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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Sprain energy consequences for damage localization and fracture mechanics

The 2023 smooth Lagrangian Crack-Band Model (slCBM), inspired by the 2020 invention of the gap test, prevented spurious damage localization during fracture growth by introducing the second gradient of the displacement field vector, named the “sprain,” as the localization limiter. The key idea was that, in the finite element implementation, the displacement vector and its gradient should be treated as independent fields with the lowest ( C 0 ) continuity, constrained by a second-order Lagrange multiplier tensor. Coupled with a realistic constitutive law for triaxial softening damage, such as microplane model M7, the known limitations of the classical Crack Band Model were eliminated. Here, we show that the slCBM closely reproduces the size effect revealed by the gap test at various crack-parallel stresses. To describe it, we present an approximate corrective formula, although a strong loading-path dependence limits its applicability. Except for the rare case of zero crack-parallel stresses, the fracture predictions of the line crack models (linear elastic fracture mechanics, phase-field, extended finite element method (XFEM), cohesive crack models) can be as much as 100% in error. We argue that the localization limiter concept must be extended by including the resistance to material rotation gradients. We also show that, without this resistance, the existing strain-gradient damage theories may predict a wrong fracture pattern and have, for Mode II and III fractures, a load capacity error as much as 55%. Finally, we argue that the crack-parallel stress effect must occur in all materials, ranging from concrete to atomistically sharp cracks in crystals.

Science & Technology - Other Topics↗
DOE OSTI2022

A phase-field model for quasi-dynamic nucleation, growth, and propagation of rate-and-state faults

Despite its critical role in the study of earthquake processes, numerical simulation of the entire stages of fault rupture remains a formidable task. The main challenges in simulating a fault rupture process include the complex evolution of fault geometry, frictional contact, and off-fault damage over a wide range of spatial and temporal scales. Here, in this paper, we develop a phase-field model for quasi-dynamic fault nucleation, growth, and propagation, which features two standout advantages: (i) it does not require any sophisticated algorithms to represent fault geometry and its evolution; and (ii) it allows for modeling fault nucleation, propagation, and off-fault damage processes with a single formulation. Built on a recently developed phase-field framework for shear fractures with frictional contact, the proposed formulation incorporates rate- and state-dependent friction, radiation damping, and their impacts on fault mechanics and off-fault damage. We show that the numerical results of the phase-field model are consistent with those obtained from well-verified approaches that model the fault as a surface of discontinuity, without suffering from the mesh convergence issue in the existing continuous approaches to fault rupture (e.g., the stress glut method). Further, through numerical examples of fault propagation in various settings, we demonstrate that the phase-field approach may open new opportunities for investigating complex earthquake processes that have remained overly challenging for the existing numerical methods.

58 GEOSCIENCES↗
DOE OSTI2021

Hydro-chemo-mechanical phase field formulation for corrosion induced cracking in reinforced concrete

Steel corrosion induced cracking in reinforced concrete structures is often caused by volumetric straining at the steel-concrete interface. This volumetric strain is mainly controlled by the rate of generation of corrosion product, which depends on the diffusion of Cl{sup −} and dissolved O{sub 2} as well as the chemical reaction at the steel-concrete interface. While many numerical modeling techniques have been proposed to tackle this complex phenomenon, most have been limited to using staggered solution schemes, where the diffusion, chemical reaction, mechanical strain, and crack fields are solved for separately. Unfortunately, such approaches introduce numerical errors that can lead to unrealistic predictions. Therefore, a coupled solution, is needed to remove the formulation induced errors and understand this complex phenomenon. To provide a unifying solution framework for corrosion induced cracking in reinforced concrete, a phase field formulation is presented and implemented with FEM algorithms. The governing equations are derived from the system's free energy and Fick's law of diffusion. The proposed formulation was first validated in 1D by comparing the modeling results with the semi-analytical solution approximated via Laurent series to avoid singularities in the complex domain. 2D plane strain solutions to the embedded rebar undergoing corrosion induced cracking with pre-cracks are also presented and compared with the approximated solutions from linear elastic fracture mechanics theory (LEFM). The modeling of crack propagation enabled by the proposed formulation is also presented along with parametric studies to reveal the roles of the fracture toughness and permeability of the concrete on the corrosion induced cracking. A case study was also conducted on H-pile steel with concrete jackets to demonstrate the feasibility of modeling corrosion induced fracture in reinforced concrete structures with complex steel-concrete interfaces.

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↗
DOE OSTI2023

Harnessing Electrochemical‐Mechanical Couplings to Improve the Reliability of Solid‐State Batteries

Abstract One key barrier to using lithium‐metal anode batteries is that metal dendrites can penetrate solid electrolytes, causing short‐circuits and battery failures. It is established that this failure is likely caused by crack propagation due to electrodeposition‐induced stresses from lithium metal. This study explores ways to harness these electrochemical‐mechanical couplings to control dendrite growth and improve battery reliability using a phase‐field model and targeted fracture experiments. The results show that dendrite growth can be effectively mitigated by applying mechanical stresses or tailoring the material's fracture toughness. This study also outlines the requirements for compressive stress to halt or deflect dendrites as a function of the overpotential and discusses the role of microstructure in this process.

Monismith, Scott↗
DOE OSTI2023

Electrochemically induced fracture in LLZO: How the interplay between flaw density and electrostatic potential affects operability

Fracture and short circuit in the Li 7 La 3 Zr 2 O 12 (LLZO) solid electrolyte are two key issues that prevent its adoption in battery cells. In this paper, we utilize phase-field simulations that couple electrochemistry and fracture to evaluate the maximum electric potential that LLZO electrolytes can support as a function of crack density. In the case of a single crack, we find that the applied potential at the onset of crack propagation exhibits inverse square root scaling with respect to crack length, analogous to classical fracture mechanics. Here, we further find that the short-circuit potential scales linearly with crack length. In the realistic case where the solid electrolyte contains multiple cracks, we reveal that failure fits the Weibull model. The failure distributions shift to favor failure at lower overpotentials as areal crack density increases. Furthermore, when flawless interfacial buffers are placed between the applied potential and the bulk of the electrolyte, failure is mitigated. When constant currents are applied, current focuses in near-surface flaws, leading to crack propagation and short circuit. We find that buffered samples sustain larger currents without reaching unstable overpotentials and without failing. Our findings suggest several mitigation strategies for improving the ability of LLZO to support larger currents and improve operability.

25 ENERGY STORAGE↗
DOE OSTI2020

Computational thermomechanics for crystalline rock. Part II: Chemo-damage-plasticity and healing in strongly anisotropic polycrystals

We present a thermal–mechanical–chemical-phase field model that captures the multi-physical coupling effects of precipitation creeping, crystal plasticity, anisotropic fracture, and crack healing in polycrystalline rock at various temperature and strain-rate regimes. This model is solved via a fast Fourier transfer solver with an operator-split algorithm to update displacement, temperature and phase field, and chemical concentration incrementally. In nuclear waste disposal in salt formation, brine inside the crystal salt may migrate along the grain boundary and cracks due to the gradient of interfacial energy and pressure. This migration has a significant implication on the permeability evolution, creep deformation, and crack healing within rock salt but is difficult to incorporate implicitly via effective medium theories compared with computational homogenization. As such, we introduce a thermodynamic framework and a corresponding computational implementation that explicitly captures the brine diffusion along the grain boundary and crack at the grain scale. Meanwhile, the anisotropic fracture and healing are captured via a high-order phase field that represents the regularized crack region in which a newly derived non-monotonic driving force is used to capture the fracture and healing due to the solution–precipitation. Numerical examples are presented to demonstrate the capacity of the thermodynamic framework to capture the multiphysics material behaviors of rock salt.

42 ENGINEERING↗
DOE OSTI2024

Intermediate Principal Stress Effects on the 3D Cracking Behavior of Flawed Rocks Under True Triaxial Compression

Crack initiation, growth, and coalescence in flawed rocks have been extensively studied for 2D (planar, penetrating) flaws under uniaxial/biaxial compression. However, little is known as to the mechanisms and processes of cracking from 3D flaws under true triaxial compression, where the intermediate principal stress (σ 2 ) is distinguished from the major and minor principal stresses. In this work, we systematically investigate the effects of σ 2 on the 3D cracking behavior of rock specimens with preexisting flaws, through the use of mechanistic simulations of mixed-mode fracture in rocks. We explore how two characteristics of σ 2 , namely, (i) its orientation with respect to the flaw and (ii) its magnitude, affect two aspects of the cracking behavior, namely, (i) the cracking pattern and (ii) the peak stress. Results show that the orientation of σ 2 exerts more control over the cracking pattern than the flaw inclination angle. The peak stress becomes highest when σ 1 is parallel to the flaw, whereas it becomes lowest when σ 2 is parallel to the flaw. Also, the effects of σ 2 magnitude are more significant when σ 2 becomes more oblique to the flaw plane. On the basis of our observations, we propose mechanisms underlying the cracking behavior of 3D flawed rocks under true triaxial compression.

58 GEOSCIENCES↗
DOE OSTI2025

GEOS-DEV/FORGE

This dataset is a repository that provides the input deck for numerical models associated with two Utah FORGE research projects: "Closing the Loop Between In situ Stress Complexity and EGS Fracture Compexity" (Project Number: 2-2446) and "Coupled Investigation of Fracture Permeability Impact on Reservoir Stress and Seismic Slip Behavior" (Project Number: 5-2428). Three kinds of simulation decks are included: (i) hydraulic fracturing simulation (HydroFrac folder), (ii) phase-field simulation (PhaseField folder), and (iii) thermo-hydro-mechanical simulation (ThermoHydroMech folder).

Cusini, Matteo [Lawrence Livermore National Labora↗
DOE OSTI2024

Quarterly Research Performance Progress Report (Q8)

As part of Task 1, we have started by testing our modeling capabilities by reproducing isothermal DFIT simulations presented in the literature. Once satisfied with the results we have started by targeting the modeling of the DFITs at conducted at well 58-32. We have a identified a specific test (cycle 4 in zone 2) as the most interesting to be model with GEOS hydraulic fracturing module. Thus, we have first produced results with an isothermal model and adjusted model parameters to get a satisfying match with field pressure data. The, we have added thermal effects and compared the modeling results with and without thermal effects to estimate how thermal effects may influence test interpretation. Models seem to suggest that, for small volumes of fluid, thermal effects are moderate. In Task 2, we have adapted GEOS phase-field formulation to be able to simulate near-wellbore hydraulic fracture nucleation and propagation. We have devised a novel formulation that, compared to other existing ones, incorporates rock strengths. We have submitted a journal publication about our work. We are currently employing this phase-field formulation to model the experiments taking place at U Pitt and help us understand the effect of various parameters. In Task 3, we have built a model of the region surround well 16A and have started modeling stage 3 stimulation because of its simpler planar geometry. After calibrating simulation parameters using known analytical solutions, we have simulated the stage 3 stimulation using our isothermal hydraulic fracturing module, varying the permeability field, the stress conditions including different physics to get a better understanding of the numerical challenges and of the effects of varying these parameters on the simulation results. In Task 4 laboratory experimentation, a set of specialized drilling and injection tools has been customized and constructed to accommodate an inclined well with an orientation of up to 30 degrees relative to material anisotropy or principal stress axes. These inclined samples have also undergone thermal stress and hydraulic fracturing at a temperature of 190 degrees Celsius. Furthermore, both vertical and deviated sampling testing setups enable an extended analysis of post-peak pressure behaviors, facilitating post-test pressure analyses such as the G-function, step rate, and fracture reopening measurements. Thus, the key components of in-situ stress estimation can be extracted and validated through our experiment, providing a solid foundation for validating existing in-situ stress estimation theories or proposing new ones. Simultaneously, we are integrating computer vision techniques with traditional experimental fracture observation methods such as multi-overcore/slicing and water-penetration fracture observation. This combination will prove beneficial in populating the hydraulic fracture patterns database, generated under challenging EGS conditions. This approach aims to deepen our understanding of the complexities in EGS reservoirs and pave the way for future data-driven investigations. Additionally, PITT has also equipped the ELE International compression machine, which is now prepared for conducting indirect tensile and fracture toughness tests. These tests will aid in characterizing how rock fabrics influence the resulting fracture patterns. Additionally, we have completed the required personnel training and gained access to Scanning Electron Microscopy (SEM) and Energy Dispersive Spectroscopy (EDS) for conducting more detailed characterization and analysis of rock fabrics, as well as the examination of thermal and hydraulically induced fracture patterns. Thus, the PITT team has effectively demonstrated the capabilities of our experimental apparatuses in exploring the thermal effects, well deviation angles, material anisotropy, and operational choices (such as circulation rate, injection fluid viscosity, and injection rate) and their impact on pressure responses and fracture trajectories under the Utah FORGE conditions.

15 GEOTHERMAL ENERGY↗
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 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

Material Fracturing and Failure Simulation Datasets

Fracturing is a fundamental physics phenomena with broad relevance across multiple domains, ranging from infrastructure integrity, aerospace durability, reservoir production, and seismic events. We present a diverse dataset of simulated fracture evolution and material failure generated from two numerical solvers: the phase-field method and the combined finite-discrete element method (FDEM). These solvers differ in formulation, physical fidelity, and computational efficiency. The dataset includes five materials: PBX, anisotropic shale, tungsten, aluminum, and steel. For each, phase-field simulations span 400,000 cases: 200,000 under uniaxial tension and 200,000 under biaxial tension. The computationally expensive FDEM simulations include 90,000 split evenly among PBX, shale, and tungsten under uniaxial loading. All simulations begin with randomized initial fracture patterns. Each entry includes temporal data capturing fracture propagation dynamics. This comprehensive dataset is designed to support the development of foundational or surrogate machine learning approaches for predicting material failure. While no such models are introduced here, the dataset lays a robust foundation for advancing future research and innovation in these areas.

36 MATERIALS SCIENCE↗
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 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 OSTI2023

Machine Learning Based Fracture Network Quantification at the IBDP CO2 Sequestration Site

This poster presents the latest results highlighted in SMART phase II task 4 of fracture network and mapping based on IBDP field data measurement. The results will be coupled into the dynamic modeling and simulation study to insight the impact of the fracture in the reservoir system. Such impacts will be applied to AI/ML development for training and test for science-informed decision making support for CO2 storage.

Kumar, Abhash↗