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DOE OSTI2025

A chain stretch-based gradient-enhanced model for damage and fracture in elastomers

Similar to quasi-brittle materials, it has been recently shown that elastomers can exhibit a macroscopically diffuse damage zone that accompanies the fracture process. In this study, we introduce a stretch-based gradient-enhanced damage (GED) model that allows the fracture to localize and also captures the development of a physically diffuse damage zone. This capability contrasts with the paradigm of the phase field method for fracture, where a sharp crack is numerically approximated in a diffuse manner. Capturing fracture localization and diffuse damage in our approach is achieved by considering nonlocal effects that encompass network topology, heterogeneity, and imperfections. These considerations motivate the use of a statistical damage function dependent upon the nonlocal deformation state. From this model, fracture toughness is realized as an output. While GED models have been classically utilized for damage modeling of structural engineering materials (e.g., concrete), they face challenges when trying to capture the cascade from damage to fracture, often leading to damage zone broadening (de Borst and Verhoosel, 2016). This deficiency contributed to the popularity of the phase-field method over the GED model for elastomers and other quasi-brittle materials. Other groups have proceeded with damage-based GED formulations that prove identical to the phase-field method (Lorentz et al., 2012), but these inherit the aforementioned limitations. To address this issue in a thermodynamically consistent framework, we implement two modeling features (a nonlocal driving force bound and a simple relaxation function) specifically designed to capture the evolution of a physically meaningful damage field and the simultaneous localization of fracture, thereby overcoming a longstanding obstacle in the development of these nonlocal strain- or stretch-based approaches. Here, we discuss several numerical examples to understand the features of the approach at the limit of incompressibility, and compare them to the phase-field method as a benchmark for the macroscopic response and fracture energy predictions.

Elastomers↗

DOE OSTI2021

Hydro-mechanical measurements and x-ray imaging of sheared crystalline rock fractures from EGS Collab experiments 1 & 2

Measuring hydro-mechanical properties of natural fractures is a prerequisite for optimizing hydraulic stimulation design and well placement. We completed experiments to characterize shear on natural fractures in schist, amphibolite, and rhyolite specimens drilled from EGS Collab Project’s field sites at the Sanford Underground Research Facility (SURF) in South Dakota. A triaxial direct shear method and coupled x-ray imaging were used to perform hydroshearing and mechanical shearing at the site’s in-situ stress conditions. This produced simultaneous measurements of fracture and matrix strength, permeability, stress-dependent aperture, dilation, and friction strength. Our results identified that only a subset of the natural fractures was weak enough for hydroshearing. Generally, hydroshearing increases fracture permeability by a factor of 10 or more and the enhancement is retainable over time. However, the shear slip does not always result in permeability enhancement. High content of phyllosilicates was found to associate with exceptionally weak fractures that also exhibited poor or even negative enhancement after stimulation. Combining our measurements with site data, we can predict that most observable fractures at the two EGS Collab sites do not meet the criteria for hydroshearing before tensile opening. In some cases, the visible fractures are low permeability and as strong as the adjacent rock. To induce hydroshearing before tensile opening, injection must target known weak and favorably oriented fractures with confirmed pre-existing permeability.

58 GEOSCIENCES↗

DOE OSTI2020

Seismicity and Stress Associated With a Fluid-Driven Fracture: Estimating the Evolving Geometry

A coupled approach, combining the theory of rate- and state-dependent friction and methods from poroelasticity, forms the basis for a quantitative relationship between displacements and fluid leak-off from a growing fracture and changes in the rate of seismic events in the region surrounding the fracture. Poroelastic Green's functions link fracture aperture changes and fluid flow from the fracture to changes in the stress field and pore pressure in the adjacent formation. The theory of rate- and state-dependent friction provides a connection between Coulomb stress changes and variations in the rate of seismic events. Numerical modeling indicates that the Coulomb stress changes can vary significantly between formations with differing properties. The relationship between the seismicity rate changes and the changes in the formation stresses and fluid pressure is nonlinear, but a transformation produces a quantity that is linearly related to the aperture changes and fluid leak-off from the fracture. The methodology provides a means for mapping changes in seismicity into fracture aperture changes and to image an evolving fracture. An application to observed microseismicity associated with a hydrofracture reveals asymmetric fracture propagation within two main zones, with extended propagation in the upper zone. Furthermore, the time-varying volume of the fracture agrees with the injected volume, given by the integration of rate changes at the injection well, providing validation of the estimated aperture changes.

58 GEOSCIENCES↗

DOE OSTI2023

Characterizing the Impacts of Multi-Scale Heterogeneity on Solute Transport in Fracture Networks

We model flow and transport in fracture networks with varying degrees of fracture-to-fracture aperture heterogeneity and network intensity to show how changes in these properties can cause the emergence of anomalous flow and transport behavior. If fracture-to-fracture aperture heterogeneity is increased in sparse networks, velocity fluctuations inhibit high flow rates and solute transport can be delayed. Surprisingly, transport can be slowed even in cases where hydraulic aperture is monotonically increased. As the intensity of the networks is increased, more connected pathways allow for particles to bypass these effects. There exists transition behavior where with relatively few connected pathways in a network, first arrival times of particles are not heavily affected by fracture-to-fracture aperture heterogeneity, but the scaling behavior of the tails is strongly influenced. These results reinforce the importance of considering multi-scale effects in fractured systems and can inform flow and transport processes in both natural and engineered fractured systems.

58 GEOSCIENCES↗

DOE OSTI2023

Emergence of Unstable Focused Flow Induced by Variable‐Density Flows in Vertical Fractures

Abstract Fluids with different densities often coexist in subsurface fractures and lead to variable‐density flows that control subsurface processes such as seawater intrusion, contaminant transport, and geologic carbon sequestration. In nature, fractures have dip angles relative to gravity, and density effects are maximized in vertical fractures. However, most studies on flow and transport through fractures are often limited to horizontal fractures. Here, we study the mixing and transport of variable‐density fluids in vertical fractures by combining three‐dimensional (3D) pore‐scale numerical simulations and visual laboratory experiments. Two miscible fluids with different densities are injected through two inlets at the bottom of a fracture and exit from an outlet at the top of the fracture. Laboratory experiments show the emergence of an unstable focused flow path, which we term a “runlet.” We successfully reproduce the unstable runlet using 3D numerical simulations and elucidate the underlying mechanisms triggering the runlet. Dimensionless number analysis shows that the runlet instability arises due to the Rayleigh‐Taylor instability (RTI), and flow topology analysis is applied to identify 3D vortices that are caused by the RTI. Even under laminar flow regimes, fluid inertia is shown to control the runlet instability by affecting the size and movement of vortices. Finally, we confirm the emergence of a runlet in rough‐walled fractures. Since a runlet dramatically affects fluid distribution, residence time, and mixing, the findings in this study have direct implications for the management of groundwater resources and subsurface applications.

Environmental Sciences & Ecology↗

DOE OSTI2024

Coupled Transport, Reactivity, and Mechanics in Fractured Shale Caprocks

Abstract Shales are low‐permeability caprocks that confine fluid, such as CO 2 , nuclear waste, and hydrogen, in storage formations. Stress‐induced fractures in shale caprocks provide pathways for fluid to leak and potentially contaminate fresh water aquifers. Fractured shales are also increasingly considered as resources for CO 2 sequestration, enhanced geothermal, and unconventional energy recovery. Injecting reactive fluids into shales introduces chemical disequilibrium, causing an onset of a series of dissolution, precipitation, and fines mobilization mechanisms. The reactions have rapid kinetics and significant impact on porosity and permeability; consequently, flow and storage properties of caprocks. While previous research has explored the separate effects of these reactions, this study aims to uncover their simultaneous occurrence and collective influence. This study unveils these highly coupled transport and reactivity mechanisms by tracking and visualizing the reaction‐induced alterations in the matrix, microcracks, and fractures of shales over time. We conducted brine injection experiments sequentially at pH 4 and 2 in a naturally fractured Wolfcamp shale sample while simultaneously imaging the dynamic processes using X‐ray computed tomography (CT). CT images are validated by finer resolution images obtained using micro‐CT and scanning electron microscopy. We also tracked the sample permeability and fluid chemistry using brine permeability and inductively coupled plasma mass spectrometry, respectively. Findings show that fluid primarily flowed through fractures, dissolving reactive minerals and mobilizing fines on fracture surfaces. Dissolution of fracture asperities under confining stress resulted in the closing of fractures. Clogging in narrow fracture pathways, caused by fines accumulation, diverted fluid flow into matrix pores.

58 GEOSCIENCES↗

DOE OSTI2022

Microbial colonization and persistence in deep fractured shales is guided by metabolic exchanges and viral predation

Background: Microbial colonization of subsurface shales following hydraulic fracturing offers the opportunity to study coupled biotic and abiotic factors that impact microbial persistence in engineered deep subsurface ecosystems. Shale formations underly much of the continental USA and display geographically distinct gradients in temperature and salinity. Complementing studies performed in eastern USA shales that contain brine-like fluids, here we coupled metagenomic and metabolomic approaches to develop the first genome-level insights into ecosystem colonization and microbial community interactions in a lower-salinity, but high-temperature western USA shale formation. Results: We collected materials used during the hydraulic fracturing process (i.e., chemicals, drill muds) paired with temporal sampling of water produced from three different hydraulically fractured wells in the STACK (Sooner Trend Anadarko Basin, Canadian and Kingfisher) shale play in OK, USA. Relative to other shale formations, our metagenomic and metabolomic analyses revealed an expanded taxonomic and metabolic diversity of microorganisms that colonize and persist in fractured shales. Importantly, temporal sampling across all three hydraulic fracturing wells traced the degradation of complex polymers from the hydraulic fracturing process to the production and consumption of organic acids that support sulfate- and thiosulfate-reducing bacteria. Furthermore, we identified 5587 viral genomes and linked many of these to the dominant, colonizing microorganisms, demonstrating the key role that viral predation plays in community dynamics within this closed, engineered system. Lastly, top-side audit sampling of different source materials enabled genome-resolved source tracking, revealing the likely sources of many key colonizing and persisting taxa in these ecosystems. Conclusions: These findings highlight the importance of resource utilization and resistance to viral predation as key traits that enable specific microbial taxa to persist across fractured shale ecosystems. We also demonstrate the importance of materials used in the hydraulic fracturing process as both a source of persisting shale microorganisms and organic substrates that likely aid in sustaining the microbial community. Moreover, we showed that different physicochemical conditions (i.e., salinity, temperature) can influence the composition and functional potential of persisting microbial communities in shale ecosystems. Together, these results expand our knowledge of microbial life in deep subsurface shales and have important ramifications for management and treatment of microbial biomass in hydraulically fractured wells.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Revealing complex subsurface dynamics with continuous seismic monitoring: Observations using distributed acoustic sensing and surface orbital vibrators during hydraulic fracturing

Understanding hydraulic fracturing is crucial to improving the stimulation of unconventional reservoirs and increasing fluid production. This study develops a novel seismic monitoring technology using distributed acoustic sensing (DAS) and surface orbital vibrators (SOV) to capture fracture seismic response and mechanical properties at high temporal intervals. We analyze continuous time-lapse vertical seismic profiling (VSP) data acquired every hour during the first nine days of treatment of an unconventional reservoir in the Austin Chalk/Eagle Field Laboratory. The VSP data contain clear seismic signals scattered from the activated fractures. The spatiotemporal changes of the fracture reflectivity revealed by the SOV/DAS data correlate well with the observations of fracture locations inferred from low-frequency DAS data. These results capture the fracture opening and closure processes, as well as highlight potential prestage activations of the fractures due to hydraulic connectivity with preexisting fracture systems. Therefore, analysis of the presented data set provides a unique opportunity to understand fracture initiation and subsequent evolution, not only in the context of unconventional resources but also in enhanced geothermal systems.

Correa, Julia↗

DOE OSTI2023

CO 2 -Responsive Fracturing Fluids for Enhanced Geothermal Systems (Final Report)

Our group has recently developed StimuFrac, a non-toxic stimuli-responsive fracturing fluid consisting of a CO 2 -reactive polymer which has shown at the lab-scale to consistently fracture rock cores at significantly lower net pressures in a range of representative geothermal pressure/temperature conditions. However, until now the mechanism/s responsible for more effective fracturing, of critical importance to optimize fracturing performance as well as strategize injection methodologies for field deployment, was not understood. In this document, we report (1) on the two main mechanisms responsible for fracturing rock at lower net pressures with StimuFrac; (2) the phase behavior of StimuFrac/CO 2 under geothermal wellbore conditions; and (3) based on high-temperature true triaxial stimulations, detailed evidence that StimuFrac/CO 2 is the best performing stimulation fluid under EGS T/P conditions as compared to water, waterless CO 2 , and CO 2 /water fracturing fluids. This is because i) it requires significantly lower volumes of CO 2 due to its reduced leak off into the formation by the crosslinked polymer solution; ii) large fractures can be generated reproducibly at both low and high CO 2 injection flow rates, and iii) the reversible (previously reported) viscosity increase of StimuFrac could be beneficial to transport proppants when they become available for EGS. These results were particularly evident for hot nearly dry rock as well as partially and nearly fully water-saturated granitic rock. GTO requires StimuFrac to be evaluated in fully water-saturated rock to determine whether the above-described performance applies under these conditions. Since (1) GTO considers there is no enough evidence for Sa different StimuFrac formulation to work below 90C (where full water-saturation in an open system is possible) and (2) no polyaxial loading frame larger than a few centimeters that can do hydraulic fracturing tests while maintaining the rock sample fully saturated with water at 200 C exists; PNNL concludes that the only way to determine if StimuFrac represents an advanced fracturing fluid alternative for EGS, is to perform a stimulation in an actual EGS reservoir.

15 GEOTHERMAL ENERGY↗

NASA NTRS1976

A fractographic study of the edge-sliding mode in fracture toughness testing

A fractographic study of Mode II fracture surfaces has been conducted for the purpose of identifying the microstructural mechanisms responsible for fracture in the edge-sliding mode. A compact shear (CS) specimen was employed to generate the fracture surfaces and also to establish Mode II fracture toughness values for Ti-6Al-4V, A533-B steel, and several aluminum alloys. In all tests, one of the two edge cracks sustained complete Mode II fracture while the other exhibited only a limited amount of subcritical crack growth. Mode II fracture surfaces, which were unique in appearance, have been examined by optical and scanning electron microscopy. It was determined that shear (or parabolic) microvoid coalescence was the dominant mechanism for Mode II fracture. It was also established that most of the surface abrasions were created by the relative sliding of the fracture surfaces during unstable fracture rather than the crack initiation process.

Jones, D. L.↗

NASA NTRS1976

Ductile fracture theories for pressurised pipes and containers

Two mechanisms of fracture are distinguished. Plane strain fractures occur in materials which do not undergo large-scale plastic deformations prior to and during a possible fracture deformation. Plane stress or high energy fractures are generally accompanied by large inelastic deformations. Theories for analyzing plane stress are based on the concepts of critical crack opening stretch, K(R) characterization, J-integral, and plastic instability. This last is considered in some detail. The ductile fracture process involves fracture initiation followed by a stable crack growth and the onset of unstable fracture propagation. The ductile fracture propagation process may be characterized by either a multiparameter (discrete) model, or some type of a resistance curve which may be considered as a continuous model expressed graphically. These models are studied and an alternative model is also proposed for ductile fractures which cannot be modeled as progressive crack growth phenomena.

Erdogan, F.↗

NASA NTRS1977

Mechanical behavior and fracture characteristics of off-axis fiber composites. 1: Experimental investigation

The mechanical behavior, fracture surfaces, and fracture modes of unidirectional high-modulus graphite-fiber/epoxy composites subjected to off-axis tensile loads were investigated experimentally. The investigation included the generation of stress-strain-to-fracture data and scanning electron microscope studies of the fractured surfaces. The results led to the identification of fracture modes and distinct fracture surface characteristics for off-axis tensile loading. The results also led to the formulation of critical for identifying and characterizing these fracture modes and their associated fracture surfaces. The results presented and discussed herein were used in the theoretical investigation and comparisons described in Part 2. These results should also provide a good foundation for identifying, characterizing, and quantifying fracture modes in both off-axis and angle-plied laminates.

Sinclair, J. H.↗

NASA NTRS1978

Metallurgical characterization of the fracture of aluminum alloys

A systematic investigation was conducted to examine the fracture behavior of the structural aluminum alloys 2024, 6061, 7075, and 7178 (in selected heat treatments) tested under several controlled conditions. The investigation included both time independent (tensile, shear, and precracked notch-bend) fractures and time dependent (fatigue and stress corrosion) fractures. Specimens were obtained from both sheet and plate material and tested in longitudinal and transverse orientations. Strain rate effects on fracture morphology were examined in tension and shear tests. Fatigue fracture studies included an examination of the influence of minimum-to-maximum-load ratio on fracture morphology. Second-phase particles observed on fracture surfaces and metallographically prepared sections and corrosion products associated with stress corrosion fractures were analyzed chemically using scanning electron microscopy and energy-dispersive X-ray analysis. Fracture morphology was related to the microstructural features, the testing conditions, and the form of commercial product.

Bhandarkar, M. D.↗

NASA NTRS1983

Fracture behavior of the Space Shuttle thermal protection system

Stable crack-growth and fracture-toughness experiments were conducted using precracked specimens machined from LI-900 reusable surface insulation (RSI) tiles of the Space Shuttle thermal protection system (TPS) at room temperature. Similar fracture experiments were conducted on fracture specimens with preexisting cracks at the interface of the tile and the strain isolation pad (SIP). Stable crack growth was not observed in the LI-900 tile fracture specimens which had a fracture toughness of 12.0 kPa sq rt of m. The intermittent subcritical crack growth at the tile-pad interface of the fracture specimens was attributed to successive local pull-outs due to tensile overload in the LI-900 tile and cannot be characterized by linear elastic fracture mechanics. No subcritical interfacial crack growth was observed in the fracture specimens with densified LI-900 tiles where brittle fracture initiated at an interior point away from the densification.

Komine, A.↗

NASA NTRS1990

Computational simulation of structural fracture in fiber composites

A methodology was developed for the computational simulation of structural fracture in fiber composites. This methodology consists of step-by-step procedures for mixed-mode fracture in generic components and an integrated computer code, Composite Durability Structural Analysis (CODSTRAN). The generic types of composite structural fracture include: (1) single and combined mode fracture in beams; 2) laminate free-edge delamination fracture; and (3) laminate center flaw progressive fracture. Structural fracture is identified by rapid changes in one or all of the following: (1) displacements, (2) frequencies, (3) the buckling loads, or (4) the strain energy release rate. These rapid changes are herein assumed to denote imminent structural fracture. Based on these rapid changes, parameters are identified which can be used as guidelines for structural fracture, inspection intervals and retirement for cause.

Chamis, Christos C.↗

NASA NTRS1990

Computational simulation of structural fracture in fiber composites

A methodology was developed for the computational simulation of structural fracture in fiber composites. This methodology consists of step-by-step procedures for mixed mode fracture in generic components and of an integrated computer code, Composite Durability Structural Analysis (CODSTRAN). The generic types of composite structural fracture include single and combined mode fracture in beams, laminate free-edge delamination fracture, and laminate center flaw progressive fracture. Structural fracture is assessed in one or all of the following: (1) the displacements increase very rapidly; (2) the frequencies decrease very rapidly; (3) the buckling loads decrease very rapidly; or (4) the strain energy release rate increases very rapidly. These rapid changes are herein assumed to denote imminent structural fracture. Based on these rapid changes, parameters/guidelines are identified which can be used as criteria for structural fracture, inspection intervals, and retirement for cause.

Chamis, C. C.↗

NASA NTRS1993

Combined mode I and mode II fracture of monolithic ceramics

The mode I, mode II, and combined mode I-mode II fracture behaviors of a coarse-grained silicon nitride, a fine-grained silicon nitride, and an alumina were investigated. These ceramics were fractured from two types of fracture initiating flaws: small surface flaws and large single edge precracks. The small surface flaws were introduced by Knoop indentation in flexural samples at various angles to the tensile stress direction and fractured in four-point bending. The samples with large precracks were fractured in the asymmetric four-point-bend geometry. The mixed-mode fracture toughness values obtained from the two flaw configurations were in good agreement with each other. All three ceramics displayed very similar mixed-mode fracture behavior, although their microstructures were not similar. Comparison of experimental data to mixed-mode fracture theories revealed that the minimum strain energy density theory best described the mixed-mode fracture behavior of all three ceramics.

Tikare, Veena↗

NASA NTRS1994

The Relationship Between Constraint and Ductile Fracture Initiation as Defined by Micromechanical Analyses

The use of small laboratory specimens to predict the integrity of large, complex structures relies on the validity of single parameter fracture mechanics. Unfortunately, the constraint loss associated with large scale yielding, whether in a laboratory specimen because of its small size or in a structure because it contains shallow flaws loaded in tension, can cause the breakdown of classical fracture mechanics and the loss of transferability of critical, global fracture parameters. Although the issue of constraint loss can be eliminated by testing actual structural configurations, such an approach can be prohibitively costly. Hence, a methodology that can correct global fracture parameters for constraint effects is desirable. This research uses micromechanical analyses to define the relationship between global, ductile fracture initiation parameters and constraint in two specimen geometries (SECT and SECB with varying a/w ratios) and one structural geometry (circumferentially cracked pipe). Two local fracture criteria corresponding to ductile fracture micromechanisms are evaluated: a constraint-modified, critical strain criterion for void coalescence proposed by Hancock and Cowling and a critical void ratio criterion for void growth based on the Rice and Tracey model. Crack initiation is assumed to occur when the critical value in each case is reached over some critical length. The primary material of interest is A516-70, a high-hardening pressure vessel steel sensitive to constraint; however, a low-hardening structural steel that is less sensitive to constraint is also being studied. Critical values of local fracture parameters are obtained by numerical analysis and experimental testing of circumferentially notched tensile specimens of varying constraint (e.g., notch radius). These parameters are then used in conjunction with large strain, large deformation, two- and three-dimensional finite element analyses of the geometries listed above to predict crack initiation loads and to calculate the associated (critical) global fracture parameters. The loads are verified experimentally, and microscopy is used to measure pre-crack length, crack tip opening displacement (CTOD), and the amount of stable crack growth. Results for A516-70 steel indicate that the constraint-modified, critical strain criterion with a critical length approximately equal to the grain size (0.0025 inch) provides accurate predictions of crack initiation. The critical void growth criterion is shown to considerably underpredict crack initiation loads with the same critical length. The relationship between the critical value of the J-integral for ductile crack initiation and crack depth for SECT and SECB specimens has been determined using the constraint-modified, critical strain criterion, demonstrating that this micromechanical model can be used to correct in-plane constraint effects due to crack depth and bending vs. tension loading. Finally, the relationship developed for the SECT specimens is used to predict the behavior of circumferentially cracked pipe specimens.

Panontin, Tina L.↗