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NASA NTRS2000

Determination of the Fracture Parameters in a Stiffened Composite Panel

A modified J-integral, namely the equivalent domain integral, is derived for a three-dimensional anisotropic cracked solid to evaluate the stress intensity factor along the crack front using the finite element method. Based on the equivalent domain integral method with auxiliary fields, an interaction integral is also derived to extract the second fracture parameter, the T-stress, from the finite element results. The auxiliary fields are the two-dimensional plane strain solutions of monoclinic materials with the plane of symmetry at x(sub 3) = 0 under point loads applied at the crack tip. These solutions are expressed in a compact form based on the Stroh formalism. Both integrals can be implemented into a single numerical procedure to determine the distributions of stress intensity factor and T-stress components, T11, T13, and thus T33, along a three-dimensional crack front. The effects of plate thickness and crack length on the variation of the stress intensity factor and T-stresses through the thickness are investigated in detail for through-thickness center-cracked plates (isotropic and orthotropic) and orthotropic stiffened panels under pure mode-I loading conditions. For all the cases studied, T11 remains negative. For plates with the same dimensions, a larger size of crack yields larger magnitude of the normalized stress intensity factor and normalized T-stresses. The results in orthotropic stiffened panels exhibit an opposite trend in general. As expected, for the thicker panels, the fracture parameters evaluated through the thickness, except the region near the free surfaces, approach two-dimensional plane strain solutions. In summary, the numerical methods presented in this research demonstrate their high computational effectiveness and good numerical accuracy in extracting these fracture parameters from the finite element results in three-dimensional cracked solids.

Lin, Chung-Yi↗

DOE OSTI2024

DECOVALEX-2023: Task F1 Final Report

DECOVALEX-2023 Task F is a comparison of models and methods for post-closure performance assessment (PA) of a deep geologic repository for radioactive waste. The general aims of Task F are to build confidence in the models, methods, and software used for PA and to stimulate additional research and development in PA methodologies. The task objectives are to motivate development of PA modelling skills and capabilities, to examine the influence of model choices on calculated repository performance, and to compare the uncertainties introduced by model choices to other sources of uncertainty. Task F involves no actual experiment or site. It is a PA modelling exercise that requires the conceptual development of hypothetical repository designs and geologic settings. Because three of the teams were interested in salt and the rest of the teams were interested in crystalline rock, Task F was split into two branches: Task F1 for crystalline rock and Task F2 for salt. This report is for Task F1, crystalline rock. Teams from seven countries (Canada, Czech Republic, Germany, Korea, Sweden, Taiwan, and United States) participated in Task F1. The teams worked together to define the features, events, and processes of the reference case repository and established a set of performance measures. In addition, they defined a set of benchmark problems designed to test and compare modelling capabilities for fracture flow and transport at different scales. The repository design and benchmark problems are documented in a Task Specification that evolved over time as the group honed the specifications. The benchmark problems verified that each team can aptly model flow and transport in fractured media in 1-, 2-, and 3-dimensions. Two general approaches were used for the 3-dimensional benchmarks: discrete fracture network (DFN) and equivalent continuous porous medium (ECPM). DFN modelling involves explicit meshing of each fracture while ECPM modelling aims to capture the effective porosity and directional permeability of each cell in a space-filling mesh as affected by intersecting fractures. In some models, a combination of the two is used, i.e., DFN for large known fractures and ECPM for the rest of the domain. Transport is solved by using either the advection-dispersion equation or particle tracking. Although some variation is observed among model breakthrough curves in the benchmark problems, there is strong agreement in breakthrough behaviour up to at least the 75 th percentile for all benchmarks. At the 90 th percentile, breakthrough results show larger differences, suggesting several models retain substantially higher fractions of tracer in regions of slower moving water. In addition to the flow and transport benchmarks, several teams completed the source term benchmark, verifying capabilities for modelling radionuclide decay and ingrowth, waste package breach, instant release fractions, fuel matrix degradation rates, and radionuclide solubility limitations. The reference case is conceptualized as a generic spent fuel repository at a depth of 450 m in fractured crystalline rock. The repository has 50 parallel backfilled drifts, each with 50 deposition holes 6 m apart. Each deposition hole contains a 4-PWR waste package and bentonite buffer. The rock domain is 5 km in length, 2 km in width, and 1 km in depth. It has 6 deterministic fractured deformation zones and a multitude of stochastic fractures. Teams generally used the ECPM approach for the entire rock or a hybrid approach in which the deterministic fracture zones are modelled with a DFN and the rest of the rock is modelled by ECPM. Of the reference case problems specified, only the results of the initial reference case problem are compared in this report. The initial problem focuses on transport from the deposition holes to the surface, i.e., it neglects waste package performance. Tracers are released at all waste package locations at time zero and tracked for their releases to the near field and ground surface. The water fluxes calculated at the ground surface entry and exit regions of the domain are similar for all models except for two that have considerably lower fluxes. For tracer transport, large differences are observed among models in the magnitude of tracer transported. Much of the difference appears to be due to how the repository is implemented and hence the different degrees of repository simplification. Models that exclude the drifts, buffer, and backfill from the domain tend to show greater release of tracers and radionuclides from the repository. The initial study presented here indicates that major differences in modelling important processes within the repository (e.g., diffusion through buffer and backfill) can produce broadly different release and transport results, especially when those processes are excluded. Even for the models that included all specified features, events, and processes, the results show significant differences and demonstrate the importance of examining multiple modelling approaches in performance assessment. The differences in results observed in this study are expected to motivate teams to either increase complexity in future versions of the reference case models or to improve methods to account for the effects of simplified features and processes. Either way, future improvements in these models are expected to produce results that more closely agree.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

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

Analysis of ZTE MRI application to sandstone and carbonate

Micro-tomography (μCT) and nuclear magnetic resonance (NMR) have been used to characterize porous media for decades. Here, Magnetic Resonance Imaging (MRI) enables direct visualization of pore architecture and many pulse sequences exist. In this work, we tested the MRI pulse sequence Zero Echo Time (ZTE) to study sandstone and carbonate for its ability to address short relaxation times. We aimed at resolving two fluid conduit scales, i.e. pores and fractures. In this research, we study tighter porous systems than those previously reported using ZTE. Additionally, Pore Cluster Analysis (PCA), combined with ZTE, can be used to analyze pore-fracture connectivity of relatively large core plugs. We show that ZTE can resolve two-scale pore systems simultaneously, i.e. fractures and pores. By combining Time-Domain NMR pore-size analysis and PCA, we show that careful selection of resolution is necessary to understand transport in porous media.

02 PETROLEUM↗

NASA NTRS1991

A three-dimensional equivalent domain integral method for cracked solids

Three-dimensional FEM analysis is presently undertaken via the general formulation of the equivalent-domain integral method for mixed-mode fracture problems in general anisotropic and nonlinear materials. In mixed-mode integrals, the total J-integral is split into three separate modes of fracture; direct and decomposition methods are effective in this separation of the modes, as presently demonstrated by their application to several pure and mixed-mode fracture problems. The results are found to agree well with those reported in the literature, and suggest the usefulness of the method as a FEM-program postprocessing subroutines.

Shivakumar, K. N.↗

NASA NTRS1991

Structural design methodologies for ceramic-based material systems

One of the primary pacing items for realizing the full potential of ceramic-based structural components is the development of new design methods and protocols. The focus here is on low temperature, fast-fracture analysis of monolithic, whisker-toughened, laminated, and woven ceramic composites. A number of design models and criteria are highlighted. Public domain computer algorithms, which aid engineers in predicting the fast-fracture reliability of structural components, are mentioned. Emphasis is not placed on evaluating the models, but instead is focused on the issues relevant to the current state of the art.

Duffy, Stephen F.↗

NASA NTRS1992

Structural design methodologies for ceramic-based material systems

Duffy, Stephen F.↗

DOE OSTI2020

Effect of Computational Schemes on Coupled Flow and Geo-Mechanical Modeling of CO 2 Leakage through a Compromised Well

Carbon capture, utilization, and storage (CCUS) describes a set of technically viable processes to separate carbon dioxide (CO 2 ) from industrial byproduct streams and inject it into deep geologic formations for long-term storage. Legacy wells located within the spatial domain of new injection and production activities represent potential pathways for fluids (i.e., CO 2 and aqueous phase) to leak through compromised components (e.g., through fractures or micro-annulus pathways). The finite element (FE) method is a well-established numerical approach to simulate the coupling between multi-phase fluid flow and solid phase deformation interactions that occur in a compromised well system. We assumed the spatial domain consists of a three-phases system: a solid, liquid, and gas phase. For flow in the two fluids phases, we considered two sets of primary variables: the first considering capillary pressure and gas pressure (PP) scheme, and the second considering liquid pressure and gas saturation (PS) scheme. Fluid phases were coupled with the solid phase using the full coupling (i.e., monolithic coupling) and iterative coupling (i.e., sequential coupling) approaches. The challenge of achieving numerical stability in the coupled formulation in heterogeneous media was addressed using the mass lumping and the upwinding techniques. Numerical results were compared with three benchmark problems to assess the performance of coupled FE solutions: 1D Terzaghi’s consolidation, Liakopoulos experiments, and the Kueper and Frind experiments. We found good agreement between our results and the three benchmark problems. For the Kueper and Frind test, the PP scheme successfully captured the observed experimental response of the non-aqueous phase infiltration, in contrast to the PS scheme. These exercises demonstrate the importance of fluid phase primary variable selection for heterogeneous porous media. We then applied the developed model to the hypothetical case of leakage along a compromised well representing a heterogeneous media. Considering the mass lumping and the upwinding techniques, both the monotonic and the sequential coupling provided identical results, but mass lumping was needed to avoid numerical instabilities in the sequential coupling. Additionally, in the monolithic coupling, the magnitude of primary variables in the coupled solution without mass lumping and the upwinding is higher, which is essential for the risk-based analyses.

deformation flow↗

DOE OSTI2025

Generalizable machine learning potentials for quantum-accurate predictions of non-equilibrium behavior in 2D materials

Machine learning interatomic potentials (ML-IAPs) are emerging as transformative tools in materials modeling, promising quantum-level accuracy at a fraction of the computational cost. However, their ability to generalize beyond equilibrium configurations and to reliably capture defect- and temperature-driven behavior remains underexplored. Here, we develop and benchmark two state-of-the-art ML-IAPs, Spectral Neighbor Analysis Potential (SNAP) and Allegro, on a comprehensive dataset for monolayer MoSe₂. Using density functional theory (DFT) as the reference, we evaluate their performance in capturing stress–strain behavior, phase transition energetics, defect evolution, edge stability, and fracture toughness. Allegro, a deep equivariant neural network potential, surpasses both SNAP and the classical Tersoff potential in accuracy, efficiency, and transferability. Importantly, both ML potentials accurately reproduce experimental fracture measurements and ab initio predictions of inversion domain formation—phenomena well beyond their training sets. Our findings establish ML-IAPs as viable replacements for traditional force fields in the study of non-equilibrium mechanical phenomena, enabling large-scale, high-fidelity simulations in 2D materials and beyond. In conclusion, this work provides a broadly applicable framework for data-driven modeling of structural and functional transformations under extreme conditions.

2D materials↗

NASA NTRS1995

Detecting gear tooth fracture in a high contact ratio face gear mesh

This paper summarized the results of a study in which three different vibration diagnostic methods were used to detect gear tooth fracture in a high contact ratio face gear mesh. The NASA spiral bevel gear fatigue test rig was used to produce unseeded fault, natural failures of four face gear specimens. During the fatigue tests, which were run to determine load capacity and primary failure mechanisms for face gears, vibration signals were monitored and recorded for gear diagnostic purposes. Gear tooth bending fatigue and surface pitting were the primary failure modes found in the tests. The damage ranged from partial tooth fracture on a single tooth in one test to heavy wear, severe pitting, and complete tooth fracture of several teeth on another test. Three gear fault detection techniques, FM4, NA4*, and NB4, were applied to the experimental data. These methods use the signal average in both the time and frequency domain. Method NA4* was able to conclusively detect the gear tooth fractures in three out of the four fatigue tests, along with gear tooth surface pitting and heavy wear. For multiple tooth fractures, all of the methods gave a clear indication of the damage. It was also found that due to the high contact ratio of the face gear mesh, single tooth fractures did not significantly affect the vibration signal, making this type of failure difficult to detect.

Zakrajsek, James J.↗

DOE OSTI2023

Multiscale spatial analysis of fracture nodes in two dimensions

Spatial arrangement of fractures as a function of scale is an important component of fracture quantification for inferential and predictive modeling. Available methods that analyze fracture spatial arrangement are based on one-dimensional spacing data; therefore, they are limited to semi-parallel fractures. Such methods cannot be applied to fracture networks in higher dimensions, particularly when fractures have different orientations. Here to characterize fracture arrangements in two dimensions, we propose using Ripley’s K-function, as a method of point pattern analysis, to quantify spatial arrangement of fracture nodes. Fracture nodes, such as barycenters, intersection points, and tips, are point-based representations of fracture locations and connectivity within the fracture network. We introduce formulations for isotropic as well as directional analyses of spatial arrangement. In addition, we derive formulations for edge correction in circular and rectangular study domains. Finally, we demonstrate applications of Ripley’s K-function on two natural fracture datasets. Our proposed method supports quantification and characterization of fracture spatial arrangements that allow practitioners to build representative models of fractures in the subsurface.

02 PETROLEUM↗

DOE OSTI2023

Peridynamic elastic waves in two-dimensional unbounded domains: Construction of nonlocal Dirichlet-type absorbing boundary conditions

The focus of this paper is on application of peridynamics (PD) to propagation of elastic waves in unbounded domains. We construct absorbing boundary conditions (ABCs) derived from a semi-analytical solution of the PD governing equation at the exterior region. This solution is made up of a finite series of plane waves, as fundamental solutions (modes), which satisfy the PD dispersion relations. The modes are adjusted to transmit the energy from the interior region (near field) to the exterior region (far field). The corresponding unknown coefficients of the series are found in terms of the displacement field at a layer of points adjacent to the absorbing boundary. This is accomplished through a collocation procedure at subregions (clouds) around each absorbing point. The proposed ABCs offer appealing advantages, which facilitate their application to PD. They are of Dirichlet-type, hence their implementation is relatively simple as no derivatives of the field variables are required. They are constructed in the time and space domains and thus application of Fourier and Laplace transforms, cumbersome for nonlocal models, is not required. At the discrete level, the modes satisfy the same numerical dispersion relations of the near field, which makes the far-field solution compatible with that of the near field. We scrutinize the performance of the proposed ABCs through several examples. So our investigation shows that the proposed ABCs perform stably in time with an appropriate level of accuracy even in problems characterized by highly-dispersive propagating waves, including crack propagation in semi-unbounded brittle solids.

42 ENGINEERING↗

DOE OSTI2022

Investigation of fracture in porous materials: a phase-field fracture study informed by ReaxFF

Microscopic features (e.g, pore shapes, sizes, and distribution) in porous material substantially affect the overall mechanical properties such as stiffness and strength. In turn, these material properties determine the macroscopic behaviors of fracture in the porous material. In certain cases, macroscopic properties can be derived from the porous skeleton and void ratio (i.e., porosity), but in many other cases, such derivation is a challenging task. This paper presents a numerical investigation of microporosity and micropore shapes effect on the macrofracture behavior in porous amorphous silica. For this study, we extend the recently-proposed combined molecular dynamic (MD) and phase-field (PF) fracture modeling approach by including different pore shapes in the atomistic domain. In the MD simulations, we adopt ReaxFF to evaluate the material properties, where four different micropore cases are considered. Based on the material properties derived from MD simulations, the macrofracture propagation of porous media is studied using hybrid PF simulation. In the characterization of the pore structure, the concept of pore ligament is proposed to relate the pore shape and the critical energy release rate. Two classical fracture problems were used to evaluate the effect of pore shape on the macrofracture behavior. The results of the case study show that although the micropore shapes change the macrofracture behaviors, these effects vary with the geometry and loading conditions of macroscopic boundary value problems. Furthermore, the case study also shows that the influence of micropore structure can be captured at the macroscopic level through the material properties derived from the MD simulations.

42 ENGINEERING↗

DOE OSTI2024

Characterizing the impact of finite matrix block size on conservative particle transport through three-dimensional fracture networks

Mass transfer of solutes between fractures and the surrounding rock matrix exerts a noticeable signature on the tail of travel time distributions. When the width of the matrix is assumed to be infinite and advective transport through the fracture is sufficiently fast, the tails of the travel time distributions exhibit a classically expected slope of ψ(t) ∝ t -3/2 . However, studies have yet to characterize how solute transfer between fractures via diffusion through finite matrix blocks influences the tail’s slope in three-dimensional fractured media. Here, in this study, we assess the impact of finite matrix block size on breakthrough curve shape at different spatio-temporal scales by con ducting particle tracking simulations in three-dimensional discrete fracture networks. We consider a variety of hydrodynamic and geostructural proper ties to determine their relative impact on the resulting travel time distributions. We observe that the impact of matrix diffusion through a finite block on travel time distributions is similar to that of an infinite matrix block when the fracture spacing is sufficiently large, matrix diffusion is relatively weak, or transport is considered at an early control plane distance. We observe that the converse of these conditions, results in deviations from the classical ψ(t) ∝ t -3/2 scaling. These results provide a first step toward developing a metric to assess when finite block size effects are expected to significantly influence transport.

58 GEOSCIENCES↗

NASA NTRS1989

Three-dimensional analysis of surface crack-Hertzian stress field interaction

The results are presented of a stress intensity factor analysis of semicircular surface cracks in the inner raceway of an engine bearing. The loading consists of a moving spherical Hertzian contact load and an axial stress due to rotation and shrink fit. A 3-D linear elastic Boundary Element Method code was developed to perform the stress analysis. The element library includes linear and quadratic isoparametric surface elements. Singular quarter point elements were employed to capture the square root displacement variation and the inverse square root stress singularity along the crack front. The program also possesses the capability to separate the whole domain into two subregions. This procedure enables one to solve nonsymmetric fracture mechanics problems without having to separate the crack surfaces a priori. A wide range of configuration parameters was investigated. The ratio of crack depth to bearing thickness was varied from one-sixtieth to one-fifth for several different locations of the Hertzian load. The stress intensity factors for several crack inclinations were also investigated. The results demonstrate the efficiency and accuracy of the Boundary Element Method. Moreover, the results can provide the basis for crack growth calculations and fatigue life prediction.

Ballarini, R.↗

NASA NTRS1991

Modeling the growth and interaction of fractures

The research objectives are to develop accurate, efficient numerical tool for fracture mechanics analysis with the capabilities of the method including the modeling of multiple site damage and the simulation of crack propagation. The fracture is modeled using a distribution of edge dislocations. Fundamental solutions for dislocations in an infinite medium, in the neighborhood of a circular inhomogeneity, and near a bi-material interface are incorporated into the procedure to allow exceptionally accurate modeling of fracture geometries involving these types of inhomogeneities. To model arbitrary (finite) domains under general boundary conditions, a combination of the dislocation methodology and boundary element techniques is used. The dislocation scheme is a natural means to model the crack(s), and the boundary element method is an effective way to model the region in which the crack is embedded. The hybrid scheme is relatively easy to use and is very accurate. The research accomplishments are presented.

Mear, Mark E.↗

DOE OSTI2021

Evaluating Effects of Shear Processing on 2D Crystalline Materials in 3D Metal Matrices: Atomistic Understanding of High Shear Deformation of Copper Graphene Composites

Composites made of copper and graphene demonstrate high strength, lubricity and enhanced electrical and thermal conductivity compared pure copper. However, manufacturing these composites at bulk volumes for industrial applications has been a big challenge. Shear deformation assisted processing is an effective method for manufacturing materials such as copper-graphene composites demonstrating ultra-fine grain structures and compositional homogeneity. Nevertheless, microstructural evolution of the composites and their property development under such conditions is not clearly understood currently. To rectify this gap in literature, high strain shear deformation of copper coated graphene foils was performed using a tribometer pin in this study. Changes in microstructure of the composite as well as the constituent components under shear deformation was correlated to process conditions. A sharp increase in the coefficient of friction attributed to rupture and smearing of graphene layer into copper substrate was observed during the shear processing. The coefficient of friction of the sheared copper/graphene composite was lower than that of pure copper, suggesting that partially worn graphene is effectively lubricious at the macroscale. A multimodal characterization of the processed region further revealed a shear deformation-induced ultrafine two-phase grain-structure consisting of copper and graphitic domains. Shear deformation reduced the copper grain size from around 50 – 100 µm to ~200 nm on an average and ~2 – 5 nm in some locations. The semicrystalline graphene films were observed to fracture into 10 – 50 µm size flakes. Oxygen enrichment was observed in the processed region. Finally, graphitic domain were identified for the first time in the copper matrix and not just at the grain boundaries providing evidence for a metastable composite microstructure as a result of solid phase processing at room temperature.

36 MATERIALS SCIENCE↗

DOE OSTI2021

An integrated numerical model for coupled poro-hydro-mechanics and fracture propagation using embedded meshes

Integrated models for fluid-driven fracture propagation and general multiphase flow in porous media are valuable to the study and engineering of several systems, including hydraulic fracturing, underground disposal of waste, and geohazard mitigation across such applications. This work extends the coupled model multiphase flow and poromechanical model of Ren et al. (2018) to admit fracture propagation (FP). The coupled XFEM-EDFM scheme utilizes a separate fracture mesh that is embedded on a static background mesh. The onset and dynamics of fracture propagation are governed by the equivalent stress intensity factor (SIF) criterion. A domain-integral method (J integral) is applied to compute this information. Additionally, an adaptive time-marching scheme is proposed to rapidly restrict and grow temporal resolution to match the underlying time-scales. The proposed model is verified with analytical solutions, and shows the capability to accurately and adaptively co-simulate fluid transport and deformation as well as the propagation of multiple fractures.

42 ENGINEERING↗