Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Phase-field fracture”

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.

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

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A multi-resolution approach to hydraulic fracture simulation

Abstract We present a multi-resolution approach for constructing model-based simulations of hydraulic fracturing, wherein flow through porous media is coupled with fluid-driven fracture. The approach consists of a hybrid scheme that couples a discrete crack representation in a global domain to a phase-field representation in a local subdomain near the crack tip. The multi-resolution approach addresses issues such as the computational expense of accurate hydraulic fracture simulations and the difficulties associated with reconstructing crack apertures from diffuse fracture representations. In the global domain, a coupled system of equations for displacements and pressures is considered. The crack geometry is assumed to be fixed and the displacement field is enriched with discontinuous functions. Around the crack tips in the local subdomains, phase-field sub-problems are instantiated on the fly to propagate fractures in arbitrary, mesh independent directions. The governing equations and fields in the global and local domains are approximated using a combination of finite-volume and finite element discretizations. The efficacy of the method is illustrated through various benchmark problems in hydraulic fracturing, as well as a new study of fluid-driven crack growth around a stiff inclusion.

58 GEOSCIENCES↗
DOE OSTI2024

Arbitrary Order Virtual Element Methods for High‐Order Phase‐Field Modeling of Dynamic Fracture

ABSTRACT Accurate modeling of fracture nucleation and propagation in brittle and ductile materials subjected to dynamic loading is important in predicting material damage and failure under extreme conditions. Phase‐field fracture models have garnered a lot of attention in recent years due to their success in representing damage and fracture processes in a wide class of materials and under a variety of loading conditions. Second‐order phase‐field fracture models are by far the most popular among researchers (and increasingly, among practitioners), but fourth‐order models have started to gain broader acceptance since their more recent introduction. The exact solution corresponding to these high‐order phase‐field fracture models has higher regularity. Thus, numerical solutions of the model equations can achieve improved accuracy and higher spatial convergence rates. In this work, we develop a virtual element framework for the high‐order phase‐field model of dynamic fracture. The virtual element method (VEM) can be regarded as a generalization of the classical finite element method. In addition to many other desirable characteristics, the VEM allows computing on polytopal meshes. Here, we use ‐conforming virtual elements and the generalized‐ time integration method for the momentum balance equation, and adopt ‐conforming virtual elements for the high‐order phase‐field equation. We verify our virtual element framework using classical quasi‐static benchmark problems and demonstrate its capabilities with the aid of numerical simulations of dynamic fracture in brittle materials.

42 ENGINEERING↗
DOE OSTI2020

Vulnerable window of yield strength for swelling-driven fracture of phase-transforming battery materials

Abstract Despite numerous experimental and theoretical investigations of the mechanical behavior of high-capacity Si and Ge Li-ion battery anodes, our basic understanding of swelling-driven fracture in these materials remains limited. Existing theoretical studies have provided insights into elasto-plastic deformations caused by large volume change phase transformations, but have not modeled fracture explicitly beyond Griffith’s criterion. Here, we use a multi-physics phase-field approach to model self-consistently anisotropic phase transformation, elasto-plastic deformation, and crack initiation and propagation during lithiation of Si nanopillars. Our computational results reveal that fracture occurs within a “vulnerable window” inside the two-dimensional parameter space of yield strength and fracture energy and highlight the importance of taking into account the surface localization of plastic deformation to accurately predict the magnitude of tensile stresses at the onset of fracture. They further demonstrate how the increased robustness of hollow nanopillars can be understood as a direct effect of anode geometry on the size of this vulnerable window. Those insights provide an improved theoretical basis for designing next-generation mechanically stable phase-transforming battery materials undergoing large volume changes.

25 ENERGY STORAGE↗
DOE OSTI2024

Phase-field modeling of thermally-grown oxide and damage evolution in environmental barrier coatings

Silicon carbide-based ceramic matrix composites protected by environmental barrier coatings (EBCs) present a promising materials solution for next-generation gas turbines. Developing more robust and efficient EBCs is therefore of significant technological importance. During the service in high-temperature oxidative environments, there is a thermally grown oxide (TGO) layer, spontaneously formed in the EBC system. TGO is recognized as a critical factor for the degradation and failure of EBCs, yet the detailed mechanisms of TGO growth and its effect on EBC failure remain unclear. In this study we develop a comprehensive chemo-mechano-phase-field model to simulate growth of the TGO in EBCs, factoring in creep and deformation, and especially the cracking behaviors. The volume expansion due to TGO growth and the resulting large inelastic deformation are addressed by using our recently developed, so-called incremental realization of inelastic deformation (IRID) algorithm, in combination with an adapted Hu-Chen spectral solver for elasticity. Simulations of TGO growth are performed considering different growth modes of TGOs determined mainly by the ratio of oxidant permeability in the topcoat to that in the TGO itself. Large-scale three-dimensional (3D) simulations are performed to model the formation of interconnecting vertical/channel cracks (often called ‘mud cracks’). The simulated crack morphology are in excellent agreement with the experimental observations from the literature. The simulations also provide insights into the cracking of EBCs and its dependence on the structure and constituent properties of the coating system. Furthermore, these results demonstrate the developed damage model can be a useful tool for design of more durable EBCs.

Cracking↗
DOE OSTI2023

Topology-enhanced mechanical stability of swelling nanoporous electrodes

Abstract Materials like silicon and germanium offer a 10-fold improvement in charge capacity over conventional graphite anodes in lithium-ion batteries but experience a roughly threefold volume increase during lithiation, which challenges ensuring battery integrity. Nanoporous silicon, created by liquid-metal-dealloying, is a potentially attractive anode design to mitigate this challenge, exhibiting both higher capacity and extended cycle lifetimes. However, how nanoporous structures accommodate the large volume change is unknown. Here, we address this question by using phase-field modeling to produce nanoporous particles and to investigate their elastoplastic swelling behavior and fracture. Our simulations show that enhanced mechanical stability results from the network topology consisting of ligaments connected by bulbous, sphere-like nodes. The ligaments forcefully resist elongation while the nodes, behaving like isolated spherical particles, experience large stresses driving fracture. However, being smaller compared to a sphere of the same volume as the entire nanoporous particle, the nodes are more protected against fracture.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Scale-bridging with the extended/generalized finite element method for linear elastodynamics

This paper presents an extended/generalized finite element method for bridging scales in linear elastodynamics in the absence of scale separation. More precisely, the GFEMgl framework is expanded to enable the numerical solution of multiscale problems through the automated construction of specially-tailored shape functions, thereby enabling high-fidelity finite element modeling on simple, fixed finite element meshes. Furthermore, this introduces time-dependencies in the shape functions in that they are subject to continuous adaptation with time. The temporal aspects of the formulation are investigated by considering the Newmark-β time integration scheme, and the efficacy of mass lumping strategies is explored in an explicit time-stepping scheme. This method is demonstrated on representative wave propagation examples as well as a dynamic fracture problem to assess its accuracy and flexibility.

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 OSTI2023

Multiscale modeling for high burnup structure formation and associated pulverization

This report summarizes the lower length scale modeling work performed in the fiscal year 2023 under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program to capture the microstrutural evolution and associated pulverization criteria in the high burnup regions. This year, the resolution mechanisms within the cluster dynamics code has been updated and it influence on the bubble growth in HBS regions at the mesoscale is studied. To improve the accuracy of phase-field models of fission gas bubble growth, a new Helmholtz free energy for high-density Xe gas is derived from a virial equation of state. Two previously used strategies for representing net vacancy production in phase-field models of fission gas bubble growth are compared with each other and with analytical models of bubble growth. The vacancy source only model is found to be more convenient to parameterize realistically compared with the vacancy source+sink model. Furthermore, the phase-field-fracture simulation have been performed using MD- informed failure stress values and realistic HBS structure obtained from the phase-field simulations. We also present the uncertainty bands on prediction of the critical stress to account for the effect of the lower length scale variabilities on the failure criteria at the mesoscale. It is observed that pulverization may occur in partially restructured regions with restructuring fraction as low as 17%. In light of this, an update to the BISON’s pulverization criteria is recommended.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Fracture Dynamics in Silicon Anode Solid-State Batteries

Solid-state batteries (SSBs) with silicon anodes could enable improved safety and energy density compared to lithium-ion batteries. However, degradation arising from the massive volumetric changes of silicon anodes during cycling is not well understood in solid-state systems. Here, we use operando X-ray computed microtomography to reveal micro- to macro-scale chemo-mechanical degradation processes of silicon anodes in SSBs. Mud-type channel cracks driven by biaxial tensile stress form across the electrode during delithiation. We also find detrimental cracks at the silicon/ solid electrolyte interface that form due to local reaction competition between neighboring domains of different sizes. Continuum phase-field damage modeling quantifies stress-driven channel cracking and shows that the lithiated silicon stress state is critical for determining the extent of interfacial fracture. This work reveals the mechanisms that govern SSBs compared to conventional lithium-ion batteries and provides guidelines for engineering chemomechanically resilient electrodes for high-energy batteries.

25 ENERGY STORAGE↗
DOE OSTI2020

An extended/generalized phase-field finite element method for crack growth with global-local enrichment

In this paper, an extended/generalized finite element method (XFEM/GFEM) for simulating quasistatic crack growth based on a phase-field method is presented. The method relies on approximations to solutions associated with two different scales: a global scale, that is, structural and discretized with a coarse mesh, and a local scale encapsulating the fractured region, that is, discretized with a fine mesh. A stable XFEM/GFEM is employed to embed the displacement and damage fields at the global scale. The proposed method accommodates approximation spaces that evolve between load steps, while preserving a fixed background mesh for the structural problem. In addition, a prediction-correction algorithm is employed to facilitate the dynamic evolution of the confined crack regions within a load step. Several numerical examples of benchmark problems in two- and three-dimensional quasistatic fracture are provided to demonstrate the approach.

multiscale↗
DOE OSTI2025

Coupled momentum balance and phase-field solver with fenicsx module

Code solves momentum balance and phase-field equations simultaneously. The differential equations are solved on a discretized domain with appropriate boundary and initial conditions using finite element method. Primary purpose of the code is to simulate brittle fracture under dynamic loading. Constitutive equations are that of linear elasticity with degradation of stress due to fracture. Small strain formulation is used.

Zecevic, Milovan↗
DOE OSTI2023

Utah FORGE 2-2446: Closing the Loop Between In-situ Stress Complexity and EGS Fracture Complexity - Workshop Presentation

This is a presentation on the Closing the Loop Between In-situ Stress Complexity and EGS Fracture Complexity project by Lawrence Livermore National Laboratory, presented by Dr. Matteo Cusini. The project's objective was to employ a combination of high-fidelity simulations and true-triaxial block fracturing tests at high temperature to explore the intricate relationship between in-situ stress and hydraulic fracture patterns and better characterize the in-situ stress at Utah FORGE. This presentation was featured in the Utah FORGE R&D Annual Workshop on September 7, 2023. The workshop provided a valuable opportunity to explore the progress made in each of the 17 Research and Development projects funded under Solicitation 2020-1 which aim to enhance our understanding of the crucial factors influencing the development of Enhanced Geothermal Systems (EGS) reservoirs and resources.

15 GEOTHERMAL ENERGY↗
DOE OSTI2026

Capturing the fractocohesive length scale in elastomers through a statistical mechanics-based gradient enhanced damage model

Here, this study aims to examine modeling flaw sensitivity in elastomers. The direct incorporation of polymer chain statistical mechanics considerations into a continuum stretch-based gradient-enhanced damage formulation, in turn, allows a representation of diffuse chain damage and fracture events that align with known micromechanical mechanisms. Through a series of numerical experiments, we simulate crack propagation and extract the fracture energy as an output of the model, while keeping track of the micromechanical signatures of diffuse chain damage that accommodate fracture propagation and eventually influence flaw sensitivity. Finally, by combining the fracture toughness and the work to rupture, we identify a fractocohesive length of the material, corresponding to the full width of the damage process zone. As the damage-to-fracture cascade in the proposed GED model is influenced by the introduction of a length scale associated with network imperfection and long-range load transfer, the emerging relationship of the two length scales is discussed, providing a potential link between microscopic damage mechanisms and the observed macroscopic fracture response.

36 MATERIALS SCIENCE↗
DOE OSTI2022

The effect of stress on the migration of He gas bubbles under a thermal gradient in Fe by phase-field modeling

Here a phase-field model is parameterized to study the effect of elastic stresses on the migration of He gas bubbles in Fe under a temperature gradient. Stresses caused by the gas bubble pressure and residual stress in the Fe matrix are considered. The dependence of He bubble migration velocity on the magnitude of the residual stress, average temperature, temperature gradient, and bubble size is measured. In agreement with a theoretical model based on surface diffusion, simulation results demonstrate that He bubbles move towards the high temperature region with velocities in Fe that are orders of magnitude faster than previously reported in UO 2 . It is found that local stresses in the matrix caused by the He bubble have negligible effect on the bubble migration process; however, residual stresses in the Fe matrix, potentially caused by processing or irradiation, can modestly modify bubble kinetics through pressure dependence of the He diffusion coefficients. Compressive residual stress decreases diffusion coefficients for bulk and surface diffusion mechanisms, thus reducing the migration velocity of the gas bubble. In contrast, tensile residual stress increases the diffusion coefficients, resulting in an increase in the gas bubble migration velocity. This pressure dependence is also consistent with a theoretical model. This phase field model lays the foundation for analysis of bubble coalescence-induced fracture in He bubble-containing steels.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Surrogate Model Integration with MOOSE XFEM for Creep Crack Growth

Ferritic-martensitic steels are key structural materials for advanced reactors but experience time-dependent deformation and damage under prolonged high temperature and irradiation, leading to creep-driven crack initiation and growth. High-fidelity models—crystal plasticity with irradiation mechanisms, phase-field for microstructural evolution, and continuum-damage viscoplasticity—capture the underlying physics but are too computationally intensive for broad design-space exploration and uncertainty quantification. This milestone advances a scalable alternative by integrating a microstructure-sensitive surrogate creep model into the Multiphysics Object-Oriented Simulation Environment (MOOSE) finite element framework and extending it to fracture via the extended finite element method (XFEM). The surrogate model, developed with collaborators at Sandia and Los Alamos National Laboratories, maps relevant microstructural descriptors to the viscoplastic response of HT9. We embed this surrogate within a coupled deformation-damage workflow in MOOSE/XFEM to simulate creep-driven crack initiation and propagation. Implementation enhancements include updates to the material interface, a plastic correction phase involving microstructure evolution, and fracture criteria to ensure numerical robustness and compatibility with the surrogate structure. Demonstrations on canonical creep benchmarks spanning uniaxial and multiaxial states show that the surrogate reproduces key trends of high-fidelity models while substantially reducing computational cost. The resulting capability bridges physics fidelity and performance, providing a practical path to a predictive, microstructure-aware assessment of creep and fracture in reactor materials.

36 - MATERIALS SCIENCE↗
DOE OSTI2023

Gradient nanostructuring via compositional means

Nanocrystalline metals are inherently unstable against thermal and mechanical stimuli, commonly resulting in significant grain growth. Also, while these metals exhibit substantial Hall-Petch strengthening, they tend to suffer from low ductility and fracture toughness. With regard to the grain growth problem, alloying elements have been employed to stabilize the microstructure through kinetic and/or thermodynamic mechanisms. And to address the ductility challenge, spatially-graded grain size distributions have been developed to facilitate heterogeneous deformation modes: high-strength at the surface and plastic deformation in the bulk. In the present work, we combine these two strategies and present a new methodology for the fabrication of gradient nanostructured metals via compositional means. Here, we have demonstrated that annealing a compositionally stepwise Pt-Au film with a homogenous microstructure results in a film with a spatial microstructural gradient, exhibiting grains which can be twice as wide in the bulk compared to the outer surfaces. Additionally, phase-field modeling was employed for the comparison with experimental results and for further investigation of the competing mechanisms of Au diffusion and thermally induced grain growth. This fabrication method offers an alternative approach for developing the next generation of microstructurally stable gradient nanostructured films.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Mechanically robust high magnetic-performance Sm-Co sintered magnets through microstructure engineering

Samarium-cobalt (Sm-Co) sintered magnets have high magnetic energy densities, great resistance to demagnetization and corrosion, and excellent thermal stability in a wide temperature range (–50–550 °C). However, the utilization of these magnets is restricted by their brittleness. Based on micromechanical and the Zener pinning model, Sm-Co sintered magnets with improved mechanical properties have been designed and fabricated via microstructure engineering. A small amount of fine Sm 2 O 3 particulates (0–3 wt%) has been incorporated into Sm 2 (CoFeCuZr) 17 sintered magnets to refine the grain size by up to approximately 50% (from 45 to 22 µm) and narrow the grain size distribution. Doping with 3 wt% Sm 2 O 3 increased the flexural strength by 62% while maintaining magnetic performance. Both grain-refined unimodal microstructure and heterogeneous laminated coarse/fine grain microstructure were formed by strategically designed assemblies of Sm 2 O 3 -added Sm-Co powder feedstock mixtures. The technology is compatible with existing magnet manufacturing processes. Numerical micromechanics simulation indicates that the fracture is dominated by intragranular mode. The mechanical strength is mainly enhanced by the additive-induced grain refinement, while the small amount of Sm 2 O 3 addition has a small direct positive contribution. Finally, these magnets will be more cost-effective, efficient, and robust for various functional applications.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Phase-field modeling of crack growth under coupled creep-fatigue

Crack growth under coupled creep-fatigue strongly influences service life of metallic components operating at high temperatures. However, there lack numerical models that enable direct simulations of crack growth and plasticity development under coupled creep-fatigue. Here, in this study, a unified phase-field model is developed for simulating crack growth under fatigue, creep, and coupled creep-fatigue. This model is able to reproduce the Paris laws for both brittle and ductile materials in pure fatigue mode, which shows that the degradation rate due to cyclic stress in ductile materials is generally larger than that in brittle materials. Fatigue simulations with different yield strengths demonstrate that plasticity facilitates crack growth in typical ductile materials. High-throughput simulations are performed under coupled creep-fatigue conditions, with varying hold-stress levels and hold-time. By analyzing crack growth rate under different hold-time, a creep-fatigue interaction term is obtained. Simulation results demonstrate that the creep-fatigue interaction is caused by smaller stress gradient and enhanced degradation rate ahead of the crack tips under coupled creep-fatigue, compared to the situation of pure fatigue. This work reveals the origin of different Paris-law exponents in brittle and ductile materials and demonstrates how the interplay between creep and fatigue affects crack growth.

36 MATERIALS SCIENCE↗