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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

On the convexity of phase-field fracture formulations: Analytical study and comparison of various degradation functions

Efficient and accurate fracture modeling is of great importance in applications where catastrophic outcomes under extreme scenarios are possible. The phase-field (PF) approach to fracture received significant attention over the past decade, due to its capability to capture complicated fracture patterns (e.g., crack merging and branching). Specifically, crack initiation and propagation are modeled via minimization of the total energy functional, which is regularized with the aid of a phase field. Despite the promising results and modeling capabilities of the PF method in many applications, the solution of fracture problems remains computationally challenging mainly due to the non-convexity of the total energy functional with respect to the combined unknown (phase field and displacement) fields. Understanding the effects of their coupling on convexity is crucial in order to address frequently encountered hurdles in fracture modeling (e.g., inefficient solvers and non-physical crack nucleation). In this paper, we develop convexity criteria for a wide class of PF fracture formulations. For this class of formulations, the second variation of the total energy functional is expressed in terms of Hessian matrices (evaluated at individual material points). Depending on the choice of geometric crack functions and degradation functions, we classify the formulations into three categories and analytically study each one separately. To study the sign of the second variation, we derive inequalities which are satisfied at material points when the Hessian matrix is locally positive semi-definite. These inequalities provide objective criteria for comparing degradation functions. Finally, the applicability of the proposed convexity criteria is demonstrated in the context of a one-dimensional problem, solved using a conventional monolithic solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Characterization of flow and transport in a fracture network at the EGS Collab field experiment through stochastic modeling of tracer recovery

Energy extraction from subsurface reservoirs is important for addressing the increasing energy demand and environmental concerns such as global warming. However, the characterization of subsurface reservoirs, particularly reservoirs dominated by fracture networks remains a challenge due to the lack of means to directly observe subsurface processes. This study explores the feasibility and efficacy of characterizing fracture flow and transport processes in an enhanced geothermal system (EGS) testbed through stochastic tracer modeling. There are two enabling factors that allow application of stochastic modeling to characterize a subsurface reservoir. First, an abundance of geological and geophysical measurements enables the development of a high-fidelity and well-constrained fracture network model. Second, high-performance computing (HPC) allows running massive realizations efficiently. Six conservative tracer tests were stochastically modeled and produced satisfactory realizations that successfully reproduce field tracer recovery data from each tracer test. The evolution of flow and transport processes in the fracture network was then analyzed from these satisfactory realizations. This work demonstrates that stochastic tracer modeling on a high-fidelity fracture network model is feasible and can provide important insights regarding flow and transport characteristics in subsurface fractured reservoirs.

58 GEOSCIENCES↗
DOE OSTI2021

Energy based fracture initiation criterion for strain-crystallizing rubber-like materials with pre-existing cracks

Fracture prediction is indispensable for polymers, like rubbers, which have a broad range of applications mainly due to their high extensibility. The phenomenon known as strain-induced crystallization further contributes to the fracture toughness of certain rubbers. Here in this study, a criterion based on internal bond energy, incorporating the effects of crystallization, is proposed to predict fracture initiation in rubber-like materials with pre-existing cracks. First, a multi-scale mechanical model is developed for characterizing the behavior of rubber when subjected to both uniaxial and biaxial deformation states. At the microscale, both the amorphous and crystalline chain segments are modeled as elastic in order to consider the energy contribution by the molecular bond distortions. This internal energy is considered along with the entropic and crystalline free energy for each chain. In the chain model, the effects of loading condition and the relative orientation of a chain on its crystallinity are taken into account. At the macroscopic scale, an existing crystallinity distribution function is adapted and a mixed finite element formulation with an augmented Lagrangian multiplier is utilized to impose the incompressibility constraint. A non-affine maximal advance path constraint based homogenization model is utilized for bridging the two scales. Its potential to account for anisotropy in the stretched network compels the model to be preferable due to its physical significance, for the purpose of fracture modeling. The rigidity of the crystallites is accounted for by proposing a crystallite distortion energy in addition to the critical bond dissociation energy, for fracture initiation to occur. The model is validated by comparison with existing experimental results for both crystallizing and non-crystallizing rubbers. In addition to its potential to predict the material behavior when subjected to uniaxial and biaxial loading, the capability of the model to quantitatively estimate the effect of crystallization on fracture initiation is also verified.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A phase-field fracture formulation for generalized standard materials: The interplay between thermomechanics and damage

Accurately modeling fracture of ductile materials poses open challenges in the field of computational mechanics due to the multiphysics nature of their failure processes. Integrating the interplay between thermodynamics and damage into ductile fracture models is vital for predicting critical failure modes. Here, in this paper, we develop a versatile phase-field (PF) framework for modeling ductile fracture, taking into account finite-strain elasto-plasticity. The framework stems from a variational formulation of constitutive relations for generalized standard materials (GSMs), whose response is described by a Helmholtz free energy and a dissipation pseudo-potential. Its variational structure is based on a minimum principle for a functional that expresses the sum of power densities for reversible and irreversible processes. By minimizing this functional with a constraint on a von Mises yield function, we derive the evolution equation for the equivalent plastic strain and an associative flow rule. This constrained optimization problem is analytically solved for a wide class of thermo-viscoplasticity models. The key innovations of the current work include (i) a cubic plastic degradation function that accounts for a non-vanishing damage-dependent yield stress, (ii) closed-form expressions of the Helmholtz free energy and dissipation pseudo-potential for three thermo-viscoplasticity models, (iii) an extended Johnson–Cook plasticity model with a nonlinear hardening law, and (iv) a plastic work heat source that depends on the plastic degradation function and a variable Taylor–Quinney (TQ) coefficient. The capabilities of the proposed framework are tested with the aid of four ductile fracture problems, including the Sandia Fracture Challenge. In each of these problems, we examine the evolution of relevant field variables such as the PF order parameter, the equivalent plastic strain, the temperature, and the internal power dissipation density, in addition to the overall structural response quantified by the force–displacement curve. These numerical studies demonstrate that the proposed framework effectively represents ductile fracture, yielding computational results that exhibit good agreement with experimental data.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Inference of phase field fracture models

The phase field approach to modeling fracture uses a diffuse damage field to represent cracks. This representation mollifies singularities that arise in computations with sharp interface models and some of the resultant difficulties in the mathematical and numerical treatment of fracture. Phase field fracture models have proven effective at representing crack propagation, branching, and merging. Specific formulations, beginning with brittle fracture, have also been shown to converge to classical solutions. Extensions to cover the range of material failure, including ductile and cohesive fracture, lead to an array of possible models. There exists a large body of literature focusing on this class of models and on the impact of model form on the predicted crack evolution. However, there have not been systematic studies into how optimal models may be chosen. Here, we take a first step in this direction by developing formal methods for identification of the best parsimonious model of phase field fracture given full-field data on the damage and deformation fields. We consider some of the main models that have been used for the degradation of elastic response due to damage and its propagation. Our approach builds upon Variational System Identification (VSI), a weak form variant of the Sparse Identification of Nonlinear Dynamics (SINDy). Furthermore, in this first communication we focus on synthetically generated data but we also consider central issues associated with the use of experimental full-field data, such as data sparsity and noise.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Effects of HFIR neutron irradiation on fracture toughness properties of standard and Ni-doped F82H

F82H is the Japanese reference reduced-activation ferritic-martensitic (RAFM) steel for fusion blanket applications. The harsh environment of a fusion reactor, such as neutron irradiation and He/H damage, can result in significant degradation of F82H fracture toughness. Therefore, understanding the fracture toughness behavior of F82H in the fusion environment is critical to ensure the long-term safe operation of the fusion reactor. Here, we summarize seven irradiation campaigns of the High Flux Isotope Reactor (HFIR) at Oak Ridge National Laboratory (ORNL) covering five variants of F82H steels, including F82H IEA, F82H Mod3, F82H doped with 1.4% natural Ni, F82H doped with 1.4% 58 Ni, and F82H doped with 1.4% 60 Ni. The irradiation temperatures covered the range from 220 °C to 530 °C and the neutron irradiation dose spanned 4 dpa to 70 dpa. The effects of neutron irradiation temperature, dose, materials composition, Ni doping, and He production on F82H fracture toughness are discussed. Our results showed that irradiation embrittlement monotonically decreased with increasing irradiation temperature until 400 °C for F82H IEA and F82H Mod3. F82H Mod3 showed better fracture toughness than F82H IEA both before and after neutron irradiation. We determined that 1.4% Ni alloying can be applied to F82H for simulating He effect in a fission reactor without jeopardizing the fracture toughness of the material. However, more studies are needed to understand the effect of high dose (>20 dpa) and He production on F82H fracture toughness.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Intrinsic and extrinsic effects on the fracture toughness of ductile metallic glasses

The potential application of metallic glasses (MGs) as structural materials demands accurate measurements of their toughness and the understanding of the underlying factors affecting it. Currently, it is challenging to precisely measure the toughness of MGs, especially ductile MGs. Measured toughness values are widely scattered, even for MGs with identical compositions. That is attributed to the combined effect of intrinsic and extrinsic factors including processing, sample geometries, and loading conditions. A fundamental understanding of the influences of these elements is thus of great significance. In the present study, molecular dynamics simulations are performed to investigate the influence of intrinsic and extrinsic effects on the fracture toughness of CuZr MGs. In particular, focused is placed on the effects of cooling rate, notch shape and size, strain rate, and temperature. The results indicate that the fracture toughness of a MG scales with the cooling rate used to prepare it. This is attributed to increased free volume content generated at high cooling rates, which enhances plastic deformation and amplifies the associated energy dissipation during plastic deformation events. Fracture toughness also increases with the strain rate, arguably due to strain rate-induced crack extension delay. Overall, the results demonstrate that the largest fracture toughness are achieved when MG samples are fabricated at high cooling rates and subjected to high strain rate deformation. In addition, results suggest that the fracture toughness decreases with increasing temperature, due to the significant decrease in strength. Here, the correlations revealed between these crucial intrinsic and extrinsic parameters and the calculated MG fracture toughness support the development of a framework to understand the root of the discrepancies in the measurement of the toughness of MGs and provide insights into the design of tough MGs for structural applications.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Predicting the Macroscopic Fracture Energy of Epoxy Resins from Atomistic Molecular Simulations

Predicting the macroscopic fracture energy of highly crosslinked glassy polymers from atomistic simulations is challenging due to the size of the process zone being large in these systems. Here, we present a scale-bridging approach that links atomistic molecular dynamics simulations to macroscopic fracture properties on the basis of a continuum fracture mechanics model for two different epoxy materials. Our approach reveals that the fracture energy of epoxy resins strongly depends on the functionality of epoxy resin and the component ratio between the curing agent (amine) and epoxide. The most intriguing part of our study is that we demonstrate that the fracture energy exhibits a maximum value within the range of conversion degrees considered (from 65% to 95%), which can be attributed to the combined effects of structural rigidity and post-yield deformability. Our study provides physical insight into the molecular mechanisms that govern the fracture characteristics of epoxy resins and demonstrates the success of utilizing atomistic molecular simulations towards predicting macroscopic material properties.

42 ENGINEERING↗
DOE OSTI2018

Advancing graph-based algorithms for predicting flow and transport in fractured rock

Discrete fracture network (DFN) models are a powerful alternative to continuum models for subsurface flow and transport simulations because they explicitly include fracture geometry and network topology, thereby allowing for better characterization of the latter's influence on flow and transport through fractured media. Recent advances in high performance computing have opened the door for flow and transport simulations in large explicit three-dimensional DFN, but this increase in model fidelity and system size comes at a huge computational cost because of the large number of mesh elements required to represent thousands of fractures (with sizes that can range several orders of magnitude, from mm to km). In most subsurface applications, fracture characteristics are only known statistically and numerous realizations are needed to bound uncertainty in flow and transport in the system, thereby exacerbating the computational burden. blackGraphs provide a simple and elegant way to characterize, query, and interrogate fracture network connectivity. We propose a DFN model reduction framework where various graph-representations are used in conjunction with high-fidelity DFN simulations to increase computational efficiency while retaining accuracy of key quantities of interest. The appropriate choice of a graph-representation, namely, which attributes of the DFN are to be represented as nodes and which ones as edges connecting those nodes, depends on the relevant scientific questions. We demonstrate that the proposed DFN model reduction framework provides an efficient means for DFN modeling through both system reduction of the DFN using graph-based properties and combining DFN and graph-based flow and transport simulations.

58 GEOSCIENCES↗
DOE OSTI2018

Friction-Stability-Permeability Evolution of a Fracture in Granite

The evolution of frictional strength, stability, and fracture permeability is intimately linked both to the seismic cycle and to the impact of hydraulic stimulation for fractured reservoirs. However, despite this importance, the poromechanical relationships between fault permeability and strength remain unclear. The present study explores this relationship via laboratory experiments for concurrent shear-flow on smooth fractures of Westerly granite. The novelty of these experiments is that the shear velocity is precisely controlled during the measurement of fracture permeability. Results indicate permeability enhancement during velocity-weakening (potentially unstable) frictional slip. To decipher key processes contributing to this response, we evaluate the state of contacting asperities and of fracture surface asperities via digital rock fracture modeling of statistically equivalent surfaces. We propose two plausible mechanisms constraining the relationship between friction and permeability evolution—one based on changes in asperity contact distribution and one on shear-induced dilation triggered by changes in fault slip velocity. Finally, these mechanisms should be taken into account in interpreting field observation such as the abrupt permeability increase of natural faults at the onset of seismic slip.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Investigation of Coupled Processes in Fractures and the Bordering Matrix via a Micro‐Continuum Reactive Transport Model

Abstract In multi‐mineral fractured rocks, the altered porous layer on the fracture surface resulting from preferential dissolution of the fast‐reacting minerals can have profound impacts on subsequent chemical‐physical alteration of the fractures. This study adopts the micro‐continuum approach to provide further understanding of reactive transport processes in the altered layer (AL), and mass exchanges with the bordering matrix and fracture. The modeling framework couples the Darcy‐Brinkman‐Stokes (DBS) solver in COMSOL Multiphysics and the geochemical modeling capability of CrunchFlow. Three‐dimensional steady state simulations with systematically varied chemical‐physical parameters of the AL were performed to examine the impacts of individual factors and processes. Our simulation results confirm previous observations that dissolution of the fast‐reacting mineral (i.e., calcite) is largely controlled by diffusion across the AL. We also show that dissolution of the slow‐reacting mineral (i.e., dolomite), which controls AL development and fracture enlargement, increases with surface area and has a complex dependence on different local rate‐limiting processes. In particular, advection can result in evident spatial variations in the local dissolution rates of dolomite, although it does not affect the bulk chemistry significantly. The difference in the spatial patterns between simulations with and without advection in the AL is more noticeable in the locations with smaller apertures, with up to 20% difference in local reaction rates. Therefore, it is important to include a full depiction of advection, diffusion, and reactions for accurately capturing local dynamics that control long‐term fracture evolution.

58 GEOSCIENCES↗
DOE OSTI2024

Complex Fluid‐Driven Fractures Caused by Crack‐Parallel Stress

Abstract Managing fluid‐driven fracture networks is crucial for subsurface resource utilization, yet the current understanding of the key controlling factors remains insufficient. While geologic discontinuities have been shown to significantly influence fracture network complexity, this study identifies another major contributor. We conducted a new set of experiments using a transparent true triaxial cell, which enabled video recording of the temporal evolution of fluid‐driven fracture paths. Using pseudo‐2D samples without macroscale structural discontinuities, we observed multiple occurrences of hydraulic fracture curving and branching under anisotropic boundary stresses. We proposed a theoretical model demonstrating that the stress parallel to the crack line in the solid matrix near the crack tip (i.e., the T ‐stress) accounts for the observed fracture curving behavior. This finding suggests that T ‐stress is an additional mechanism contributing to the complexity of fluid‐driven fracture networks in the subsurface, besides the geologic discontinuities.

58 GEOSCIENCES↗
DOE OSTI2020

Transient flow modeling in fractured media using graphs

In this work, we describe a method to simulate transient fluid flows in fractured media using an approach based on graph theory. Our approach builds on past work where the graph-based approach was successfully used to simulate steady-state fluid flows in fractured media. We find a mean computational speedup of the order of 1400 from an ensemble of a 100 discrete fracture networks in contrast to the O(10 4 ) speedup that was obtained for steady-state flows earlier. However, the transient flows considered here involve an additional degree of complexity that was not present in the steady-state flows considered previously with a graph-based approach, that of time marching and solution of the flow equations within a time-stepping scheme. We verify our method with an analytical test case and demonstrate its use on a practical problem related to fluid flows in hydraulically fractured reservoirs. By enabling the study of transient flows, we create an opportunity for a wide set of possibilities where a steady-state approximation is not sufficient, such as the example motivated by hydraulic fracturing that we present here. This work validates the concept that graphs are able to reliably capture the topological properties of the fracture network and serve as effective surrogates in an uncertainty-quantification framework.

58 GEOSCIENCES↗
DOE OSTI2016

Peculiar features of boron distribution in high temperature fracture area of rapidly quenched heat-resistant nickel alloy

This article comprises the results of comprehensive study of the structure and distribution in the high temperature fracture area of rapidly quenched heat-resistant superalloy of grade EP741NP after tensile tests. The structure and boron distribution in the fracture area are studied in detail by means of direct track autoradiography in combination with metallography of macro- and microstructure. A rather extensive region of microcracks generation and intensive boron redistribution is detected in the high temperature fracture area of rapidly quenched nickel superalloy of grade EP741NP. A significant decrease in boron content in the fracture area and formation of elliptically arranged boride precipitates are revealed. The mechanism of intense boron migration and stability violation of the structural and phase state in the fracture area of rapidly quenched heat-resistant nickel superalloy of grade EP741NP is proposed on the basis of accounting for deformation occurring in the fracture area and analysis of the stressed state near a crack.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Fracture detection and imaging through relative seismic velocity changes using distributed acoustic sensing and ambient seismic noise

Fracture systems are important pathways for fluid and solute transport and exert a critical influence on the hydraulic properties of aquifers and reservoirs. Therefore, detailed knowledge of fracture locations, connections, and evolution is crucial for both groundwater and energy applications (e.g., enhanced geothermal, oil and gas recovery, carbon sequestration, and wastewater injection). The innovative combination of distributed acoustic sensing (DAS) and ambient seismic noise techniques has the potential to detect and characterize fracture systems at high-spatial and temporal resolution without an active source. To test this, we conducted a multiphysics field experiment at Blue Canyon Dome, New Mexico. A novel energetic material developed by Sandia National Laboratories was used to generate fractures in two separate stimulations. Ambient noise was recorded before and after each stimulation using fiber-optic cables installed in the outer annulus of four boreholes surrounding the stimulation hole at a radius of 1.2 m. The Python package MSNoise was used to compute crosscorrelations and measure changes in velocity between each time period relative to the initial (prestimulation) time period. The majority of channel pairs showed a velocity reduction (average –3% relative velocity change) following both stimulations. We used a 3D Bayesian tomography approach to resolve spatial variations by utilizing differences between channel pairs. Results showed that the greatest velocity reduction was concentrated near the center of the test area and suggested the presence of a near-vertical fracture, oriented northeast to southwest for depths >19 m below ground surface and extending slightly to the southwest corner. Finally, these results were generally consistent with crosshole seismic tomography time-lapse images. DAS technology provides valuable sensing capability and — when used with a passive seismic approach — shows great promise for monitoring and characterization of fractured-rock systems.

58 GEOSCIENCES↗
DOE OSTI2022

Adhesively-bonded Metal-CFRTP Bi-materials: Enhanced Crack Growth Resistance via Plasma and Quantified Fracture via Size Effect Method

This work investigated air plasma effect on the Mode I crack growth resistance of adhesively-bonded metal-CFRTP dissimilar joints by using aluminum alloy (AA6061) and short-carbon-fiber-reinforced polyamide 66 (CFRPA66) as an example, and the Double Cantilever Beam (DCB) fracture testing as an evaluation method. The results show that air plasma treatment can significantly improve the fracture resistance of adhesively-bonded AA6061-CFRPA66 dissimilar joints with about 140% enhanced Mode I fracture energy in maximum compared to non-treated ones. The quantified fracture energies from size effect method for both non-treated and plasma-treated cases are geometry-independent, whereas this is not true for modified beam theory causing geometry-dependent results. The foregoing improvement was confirmed from the failure surface morphology of plasma-treated specimens, showing fibers peeling off from CFRPA66 surface due to plasma-enhanced bonding between CFRPA66 and adhesive by the formation of covalent bonds at their interface. This study demonstrated air plasma as an efficient surface modification method to enhance the fracture resistance of adhesively-bonded metal-CFRTP dissimilar joints, and size effect method as a characterization method to properly quantify their fracture properties. These aspects are valuable in the area of multi-materials joining.

Plasma, Adhesive Bonding, Slow Crack Growth, fract↗
DOE OSTI2020

Value-of-Information Analysis of a Fracture Prediction Method

A core-based fracture prediction method is used to illustrate a Value of Information (VOI) decision-analysis protocol to inform completion decisions in tight-gas sandstones. The ratio of late host-rock cement to available pore volume or degradation index uses petrographic observations of cement distributions in core (including sidewall cores) to predict whether nearby but unsampled fractures (widths > 0.5 to 1 mm) are sealed (non-conductive) or open (conductive). Measurements from four sandstone plays suggest that the index correctly predicts open vs. sealed fractures with an accuracy in excess of 80%. The value added is calculated using Bayesian inference in which accuracy of the index serves as the likelihood of the prior distribution of open fractures to assess the posterior probability that data represent a useful predictor of producibility. VOI of the prediction method is more than three times the cost to acquire the data. VOI is most sensitive to play-specific geologic and cost parameters including cost to drill, expected revenue from a successful well, cost of completion, cost of acquiring data for the index, and fracture probability distributions. The approach provides a way to value acquiring fracture data and points to a need for zone-specific production data in tight-gas sandstones.

02 PETROLEUM↗
DOE OSTI2025

Geochemical Impact of Acid Spearhead and Slickwater Stimulation on Wolfcamp Shale from the Hydraulic Fracturing Test Site

The Hydraulic Fracturing Test Site 1 (HFTS-1) was a field study performed in the Wolfcamp Formation in the West Texas Permian (Midland) Basin, USA, with a focus on improving the efficiency of hydraulic fracturing. Investigating site-specific rock-fluid geochemical interactions during hydraulic fracturing is an important step to understanding the impact on formation shale porosity, permeability, and long-term shale gas production. During field operations in this region, hydraulic fracturing fluid (HFF) injection usually starts with a concentrated acid spearhead for rapid rock dissolution, followed by the injection of near-neutral pH slickwater containing chemicals and proppants. A multistep sequential injection approach was used to investigate different stages of rock-fluid interactions. The carbonate content in the host rock is important when acid spearhead is considered, as carbonate mineral dissolution is rapid and can result in porosity and permeability changes in the shale matrix. Here, in this study, we designed flow-through experiments using fractured carbonate-rich and clay-rich Wolfcamp shale cores with (1) a short-time acid soaking step and (2) a long-term slickwater flow-through step to simulate the injection method used at HFTS-1. The fluid chemistry was analyzed. A thorough mineralogical progression [e.g., Calcium (Ca) dissolution and iron (Fe) redox progression] in the cores during HFF injection was also characterized and imaged by synchrotron microprobe. Reactive transport modeling was performed based on the experimental setup. The results showed that the acid spearhead is a crucial step in creating a reaction front by mineral dissolution, especially in carbonate-rich shales. A slight layer of ferrihydrite precipitated during the slickwater flow-through period. This study provides insights into potential geochemical impact due to hydraulic fracturing operations in the Permian Basin.

clastic rock↗