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All sources NASA NTRS DOE OSTI

DOE OSTI2019

Continuum stress intensity factors from atomistic fracture simulations

Stress intensity factors (SIFs) are utilized in continuum fracture mechanics to quantify the stress fields surrounding a crack in a homogeneous material in the linear elastic regime. Critical values of the SIFs define an intrinsic measure of the resistance of a material to propagate a crack. At atomic scales, yet, fracture occurs as a series of atomic bonds breaking, differing from the continuum description. As a consequence, a formal analog of the continuum SIFs calculated from atomistic simulations can have spatially localized, microstructural contributions that originate from varying bond configurations. The ability to characterize fracture at the atomic scale in terms of the SIFs offers both an opportunity to probe the effects of chemistry, as well as how the addition of a microstructural component affects the accuracy. We present a novel numerical method to determine SIFs from molecular dynamics (MD) simulations. The accuracy of this approach is first examined for a simple model, and then applied to atomistic simulations of fracture in amorphous silica. MD simulations provide time and spatially dependent SIFs, with results that are shown to be in good agreement with experimental values for fracture toughness in silica glass.

42 ENGINEERING↗

NASA NTRS1988

Numerical fracture simulation of compact and bend specimens

An elastic-plastic finite-element analysis with a critical crack-tip-opening displacement criterion was used to simulate fracture of various size compact and bend specimens made of HY-130 steel. From the calculated load-crack-extension and load-displacement curves, J-resistance (J-R) curves were determined by several methods. The simulated 3-R curves were insensitive to specimen size up to maximum load but were sensitive to specimen configuration for crack extensions greater than 10 percent of the initial uncracked ligament length.

Shivakumar, K. N.↗

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↗

NASA NTRS2011

Surrogate Modeling of High-Fidelity Fracture Simulations for Real-Time Residual Strength Predictions

A surrogate model methodology is described for predicting, during flight, the residual strength of aircraft structures that sustain discrete-source damage. Starting with design of experiment, an artificial neural network is developed that takes as input discrete-source damage parameters and outputs a prediction of the structural residual strength. Target residual strength values used to train the artificial neural network are derived from 3D finite element-based fracture simulations. Two ductile fracture simulations are presented to show that crack growth and residual strength are determined more accurately in discrete-source damage cases by using an elastic-plastic fracture framework rather than a linear-elastic fracture mechanics-based method. Improving accuracy of the residual strength training data does, in turn, improve accuracy of the surrogate model. When combined, the surrogate model methodology and high fidelity fracture simulation framework provide useful tools for adaptive flight technology.

Spear, Ashley D.↗

NASA NTRS2011

Surrogate Modeling of High-Fidelity Fracture Simulations for Real-Time Residual Strength Predictions

A surrogate model methodology is described for predicting in real time the residual strength of flight structures with discrete-source damage. Starting with design of experiment, an artificial neural network is developed that takes as input discrete-source damage parameters and outputs a prediction of the structural residual strength. Target residual strength values used to train the artificial neural network are derived from 3D finite element-based fracture simulations. A residual strength test of a metallic, integrally-stiffened panel is simulated to show that crack growth and residual strength are determined more accurately in discrete-source damage cases by using an elastic-plastic fracture framework rather than a linear-elastic fracture mechanics-based method. Improving accuracy of the residual strength training data would, in turn, improve accuracy of the surrogate model. When combined, the surrogate model methodology and high-fidelity fracture simulation framework provide useful tools for adaptive flight technology.

Spear, Ashley D.↗

DOE OSTI2025

Impact of position and density of nanoscale voids on fracture initiation in iron from phase field fracture simulation

Understanding the impact of these bubbles on crack propagation, like that of helium bubble-induced cracking in irradiated materials is incredibly complex. A useful first study towards understanding bubble effects on fracture is to examine how voids impact fracture first. In this work, we used phase-field fracture simulations to examine the influence of voids and their distribution on Mode I fracture in Fe. Assuming brittle fracture, two simulation configurations were considered: (1) nanoscale systems with one or two voids, and (2) nanoscale systems with an experimentally relevant distribution of voids, with up to 20% void area. Results from simulations with one and two voids showed that voids within 10 nm of a crack tip reduce the stress required for crack growth, with the magnitude of reduction depending on void-to-crack orientation. Comparisons with linear elastic fracture mechanics and evaluation of one versus two void systems revealed deviations from linear superposition, implying complex interactions between void and crack tip stress fields. In multi-void simulations, as void sizes increase, the nearest void to the crack tip exerts a greater influence on fracture stress than the overall porosity. Furthermore this study provides valuable insights into the relationship between void size and concentration, and the stress necessary for crack growth, marking a step forward towards understanding He bubble-induced fracture in ferrous materials.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Ductility mechanisms in complex concentrated refractory alloys from atomistic fracture simulations

The striking variation in damage tolerance among refractory complex concentrated alloys is examined through the analysis of atomistic fracture simulations, contrasting behavior in elemental Nb with that in brittle NbMoTaW and ductile Nb45Ta25Ti15Hf15. We employ machine-learning interatomic potentials (MLIPs), including a new MLIP developed for NbTaTiHf, in atomistic simulations of crack tip extension mechanisms based on analyses of atomistic fracture resistance curves. While the initial behavior of sharp cracks shows good correspondence with the Rice theory, fracture resistance curves reveal marked changes in fracture modes for the complex alloys as crack extension proceeds. In NbMoTaW, compositional complexity appears to promote dislocation nucleation relative to pure Nb, despite theoretical predictions that the alloy should be relatively more brittle. In Nb45Ta25Ti15Hf15, alloying alters the fracture mode compared to elemental Nb, promoting crack tip blunting and enhancing resistance to crack propagation.

Computational methods↗

DOE OSTI2021

Verification of Coupled Hydraulic Fracturing Simulators Using Laboratory-Scale Experiments

In this work, we aim to verify the predictions of the numerical simulators, which are used for designing field-scale hydraulic stimulation experiments. Although a strong theoretical understanding of this process has been gained over the past few decades, numerical predictions of fracture propagation in low-permeability rocks still remains a challenge. Against this background, we performed controlled laboratory-scale hydraulic fracturing experiments in granite samples, which not only provides high-quality experimental data but also a well-characterized experimental set-up. Using the experimental pressure responses and the final fracture sizes as benchmark, we compared the numerical predictions of two coupled hydraulic fracturing simulators—CSMP and GEOS. Both the simulators reproduced the experimental pressure behavior by implementing the physics of Linear Elastic Fracture Mechanics (LEFM) and lubrication theory within a reasonable degree of accuracy. The simulation results indicate that even in the very low-porosity (1–2 %) and low-permeability (10 -18 m 2 - 10 -19 m 2 ) crystalline rocks, which are usually the target of EGS, fluid-loss into the matrix and unsaturated flow impacts the formation breakdown pressure and the post-breakdown pressure trends. Therefore, underestimation of such parameters in numerical modeling can lead to significant underestimation of breakdown pressure. The simulation results also indicate the importance of implementing wellbore solvers for considering the effect of system compressibility and pressure drop due to friction in the injection line. The varying injection rate as a result of decompression at the instant of fracture initiation affects the fracture size, while the entry friction at the connection between the well and the initial notch may cause an increase in the measured breakdown pressure.

15 GEOTHERMAL ENERGY↗

DOE OSTI2021

An Enhanced Virtual Crack Closure Technique for Stress Intensity Factor Calculation along Arbitrary Crack Fronts and the Application in Hydraulic Fracturing Simulation

The virtual crack closure technique (VCCT) is widely used for calculating energy release rates along crack fronts and modeling the propagation of cracks in solid materials. Although the VCCT formulation for smooth crack fronts has been sufficiently addressed in the literature, the application of VCCT to a nonsmoothed crack front with sharp corners warrants further investigation. In this study, we describe an enhanced VCCT to calculate energy release rates and stress intensity factors for cracks with arbitrary shapes in 3D domains discretized on structured grids. The formulations of the enhanced VCCT were developed and implemented into a multiphysics simulation environment capable of simulating crack propagation in the framework of linear elastic fracture mechanics. Comparisons with existing analytical/numerical solutions and other VCCT approaches were performed to verify the enhanced VCCT in terms of SIF calculation along nonsmoothed crack fronts. We then applied the enhanced VCCT to a hydraulically driven penny-shaped fracture problem to further demonstrate its capability to simulate nonsmoothed fracture propagation.

02 PETROLEUM↗

DOE OSTI2015

Dynamic Fracture Simulations of Explosively Loaded Cylinders

This report documents the modeling results of high explosive experiments investigating dynamic fracture of steel (AerMet® 100 alloy) cylinders. The experiments were conducted at Lawrence Livermore National Laboratory (LLNL) during 2007 to 2008 [10]. A principal objective of this study was to gain an understanding of dynamic material failure through the analysis of hydrodynamic computer code simulations. Two-dimensional and three-dimensional computational cylinder models were analyzed using the ALE3D multi-physics computer code.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

X-ray CT characterization and fracture simulation of ASR damage of glass particles in alkaline solution and mortar

The alkali-silica reaction (ASR) damage in reactive aggregates affects the long-term durability of the concrete infrastructure. The generated ASR gel can expand by imbibing water from the pore solution and the resulting expansion pressure causes the aggregate fracture. This study aims to simulate the development of ASR damage in glass particles of two types of samples (glass in alkali solution and glass mortars). The dynamic micro X-ray CT technique was conducted to monitor the crack propagation in glass aggregates at different reaction stages (up to 64 hrs). The Boundary Element Method (BEM) and Displacement Discontinuity Method (DDM) were used to efficiently simulate the crack propagation within irregular glass particles under gel expansion pressures. The aggregate boundaries were built with the BEM elements and the initial cracks were meshed with the DDM elements. The estimated expansion pressure was applied to the initial crack surfaces. The discontinuous displacements and stresses were calculated along the crack path and crack tip. The mixed-mode Stress Intensity Factors (SIFs) were calculated based on plane stress conditions. The maximum circumferential stress criteria was used to simulate the propagation of cracks along a specific angle. The simulation results include the simulated crack path and the combined SIFs changing with the increments. With the estimate expansion pressure, the glass particle damages were simulated within conditions of alkali solution and confined motar samples. The predicted crack propagation path was compared with the X-ray CT imaging data. The comparison results demonstrate the DDM has the ability to predicting the ASR damage propagation inside aggregates.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Simulating Fracture Sealing by Granular LCM Particles in Geothermal Drilling

Lost circulation occurs when the returned fluid is less than what is pumped into the well due to loss of fluid to pores or fractures. A lost-circulation event is a common occurrence in a geothermal well. Typical geothermal reservoirs are often under-pressured and have larger fracture apertures. A severe lost-circulation event is costly and may lead to stuck pipe, well instability, and well abandonment. One typical treatment is adding lost-circulation materials (LCMs) to seal fractures. Conventional LCMs fail to properly seal fractures because their mechanical limit is exceeded at elevated temperatures. In this paper, parametric studies in numerical simulations are conducted to better understand different thermal effects on the sealing mechanisms of LCMs. The computational fluid dynamics (CFDs) and the discrete element method (DEM) are coupled to accurately capture the true physics of sealing by granular materials. Due to computational limits, the traditional Eulerian–Eulerian approach treats solid particles as a group of continuum matter. With the advance of modern computational power, particle bridging is achievable with DEM to track individual particles by modeling their interactive forces between each other. Particle–fluid interactions can be modeled by coupling CFD algorithms. Fracture sealing capability is investigated by studying the effect of four individual properties including fluid viscosity, particle size, friction coefficient, and Young’s modulus. It is found that thermally degraded properties lead to inefficient fracture sealing.

15 GEOTHERMAL ENERGY↗

NASA NTRS1992

Finite-element analyses and fracture simulation in thin-sheet aluminum alloy

A two-dimensional, elastic-plastic finite-element analysis was used with a critical crack-tip-opening angle (CTOA) fracture criterion to model stable crack growth in thin-sheet 2024-T3 aluminum alloy under monotonic loading after precracking at different cyclic stress levels. Tests were conducted on three types of specimens: middle-crack, three-hole-crack and blunt-notch tensile specimens. An experiment technique was developed to measure CTOA during crack growth initiation and stable tearing using a high-resolution video camera and recorder. Crack front shapes were also measured during initiation and stable tearing using a fatigue marker-load technique. Three-dimensional elastic-plastic finite-element analyses of these crack shapes for stationary cracks were conducted to study the crack-front opening displacements. Predicted load against crack extension on middle-crack tension specimens agreed well with test results even for large-scale plastic deformations. The analyses were able to predict the effects of specimen size and precracking stress history on stable tearing. Predicted load against load-line displacements agreed well with test results up to maximum load bu the analyses tended to overpredict displacements as crack grew beyond the maximum load under displacement-controlled conditions. During the initiation phase, the measured CTOA values were high but decreased and remained nearly constant after a small amount of stable tearing. The constant value of CTOA agree well with the calculated value from the finite-element analysis. The larger CTOA values measured at the sheet surface during the initiation phase may be associated with the crack tunneling observed in the tests. Three-dimensional analyses for nonstraight crack fronts predicted much higher displacements near the free surface than in the interior.

Newman, J. C., Jr.↗

DOE OSTI2024

Poromechanical cohesive interface element with combined Mode I-II cohesive zone elastoplasticity for simulating fracture in fluid-saturated porous media

A combined Mode I-II cohesive zone (CZ) elasto-plastic constitutive model, and a two-dimensional (2D) cohesive interface element (CIE) are formulated and implemented at small strain within an ABAQUS User Element (UEL) for simulating 2D crack nucleation and propagation in fluid-saturated porous media. Here, the CZ model mitigates problems of convergence for the global Newton-Raphson solver within ABAQUS, which when combined with a viscous stabilization procedure allows for simulation of post-peak response under load control for coupled poromechanical finite element analysis, such as concrete gravity dam stability analysis. Verification examples are presented, along with a more complex ambient limestone-concrete wedge fracture experiment, water-pressurized concrete wedge experiment, and concrete gravity dam stability analyses. A calibration procedure for estimating the CZ parameters is demonstrated with the limestone-concrete wedge fracture process. For the water-pressurized concrete wedge fracture experiment it is shown that the inherent time-dependence of the poromechanical CIE analysis provides a good match with experimental force versus displacement results at various crack mouth opening rates, yet misses the pore water pressure evolution ahead of the crack tip propagation. This is likely a result of the concrete being partially-saturated in the experiment, whereas the finite element analysis assumes fully water saturated concrete. For the concrete gravity dam analysis, it is shown that base crack opening and associated water uplift pressure leads to a reduced Factor of Safety, which is confirmed by separate analytical calculations.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1989

Numerical fracture simulation of bend specimens using a CTOD criterion

Stable crack growth in 50-mm-thick side-grooved three-point bend specimens of HY-130 steel is modeled numerically. A two-dimensional elastoplastic FEM formulation incorporating a CTOD fracture criterion is developed analytically, and the theoretical predictions are compared with experimental data in graphs. Good general agreement is obtained, except for the crack extension, which was typically overpredicted. The value of the J integral at crack initiation is found to be 83 kJ/sq m.

Shivakumar, K. N.↗

DOE OSTI2019

Use of Neutron Flux Calculated by Shift in a Grizzly Reactor Pressure Vessel Fracture Simulation

The reactor pressure vessel (RPV) plays the critical role of containing the reactor and coolant in a light water reactor nuclear power plant, and must be able to safely perform this function under a variety of normal and off-normal transient loading conditions. The RPV is subjected to harsh environmental conditions (elevated temperature and high neutron flux) whenever the plant is operating, which leads to embrittlement of the steel over time. RPVs contain populations of flaws introduced during the manufacturing process, and the primary safety concern is that during a transient event, a fracture could initiate at the site of one of these flaws and lead to rupture of the RPV. RPVs are very rugged structures, and the probability of this occurring is very low, but as the RPV's steel becomes embrittled over time, its resistance to fracture decreases and this becomes more likely. Assessing the likelihood of RPV fracture during a transient event involves performing a probabilistic fracture mechanics analysis, in which random sampling procedures are used to assess the probability of fracture of a population of flaws. Grizzly offers unique capabilities for modeling the RPV using 1D, 2D, or 3D representations, taking advantage of parallel computing for this type of analysis. One of the important inputs to Grizzly is the spatial distribution of the neutron fluence, which has a large impact on the material embrittlement, and should thus be characterized as accurately as possible. The VERA core simulator developed by the CASL program takes advantage of high performance computing resources to perform high-fidelity multiphysics simulations of reactor physics, including the effects of neutron transport, fuel performance, and thermal hydraulics. Recently a capability was developed to also evaluate neutron fluxes away from the reactor core through the Shift code. This allows for a detailed 3D map of the spatial variation of the fluence in components such as the RPV to be computed, which is ideal for use with Grizzly. This report documents a procedure developed to use the fluences computed in Shift in a Grizzly simulation, which allows for improved realisim in the prediction of the effects of environmental exposure on propensity for reactor pressure vessel fracture. This capability demonstrated on RPVs with multiple types of configurations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Synergistic foam stabilization and transport improvement in simulated fractures with polyelectrolyte complex nanoparticles: Microscale observation using laser etched glass micromodels

Inaccessibility to direct pore scale observation in hydrocarbon recovery of tight shale formations poses a great challenge to water-energy nexus initiatives and necessitates the use of high throughput technologies to emulate environmentally friendly processes. Herein, we employ a precise glass micromodel fabrication and visualization method to isolate the supercritical CO 2 bubbles surrounded by CO 2 -water lamella prepared in saline produced water stabilized with molecular complexation of zwitterionic surfactants (ZS) and polyelectrolyte complex nanoparticles (PECNP). The Selective Laser Enhanced Etching (SLE) technique was selected for micromodel simulation of high-pressure flow. Two representative designs, (1) fracture/micro-crack network 28 and (2) fracture/matrix were etched on fused silica glass with a laser printing machine and scCO 2 foam was injected to study the foamability, propagation, stability, and fluid loss properties. The highly monodispersed and uniformly distributed array of scCO 2 bubbles were detected in flow of scCO 2 foam in highly saline brine containing ionic complexes of positively charged PECNPs and ZS, whereas foam flow with the lamella containing ZS in fractures offered a noticeably large and polydisperse array of scCO 2 bubbles. scCO 2 bubble motion and deformation were traced, and local description of foam flow was visually examined. The confined array of scCO 2 bubbles stabilized by ZS in microcracks was affected by bubble growth and coalescence, whereas the super-populated array of monodispersed scC O2 bubbles with lamella containing complexes of PECNP and ZS were able to fill the channels with stable configurations within the timeframe of comparative stability measurements. The ability of complex fluid to prevent the formation damage was evaluated through fluid loss visualization in micromodels. Probing scCO 2 foam transport in homogenous porous media revealed smaller volume leak-off for scCO 2 foam containing PECNP-ZS ionic complexes.

04 OIL SHALES AND TAR SANDS↗

DOE OSTI2016

Cavitation-based hydro-fracturing simulator

An apparatus 300 for simulating a pulsed pressure induced cavitation technique (PPCT) from a pressurized working fluid (F) provides laboratory research and development for enhanced geothermal systems (EGS), oil, and gas wells. A pump 304 is configured to deliver a pressurized working fluid (F) to a control valve 306, which produces a pulsed pressure wave in a test chamber 308. The pulsed pressure wave parameters are defined by the pump 304 pressure and control valve 306 cycle rate. When a working fluid (F) and a rock specimen 312 are included in the apparatus, the pulsed pressure wave causes cavitation to occur at the surface of the specimen 312, thus initiating an extensive network of fracturing surfaces and micro fissures, which are examined by researchers.

15 GEOTHERMAL ENERGY↗