Double Torsion Method Research Articles

Inversion-based correction of Double-Torsion (DT) subcritical crack growth tests for crack profile geometry

Because of its simplicity and the ability to produce a stable, slow-propagating crack, the Double-Torsion (DT) method has been used widely for investigating the critical and subcritical propagation of a slow-propagating tensile (mode-I) crack. However, to determine the complex relationship between the crack velocity vc vs. the strain energy release rate G (or the stress intensity factor K) from laboratory measurements, several corrections must be made to account for the impact of sample and crack geometry. Particularly, DT test typically produces a crack with a curved edge profile instead of a straight line, causing the local vc and G vary along the crack front. The experimentally measured vc and G data merely reflect collective, averaged behavior of the crack. This makes inversion for the intrinsic, “true” crack growth kinetics necessary, based upon the knowledge of the crack geometry. Simple and effective correction methods have been proposed and validated for the slow, chemical-reaction-controlled part (Region I) of the vc−G curve. However, reliable methods for the highly nonlinear, transport-dominated part (Region II) and its sudden transition to the dynamic propagation part (Region III) are still lacking. In this paper, we propose a method for determining the intrinsic vc−G relationship across all three Regions based upon DT test data, using a simple model function and its numerical inversion. The performance of this approach is examined and demonstrated using both synthetic and laboratory data for subcritical crack growth in soda lime glass.

Double Torsion testing of thin porous zirconia supports for energy applications: Toughness and slow crack growth assessment

Thin, porous zirconia-based ceramic components are of high interest in energy application devices where they are used as structural ceramics. Mechanical reliability of such devices is not only dependent on the fracture toughness of the ceramic components, but also on their sensitivity to slow crack growth (SCG). In this work, the fracture toughness and SCG behavior of porous (4.5–45.5%) and thin (∼ 0.25 mm) 3Y-TZP ceramics are investigated using the Double Torsion method. The analysis of the double torsion data, previously developed for dense materials, was here assessed and adapted. The compliance of the samples was observed to change linearly with crack length and the measured stress intensity factor was dependent on crack length, as for dense materials. This dependency decreased by increasing the sample porosity. For all materials, the ratio of the SCG threshold to fracture toughness was of 0.56 ± 0.06.

Salinity, pH, and temperature controls on fracture mechanical properties of three shales and their implications for fracture growth in chemically reactive fluid environments

Using the double torsion method, we investigated the fracture mechanical properties of clay-rich Woodford and Mancos Shales, and carbonate-rich Marcellus Shale under conditions of varying fluid salinity, pH, and temperature. Both fracture toughness and subcritical fracture growth properties for clay-rich Woodford and Mancos Shales are sensitive to fluid salinity but not sensitive to pH. With increasing salinity, mean fracture toughness increased up to 34% and 39% for Woodford and Mancos Shale, respectively, and mean subcritical fracture growth index increased up to 99% for Woodford Shale. In contrast, fracture toughness for carbonate-rich Marcellus Shale is unaffected by fluid chemistry, but subcritical fracture growth index increases with increasing pH. Subcritical fracture growth index is reduced by 51% with a decrease in pH from 7 to 1.2. Clay–water interaction is identified as the mechanism for enhanced subcritical fracture growth in clay-rich Woodford and Mancos Shales while enhanced calcite dissolution is accountable for the positive correlation between pH and subcritical fracture growth index in carbonate-rich Marcellus Shale. Increasing solution temperature from 23 °C to 63 °C shifts the K–V curves toward lower stress intensity and amplifies the salinity dependence in the shift of the K–V curves for Woodford Shale. The increase in subcritical fracture growth rate at elevated temperature observed in both clay-rich and carbonate-rich shales is interpreted to reflect faster diffusion rates of fluid from the propagating fracture into the matrix at elevated temperature. Our results emphasize the dependence of critical and subcritical fracture behavior on fluid chemical environment with implications for hydraulic fracture growth in shale reservoirs, and for caprock integrity of wastewater and CO2 storage reservoirs. In these applications, fluid chemistry can both strengthen and weaken caprocks depending on caprock lithology and induced changes in formation water chemistry.

Effect of Water on Fracture Mechanical Properties of Shales

AbstractRecognition of the potential for subcritical fracture growth of rocks is essential for the evaluation of long‐term stability of fluids trapped in geologic structures. In shales, subcritical fracture growth may control migration of hydrocarbons in source rock and unconventional reservoirs and of sequestered CO2 across top seals. Using the double torsion method, we investigated the mode‐I fracture mechanical properties of three shales of different composition, namely, Woodford Shale, Mancos Shale, and Marcellus Shale, under water‐saturated conditions, in ambient air, and in dry CO2 gas conditions to systematically investigate the effect of water on the fracture growth properties of shales. The clay‐rich (illite with minor kaolinite) Woodford and Mancos Shales demonstrate a strong water‐weakening effect despite their low smectite content, with the fracture toughness reduced by up to 54% and the subcritical fracture growth index by up to 77% under water‐saturated conditions compared to tests in ambient air. Carbonate‐rich Marcellus Shale, in contrast, displays negligible water‐weakening effects. The clay‐CO2 interaction is minor for the three shales. Specimens treated with a hydrophobic surface coating were also tested to limit water‐weakening effects to the fracture tip. Data from these tests reveal rate‐dependent stress intensity factor‐velocity curves for clay‐rich Woodford and Mancos Shales suggesting a competition between mechanical fracture growth and physicochemical water‐rock interactions. Our results suggest that subcritical failure by water‐enhanced subcritical fracture growth could significantly increase brittle failure in clay‐rich shales.

Effect of CO2–brine–rock interaction on fracture mechanical properties of CO2 reservoirs and seals

The effect of CO2–water–rock interactions on fracture mechanical properties of reservoir and seal rocks due to injection of CO2 in the subsurface may impact long-term (102–104 yr) storage security. At the Crystal Geyser and Salt Wash field sites near Green River, Utah, sandstone of the Salt Wash Member of the Morrison Formation and Mancos Shale have undergone chemical alteration associated with flow of CO2-bearing water under natural conditions over geologic time scales of 103–105 yrs. To quantify the effects of these diagenetic changes on rock fracture mechanical properties we conducted opening-mode fracture mechanics tests using the double torsion method on a suite of CO2-altered and unaltered siliciclastic samples. We show that dissolution of hematite and carbonate cement in Entrada Sandstone by CO2-rich brine lowers fracture toughness by nearly 40% relative to adjacent, unaltered samples from the same unit. In contrast, precipitation of calcite pore cement in a sandstone of the Salt Wash Member of the Morrison Formation, attributed to CO2 degassing during upward fluid flow along the Little Grand Wash Fault, results in a 100–700% increase in fracture toughness. Similarly, precipitation of carbonate mineral cements and replacement of matrix measurably strengthens Mancos Shale, considered a regional top seal. Subcritical fracture growth index (SCI) which quantifies reaction-assisted subcritical fracture propagation is also affected by CO2-related alteration. Based on previous numerical simulations of fracture network growth with varying fracture mechanical parameters, we find that the measured variations in fracture mechanical properties qualitatively match observed differences in opening-mode fracture distributions along the fault, with short, non-connected fractures in CO2-bleached rock, long, throughgoing fractures in calcite-cemented shale, and short, closely spaced, interconnected fracture networks in highly altered rock directly adjacent to fault conduits. Our fracture mechanics tests demonstrate that fracture mechanical properties of reservoir and seal rock can change as a result of chemical CO2–brine–rock interaction. These chemical interactions may favor or inhibit subcritical fracture growth processes and thus reservoir and seal flow properties. In regions of CO2-related mineral dissolution, subcritical fracture growth may reduce seal integrity over time scales beyond those of active injection and reservoir monitoring, thus negatively affecting seal integrity over the expected design lifetime of a CO2 reservoir.

Subcritical crack growth and lifetime prediction of chemically strengthened aluminosilicate glass

The effect of residual stress on subcritical crack growth in chemically strengthened aluminosilicate glass in air and water was firstly investigated using the double torsion (DT) technique. An experimental evaluation procedure was developed based on the DT method. The research demonstrates that high compressive stress (CS) and low central tension (CT) in chemically strengthened glass are beneficial in improving crack growth index and decreasing susceptibility to fatigue. Chemically strengthened glass with high CS and low CT exhibits a smaller proof-test ratio, which indicates better survival characteristics. The results are useful in designing the strength and optimizing the strengthening process by ion exchange to obtain a more robust glass with long service lifetime.

Effects of relative humidity and temperature on subcritical crack growth in rock

In order to ensure long-term stability of structures in a rock mass, the study of time-dependent fracturing is essential. We have therefore investigated the effects of relative humidity and temperature on subcritical crack growth in rock experimentally on samples of Kumamoto andesite, Oshima granite, Berea sandstone, Shirahama sandstone and Kushiro sandstone using the Double Torsion method. All experiments were conducted in moist air. Our results show that, in experiments conducted under the same relative humidity, crack velocity in igneous rocks increased with increasing temperature, in agreement with previous studies. On the other hand, the change of the crack velocity in sandstones at a given stress intensity factor was unclear when the temperature increased under a constant relative humidity in air. Our results also show that, in experiments conducted at the same temperature, crack velocity increased dramatically with increasing relative humidity. This increase is much larger than that expected from the conventional concept based on the theory of stress corrosion. The increase of the crack velocity was larger for sandstone which contained larger amount of clays. We conclude that subcritical crack growth in rock in air is affected remarkably by the relative humidity and the existence of clays.

Determination of the critical stress intensity factor (KIC) of compacted pharmaceutical powders by the double torsion method.

The critical stress intensity factor KIC has been determined for compacts prepared at different pressures from both Avicel PH101 and sorbitol "Instant', by means of a double torsion method. This method avoids the need for displacement measurement and the introduction of notch into the specimens, both of which present problems with pharmaceutical materials. Measurements of fracture loads for such specimens were reproducible. The values of KIC derived for both materials were found to increase linearly with increase in compaction pressure and linearly with decrease in specimen porosity. Extrapolation of the latter relationship to zero porosity gave values of 1.81 and 0.69 MN m-3/2 for the KIC of Avicel PH101 and sorbitol "Instant', respectively.

Fracture behaviour of a self-healing microcapsule-loaded epoxy system

The effect of temperature on the fracture behaviour of a microcapsule-loaded epoxy matrix was investigated. Microencapsulated epoxy and mercaptan-derivative healing agents were incorporated into an epoxy matrix to produce a polymer composite capable of self-healing. Maximum fracture loads were measured using the double-torsion method. Thermal aging at 55 and 110°C for 17 hours (hrs) was applied to heal the pre-cracked samples. The addition of microcap- sules appeared to increase significantly the load carrying capacity of the epoxy after healing. Once healed, the composites achieved as much as 93-171% of its virgin maximum fracture load at 18, 55 and 110°C. The fracture behavior of the micro- capsule-loaded epoxy matrix was influenced by the healing temperature. The high self-healing efficiency may be attributed to the result of the subsurface micro-crack pinning or deviation, and to a stronger microencapsulated epoxy and mercaptan- derivative binder than that of the bulk epoxy. The results show that the healing temperature has a significant effect on recov- ery of load transferring capability after fracture.

Subcritical crack growth and long-term strength in rock and cementitious material

High-strength and ultra low-permeability concrete (HSULPC) is a strong candidate for a radioactive waste package containing transuranic radionuclides (TRU waste) for geological disposal. Knowledge of the time-dependent fracturing of HSULPC and surrounding rock mass is essential to assess the long-term stability of such underground repositories. We have measured crack velocity in andesite and HSULPC both in air and water to examine subcritical crack growth by the Double-Torsion method. In air, the crack velocity in andesite increased when the temperature and relative humidity increased. On the other hand, the temperature and relative humidity had little effect on the crack velocity in HSULPC in air. In water, the crack velocity increased when the temperature was higher for both andesite and HSULPC. Using these experimental results, the long-term strength was estimated. It was shown that the long-term strength of HSULPC was higher than that of andesite. In air, the long-term strength for andesite was affected by the temperature and relative humidity. The long-term strength for andesite decreased when the temperature or relative humidity increased. For HSULPC, the change of the long-term strength with varying temperature or relative humidity was smaller than andesite in air. In water, the long-term strength for both materials decreased with increasing the temperature. Comparing the long-term strength of andesite and HSULPC at the same environmental conditions, it was recognized that the decrease of the long-term strength of HSULPC is smaller than that of andesite. The long-term strength in water was smaller than that in air for both materials.

Effect of Surrounding Environment on Subcritical Crack Growth Index and Long-Term Strength for Rock

Study of subcritical crack growth is important in estimating the long-term strength of rock and in ensuring the long-term stability of structures in a rock mass. The long-term strength is affected by the value of subcritical crack growth index (SCGI). However, the effect of environmental conditions on SCGI has not been clarified. In this study, we have estimated SCGI under various environmental conditions on a sample of Kumamoto andesite, using the Double-Torsion method. We show that the SCGI decreased when the temperature is higher in both air and water; the SCGI in water is smaller than that in air. When the relative humidity of the air increased, SCGI tended to be smaller and at 90 % relative humidity was close to the value in water. Under alkali conditions, the SCGI decreased slightly. Using the values of SCGI, the long-term strength was estimated and it is shown that the long-term strength decreased when SCGI was smaller. It is concluded that SCGI and the long-term strength is affected by the surrounding environment, specifically by the temperature and water. To ensure the long-term stability of rock, the control of the temperature and water migration is important.

砂岩の破壊靭性に及ぼす湿度の影響

The effect of the humidity on the fracture toughness in sandstone in air was investigated experimentally. Rocks used in this study were Berea sandstone, Shirahama sandstone and sandstone obtained at Kushiro coalmine (Kushiro sandstone). Double-Torsion method was used in this study to measure the fracture toughness to compare the results to those of subcritical crack growth. All measurements were conducted under the same temperature and different relative humidity to investigate the effect of the humidity.It was shown that the humidity affected the fracture toughness. The fracture toughness decreased with the increase of the humidity. The decrease of the fracture toughness was more remarkable when the content of clays in rock was higher. It is considered that the amount of clays had a significant effect on the change of the fracture toughness of sandstone. Degradation of clays with increasing the water content is considered to affect the decrease of the fracture toughness. It was shown that the decrease of the fracture toughness with increasing the humidity was less than the decrease of the stress intensity factor for subcritical crack growth. This was caused because stress corrosion had less effect on the fracture toughness. It is concluded that the crack growth in sandstone is affected by the humidity and the content of clays.

砂岩のサブクリティカルき裂進展に及ぼす湿度の影響

The effect of the humidity on subcritical crack growth in sandstone in air was investigated experimentally. Rocks used in this study were Berea sandstone, Shirahama sandstone and sandstone obtained at Kushiro coalmine (Kushiro sandstone). Double-Torsion method was used in this study to measure the crack velocity and the stress intensity factor. All experiments were conducted under the same temperature and different relative humidity to investigate the effect of the humidity.It was shown that the humidity affected the crack velocity strongly. The crack velocity increased with the increase of the humidity. The increases of the crack velocity were much larger than that estimated from the classical stress corrosion theory. The increases of the crack velocity in Shirahama sandstone and Kushiro sandstone were larger than that in Berea sandstone by several orders of magnitude. This difference may be due to the difference of the rock fabric. Shirahama sandstone and Kushiro sandstone include clay minerals much more than Berea sandstone. It is probable that the fracture resistance of clay decreased due to the increase of the humidity. Consequently, large increases of the crack velocity occurred in Shirahama sandstone and Kushiro sandstone. It is concluded that the humidity has the strong effect on subcritical crack growth in sandstone and the control of the humidity is important to prevent the weakening of rock.

Subcritical Crack Growth and Long-Term Strength in Rock and High-Strength and Ultra Low-Permeability Concrete

High-strength and ultra low-permeability concrete (HSULPC) is a strong candidate for a radioactive waste package containing transuranic radionuclides (TRU waste) for geological disposal. The information and knowledge of the time-dependent fracturing of HSULPC and surrounding rock mass are essential to assess the long-term stability of such underground repositories. Here we measured crack velocity in andesite and HSULPC both in air and water to examine slow crack growth (subcritical crack growth) by Double-Torsion method. In air, the crack velocity in andesite increased when the temperature increased. On the other hand, the temperature had little effect on the crack velocity in HSULPC in air. In water, the crack velocity increased when the temperature was higher for both andesite and HSULPC. By using the experimental results of subcritical crack growth, the long-term strength was estimated based on the model of a single crack subjected to tension in an infinite plate. It was shown that the long-term strength of HSULPC was higher than that of andesite. When the temperature increased, the long-term strength of andesite both in air and water and that of HSULPC in water decreased. The long-term strength in water was smaller than that in air for both materials. It is concluded that water remarkably affects subcritical crack growth and the long-term strength in these materials.

火成岩のサブクリティカルき裂進展に及ぼす湿度の影響

The effect of the humidity on subcritical crack growth in igneous rock in air was investigated experimentally. Rocks used in this study were Kumamoto andesite and Oshima granite. Double-Torsion method was used in this study to measure the crack velocity and the stress intensity factor. All experiments were conducted under the same temperature and different relative humidity to investigate the effect of the humidity.It was shown that the humidity affected the crack velocity strongly. The crack velocity increased with the increase of the humidity. The crack velocity increased by 1 ∼ 4 orders of magnitude when the humidity increased threefold or fourfold. This increase is larger than that estimated from the classical stress corrosion theory. It is concluded that the humidity has the strong effect on subcritical crack growth in rock and the control of the humidity is important to prevent the weakening of rock.

Fracture toughness, strength and slow crack growth in a ceria stabilized zirconia–alumina nanocomposite for medical applications

Mechanical properties and slow crack growth (SCG) behavior of a 10Ce-TZP/Al 2O 3 nanocomposite currently developed as a biomaterial are considered. Fracture toughness is determined for sharp, long (double torsion) and short (indentation) cracks and a good agreement is found between the two types of cracks. The main toughening mechanism in the nanocomposite is the tetragonal to monoclinic phase transformation of the ceria-stabilized zirconia (Ce-TZP) phase. Transformation at the surface of ground specimens leads to surface compressive induced stresses and an increase in strength. Crack velocity curves ( V– K I curves) are obtained under static and cyclic fatigue using the double torsion method. The static V– K I curve in air reveals the three stages characteristic of stress corrosion with a threshold K I0 ∼ 4.5 MPa m 1/2 and a fracture toughness of 8.8 MPa m 1/2 significantly higher than those of currently used inert bioceramics (i.e. alumina and Y-TZP). A crack growth accelerating effect is shown under cyclic loading, correlated with a decrease in the threshold. However, the cyclic fatigue threshold (4 MPa m 1/2) still stands above that of current biomedical grade alumina and zirconia.

The predictions and applications of fatigue lifetime in alumina and zirconia ceramics

The lifetime prediction of ceramics has been discussed on the basis of the relation between the stress intensity factor K I and the crack velocity V. In this paper, the effects of both cyclic loading and water environment on the K I– V characteristics were studied by the crack growth tests using the double torsion method under static and cyclic loading in both environments of air and water for alumina and zirconia ceramics. The K I– V characteristics determined by the double torsion method were used to predict time-to-failure under cyclic fatigue of alumina and zirconia ceramics. The predictions agreed qualitatively with the experimental results.

Crack propagation behavior and lifetime prediction in alumina and zirconia

The lifetime prediction of ceramics is discussed on the basis of the relationship between stress intensity factor KI and crack velocity v. The effects of water environment, the cyclic loading and microstructure of material on KI-v characteristics are studied by carrying out the crack growth tests by the double torsion (DT) method under the static and cyclic loading in both environments of air and water for alumina and zirconia. KI-v characteristics determined by the double torsion method are used to predict time-to-failure under the cyclic loading of alumina and zirconia ceramics. The predictions agree qualitatively with the experimental results.

Investigation of Slow Crack Growth in Dense Hydroxyapatite Using the Double Torsion Method

Investigation of Slow Crack Growth in Dense Hydroxyapatite Using the Double Torsion Method

Slow crack growth study of plaster using the double torsion method

Double torsion tests were performed to study slow crack growth (SCG) behavior of dry plaster. Preliminary, the fracture toughness K Ic was measured, and higher value than that obtained with notched beams in bending test was found. This can be attributed to interactions between the surfaces of the initial crack in the DT samples. For SCG investigation, both load relaxation and constant loading tests were conducted. It is found that the relaxation method is not suitable for quantitative determination of the SCG law. Indeed, the load relaxation is very limited for dry samples and cannot be correlated to the crack propagation observed on the tensile surface. The constant loading results show that subcritical crack propagation occurs at K I values lower than 30% K Ic. This can be explained by the linkage of the main propagating crack with secondary cracks, the nucleation of which occurs at very low applied stresses.