SEARCH · Engineering Papers

Results for “phase field models”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

All sources NASA NTRS DOE OSTI

DOE OSTI2019

Phase-field modeling of stacking structure formation and transition of δ-hydride precipitates in zirconium

d-hydride structures in Zr nuclear fuel-rod cladding significantly affect mechanical properties. In this work, a micromechanical phase-field model is developed to investigate the effect of interfacial energy anisotropy and elastic interaction on the nucleation, stacking structure formation, and stacking structure transition of d-hydride precipitates. It is found that the nucleation probability and growth of d-hydride near pre-existing hydrides are strongly spatially dependent. Results show that (1) the d-hydride precipitate has a platelet-like shape. The large shear deformation associated with lattice mismatches and a small interfacial energy of its broad interface cause the orientation of the plate-like d-hydride off the basal plane a small angle of approximately 14.7°. (2) Stress-induced nucleation of d-hydride precipitates near a pre-existing hydride results in the unique stacking structure formation of d-hydride precipitates. (3) The morphology and alignment of hydride stacking structures, called as macroscopic hydrides which consist of microscopic hydrides with certain stacking sequences, change under stresses. The alignment of macroscopic hydrides changes from along the circumferential direction to along the radial direction under tensile hoop stress while the orientation of microscopic hydrides remains parallel to the basal plane. These results are in agreement with experimental observations. The simulations reveal that stress-induced heterogeneous nucleation and growth is the mechanism for the formation and transition of unique macro-hydride stacking structures observed in in Zr nuclear fuel-rod cladding.

Han, G. M.↗

DOE OSTI2017

A Rate-Theory–Phase-Field Model of Irradiation-Induced Recrystallization in UMo Nuclear Fuels

Experiments showed that recrystallization dramatically speeds up the gas bubble swelling kinetics in metallic UMo fuels. In this work a recrystallization model is developed to study the effect of microstructures and radiation conditions on recrystallization kinetics. The model integrates the rate theory of intra-granular gas bubble and interstitial loop evolution and a phase field model of recrystallization zone evolution. A fast passage method is employed to describe one dimensional diffusion of interstitials which have diffusivity several order magnitude larger than that of the fission gas Xe. With the model, the effect of grain sizes on recrystallization kinetics is simulated.

Hu, Shenyang↗

DOE OSTI2015

Brittle fracture phase-field modeling of a short-rod specimen

Predictive simulation capabilities for modeling fracture evolution provide further insight into quantities of interest in comparison to experimental testing. Based on the variational approach to fracture, the advent of phase-field modeling achieves the goal to robustly model fracture for brittle materials and captures complex crack topologies in three dimensions.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Phase field modeling of dislocations and obstacles in InSb

We present a phase-field dislocation dynamics (PFDD) model informed by first-principle calculations to elucidate the competitive dislocation nucleation and propagation between the glide and shuffle sets in InSb diamond cubic crystal. The calculations are directly informed with generalized stacking fault energy curves on the (111) slip plane for both the “glide set,” with the smaller interplanar spacing, and the “shuffle set,” with the larger interplanar spacing. The formulation also includes elastic anisotropy and the gradient term associated with the dislocation core. The PFDD calculations show that under no stress the equilibrium structure of screw glide set dislocations dissociates into Shockley partials, while those of the shuffle set dislocations do not dissociate, remaining compact. The calculated dislocation core widths of these InSb dislocations agree well with the measured values for other semiconductor materials, such as Si and GaN. We find that a shuffle set dislocation emits from a dislocation source at an applied stress about three times smaller than that needed to emit leading and trailing partials successively on the glide set plane. Once the partial dislocations in the glide set are emitted, they propagate faster than the shuffle set perfect dislocation at the same stress level.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Phase-field modeling of alloy oxidation at high temperatures

Oxide growth is a complex process involving transport of reactive species, heterogeneous reactions, and microstructure evolution. Predicting oxidation kinetics and especially the oxide morphological change has been a long-standing challenge. Here we develop a phase-field model for predicting the oxide growth kinetics of a multicomponent alloy during high temperature oxidation, focusing on internal oxidation (non-protective) and its transition to external oxidation (protective). In this work, the predicted kinetics and oxide morphology are analyzed and compared to the classical Wagner’s theory and an existing analytical model by Zhao and Gleeson. Some assumptions used in the analytical models and the limitation are discussed. In addition, it is demonstrated that the morphology and distribution of the initial oxide nuclei play an important role in the later stage oxide connectivity and thus the transition to external oxidation.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Phase Field Modeling of Corrosion for Design of Next-Generation Magnesium-Aluminum Vehicle Joints

In this study, WPI and its partners sought to understand galvanic corrosion in Mg-Al friction stir weld (FSW) joints. Unlike fusion welds, FSW is done in the solid state. This limits (but does not eliminate) the formation of brittle Al-Mg intermetallics, resulting in better joint strength and corrosion resistance. This study aimed to understand corrosion behavior of Mg-Al FSW joints by using a Cahn-Hilliard phase field electrochemistry model based on the work of Pongsaksawad et al. Its context challenge problem was an ultra-light door designed by Magna with 6061-Al sheet outer and ZEK100-Mg sheet inner panels, joined by an adhesive and FSW. Unlike most FSW joints, which weld through the softer material into the harder one, the Al sheet’s hem joint around Mg required the FSW tool to through the harder Al into the softer Mg, which was itself a challenge. Despite this challenge, PNNL succeeded in consistently making very strong FSW lap joints, by using a triflute tool and power control. Characterization showed mostly separate Al and Mg regions in the weld, usually with a hook protruding from Al into Mg, which likely contributed to high joint strength. Nanohardness mapping showed higher hardness in thin Mg swirls into the Al nugget, likely due to the intermetallics. The study used the industry standard SAE J2334 Cyclic Corrosion Test (CCT) to simulate corrosion conditions over the life of a vehicle, as well as linear polarization testing and ASTM G71 pitting corrosion testing. Corrosion reactions were: H 2 O + ½O 2 + 2e - → 2OH - at the Al cathode, and either Mg → Mg 2+ + 2e - or Mg + 2OH - → Mg(OH) 2 + 2e - at the Mg anode, with electron transfer through the joint. Mass loss increased with Al section length, supporting the hypothesis that galvanic corrosion in Al-Mg joints is limited by the cathodic reaction. Both pitting corrosion (first anode reaction) and hydroxide film formation (second reaction) were observed. The J2334 CCT test method was slightly modified, adding a chromium solution cleaning step after each week of corrosion testing, in order to remove Mg oxides and hydroxides and accurately measure mass loss over time. That said, FSW joints treated in this way did not did not exhibit significant reduction in lap shear strength of the joints vs. newly welded samples which had not undergone corrosion. Corrosion appeared to consist mainly of pitting in Mg in a way which did not directly affect the bond between the materials where the joints failed. A Cahn-Hilliard phase field model coupled with electrical potential described the electronically mediated galvanic corrosion electrochemical reactions described above in the four-component Al-Mg-H 2 O-(H 2 O+½O 2 ) system. This 2-D model successfully predicted Mg(OH)₂ formation at the anode in some circumstances, and Mg pitting corrosion in others, and showed the correct electric field directions in both cases. The model predicted Mg pit corrosion depth within a factor of two of measured pits.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2014

Phase-field modeling of switchable diode-like current-voltage characteristics in ferroelectric BaTiO{sub 3}

A self-consistent model has been proposed to study the switchable current-voltage (I-V) characteristics in Cu/BaTiO{sub 3}/Cu sandwiched structure combining the phase-field model of ferroelectric domains and diffusion equations for ionic/electronic transport. The electrochemical transport equations and Ginzburg-Landau equations are solved using the Chebyshev collocation algorithm. We considered a single parallel plate capacitor configuration which consists of a single layer BaTiO{sub 3} containing a single tetragonal domain orientated normal to the plate electrodes (Cu) and is subject to a sweep of ac bias from −1.0 to 1.0 V at 25 °C. Our simulation clearly shows rectifying I-V response with rectification ratios amount to 10{sup 2}. The diode characteristics are switchable with an even larger rectification ratio after the polarization direction is flipped. The effects of interfacial polarization charge, dopant concentration, and dielectric constant on current responses were investigated. The switchable I-V behavior is attributed to the polarization bound charges that modulate the bulk conduction.

36 MATERIALS SCIENCE↗

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↗

DOE OSTI2021

Kinetics of solid–liquid interface motion in molecular dynamics and phase-field models: crystallization of chromium and silicon

The results of molecular dynamics (MD) simulations of the crystallization process in one-component materials and solid solution alloys reveal a complex temperature dependence of the velocity of the crystal–liquid interface featuring an increase up to a maximum at 10–30% undercooling below the equilibrium melting temperature followed by a gradual decrease of the velocity at deeper levels of undercooling. At the qualitative level, such non-monotonous behaviour of the crystallization front velocity is consistent with the diffusion-controlled crystallization process described by the Wilson–Frenkel model, where the almost linear increase of the interface velocity in the vicinity of melting temperature is defined by the growth of the thermodynamic driving force for the phase transformation, while the decrease in atomic mobility with further increase of the undercooling drives the velocity through the maximum and into a gradual decrease at lower temperatures. At the quantitative level, however, the diffusional model fails to describe the results of MD simulations in the whole range of temperatures with a single set of parameters for some of the model materials. The limited ability of the existing theoretical models to adequately describe the MD results is illustrated in the present work for two materials, chromium and silicon. It is also demonstrated that the MD results can be well described by the solution following from the hodograph equation, previously found from the kinetic phase-field model (kinetic PFM) in the sharp interface limit. The ability of the hodograph equation to describe the predictions of MD simulation in the whole range of temperatures is related to the introduction of slow (phase field) and fast (gradient flow) variables into the original kinetic PFM from which the hodograph equation is obtained. The slow phase-field variable is responsible for the description of data at small undercoolings and the fast gradient flow variable accounts for local non-equilibrium effects at high undercoolings. The introduction of these two types of variables makes the solution of the hodograph equation sufficiently flexible for a reliable description of all nonlinearities of the kinetic curves predicted in MD simulations of Cr and Si. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

Science & Technology - Other Topics↗

DOE OSTI2021

Wide-blocky veins explained by dependency of crystal growth rate on fracture surface type: Insights from phase-field modeling

Vein microstructures contain a wealth of information on coupled chemical and mechanical processes of fracturing, fluid transport, and crystal growth. Numerical simulations have been used for exploring the factors controlling the development of vein microstructures; however, they have not been quantitatively validated against natural veins. Here we combined phase-field modeling with microtextural analysis of previously unexplained wide-blocky calcite veins in natural limestone and of the fresh fracture surface in this limestone. Results show that the wide-blocky vein textures can only be reproduced if ~10%–20% of crystals grow faster than the rest. This fraction corresponds to the amount of transgranularly broken grains that were observed on the experimental fracture surfaces, which are dominantly intergranular. We hypothesize that transgranular fractures allow faster growth of vein minerals due to the lack of clay coatings and other nucleation discontinuities that are common along intergranular cracks. Our simulation results show remarkable similarity to the natural veins and reproduce the nonlinear relationship between vein crystal width and vein aperture. This allows accurate simulations of crystal growth processes and related permeability evolution in fractured rocks.

Geology↗

DOE OSTI2025

Thermo-Mechanical Phase-Field Modeling of Fracture in High-Burnup UO2 Fuels Under Transient Conditions

This study presents a novel multiphysics phase-field fracture model to analyze high-burnup uranium dioxide (UO2) fuel behavior under transient reactor conditions. Fracture is treated as a stochastic phase transition, which inherently accounts for the random microstructural effects that lead to variations in the value of fracture strength. Moreover, the model takes into consideration the effects of temperature and burnup on thermal conductivity. Therefore, the model is able to predict crack initiation, propagation, and complex morphologies in response to thermal gradients and stress distributions. Several simulations were conducted to investigate the effects of operational and transient conditions on fracture behavior and the resulting cracking patterns. High-burnup fuels exhibit reduced thermal conductivity, elevating temperature gradients and resulting in extensive radial and circumferential cracks. Transient heating rates and temperatures significantly affect fracture patterns, with higher heating rates generating steeper gradients and more irregular crack trajectories. This approach provides critical insights into fuel integrity during accident scenarios and supports the safety evaluation of extended burnup limits.

Chemistry↗

DOE OSTI2017

Quantification of flexoelectricity in PbTiO 3 /SrTiO 3 superlattice polar vortices using machine learning and phase-field modeling

Flexoelectricity refers to electric polarization generated by heterogeneous mechanical strains, namely strain gradients, in materials of arbitrary crystal symmetries. Despite more than 50 years of work on this effect, an accurate identification of its coupling strength remains an experimental challenge for most materials, which impedes its wide recognition. Here, we show the presence of flexoelectricity in the recently discovered polar vortices in PbTiO 3 /SrTiO 3 superlattices based on a combination of machine-learning analysis of the atomic-scale electron microscopy imaging data and phenomenological phase-field modeling. By scrutinizing the influence of flexocoupling on the global vortex structure, we match theory and experiment using computer vision methodologies to determine the flexoelectric coefficients for PbTiO 3 and SrTiO 3 . Here, our findings highlight the inherent, nontrivial role of flexoelectricity in the generation of emergent complex polarization morphologies and demonstrate a viable approach to delineating this effect, conducive to the deeper exploration of both topics.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Pressure-induced switching in ferroelectrics: Phase-field modeling, electrochemistry, flexoelectric effect, and bulk vacancy dynamics

Pressure-induced polarization switching in ferroelectric thin films has emerged as a powerful method for domain patterning, allowing us to create predefined domain patterns on free surfaces and under thin conductive top electrodes. However, the mechanisms for pressure-induced polarization switching in ferroelectrics remain highly controversial, with flexoelectricity, polarization rotation and suppression, and bulk and surface electrochemical processes all being potentially relevant. Here we classify possible pressure-induced switching mechanisms, perform elementary estimates, and study in depth using phase-field modeling. Finally, we show that magnitudes of these effects are remarkably close and give rise to complex switching diagrams as a function of pressure and film thickness with nontrivial topology or switchable and nonswitchable regions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Local and nonlocal phase-field models of tumor growth and invasion due to ECM degradation

We present and analyze new multi-species phase-field mathematical models of tumor growth and ECM invasion. The local and nonlocal mathematical models describe the evolution of volume fractions of tumor cells, viable cells (proliferative and hypoxic cells), necrotic cells, and the evolution of matrix-degenerative enzyme (MDE) and extracellular matrix (ECM), together with chemotaxis, haptotaxis, apoptosis, nutrient distribution, and cell-to-matrix adhesion. We provide a rigorous proof of the existence of solutions of the coupled system with gradient-based and adhesion-based haptotaxis effects. In addition, we discuss finite element discretizations of the model, and we present the results of numerical experiments designed to show the relative importance and roles of various effects, including cell mobility, proliferation, necrosis, hypoxia, and nutrient concentration on the generation of MDEs and the degradation of the ECM.

Mathematics↗

DOE OSTI2022

Phase-field modeling of crack growth and mitigation in solid oxide cells

Fracture and crack growth is one of the main degradation mechanisms in solid oxide cells (SOCs). However, the modeling of crack growth in SOCs is challenging due to their complex microstructures and possible plasticity development within the Ni particles in Ni-based SOC electrodes. In this study, a phase-field fracture model is developed, which incorporates the SOC microstructures and phase-dependent material properties, including yield strength, fracture toughness in the bulk and at the interphase boundaries. The model is employed to study crack initiation and growth under thermal and redox cycling on the hydrogen electrode side of SOCs. The simulation results demonstrate that under thermal cycling, work-zone cracking dominates in electrolyte-supported SOCs with cracks initiated at the triple-phase boundaries, while only minor mechanical degradation occurs in hydrogen-electrode-supported SOCs after hundreds of thermal cycles. Under redox cycling, through-cracking of yttria-stabilized zirconia (YSZ) in the hydrogen electrode and electrolyte layers dominates. Finally, the simulation results suggest several crack-mitigation strategies, including decreasing the porosity in the hydrogen electrode support layer and synchronizing thermal strain to balance oxidation strain.

08 HYDROGEN↗

DOE OSTI2021

A multi-phase-field model of topological pattern formation during electrochemical dealloying of binary alloys

Porous metal structures produced by electrochemical dealloying have been extensively studied for use in various applications that require high surface areas. A new comprehensive multi-phase-field (MPF) model is proposed to study topological porous patterns formed by spontaneously etching a bulk binary alloy that involves electrochemical reactions, bulk and surface diffusion, ion transport, applied electrode potential, and charge conservation. The governing equations for the alloy-porous cluster-electrolyte system account for a generalized Butler-Volmer electrochemical reaction and are in accordance with the classical nucleation theory. Based on a quantitative examination of the effects of electrode potential and precursor composition, the simulation results reproduce typical phenomena including passive surface dealloying, active porosity evolution, critical potential, and characteristic length scale in two-dimension (2-D) and three-dimension (3-D). To consider more complicated dealloying systems, the evolutions of a bimodal porous metal structure, nanocomposite, and nested porous network with a structured hierarchy are investigated. Finally, the proposed model can be a useful tool for understanding and predicting the morphology evolution of diverse porous structures during electrochemical dealloying.

Hierarchical porous structure↗

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↗