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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Energy Budget of Brittle Fracturing in Granite Under Stress Relaxation and Creep
Creep and relaxation are the two major time-dependent fracturing processes in rocks. While a considerable amount of research has been done in understanding these two mechanisms, critical gaps remain regarding how different energy components evolve during time-dependent fracturing processes in rocks. In this study, a series of relaxation and creep experiments were conducted on prismatic Barre granite specimens in the laboratory to estimate the energy budget of brittle fracturing in granite. For the input energy, the work done by the machine (W) is calculated and for the output energy the radiated seismic energy (E R ), released in the form of acoustic emissions (AEs), is calculated as the only measurable output energy component in the conducted experiments. The low-frequency plateau (Ω 0 ) and corner frequency (f 0 ) for each AE waveform was estimated by fitting the observed AE spectra with the theoretical spectra using the Omega model. These parameters were used to estimate the seismic moments (M 0 ) based on the radiation pattern for the double couple (shear) and non-double-couple (non-shear) events. The range of f 0 and M 0 varied from 150 to 750 kHz and 10 –4 to 10 –1 N m, respectively. Moment magnitude (M w ) varied in a wider range from –9 to –6 in creep and –8.5 to –7 in relaxation. Stress drops (Δ σ ) and source radius (r) were estimated for the AEs using Brune’s model. Here, the results report on three primary observations: (1) the effects of different source mechanisms on the estimated source parameters showed that M 0 and Δ σ were higher for DC events as compared to NDC in both relaxation and creep. (2) The radiation efficiency in the case of creep is 70% higher as compared to relaxation and, (3) the stress drop estimated in relaxation and creep demonstrated a breakdown in scaling with the seismic moment.
58 GEOSCIENCES↗
Fracture angle and strain-energy-density-factor of a crack at hole at an arbitrary angle
For both the maximum stress criterion and strain-energy-density-factor (S) theory, fracture angle (the initial angle of crack growth) is predicted by using opening and sliding mode stress intensity factors. These theoretical predictions are consistent with experimental fracture angles. For the S theory, the crack spreads in the direction of the negative fracture angle in a plane for which S is a minimum. This quantity was obtained analytically. The experimental data of the critical S on plexiglass fracture specimens remains essentially constant.
Hsu, Y. C.↗
The peel test in experimental adhesive fracture mechanics
Several testing methods have been proposed for obtaining critical energy release rate or adhesive fracture energy in bond systems. These tests include blister, cone, lap shear, and peel tests. Peel tests have been used for many years to compare relative strengths of different adhesives, different surface preparation techniques, etc. The present work demonstrates the potential use of the peel test for obtaining adhesive fracture energy values.
Anderson, G. P.↗
Assessment of four strain energy decomposition methods for phase field fracture models using quasi-static and dynamic benchmark cases
Abstract Strain energy decomposition methods in phase field fracture models separate strain energy that contributes to fracture from that which does not. However, various decomposition methods have been proposed in the literature, and it can be difficult to determine an appropriate method for a given problem. The goal of this work is to facilitate the choice of strain decomposition method by assessing the performance of three existing methods (spectral decomposition of the stress or the strain and deviatoric decomposition of the strain) and one new method (deviatoric decomposition of the stress) with several benchmark problems. In each benchmark problem, we compare the performance of the four methods using both qualitative and quantitative metrics. In the first benchmark, we compare the predicted mechanical behavior of cracked material. We then use four quasi-static benchmark cases: a single edge notched tension test, a single edge notched shear test, a three-point bending test, and a L-shaped panel test. Finally, we use two dynamic benchmark cases: a dynamic tensile fracture test and a dynamic shear fracture test. All four methods perform well in tension, the two spectral methods perform better in compression and with mixed mode (though the stress spectral method performs the best), and all the methods show minor issues in at least one of the shear cases. In general, whether the strain or the stress is decomposed does not have a significant impact on the predicted behavior.
Zhang, Shuaifang↗
Vacancy-Mediated Increases in Brine–Salt Surface Energies
Salt formations have been explored for the permanent isolation of spent nuclear fuel based on their high thermal conductivity, self-healing nature, and low hydraulic permeability to brine flow. Vacancy defect concentrations in salt complicate fracture mechanics not driven by dislocation dynamics and can influence the resulting surface structure. Classical molecular dynamic simulations were used to simulate tensile testing of salt crystals (halite) with vacancy defect concentrations of up to 0.5 defects/nm 3 . Increasing defect concentrations resulted in a decrease in ultimate tensile strength and fracture surface energies, driven by increased surface roughness rather than changes in the amount of surface area. Brine–salt surface energies of the fractured surfaces were 0.22 to 0.26 J/m 2 , significantly higher than values reported for atomically flat (100) surfaces at the same brine composition. This change in surface energy increased the brine–salt dihedral angle by ~27°. The dihedral angle threshold for percolation in salt is 60°, and a 27° increase due to rough fracture surfaces identifies a reduction in porosity percolation and a decrease in salt permeability. Therefore, bedded salt and salt domes may be even more stable than those previously predicted from dihedral angle calculations.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Tensile Creep Fracture of Polycrystalline Near-Stoichiometric NiAl
Tensile creep fracture behavior of polycrystalline near-stoichiometric NiAl has been studied between 700 and 1200 K under initial applied stresses varying between 10 and 200 MPa. The stress exponent for fracture varied between 5.0 and 10.7 while the activation energy for fracture was 250 +/- 22 kJ/mol. The fracture life was inversely proportional to the secondary creep rate in accordance with the Monkman-Grant relation although there was extensive scatter in the data. This observation suggests that the fracture life for near-stoichiometric NiAl was influenced by creep under these stress and temperature conditions. Several different fracture morphologies were observed. Transgranular ductile cleavage fracture occurs at 700 K and at the higher stresses at 800 K. The fracture mode transitions to transgranular creep fracture at 900 and 1000 K and at lower stresses at 800 K, while plastic rupture and grain boundary cavitation occur at 1100 and 1200 K. An experimental fracture mechanism map is constructed for near-stoichiometric NiAl.
Raj, Sai V.↗
Experimental investigation on fracture of viscoelastic materials under biaxial-stress fields.
Fracture behavior of viscoelastic materials under various biaxial stress fields, determining total strain energy at fracture
Lim, C. K.↗
A simplified approach to strain energy release rate computations for interlaminar fracture of composites
A simple approach for the strain energy release rate computations based on the finite element method and a singular fitting model is presented. The model uses the stress and displacement distributions at the delamination front. The method is applied to a mixed-mode double cracked-lap-shear composite configuration. The strain energy release rate components predicted by the model are compared with the finite element crack-closure method. The effect of the mesh size on the stress and displacement distribution is isolated. The strain energy release rates predicted by relatively coarse mesh sizes are in good agreement with the finite element crack closure method.
Armanios, Erian A.↗
A Low-Frequency Electrode Array Tool for Fracture Diagnostics in Steel-Cased Wellbores
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02 PETROLEUM↗
Growth characteristics of a plane crack subjected to three-dimensional loading
The closed form expressions for the stress intensity factors due to concentrated forces applied to the surfaces of a half plane crack in an infinite body are used to generate solutions for distributed loads in this geometry. The stress intensity factors for uniformly distributed loads applied over a rectangular portion of the crack surface are given in closed form. An example of non-uniformly distributed loads which can be treated numerically is also included. In particular, combinations of normal and shear stresses on the crack which simulate the case of loading at an angle to the crack front are considered. The resulting stress intensity factors are combined with the strain energy density fracture criterion for the purpose of predicting the most likely direction of crack propagation. The critical value of the energy density factor can then be used for determining the allowable load on a specimen with a crack front not perpendicular to the tensile axis.
Hartranft, R. J.↗
Influence of Nanoconfinement and Elevated Temperatures on Geocolloid-Facilitated Transport of Energy related Contaminants
Fossil fuels obtained using hydraulic fracturing and nuclear energy are deemed crucial for meeting the current and future energy demands of the United States. The utilization of these resources, especially fossil fuels from hydraulic fracturing, has increased rapidly within the last decade. However, with the increasing levels of hydraulic fracturing activities, the occurrence and fate of chemicals used in these processes in the geosystem, as well as the potential consequences of their interactions with environment and geosystems (e.g. mineral-based geocolloids and geosurfaces), have been increasingly recognized as issues warranting consideration owing to the toxic nature of these chemicals. Scientific results originated from this project has brought better understandings on how such contaminants can preferentially or adversely interact with geosystems and how geocolloids can facilitate their transport by realistically mimicking geological conditions and environments in the laboratory level for the first time. Based on such knowledge, it may eventually lead to the development of mitigation strategies for reducing and minimizing the transport and wide distribution of contaminants and pollutants. This aspect is important for the society to ensure that energy-related contaminants do not find their way to waterbodies that are used as drinking water or irrigation. The project is also anticipated to increase public awareness about potential adverse effects of energy systems on the geosphere and environment and may motivate society to consider better mitigation strategies to prevent such occurrences.
(Nano)Confinement↗
Seismic Survey 2016 Data at Crescent Valley, Nevada
In September 2016, 989 vertical-component seismic instruments were deployed for 75 hours at the Crescent Valley greenfield geothermal play area in Nevada. Data were recorded 12/9/16 - 12/15/16. Data are stored in individual files in one-minute increments in SEGD formats. See the metadata in Crescent Valley Station Locations.sp1, Crescent Valley Observer Logs.xls, and the attached Metadata link for details about the seismic station locations, seismic data logger specifications, instrumentation specifications, descriptions of data, a fracture finding summary, and the final report for the 2016 seismic survey done in Crescent Valley, Nevada. Note that no discrete events were identified, and a 1750m x 2250m x 300m PSET volume of acoustic energy was delivered.
15 GEOTHERMAL ENERGY↗
The homogenous alternative to biomineralization: Zn- and Mn-rich materials enable sharp organismal “tools” that reduce force requirements
We measured hardness, modulus of elasticity, and, for the first time, loss tangent, energy of fracture, abrasion resistance, and impact resistance of zinc- and manganese-enriched materials from fangs, stings and other “tools” of an ant, spider, scorpion and nereid worm. The mechanical properties of the Zn- and Mn-materials tended to cluster together between plain and biomineralized “tool” materials, with the hardness reaching, and most abrasion resistance values exceeding, those of calcified salmon teeth and crab claws. Atom probe tomography indicated that Zn was distributed homogeneously on a nanometer scale and likely bound as individual atoms to more than ¼ of the protein residues in ant mandibular teeth. This homogeneity appears to enable sharper, more precisely sculpted “tools” than materials with biomineral inclusions do, and also eliminates interfaces with the inclusions that could be susceptible to fracture. Based on contact mechanics and simplified models, we hypothesize that, relative to plain materials, the higher elastic modulus, hardness and abrasion resistance minimize temporary or permanent tool blunting, resulting in a roughly 2/3 reduction in the force, energy, and muscle mass required to initiate puncture of stiff materials, and even greater force reductions when the cumulative effects of abrasion are considered. We suggest that the sharpness-related force reductions lead to significant energy savings, and can also enable organisms, especially smaller ones, to puncture, cut, and grasp objects that would not be accessible with plain or biomineralized “tools”.
59 BASIC BIOLOGICAL SCIENCES↗
Utah FORGE 5-2419: Temperature Testing of Proppants for EGS and Stimulation of Electromagnetic Fracture Mapping Using Electrically-Conducive Proppants - 2024 Annual Workshop Presentation
This is a presentation on the Temperature Testing of Proppants for EGS and Stimulation of Electromagnetic Fracture Mapping Using Electrically-Conducive Proppants by Stevens Institute of Technology, presented by Cheng Chen. This video slide presentation discusses well controlled laboratory experiments testing the high-temperature performance of electrically-conductive and non-electrically-conductive proppants in maintaining fractures hydraulic and electrical conductivities to understand and quantify the thermal-hydrologic-mechanical-chemical mechanisms that regulate the observed behaviors. This will be tested using proppant/fracture imaging via borehole electromagnetic measurements. This presentation was featured in the Utah FORGE R&D Annual Workshop on August 15, 2024.
15 GEOTHERMAL ENERGY↗
Utah FORGE 5-2615: Thermo-poromechanical Response of Fractured Rock - Workshop Presentation
This is a presentation on the Experimental Determination and Modeling-Informed Analysis of Thermo-poromechanical Response of Fractured Rock for Application to Utah FORGE project by the University of Oklahoma, presented by Dr. Ahmad Ghassemi, McCasland Chair Prof. The project objective is to improve understanding and control of coupled thermo-poromechanical (or thermo-hydro-mechanical- TPM) processes in reservoir development, and to study any role in interpretations of the fracture closure. This presentation was featured in the Utah FORGE R&D Annual Workshop on September 8, 2023. The workshop provided a valuable opportunity to explore the progress made in each of the 17 Research and Development projects funded under Solicitation 2020-1 which aim to enhance our understanding of the crucial factors influencing the development of Enhanced Geothermal Systems (EGS) reservoirs and resources.
15 GEOTHERMAL ENERGY↗
Utah FORGE: Seismic DAS and Geophone Borehole Data Processing and 3D Imaging of Vp/Vs Ratio in the 2024 Stimulated Reservoir
This dataset includes a final report and a 3D velocity model derived from seismic DAS and geophone borehole data collected during the April 2024 stimulation of the reservoir at Utah FORGE. The report details the processing of over 50,000 P- and S-wave travel times used in a tomographic inversion to estimate the Vp/Vs ratio, revealing anomalies adjacent to wells 16A and 16B that may be associated with injected fracturing fluids. Additionally, Wadati analysis of more than 27,000 pairs of differential P- and S-wave travel times supports this interpretation with a high Vp/Vs estimate of 1.86, averaged over the dimensions of the earthquake cluster. The accompanying data file provides a 3D model of P- and S-wave velocities and Vp/Vs ratios, structured with spatial coordinates and velocity values.
15 GEOTHERMAL ENERGY↗