Mathematical theories of brittle fracture.
Strain energy for two and three dimensional crack systems subjected to varying loads, detailing loading and crack geometry effects on fracture criterion
Liebowitz, H.↗
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Fracture toughness of schist, amphibolite, and rhyolite from the Sanford Underground Research Facility (SURF), Lead, South Dakota
The Cracked Chevron Notched Brazilian Disc (CCNBD) method was selected for Mode I fracture toughness tests on Poorman schist, Yates amphibolite, and rhyolite dikes from the EGS Collab site at the SURF in Lead, South Dakota. The effects of lithology, anisotropy, and loading rate were investigated. Fracture toughness was greatest in amphibolite, with schist and rhyolite having similar toughness values ($K$ amphibolite > $K$ rhyolite ≈ $K$ schist ). The effects of anisotropy on fracture toughness were investigated in the foliated schist samples. Schist samples were prepared in three geometries (divider, arrester, and short transverse) which controlled how the fracture would propagate relative to foliations. The divider geometry was strongest and short transverse geometry was the weakest ($K$ divider > $K$ arrester > $K$ shorttransverse ). Fracture toughness was observed to decrease with decreasing loading rate. Optical and SEM microscopy revealed that for the short transverse geometry, fractures tended to propagate along grain boundaries, whereas in arrester and divider geometries fractures tended to propagate through grains. In foliated samples, the tortuosity of the fracture observed in thin section was greater in arrester and divider geometries than in short transverse geometries.
58 GEOSCIENCES↗
Evaluation of Lost Circulation Material Sealing for Geothermal Drilling
Lost circulation is a pervasive problem in geothermal wells that can create prohibitive costs during drilling. The main issue with treatment is that the mechanism of plug formation is poorly understood. Here we applied two experimental approaches to characterize the clogging effectiveness of different materials. Fracture flow tests with different geometries were conducted with various individual materials and mixtures at relevant conditions. A high-temperature flow loop system was also developed to inject single- and mixed-material plugs into a gravel pack with a non-uniform geometry to compare with the fracture tests. The fracture tests revealed that single materials tended to form no plug or an unstable plug, while mixtures of materials were uniformly better at sealing fractures. Gravel pack tests at high temperatures show most of the materials are intact but degraded. The fibrous materials can create partial or unstable plugs in the gravel pack, but mixed-material plugs are far more effective at clogging. Both test types suggest that (1) mixed materials are more effective at blocking fluid flow and (2) fibrous materials seal fracture openings better, while granular materials seal inside fractures or pore throats better. Further research is needed to study the long-term stability of different plug configurations.
clogging tests↗
The load separation technique in the elastic-plastic fracture analysis of two- and three-dimensional geometries
Load separation is the representation of the load in the test records of geometries containing cracks as a multiplication of two separate functions: a crack geometry function and a material deformation function. Load separation is demonstrated in the test records of several two-dimensional geometries such as compact tension geometry, single edge notched bend geometry, and center cracked tension geometry and three-dimensional geometries such as semi-elliptical surface crack. The role of load separation in the evaluation of the fracture parameter J-integral and the associated factor eta for two-dimensional geometries is discussed. The paper also discusses the theoretical basis and the procedure for using load separation as a simplified yet accurate approach for plastic J evaluation in semi-elliptical surface crack which is a three-dimensional geometry. The experimental evaluation of J, and particularly J(sub pl), for three-dimensional geometries is very challenging. A few approaches have been developed in this regard and they are either complex or very approximate. The paper also presents the load separation as a mean to identify the blunting and crack growth regions in the experimental test records of precracked specimens. Finally, load separation as a methodology in elastic-plastic fracture mechanics is presented.
Sharobeam, Monir H.↗
Revisiting the first Sandia Fracture Challenge with transient deformation heating and strain localization considerations
In this study, we present a systematic experimental study and accompanying theoretical analysis of the dependence of ductile fracture on strain localization, strain hardening rates, deformation-induced thermal softening, and transient heat conduction under spatially uniform as well as spatially heterogeneous deformation. Spatially uniform cases are studied via standard dogbone shaped specimens subject to uniaxial tension. Spatially heterogeneous deformation is studied via the so-called Sandia Fracture Challenge (SFC) specimen, which is a standard compact tension specimen modified with three machined holes in front of a blunt notch. We utilize the same precipitation hardened martensitic stainless steel used in the first SFC experiments, i.e. 15-5 PH with an H1075 heat treatment. We also study 15-5 PH in Condition A and with the H900 heat treatment, each of which has a different hardening behavior and ductility. We find that the ductility does not correlate with the deformation to first crack initiation in the SFC specimen. Instead, hardening rates are better correlated. Moreover, a re-examination finds that an accurate calibration of the hardening rates is strongly correlated with accurate blind predictions of ductile fracture in the SFC specimens. Given that thermal softening can greatly affect hardening rates, we provided a thermographic analysis of deformation-induced heating and transient heat transfer in both the dogbone shaped samples and the SFC specimens. Transient heating in stainless steels is found to have first-order effects on the strain at the onset of necking, strain to fracture, as well as strain localization and ductile fracture in complex geometries even under so-called quasi-static loading rates.
42 ENGINEERING↗
Computationally Efficient Multiscale Neural Networks Applied to Fluid Flow in Complex 3D Porous Media
Abstract The permeability of complex porous materials is of interest to many engineering disciplines. This quantity can be obtained via direct flow simulation, which provides the most accurate results, but is very computationally expensive. In particular, the simulation convergence time scales poorly as the simulation domains become less porous or more heterogeneous. Semi-analytical models that rely on averaged structural properties (i.e., porosity and tortuosity) have been proposed, but these features only partly summarize the domain, resulting in limited applicability. On the other hand, data-driven machine learning approaches have shown great promise for building more general models by virtue of accounting for the spatial arrangement of the domains’ solid boundaries. However, prior approaches building on the convolutional neural network (ConvNet) literature concerning 2D image recognition problems do not scale well to the large 3D domains required to obtain a representative elementary volume (REV). As such, most prior work focused on homogeneous samples, where a small REV entails that the global nature of fluid flow could be mostly neglected, and accordingly, the memory bottleneck of addressing 3D domains with ConvNets was side-stepped. Therefore, important geometries such as fractures and vuggy domains could not be modeled properly. In this work, we address this limitation with a general multiscale deep learning model that is able to learn from porous media simulation data. By using a coupled set of neural networks that view the domain on different scales, we enable the evaluation of large ( $$>512^3$$ > 512 3 ) images in approximately one second on a single graphics processing unit. This model architecture opens up the possibility of modeling domain sizes that would not be feasible using traditional direct simulation tools on a desktop computer. We validate our method with a laminar fluid flow case using vuggy samples and fractures. As a result of viewing the entire domain at once, our model is able to perform accurate prediction on domains exhibiting a large degree of heterogeneity. We expect the methodology to be applicable to many other transport problems where complex geometries play a central role.
36 MATERIALS SCIENCE↗
Investigation of flaw geometry and loading effects on plane strain fracture in metallic structures
The effects on fracture and flaw growth of weld-induced residual stresses, combined bending and tension stresses, and stress fields adjacent to circular holes in 2219-T87 aluminum and 5AI-2.5Sn(ELI) titanium alloys were evaluated. Static fracture tests were conducted in liquid nitrogen; fatigue tests were performed in room air, liquid nitrogen, and liquid hydrogen. Evaluation of results was based on linear elastic fracture mechanics concepts and was directed to improving existing methods of estimating minimum fracture strength and fatigue lives for pressurized structure in spacecraft and booster systems. Effects of specimen design in plane-strain fracture toughness testing were investigated. Four different specimen types were tested in room air, liquid nitrogen and liquid hydrogen environments using the aluminum and titanium alloys. Interferometry and holograph were used to measure crack-opening displacements in surface-flawed plexiglass test specimens. Comparisons were made between stress intensities calculated using displacement measurements, and approximate analytical solutions.
Hall, L. R.↗
Geometry and relative age of large patterned fractures in southern Acidalia Planitia, Mars
Extraordinary patterned fractures occur in Elysium, Utopia, and Acidalia Planitiae of Mars. Theories as to their origin range from permafrost patterning to tectonic fracturing. Recent studies indicate the patterned fractures may be a surface reflection of rough, buried terrane in which fracturing occurs as a result of differential compaction. The patterned terrane in the southern portion of the Acidalia region (MC4-SE, MC4-SC) is being studied to determine its age relative to other terranes and events, and to constrain models for the origin of the fractures. Fracturing in this area occurs between 5 and 25 degrees west longitude and 37 and 50 degrees north latitude. Many fracture patterns are roughly polygonal, with polygons ranging in size from approximately 11 to 32 km in diameter. Fracture traces range from the limit of resolution (10's of meters) to 35 km in length.
Borrello, Murray C.↗
Flaw-insensitive fracture of a micrometer-sized brittle metallic glass
Brittle materials, such as oxide glasses, are usually very sensitive to flaws, giving rise to a macroscopic fracture strength that is much lower than that predicted by theory. The same applies to metallic glasses (MGs), with the important difference that these glasses can exhibit certain plastic strain prior to catastrophic failure. Here we consider the strongest metallic alloy known, a ternary Co 55 Ta10B 35 MG. In this work, we show that this macroscopically brittle glass is flaw-insensitive at the micrometer scale. This discovery emerges when testing pre-cracked specimens with self-similar geometries, where the fracture stress does not decrease with increasing pre-crack size. The fracture toughness of this ultra-strong glassy alloy is further shown to increase with increasing sample size. Both these findings deviate from our classical understanding of fracture mechanics, and are attributed to a transition from toughness-controlled to strength-controlled fracture below a critical sample size.
36 MATERIALS SCIENCE↗
Fracture toughness testing of polymer matrix composites
A review of the interlaminar fracture indicates that a standard specimen geometry is needed to obtain consistent fracture toughness measurements in polymer matrix composites. In general, the variability of measured toughness values increases as the toughness of the material increases. This variability could be caused by incorrect sizing of test specimens and/or inconsistent data reduction procedures. A standard data reduction procedure is therefore needed as well, particularly for the tougher materials. Little work has been reported on the effects of fiber orientation, fiber architecture, fiber surface treatment or interlaminar fracture toughness, and the mechanisms by which the fibers increase fracture toughness are not well understood. The little data that is available indicates that woven fiber reinforcement and fiber sizings can significantly increase interlaminar fracture toughness.
Grady, Joseph E.↗
Validation of Proposed Metrics for Two-Body Abrasion Scratch Test Analysis Standards
Abrasion of mechanical components and fabrics by soil on Earth is typically minimized by the effects of atmosphere and water. Potentially abrasive particles lose sharp and pointed geometrical features through erosion. In environments where such erosion does not exist, such as the vacuum of the Moon, particles retain sharp geometries associated with fracturing of their parent particles by micrometeorite impacts. The relationship between hardness of the abrasive and that of the material being abraded is well understood, such that the abrasive ability of a material can be estimated as a function of the ratio of the hardness of the two interacting materials. Knowing the abrasive nature of an environment (abrasive)/construction material is crucial to designing durable equipment for use in such surroundings. The objective of this work was to evaluate a set of standardized metrics proposed for characterizing a surface that has been scratched from a two-body abrasion test. This is achieved by defining a new abrasion region termed Zone of Interaction (ZOI). The ZOI describes the full surface profile of all peaks and valleys, rather than just measuring a scratch width. The ZOI has been found to be at least twice the size of a standard width measurement; in some cases, considerably greater, indicating that at least half of the disturbed surface area would be neglected without this insight. The ZOI is used to calculate a more robust data set of volume measurements that can be used to computationally reconstruct a resultant profile for de tailed analysis. Documenting additional changes to various surface roughness par ameters also allows key material attributes of importance to ultimate design applications to be quantified, such as depth of penetration and final abraded surface roughness. Further - more, by investigating the use of custom scratch tips for specific needs, the usefulness of having an abrasion metric that can measure the displaced volume in this standardized manner, and not just by scratch width alone, is reinforced. This benefit is made apparent when a tip creates an intricate contour having multiple peaks and valleys within a single scratch. The current innovation consists of a software- driven method of quantitatively evaluating a scratch profile. The profile consists of measuring the topographical features of a scratch along the length of the scratch instead of the width at one location. The digitized profile data is then fed into software code, which evaluates enough metrics of the scratch to reproduce the scratch from the evaluated metrics. There are three key differences between the current art and this innovation. First, scratch width does not quantify how far from the center of the scratch damage occurs (ZOI). Second, scratch width does not discern between material displacement and material removal from the scratch. Finally, several scratches may have the same width but different zones of interactions, different displacements, and different material removals. The current innovation allows quantitative assessment of all three.
Street, Kenneth W., Jr.↗
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↗
Development of a Fatigue Crack Growth Coupon for Highly Plastic Stress Conditions
This paper presents an analytical approach used to develop a novel fatigue crack growth coupon for a highly plastic 3-D stress field condition. The flight hardware investigated in this paper is a large separation bolt that fractures using pyrotechnics at the appointed time during the flight sequence. The separation bolt has a deep notch that produces a severe stress concentration and a large plastic zone when highly loaded. For this geometry, linear-elastic fracture mechanics (LEFM) techniques are not valid due to the large nonlinear stress field. Unfortunately, industry codes that are generally available for fracture mechanics analysis and fatigue crack growth (e.g. NASGRO (11) are limited to LEFM and are available for only a limited number of geometries. The results of LEFM based codes are questionable when used on geometries with significant plasticity. Therefore elastic-plastic fracture mechanics (EPFM) techniques using the finite element method (FEM) were used to analyze the bolt and test coupons. scale flight hardware is very costly in t e r n of assets, laboratory resources, and schedule. Therefore to alleviate some of these problems, a series of novel test coupons were developed to simulate the elastic-plastic stress field present in the bolt.
Allen, Phillip A.↗
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.↗
EVALUATION OF SPECIMEN GEOMETRY AND TESTING PARAMETERS FOR HYDROGEN-ASSISTED FRACTURE MEASUREMENTS
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San Marchi, Christopher William [Sandia National L↗
Evaluation of specimen geometry and testing parameters for hydrogen-assisted fracture measurements
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San Marchi, Christopher William [Sandia National L↗
Fracture Description of the HFTS-2 Slant Core, Delaware Basin, West Texas
Previous work in the Midland Basin Hydraulic Fracture Test Site project (HFTS1) has shown the value of core recovered from a stimulated volume in providing information on the geometry and extent of hydraulic fractures. This project (HFTS2) is in the Wolfcamp Formation of the Delaware Basin. A slant core through the stimulated volume was acquired above and below a stimulated well and the results of the fracture description are presented here. Here, nine, 3-inch-diameter whole cores from the slant well were examined for fractures prior to slabbing, together with a CT scan of the core. We used criteria developed during the HFTS1 project to identify hydraulic, natural, drilling-induced and core-handling fractures. Material collected from a few fracture faces was cleaned, sieved, and examined under a microscope to look for proppant. A total of 1261 fractures, including 500 hydraulic fractures, were described in 948 feet of core. Hydraulic fractures are not evenly distributed through the cores; they tend to occur in clusters. Many are remarkably planar, smooth, and featureless, while others have twist hackles, steps, plumose, and kinks. Natural, subvertical fractures, mostly less than 1 mm in width, sealed with blocky calcite, are oriented NE-SW (Set 1) and WNW-ESE (Set 2). Two Set 1 fractures have drusy cement on parted faces and were possibly open prior to drilling. A few subvertical sealed fractures with different orientations are also present. Bed-parallel natural fractures, most having fibrous cement (beef), and some showing top-to-north bed-parallel shear are present. Faults with normal/oblique movement were found in one part of the core. Drilling induced and core-handling breaks were identified in all cores, and were also noted to have reactivated some natural fractures. The results from this work will allow hydraulic fracture distribution relative to the stimulated well to be assessed. The number of fractures is generally greater than the number of perforations, but these can be compared for different stages and perforation clusters. Surface features provide information about the direction of hydraulic fracture propagation and about segmentation and bifurcation that might increase the number of fracture strands. Reactivation of natural fractures, including bedding-parallel fractures, occurs although the mechanism of parting is mostly unknown. The wider HFTS2 project will make use of this fracture description to improve hydraulic fracture modeling (geomechanics and engineering), to help explain pressure depletion and fiber optics observations (reservoir depletion and frac geometry), to help verify indirect fracture diagnostic techniques such as microseismic monitoring (geophysics), and to help calibrate horizontal well image logs.
58 GEOSCIENCES↗
New Fracture Diagnostic Tool for Unconventionals: High-Resolution Distributed Strain Sensing via Rayleigh Frequency Shift during Production in Hydraulic Fracture Test 2
Fiber Optic monitoring in unconventional reservoirs has proven to be an invaluable diagnostic tool for assessing both near-wellbore stimulation effectiveness and to help describe the far-field frac geometries created by hydraulic fracture stimulation. Unfortunately, gaining any detailed qualitative and quantitative understanding of the near-wellbore frac geometry or cluster/stage productivity during production via Fiber Optic (FO) has proven to be more difficult, particularly in wells producing liquids. A new FO diagnostic method, Distributed Strain Sensing based on Rayleigh Frequency Shift (DSS-RFS), first demonstrated for oil and gas applications in the Hydraulic Test Site 2 (HFTS2) provides new insights about the characteristics of near-wellbore-region (NWR) during production. DSS-RFS is different from other FO strain measurements because it relies on accurate measurement of frequency shifts of Rayleigh backscattered spectrum obtained by scanning the fiber with a coherent optical time-domain reflectometer with a range of laser frequencies using a tunable-wavelength laser system. Changes in strain are measured with an extremely high spatial resolution of 20 cm and with high signal-to-noise ratios over long distances. In HFTS2, strain changes for the entire wellbore have been measured twice during scheduled shut-in and reopening operations (February 2020 and September 2020). After removing temperature effects, consistent strain changes have been observed at the location of most perforation clusters. These are caused by near wellbore fracture aperture changes due to pressure increases during shut-in within the near-wellbore fracture network. The strain-change patterns from the DSS-RFS during shut-in correlate very well with the location of clusters and allow for the definition of extending intervals with positive strain signals at each cluster and slightly compressing intervals with negative strain signals between the clusters and in the non stimulated intervals. The locations of the measured positive strain peaks also show good correspondence to DAS acoustic intensity measurements acquired during the stimulation. The geometry and magnitude of the strain changes differ significantly between the two tested completion designs in the same well. During shut in and reopening each cluster exhibit its own strain-change / pressure path. In addition, the September 2020 dataset also revealed the existence of small but measurable strain changes as consequence of pressure decline during production. These strain changes also correlate well with the presence of producing clusters, but the strain-rate signals are opposite to that obtained during shut-in and reopening operations. Although Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/21URTC/2-21URTC/D021S031R002/2477551/urtec-2021-5408-ms.pdf/1 by Carol Worster on 28 February 2022 URTeC 5408 2 we are still in the early stages of exploring the potential of this novel FO technique, we believe that the highly detailed information contained in the measurement of strain changes using DSS-RFS during production can significantly improve our understanding of near-wellbore hydraulic fracture characteristics and the relationships between stimulation and production from unconventional oil and gas wells.
04 OIL SHALES AND TAR SANDS↗