Fracture toughness and subcritical crack growth during high-temperature tensile deformation of Westerly granite and Black gabbro

doi:10.1016/0031-9201(85)90113-X

Physics of the Earth and Planetary Interiors

Volume 39, Issue 1, June 1985, Pages 33-51

https://doi.org/10.1016/0031-9201(85)90113-X Get rights and content

Abstract

The double torsion testing method has been used to determine catastrophic and subcritical crack propagation parameters for pre-cracked specimens of Westerly granite and Black gabbro under a number of environmental conditions.

The critical stress intensity factor for catastrophic crack propagation (fracture toughness) of granite and gabbro has been measured at temperatures from 20 to 400°C, in a vacuum. At 20°C, the fracture toughness of Westerly granite was $1.79 ± 0.02 MPa · m^{12}$ , and for two blocks of Black gabbro it was $3.03 ± 0.08 MPa · m^{12}$ and $2.71 ± 0.15 MPa · m^{12}$ , respectively. These values are very close to those reported by other investigators for tests conducted in air of ambient humidity at room temperature. For both rocks, fracture toughness at first increased slightly, and then decreased steadily on raising the temperature above ambient conditions. This behaviour is explained in terms of the density and distribution of thermally induced microcracks, as determined by quantitative optical microscopy.

Subcritical crack growth behaviour has been studied at temperatures up to 300°C, and under water vapour at pressures of 0.6 to 15 kPa. Both the load relaxation and incremental constant displacement rate forms of the double torsion testing method were utilised to generate stress intensity factor/crack velocity diagrams. Crack growth was measured over the velocity range 5 × 10⁻³ to 10⁻⁷ m · s⁻¹. Increasing both temperature and water vapour pressure resulted in substantially higher crack growth rates. The overall effect of raising the temperature over the range studied here (20–300°C) was to increase the crack growth rate in granite and gabbro by ∼5 and 7 orders of magnitude, respectively, at constant stress intensity factor and vapour pressure of water. For both rocks, the slopes of stress intensity factor/crack velocity curves were sensitive to changes in both temperature and water vapour pressure at low values of the latter parameter. Slopes fell substantially on raising the water vapour pressure, but were relatively insensitive to changes in temperature at these higher pressures. No subcritical crack growth limit was encountered.

Estimates of the uncertainty in our experimental data are given. From the results of multiple load relaxation experiments on Westerly granite specimens, we estimate the uncertainty in position of stress intensity factor/crack velocity curves along the stress intensity axis to be c. 10% of the fracture toughness, and the uncertainty in slope of such curves to be c. 12%.

Problems associated with the extrapolation of our experimental data to regions of higher effective confining pressure in the Earth's crust are discussed.

References (41)

B.K. Atkinson
Fracture toughness of Tennessee sandstone and Carrara marble using the double torsion method
Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
(1979)
B.K. Atkinson
Stress corrosion and the rate-dependent tensile failure of a fine-grained quartz rock
Tectonophysics
(1980)
B.K. Atkinson
Subcritical crack propagation in rocks: theory, experimental results and applications
J. Struct. Geol.
(1982)
R.S.C. Wai et al.
Thermal stress analysis in rocks with nonlinear properties
Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
(1982)
T. Waza et al.
The effect of water on the subcritical crack growth in silicate rocks
Tectonophysics
(1980)
B.J.S. Wilkins
Slow crack growth and delayed failure of granite
Int. J. Rock Mech. Min. Sci. Geomech. Abstr.
(1980)
O.L. Anderson et al.
Stress corrosion theory of crack propagation with application to geophysics
Rev. Geophys. Space Phys.
(1977)
B.K. Atkinson
A fracture mechanics study of subcritical tensile cracking of quartz in wet environments
Pure Appl. Geophys.
(1979)
B.K. Atkinson
Subcritical crack growth in geological materials
J. Geophys. Res.
(1984)
B.K. Atkinson et al.
Acoustic emission during stress corrosion cracking in rocks

B.K. Atkinson et al.

Mechanisms of fracture and friction of crustal rocks in simulated geologic environments

Semiannual Technical Report to the Managers of the US National Earthquake Hazards Reduction Program

(1980)

B.K. Atkinson et al.

Acoustic response and fracture mechanics of granite subjected to thermal and stress cycling experiments

S.J. Bauer et al.

Effects of slow uniform heating on the physical properties of Westerly and Charcoal granites

R.J. Charles

Static fatigue of glass

J. Appl. Physics

(1958)

L.S. Costin et al.

Time-dependent crack growth and failure in brittle rock

J.D. Dunning et al.

Chemomechanical weakening in the presence of surfactants

J. Geophys. Res.

(1980)

A.G. Evans

A method for evaluating the time-dependent failure characteristics of brittle materials—and its application to polycrystalline alumina

J. Mater. Sci.

(1972)

E.R. Fuller

An evaluation of double torsion testing—Analysis

J.E. Gordon

The New Science of Strong Materials

J.P. Henry et al.

Experimental study of crack propagation in calcite rocks

Int. J. Roch Mech. Min. Sci. Geomech. Abstr.

(1978)

Cited by (213)

Shear behavior of thermally damaged rock using the bonded-particle model based on moment tensor
2024, Geothermics
It is critical to understand the temperature-dependent shear behavior of rock in exploiting deep natural resources-geothermal energy, coal, and oil. The shear behavior of thermally damaged rock needs to be further clarified from a micromechanical perspective. In this study, a series of direct shear tests are performed on thermally damaged sandstone using the bonded-particle model (BPM) with thermal formulation to investigate the temperature-dependent behavior. The macro mechanical properties and micro acoustic emission (AE) responses based on a moment tensor algorithm are derived from numerical models to provide insight into the temperature dependence of the mechanical behavior of sandstone. The simulated results indicate that high temperature can induce microcracks, a form of thermally induced damage. Thermally induced damage is a principal cause of the degradation of rock's mechanical properties. Generally, the maximum magnitudes of tensile, shear, and implosive events that can be tolerated without damage decrease gradually as the temperature increases. Also, AE b-value are closely associated with temperature. The findings of this study provide new insights into the shear responses and failure behaviors of rocks at different temperatures, and further aid deep natural resource exploitation when thermal and mechanical properties are coupled. The findings of this study provide new insights into the shear responses and failure behaviors of rocks at different temperatures. These insights could be valuable for optimizing deep natural resource exploitation, particularly when considering the coupling of thermal and mechanical properties.
Thermal treatment effects on rock fracture behaviour under three loading modes: A comparative analysis of granite and mudstone
2024, Engineering Failure Analysis
Temperature and thermal damage have a major impact on the behaviour of fractures in the earth’s crust. For deep earth engineering such as underground coal gasification, geothermal energy extraction, and nuclear waste repositories, developing fracture criteria governing the propagation of fractures under thermal effect is crucial. As a result, the ability of stress, energy, and strain-based fracture criteria to predict rock fracture behavior both before and after thermal treatment is assessed in this paper considering two rock types; granite, and mudstone, which are very different from one another in terms of their mineralogical composition and mechanical properties. The overall findings showed that the energy-based criterion was more effective in predicting fracture parameters both before and after thermal treatment than the stress and strain-based criteria. Specifically, after thermal treatment at 500 °C for the granite, and at any temperature for the mudstone, the strain-based criterion was no longer valid. It was found that the temperature and loading mode have a significant impact on the granite’s transition from brittle to ductile, where this transition can occur at an approximated temperature of 460 °C. Meanwhile, an increase in brittleness with rising temperature was noted in mudstone. Moreover, the Fracture Process Zone (FPZ) size was predicted by the energy-based criterion to be greater than that predicted by stress and strain-based criteria. It was found that the FPZ size is proportional to the brittleness degree of the two rock types, which is considerably impacted by thermal treatment. In addition, this study discusses several critical areas in rock fracture mechanics in the presence of thermal effects including fracture envelopes under mixed mode loading I/II, fracture stress, and initial crack extension angle. All of these are of high importance in assessing the safety and stability of rock structures in the presence of thermal effects.
Failure mechanism of hot dry rock under the coupling effect of thermal cycling and direct shear loading path
2024, International Journal of Rock Mechanics and Mining Sciences
Inducing shear failure in reservoir rocks is a critical strategy for enhancing hot dry rock resource exploitation, as it promotes the development of an extensive fracture network. In this study, granite was subjected to direct shear tests under three distinct temperatures and five thermal cycling treatments. Utilizing acoustic emission (AE) and digital image correlation (DIC) techniques, the shear failure traits and the evolutionary patterns of cracks in granite under diverse thermal cycling treatments were probed. Experimental results reveal that the direct shear strength of granite initially decreases, subsequently rebounds with increasing thermal cycles, and exhibits a steady decrease with temperature increase. Effects of thermal shock provoke a surge in AE counts and energy during the initial half of the shearing process, steering the failure mode of the samples from brittle to plastic. Furthermore, the macro crack morphology changes from a singular shear crack to a pair of parallel shear cracks, becoming intricately complex at elevated temperatures (600 °C). Additionally, the initiation of the main shear crack in granite consistently manifests a mixed tensile-shear failure, with the proportion of shear action displaying a positive correlation with temperature. In contrast, the proximal secondary cracks are purely tension-initiated. Finally, a competitive mechanism between rock strengthening and weakening induced by thermal cycles treatment was proposed to explain the remarkable rebound in direct shear strength following thermal cycling treatment. The current work provides insights for the mechanism of shear failure in rocks under different thermal cycling conditions in geothermal reservoir stimulation.
Experimental study on mode I fracture characteristics of heated granite subjected to water and liquid nitrogen cooling treatments
2024, Engineering Fracture Mechanics
Liquid nitrogen (LN₂) cryogenic fracturing, as a kind of waterless fracturing, is being considered for its potential to enhance the permeability of hot dry rock (HDR) reservoirs. The model I fracture behavior of HDR plays a pivotal role in the HDR fracturing. Therefore, this study focuses on the fracture behavior of the heated granite subjected to water cooling (WC) and liquid nitrogen cooling (LNC) under mode I load. The micro-cracking mechanism of the high-temperature granite under the rapid cooling treatment is analyzed based on the thermo-mechanical coupling grain-based model (GBM). The results indicate that the change in the fracture toughness with the granite temperature has obvious segmental characteristics and the temperature of 200 ℃ is a critical point. Before the critical temperature, the trend of fracture toughness is indistinct with the granite temperature for both cooling methods. However, beyond the critical temperature, the fracture toughness obviously decreases with the increase in the granite temperature, and the LNC is more effective at reducing fracture toughness compared to the WC. With increasing the granite temperature, shear cracks occur earlier during the three-point bending test. A higher proportion of tensile fractures after the LNC treatment is induced by mode I load than after the WC treatment, especially at high granite temperatures. Compared to the WC, the LNC can generate a greater number of microcracks inside the granite, which further results in smaller fracture damage of the LNC-treated granite during mode I load. Ultimately, this leads to improved stimulation performance in terms of reduced fracture resistance and decreased fracture energy requirements for the high-temperature granite cooled by LN₂. The results can enhance the understanding of distinctions between LN₂ cryogenic fracturing and hydraulic fracturing in geothermal exploitation.
Storage integrity during underground hydrogen storage in depleted gas reservoirs
2023, Earth-Science Reviews
The transition from fossil fuels to renewable energy sources, particularly hydrogen, has emerged as a central strategy for decarbonization and the pursuit of net-zero carbon emissions. Meeting the demand for large-scale hydrogen storage, a crucial component of the hydrogen supply chain, has led to the exploration of underground hydrogen storage as an economically viable solution to global energy needs. In contrast to other subsurface storage options such as salt caverns and aquifers, which are geographically limited, depleted gas reservoirs have garnered increasing attention due to their broader distribution and higher storage capacity. However, the safe storage and cycling of hydrogen in depleted gas reservoirs require the preservation of high stability and integrity in the caprock, reservoir, and wellbore. Nevertheless, there exists a significant gap in the current research concerning storage integrity in underground hydrogen storage within depleted gas reservoirs, and a systematic approach is lacking. This paper aims to address this gap by reviewing the primary challenges associated with storage integrity, including geochemical reactions, microbial activities, faults and fractures, and perspectives on hydrogen cycling. The study comprehensively reviews the processes and impacts, such as abiotic and biotic mineral dissolution/precipitation, reactivation and propagation of faults and fractures in caprock and host-rock, wellbore instability due to cement degradation and casing corrosion, and stress changes during hydrogen cycling. To provide a practical solution, a technical screening tool has been developed, considering controlling variables, risks, and consequences affecting storage integrity. Finally, this paper highlights knowledge gaps and suggests feasible methods and pathways to mitigate these risks, facilitating the development of large-scale underground hydrogen storage in depleted gas reservoirs.
Machine learning models for predicting rock fracture toughness at different temperature conditions
2023, Case Studies in Construction Materials
The rock fracture toughness (RFT) is significantly influenced by thermal treatments. Accurate evaluation of RFT at different temperatures holds great importance in the fields of geotechnical engineering. Current analytical and empirical models, based on our current but incomplete understanding of the fracture mechanics theory, are unable to produce a priori predictions of RFT. As a result, researchers have to rely on experiments, which are often costly and time-consuming, to understand external environment, internal factors and RFT links in rocks. This research explores the potential of employing machine learning (ML) models as an effective approach to address such challenges. Six ML models are presented, including support vector machine (SVM), random forest (RF), back propagation neural network (BPNN), back propagation-particle swarm optimization (BP-PSO), convolutional neural network (CNN), and radial basis function neural network (RBF). These models are applied using a dataset of 297 samples derived from previous studies involving semi-circle bend tests. The dataset encompasses 15 input variables, including sample radius, sample thickness, notch length, support span, inclination angle of the notch, tensile strength, uniaxial compressive strength, density, quartz content, feldspar content, gypsum content, clay content, other minerals, loading rate, and temperature. The results of three statistical metrics (root mean square error (RMSE), coefficient of determination (R²), and mean absolute error (MAE)) confirm that the ML models are able to predict the temperature-dependent RFT in modes I, II and III with high accuracy. The results demonstrated that the SVM model shows a better performance than the other five models. In the case of testing dataset, the RMSE, MAE and R² values for SVM model are 0.1122 MPa·m^1/2, 0.0829 MPa·m^1/2 and 0.9506, respectively. Additionally, feature importance analysis highlights that the temperature and inclination angle are the most influential variables affecting the RFT.

View all citing articles on Scopus

View full text

Fracture toughness and subcritical crack growth during high-temperature tensile deformation of Westerly granite and Black gabbro

Abstract

Int. J. Rock Mech. Min. Sci. Geomech. Abstr.

Tectonophysics

J. Struct. Geol.

Int. J. Rock Mech. Min. Sci. Geomech. Abstr.

Tectonophysics

Int. J. Rock Mech. Min. Sci. Geomech. Abstr.

Stress corrosion theory of crack propagation with application to geophysics

Rev. Geophys. Space Phys.

A fracture mechanics study of subcritical tensile cracking of quartz in wet environments

Pure Appl. Geophys.

Subcritical crack growth in geological materials

J. Geophys. Res.

Acoustic emission during stress corrosion cracking in rocks

Mechanisms of fracture and friction of crustal rocks in simulated geologic environments

Semiannual Technical Report to the Managers of the US National Earthquake Hazards Reduction Program

Acoustic response and fracture mechanics of granite subjected to thermal and stress cycling experiments

Effects of slow uniform heating on the physical properties of Westerly and Charcoal granites

Static fatigue of glass

J. Appl. Physics

Time-dependent crack growth and failure in brittle rock

Chemomechanical weakening in the presence of surfactants

J. Geophys. Res.

A method for evaluating the time-dependent failure characteristics of brittle materials—and its application to polycrystalline alumina

J. Mater. Sci.

An evaluation of double torsion testing—Analysis

The New Science of Strong Materials

Experimental study of crack propagation in calcite rocks

Int. J. Roch Mech. Min. Sci. Geomech. Abstr.