while SC[001] undergoes only plastic yielding. The TMPT induced by compressive loading exhibits shape memory effect (SME) below the equilibrium transformation temperature and pseudoelasticity above it, while the critical transformation stress increases with increasing loading temperature. The irrecoverable plastic strain is found to trap a part of the monoclinic phase, which prevents a complete reverse transformation. The polycrystalline cases also display SME and PE at low and high temperatures, respectively. Due to the orientation differences between grains and the stress concentrations at geometric nonlinearities, plastic deformation occurs in polycrystalline YSTZ for an applied load less than the yield stress. The results suggest a possible limitation of plasticity and an improvement of the shape recovery of YSTZ if one can control the orientation of the grains and/or increase the density of stacking faults at the GBs during material processing.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model

This work presents phase field fracture modeling in heterogeneous porous media. We develop robust and efficient numerical algorithms for pressure-driven and fluid-driven settings in which the focus relies on mesh adaptivity in order to save computational cost for large-scale 3D applications. In the fluid-driven framework, we solve for three unknowns pressure, displacements and phase field that are treated with a fixed-stress iteration in which the pressure and the displacement–phase-field system are decoupled. The latter subsystem is solved with a combined Newton approach employing a primal–dual active set method in order to account for crack irreversibility. Numerical examples for pressurized fractures and fluid filled fracture propagation in heterogeneous porous media demonstrate our developments. Finally in particular, mesh refinement allows us to perform systematic studies with respect to the spatial discretization parameter.

42 ENGINEERING↗