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DOE OSTI2013

Natural time analysis of critical phenomena: The case of pre-fracture electromagnetic emissions

Criticality of complex systems reveals itself in various ways. One way to monitor a system at critical state is to analyze its observable manifestations using the recently introduced method of natural time. Pre-fracture electromagnetic (EM) emissions, in agreement to laboratory experiments, have been consistently detected in the MHz band prior to significant earthquakes. It has been proposed that these emissions stem from the fracture of the heterogeneous materials surrounding the strong entities (asperities) distributed along the fault, preventing the relative slipping. It has also been proposed that the fracture of heterogeneous material could be described in analogy to the critical phase transitions in statistical physics. In this work, the natural time analysis is for the first time applied to the pre-fracture MHz EM signals revealing their critical nature. Seismicity and pre-fracture EM emissions should be two sides of the same coin concerning the earthquake generation process. Therefore, we also examine the corresponding foreshock seismic activity, as another manifestation of the same complex system at critical state. We conclude that the foreshock seismicity data present criticality features as well.

58 GEOSCIENCES↗

DOE OSTI2013

Islands stretch test for measuring the interfacial fracture energy between a hard film and a soft substrate

We present a technique for measuring the interfacial fracture energy, {Gamma}{sub i}, between a hard thin film and a soft substrate. A periodic array of hard thin islands is fabricated on a soft substrate, which is then subjected to uniaxial tension under an optical microscope. When the applied strain reaches a critical value, delamination between the islands and the substrate starts from the edge of the islands. As the strain is increased, the interfacial cracks grow in a stable fashion. At a given applied strain, the width of the delaminated region is a unique function of the interfacial fracture energy. We have calculated the energy release rate driving the delamination as a function of delamination width, island size, island thickness, and applied strain. For a given materials system, this relationship allows determination of the interfacial fracture energy from a measurement of the delamination width. The technique is demonstrated by measuring the interfacial fracture energy of plasma-enhanced chemical vapor deposition SiN{sub x} islands on a polyimide substrate. We anticipate that this technique will find application in the flexible electronics industry where hard islands on soft substrates are a common architecture to protect active devices from fracture.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2015

Statistical features of magnetic noise in mixed-type impact fracture

We study the statistical features of magnetic noise accompanying the dynamic fracture of steel samples during mixed type fracture, where the overall ductile character of crack propagation is interrupted by a sudden brittle jump. The structure of the voltage time series is investigated by identifying discrete peaks which correspond to elementary steps of the jerky cracking process. We show that the height, duration, area, and energy of peaks have power law distributions with exponents falling close to the corresponding values of pure ductile fracture. For single peaks, a power law correlation of the height and area with the width is evidenced; however, the mixed nature of fracture gives rise to a crossover between two regimes of different exponents. The average pulse shape of micro-cracking events has a parabolic form with a right handed asymmetry similarly to quasi-static fracture propagation. The asymmetry emerges due to stress localization at the advancing crack front.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2014

A novel pillar indentation splitting test for measuring fracture toughness of thin ceramic coatings

Fracture toughness is an important material property that plays a role in determining the in-service mechanical performance and adhesion of thin ceramic films. Unfortunately, measuring thin film fracture toughness is affected by influences from the substrate and the large residual stresses that can exist in the films. In this paper, we explore a promising new technique that potentially overcomes these problems based on nanoindentation testing of micro-pillars produced by focused ion beam milling of the films. By making the pillar diameter approximately equal to its length, the residual stress in the pillar’s upper portion is almost fully relaxed, and when indented with a sharp Berkovich indenter, the pillars fracture by splitting at reproducible loads that are readily quantified by a sudden displacement excursion in the load displacement behavior. Cohesive finite element simulations are used to analyze and develop, for a given material, a simple relation between the critical load at failure, pillar radius, and fracture toughness. The main novel aspect of this work is that neither crack geometries nor crack sizes need to be measured post test. Furthermore, the residual stress can be measured at the same time with toughness, by comparing the indentation results from the stress-free pillars and the as-deposited film. The method is tested on three different hard coatings formed by physical vapor deposition: titanium nitride, chromium nitride, and a CrAlN/Si 3 N 4 nanocomposite. Results compare well to independently measured values of fracture toughness for the three brittle films. The technique offers several benefits over existing methods.

42 ENGINEERING↗

DOE OSTI2022

Understanding the Elastic, Plastic, and Damage Features in Fracturing of Self-reinforced Thermoplastic Composites via Non-destructive Digital Imaging Correlation

This work demonstrated the utilization of non-destructive Digital Imaging Correlation (DIC) method to characterize the elastic, plastic, and damage features during the Mode I intra-laminar fracturing process of self-reinforced thermoplastic composites by using a self-reinforced polypropylene (PP) composite as an example. The DIC results clearly showed the development of huge plastic zone (PZ) and non-negligible Fracture Process Zone (FPZ) in front of the notch tip during the fracturing process, and the geometries and sizes of the foregoing zones at the peak load were further quantified. Such an interesting fracturing behavior of self-reinforced thermoplastic composites is way different from brittle materials (e.g., glass, acrylic, etc.), ductile materials (e.g., aluminum, steel, etc.), and even quasi-brittle materials (e.g., concrete, nanoparticle-reinforced composites, tough ceramics, wood, cement, carbon/glass fiber-reinforced polymers, etc.). Thus, understanding the elastic, plastic, and damage features is the first step before better characterizing the material fracture properties of self-reinforced thermoplastic composites through new analytical methods and computational modeling. These efforts are of utmost importance for wide applications of self-reinforced thermoplastic composites in various engineering fields in the future.

Lightweight Composites, Self-reinforced Thermoplas↗

DOE OSTI2014

Elongational rheology and cohesive fracture of photo-oxidated LDPE

It was found recently that low-density polyethylene (LDPE) samples with different degrees of photo-oxidation represent an interesting system to study the transition from ductile to cohesive fracture and the aspects of the cohesive rupture in elongational flow. Sheets of LDPE were subjected to photo-oxidation in the presence of air using a xenon lamp to irradiate the samples for times between 1 day and 6 weeks. Characterisation methods included Fourier transform infrared spectroscopy, solvent extraction method, and rheology in shear and uniaxial extensional flows. Linear viscoelasticity was increasingly affected by increasing photo-oxidation due to crosslinking of LDPE, as corroborated by the carbonyl index, acid and aldehydes groups, and gel fraction. The molecular stress function model was used to quantify the experimental data, and the nonlinear model parameter β was found to be correlated with the gel content. The uniaxial data showed that the transition from ductile to cohesive fracture was shifted to lower elongational rates, the higher the gel content was. From 2 weeks photo-oxidation onwards, cohesive rupture occurred at every strain rate investigated. The true strain and true stress at cohesive fracture as well as the energy density applied to the sample up to fracture were analyzed. At low gel content, rupture was mainly determined by the melt fraction while at high gel content, rupture occurred predominantly in the gel structure. The strain at break was found to be independent of strain rate, contrary to the stress at break and the energy density. Thus, the true strain and not the stress at break or the energy density was found to be the relevant physical quantity to describe cohesive fracture behavior of photo-oxidated LDPE. The equilibrium modulus of the gel structures was correlated with the true strain at rupture. The stiffer the gel structure, the lower was the deformation tolerated before the sample breaks.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Identifying Backbones in Three-Dimensional Discrete Fracture Networks: A Bipartite Graph-Based Approach

In this paper, we present a graph-based method to identify primary flow and transport sub-networks in three-dimensional discrete fracture networks (DFNs). The structure of a DFN lends itself to the use of graphs as a coarse-scale representation that retains the multiscale nature of flow and transport through fracture media. We develop a bipartite graph representation that integrates fracture network topology, fracture geometry, and hydraulic properties. We show that the two most common graph-representations of DFNs, vertices representing intersections and vertices representing fractures, are projections of this bipartite graph thereby providing a generalization of previous DFN-graph frameworks. The primary subnetworks in each DFN are identified by running a heuristic algorithm that determines the edge-disjoint shortest paths through the graph which correspond to the regions where the fastest transport occurs. The method does not have any user-defined parameters and terminates in a finite number of steps. The quality of the method is demonstrated by comparing transport simulations on the identified primary subnetwork and full network, which are in good agreement for early and middle times. In conclusion, these estimates of the first passage times can be achieved with close to an order of magnitude reduction of computational expense using the proposed method.

58 GEOSCIENCES↗

DOE OSTI2013

Modeling the Fracture of Ice Sheets on Parallel Computers

The objective of this project was to investigate the complex fracture of ice and understand its role within larger ice sheet simulations and global climate change. This objective was achieved by developing novel physics based models for ice, novel numerical tools to enable the modeling of the physics and by collaboration with the ice community experts. At the present time, ice fracture is not explicitly considered within ice sheet models due in part to large computational costs associated with the accurate modeling of this complex phenomena. However, fracture not only plays an extremely important role in regional behavior but also influences ice dynamics over much larger zones in ways that are currently not well understood. To this end, our research findings through this project offers significant advancement to the field and closes a large gap of knowledge in understanding and modeling the fracture of ice sheets in the polar regions. Thus, we believe that our objective has been achieved and our research accomplishments are significant. This is corroborated through a set of published papers, posters and presentations at technical conferences in the field. In particular significant progress has been made in the mechanics of ice, fracture of ice sheets and ice shelves in polar regions and sophisticated numerical methods that enable the solution of the physics in an efficient way.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Initial Fracture Propagation Modeling of Graphite Components with Grizzly

Graphite has historically been extensively used in power reactor cores and will be used in multiple types of advanced reactors currently under development. These graphite structural components can experience significant stresses due to nonuniform volumetric strains induced by irradiation and thermal expansion, which can lead to fracture. Robust tools for predicting fracture initiation and propagation in graphite structural components in nuclear reactors are important for evaluating component integrity, developing design standards, and interpreting experimental results to characterize graphite performance. The U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation program has been developing degradation models for other structural components in nuclear reactors within the Grizzly and BlackBear codes. This report documents an effort to develop initial capabilities for modeling graphite fracture within these codes, building on prior efforts to model fracture in other materials. Major elements of this effort include developing a new system for modeling fracture nucleation and growth in two dimensions using the extended finite element method and incorporating a damage and plasticity model. These capabilities are applied here to model a representative graphite component and a splitting disc experiment used to obtain tensile strength.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Predicting Fracture Porosity Evolution in Sandstone

To better understand the porosity, strength, chemical reactivity, and patterns of fractures in the subsurface, we used evidence from mineral deposits in open fractures to unravel how fracture growth and diagenesis interact to create and destroy fracture porosity. Quartz cement textures and associated fluid inclusions and thermal histories provided data used to infer the duration and rates at which fractures open.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Dynamic Binary Complexes (DBC) as Super-Adjustable Viscosity Modifiers for Hydraulic Fracturing Fluids

In the preceding project year two, we refined three DBC formulations from a selection of over 50 different chemistries. The optimization study primarily encompassed testing for (i) reversibility extent, (ii) performance in the presence of chemical additives, (iii) adhesion and friction behavior during displacement in wellbores and pipelines, (iv) corrosion protection performance, and (v) injection performance with model fracture systems at the laboratory scale. Highly promising results obtained from all these tests signify the significant potential of DBCs in enhancing hydrocarbon recovery from unconventional reservoirs. The primary activities in the third project year included publishing experimental findings across multiple articles and conducting outreach initiatives. Throughout the year, we undertook tasks such as replicating experimental results, further optimizing various formulations and their associated experimental sets, and conducting additional tests to address missing components based on reviewer feedback and suggestions. We also explored the surfactant and friction-reduction aspects of selected formulations through drag reduction tests. In addition, we constructed an improved fracturing performance setup and performed flow injection tests. The specific DBC formulations focused on during this project period were A8/B1, A12/B5, and A10/B12. We also obtained results for additional DBC formulations and a select few commercial fracturing fluids for the purpose of comparison. Within the project's scope, we aim to enhance the experimental findings with the development of various models. The first two years focused on two key aspects: (i) the creation of a high-fidelity hydraulic fracturing model for non-Newtonian fluids to gain insights into the implementation of DBC fluids in fracking environments, and (ii) the development of a multiphase flow simulator for estimating total production, fluid saturation in the reservoir, and the creation of a fracture propagation model and kinetic Monte Carlo (kMC) models for diverse applications. In the third year, we delved into the fundamental nanostructural properties of DBCs, exploring aspects such as material chemistry, pH tunability, and control of DBC formation and stability. Subsequently, in the extension year, we conducted a systematic investigation of various building blocks containing primary, secondary, and tertiary amine functional groups to understand their impact on rheological and viscoelastic properties. Furthermore, we explored a Dissipative Particle Dynamics (DPD) model to simulate self-assembly processes with precision, creating a high-fidelity representation of relevant nanostructures. The tasks performed this year with the significant results obtained have been discussed in Section 2.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

FracML: A Machine Learning Based Tool to Quantify Reservoir Scale Fracture Network for CO2 Storage

Poster on “FRACML: A Machine Learning Based Tool to Quantify Reservoir Scale Fracture Network for CO2 Storage” for the CCUS 2025 conference held in Houston, Texas March 3-5, 2025. The accurate characterization of subsurface fracture networks is essential for the secure operation of carbon capture, utilization, and storage (CCUS) projects. A thorough understanding of the spatial distribution of subsurface faults and fractures is crucial for predicting CO2 plume evolution and minimizing risks such as potential leakage into overlying formations or induced seismicity. In this context, robust fracture network quantification plays a pivotal role in reservoir management, providing the data necessary to fine-tune operational parameters, and ensure the environmental and economic viability of CCUS projects. As part of the U.S. Department of Energy’s SMART (Science-informed Machine Learning for Accelerating Real-time Decisions in Subsurface Applications) initiative, we focused on the development and application of a machine learning-based tool (FRACML) designed to quantify and map fracture networks using real-world (non-synthetic) data from an active CO2 injection site. Our objective is to demonstrate the utility of this tool in improving operational efficiency and safety across CCUS sites.

artifical intelligence / machine learning (AI/ML)↗

NASA NTRS1988

Fracture resistance of a TiB2 particle/SiC matrix composite at elevated temperature

The fracture resistance of a commercial TiB 2 particle/SiC matrix composite was evaluated at temperatures ranging from 20 to 1400 °C. A laser interferometric strain gauge (LISG) was used to continuously monitor the crack mouth opening displacement (CMOD) of the chevron-notched and straight-notched, three-point bend specimens used. Crack growth resistance curves (R-curves) were determined from the load versus displacement curves and displacement calibrations. Fracture toughness, work-of-fracture, and R-curve levels were found to decrease with increasing temperature. Microstructure, fracture surface, and oxidation coat were examined to explain the fracture behavior.

Fracture↗

DOE OSTI2014

Stimuli Responsive/Rheoreversible Hydraulic Fracturing Fluids for Enhanced Geothermal Energy Production (Part II)

We have used an environmentally friendly and recyclable hydraulic fracturing fluid - diluted aqueous solutions of polyallylamine or PAA – for reservoir stimulation in Enhanced Geothermal System (EGS). This fluid undergoes a controlled and large volume expansion with a simultaneous increase in viscosity triggered by CO2 at EGS temperatures. We are presenting here the results of laboratory-scale hydraulic fracturing experiment using the fluid on small cylindrical rock cores (1.59 cm in diameter and 5.08 cm in length) from the Coso geothermal field in California. Rock samples consisted of Mesozoic diorite metamorphosed to greenschist facies. The experiments were conducted on 5 samples for realistic ranges of pressures (up to 275 bar) and temperatures (up to 210 °C) for both the rock samples and the injected fluid. After fracturing, cores were subjected to a CO2 leakage test, injection of KI solution, and X-ray microtomography (XMT) scanning to examine the formation and distribution of fractures. The design and conduct of these experiments will be presented and discussed in details. Based on the obtained XMT images, Computational Fluid Dynamics (CFD) simulations were then performed to visualize hydraulic fractures and compute the bulk permeability. OpenFOAM (OpenCFD Ltd., Reading, UK), was used to solve the steady state simulation. The flow predictions, based upon the laminar, 3-D, incompressible Navier-Stokes equations for fluid mass and momentum, show the remarkable stimulation of the permeability in the core samples and demonstrate the efficiency of such a CO2 triggered fluid in EGS.

CO2-activated↗

DOE OSTI2018

An Overview of the EGS Collab Project: Field Validation of Coupled Process Modeling of Fracturing and Fluid Flow at the Sanford Underground Research Facility, Lead, SD

Enhanced Geothermal Systems (EGS) development will require an ability to accurately predict the flow rates and temperatures of the production wells. While simple in concept, complex heterogeneous fracture pathways can lead to channeling, short-circuiting, and premature thermal breakthrough complicating EGS. The EGS Collab project will establish a suite of intermediate-scale (~10-20 m) field test beds coupled with stimulation and interwell flow tests to provide a basis to better understand the fracture geometries and processes that control heat transfer between rock and stimulated fractures. These experiments will provide a means of testing tools, codes, and concepts that could later be employed under geothermal reservoir conditions at FORGE and in EGS. We will perform well-controlled, in situ experiments focused on rock fracture behavior and permeability enhancement. Pre- and post-test modeling of each test will allow for model prediction and validation. Comprehensive instrumentation will be used to collect high-quality, high-resolution geophysical and fracture characterization and fluid flow data. ,These data will be analyzed and compared with models and field observations to further elucidate the basic relationships between stress, induced seismicity, and permeability enhancement. To the maximum extent achievable, we will observe and quantify other key governing parameters that impact permeability, and attempt to understand how these parameters might change throughout the development and operation of an EGS project with the goal of enabling commercial viability of EGS. The Sanford Underground Research Facility (SURF) in South Dakota was selected as the EGS Collab project experimental site based on the evaluation of information from several sites. Our team has designed and constructed the first field experiment planned for this project, which is supported by the US Department of Energy’s Geothermal Technologies Office.

EGS, FORGE, field fracture stimulation and flow ex↗

DOE OSTI2025

A review of thermo-hydro-mechanical modeling of coupled processes in fractured rock: From continuum to discontinuum perspective

Coupled thermo-hydro-mechanical (THM) processes in fractured rock are playing a crucial role in geoscience and geoengineering applications. Diverse and conceptually distinct approaches have emerged over the past decades in both continuum and discontinuum perspectives leading to significant progress in their comprehending and modeling. This review paper offers an integrated perspective on existing modeling methodologies providing guidance for model selection based on the initial and boundary conditions. By comparing various models, one can better assess the uncertainties in predictions, particularly those related to the conceptual models. The review explores how these methodologies have significantly enhanced the fundamental understanding of how fractures respond to fluid injection and production, and improved predictive capabilities pertaining to coupled processes within fractured systems. It emphasizes the importance of utilizing advanced computational technologies and thoroughly considering fundamental theories and principles established through past experimental evidence and practical experience. The selection and calibration of model parameters should be based on typical ranges and applied to the specific conditions of applications. The challenges arising from inherent heterogeneity and uncertainties, nonlinear THM coupled processes, scale dependence, and computational limitations in representing field scale fractures are discussed. Realizing potential advances on computational capacity calls for methodical conceptualization, mathematical modeling, selection of numerical solution strategies, implementation, and calibration to foster simulation outcomes that intricately reflect the nuanced complexities of geological phenomena. Future research efforts should focus on innovative approaches to tackle the hurdles and advance the state-of-the-art in this critical field of study.

Coupling scheme↗

DOE OSTI2014

Impact of velocity correlation and distribution on transport in fractured media: Field evidence and theoretical model

Flow and transport through fractured geologic media often leads to anomalous (non-Fickian) transport behavior, the origin of which remains a matter of debate: whether it arises from variability in fracture permeability (velocity distribution), connectedness in the flow paths through fractures (velocity correlation), or interaction between fractures and matrix. Here we show that this uncertainty of distribution- versus correlation-controlled transport can be resolved by combining convergent and push-pull tracer tests because flow reversibility is strongly dependent on velocity correlation, whereas late-time scaling of breakthrough curves is mainly controlled by velocity distribution. We build on this insight, and propose a Lagrangian statistical model that takes the form of a continuous time random walk (CTRW) with correlated particle velocities. In this framework, velocity distribution and velocity correlation are quantified by a Markov process of particle transition times that is characterized by a distribution function and a transition probability. Our transport model accurately captures the anomalous behavior in the breakthrough curves for both push-pull and convergent flow geometries, with the same set of parameters. Thus, the proposed correlated CTRW modeling approach provides a simple yet powerful framework for characterizing the impact of velocity distribution and correlation on transport in fractured media.

58 GEOSCIENCES↗

DOE OSTI2015

Multiporosity flow in fractured low-permeability rocks: Extension to shale hydrocarbon reservoirs

We presented a multiporosity extension of classical double and triple-porosity fractured rock flow models for slightly compressible fluids. The multiporosity model is an adaptation of the multirate solute transport model of Haggerty and Gorelick (1995) to viscous flow in fractured rock reservoirs. It is a generalization of both pseudo steady state and transient interporosity flow double-porosity models. The model includes a fracture continuum and an overlapping distribution of multiple rock matrix continua, whose fracture-matrix exchange coefficients are specified through a discrete probability mass function. Semianalytical cylindrically symmetric solutions to the multiporosity mathematical model are developed using the Laplace transform to illustrate its behavior. Furthermore, the multiporosity model presented here is conceptually simple, yet flexible enough to simulate common conceptualizations of double and triple-porosity flow. This combination of generality and simplicity makes the multiporosity model a good choice for flow modelling in low-permeability fractured rocks.

58 GEOSCIENCES↗