Crack Closure Stress Research Articles

Research on the Mechanical Properties and Damage Constitutive Model of Multi-Shape Fractured Sandstone under Hydro-Mechanical Coupling

In this paper, mechanical property tests of sandstone with multiple shapes of prefabricated fractures (single, T-shaped, and Y-shaped fractures) are carried out through the MTS815 rock mechanics testing machine and the Teledyne ISCO D-Series Pumps system. Considering the hydro-mechanical coupling effects, the experiments reveal the key thresholds, strength characteristics and deformation laws of multi-shape fractured sandstones during the progressive failure process. According to the elastic-plastic theory, the continuous damage theory and the statistical damage theory, a new damage model is constructed, which fully reflects the coupled effects among water, micro flaws and macroscopic prefabricated fractures. The crack closure stress σcc, crack initiation stress σci and damage stress σcd of multi-shape fractured sandstone samples are determined by the proposed volumetric strain response method. In the range of 0–90°, the σcc and σci of the multi-shape fractured sandstone samples are different, as well as the angles when the σcd and peak strength (σc) reach their peak values. The stress ratios (the σcc/σc, σci/σc, and σcd/σc are collectively referred to as stress ratios) are hardly affected by the shape and inclination of the fractures inside the rock. According to strength analysis and deformation characteristics, the weakening effect of water has less of an influence on the strength than prefabricated fractures. The stress–strain curve obtained, based on the hydro-mechanical coupling test, is in good agreement with the theoretical curve generated by the damage constitutive model, verifying the rationality of the damage constitutive model. In addition, the fracture inclination only affects the numerical value of the total damage variable of multi-shape fractured sandstone samples, and has minor effects on its variation trend.

Nonlinear statistical damage constitutive model of granite based on the energy dissipation ratio

The stress–strain curves and mechanical properties of Shuangjiangkou granite were obtained using five groups of conventional triaxial tests under various confining pressures using MTS815 rock test equipment. From the microscale, mesoscale, and macroscale perspectives, four types of mechanisms that contribute to energy dissipation during granite deformation were investigated. Based on the energy dissipation ratio, a new approach for estimating crack closure stress and damage stress is proposed. The energy dissipation ratio was substituted into the Weibull distribution function, and then a new nonlinear statistical damage constitutive model of granite based on the energy dissipation ratio was constructed after Biot’s theory was modified per the Lemaitre strain equivalence principle. By comparing experimental data with theoretical values estimated by the model, the model’s rationality and correctness were confirmed.

A new method to determine the crack closure stress based on stress difference

Crack closure stress is a key stress threshold of rocks under compression, the determination of which is of great significance to the evaluation of macroscopic deformation behavior and microscopic fracture evolution characteristics of rocks. Based on the applicability and analysis of the existing methods, a novel method called axial stress difference (ASD) method on the basis of axial stress - axial strain curve is proposed. This method reduces the dependence on the elastic modulus which restricts the promotion of previous methods, and can objectively acquire the crack closure stress by the identification of the onset point of linearly elastic stage of axial stress - axial strain curves. Then, the crack closure stress of rock materials under uniaxial and triaxial compression obtained by the ASD method is compared with the counterparts from other methods. The results obtained by the ASD method are close to that by other methods, which can also be verified by the small standard deviation and coefficient of variation. Since the International Society for Rock Mechanics and Rock Engineering (ISRM) has not yet recommended standard methods for solving the crack closure stress, this method can be an effective supplement to the existing methods.

Fatigue crack growth under mixed mode I-II loading with a single tensile overload at negative load ratios

Fatigue crack growth (FCG) behavior under mixed mode loading has been received extensive attention, including overload condition. The mixed mode I-II fatigue crack growth behavior of commercial pure titanium (CP-Ti) with tensile overload at negative load ratios was investigated by experiment and finite element method (FEM). The effects of loading angle, load ratio and overload on mixed mode I-II fatigue crack growth were discussed with a modified compact-tensile-shear (CTS) specimen. The mechanism of mixed mode crack growth with overload was revealed. Fatigue crack growth path and fatigue crack growth rate (FCGR) with/without overload were compared experimentally, and overload retardation effect was investigated. The variation of plastic zone and the distribution of stress and strain were simulated through finite element method. The mechanism of overload retardation effect of mixed mode I-II crack growth under compressive load was illustrated by microscopic perspective, crack closure and residual compressive stress at crack tip, and the weakening effect of mode II shear component and compressive load effect on overload retardation effect was demonstrated.

Effect of crack-tip deformation on fatigue crack growth: A comparative study under overload/underload conditions

With the aim to provide the structural design stage with data on the crack retardation/acceleration effects caused by overload/underload and to explore the corresponding mechanisms, we conducted a series of comparative fatigue crack growth rate (FCGR) tests on S355J2W+N steel. The various amplitudes of overload/underload were investigated comprehensively under different stress-ratio baseline loads for single and periodic overloading/underloading processes. Moreover, the crack-tip deformation behaviors (i.e., the strain/stress fields and crack closure responses following the overload/underload) were observed using a digital image correlation (DIC) technique and calculated through the finite element analysis. The relevant fracture morphologies and crack-tip dislocation structures were characterized and analyzed. The results showed that the crack propagation cycles could be influenced to different degrees by a single overload (OL), a single underload (UL), and periodic underloads (PULs). Compared with the transient crack acceleration induced by a UL, a lasting crack growth retardation occurred following an OL. The OL&UL sequences had various effects on the changes in FCGR. Furthermore, a higher stress-ratio baseline loading and larger-amplitude OL increased the retardation effect; a lower stress-ratio baseline loading and larger-amplitude UL enhanced the acceleration effect. The degrees of crack retardation or acceleration following the OL/UL were determined by the changes in the crack closure and residual stress state near crack tip, which were closely related to the baseline loading stress ratio and local residual strain characteristics. Correspondingly, the OL and PULs also changed the dislocation density and structures in the microscopic view.

Measuring crack growth and related opening and closing stresses using continuous potential drop recording

To improve resolution of in-situ measurement of crack closure and opening in fatigue, potential drop (PD) measurement technique has been further developed to measure thousands of times through each load cycle with high precision. The results are interpreted with physical phenomena like strain, Poisson’s effect, piezo-resistivity, plasticity, and crack growth. Application of the technique to fatigue crack growth tests on aluminum 2024-T3 CCT specimens at different maximum stresses and stress ratios, demonstrate that indeed variations in PD can be associated to development of plasticity and crack opening and closure. Hence, the technique allows to measure timing and magnitude of crack opening and closure stresses in-situ in fatigue crack growth experiments.

Mechanisms of fatigue crack growth in Ti-6Al-4V alloy subjected to single overloads

The relative importance of crack closure and residual stresses on fatigue crack growth (FCG), which is controversial, is studied here. FCG is predicted numerically in CT specimens of Ti-6Al-4V alloy submitted to single overloads, assuming that crack tip plastic strain is the driving force. The numerical procedure, which includes the effects of crack tip blunting, material hardening, crack closure and partial crack closure, was found to be very robust and to give correct trends. The high strength material studied showed relatively small overload affected zones (<0.5 mm), which is even more pronounced under plane strain conditions. The comparison of numerical results with and without contact of crack flanks showed that crack closure is responsible for the effect of overloads on FCG rate behaviour, while the effect of residual stresses is not relevant for the material studied. The transient behaviour obtained after an overload is unattainable without considering the contact of the crack flanks.

Strength and energy exchange of deep sandstone under high hydraulic conditions

To investigate the influence of confining pressure and pore water pressure on strength characteristics, energy storage state and energy release intensity at peak failure of deep sandstone, a series of triaxial compression tests under hydraulic coupling conditions are carried out. By analyzing the process of rock deformation and failure, the stress thresholds of the rock are obtained. The change trend of total energy density, elastic energy density and dissipated energy density of deep sandstone in the pre-peak stage is obtained by the graphical integration method. By comparing the dynamic energy storage level of rocks under different confining pressures, the influence of pore water pressure on the energy dissipation at stress thresholds of crack closure stress, crack initiation stress, crack damage stress and peak stress is analyzed. Based on the ratio of pre-peak total energy density to post-peak total energy density, the interaction mechanism of confining pressure and pore water pressure for the rock burst proneness of deep sandstone is studied. The experimental results show that the peak stress of sandstone increases with the increase of confining pressure, while the existence of pore water pressure can weaken the peak stress of sandstone. In the stress stage from crack closure stress to peak stress, the dynamic energy storage level of rock presents a trend of the inverse “check mark”. Meanwhile, the larger the confining pressure, the higher the energy storage level of rock. However, the pore water pressure increases the degree of energy dissipation of rock and reduces the energy storage capacity of rock, and the degree of dissipation is linear with pore water pressure. The increase of confining pressure aggravates the instability and failure of deep sandstone, while pore water pressure has the opposite effect. The research results will provide necessary data support for the stability analysis of rock mass excavation in sandstone stratum under high stress and high pore water pressure.

Elasto-plastic behavior of the Fontainebleau sandstone based on a refined continuous strain deviation approach

The elasto-plastic behavior of the Fontainebleau sandstone is studied from experimental and numerical points of view on the basis of a series of conventional triaxial compression tests. Five distinct stages of the axial strain curve are quantified in terms of four stress thresholds (crack closure stress σcc , crack initiation stress σci , crack damage stress σcd and short-term peak strength σp ). The onset of dilation and total volumetric strain reversal occur at axial stress level 30–50% and 50–80% of σp , respectively. A refined continuous strain deviation (RCSD) method is proposed to more accurately define the elastic parameters. Other internal state variables are determined accordingly. Some important information are gained as follows: (1) the Poisson’s ratio decreases with the increase of the confining pressure; (2) at the same stress level, the higher of the confining pressure, the smaller of the negative plastic volumetric strain (dilatancy); (3) the evolution of the friction-like coefficient and the plastic volumetric strain can be described with an exponential function and a hyperbolic function, respectively. A strictly experimental based constitutive model is proposed to study the elasto-plastic behavior of the Fontainebleau sandstone. All numerical aspects including formulations, algorithms and experimental validations, are presented in detail.

Impact of the initial crack volume on the intact behavior of a bonded particle model

The flat-jointed (FJ) contact model implemented in the particle flow code resolves the long-standing issue of the code producing unrealistically low ratios of uniaxial compressive strength (UCS) to direct tensile strength. Despite the improvements introduced with the FJ model, an FJ sample calibrated to the UCS still produces a crack initiation stress much lower than the expected value of approximately 0.4 UCS, as commonly observed in laboratory compression tests for most rocks. In this study, we investigated the role of initial crack volume on the crack initiation stress of a rock. We found that the microcracks among the mineral grains and their associated void space played a major role in controlling the stress magnitude associated with crack initiation. We also observed that the closure of these cracks between mineral grains was the primary driver of the crack closure phase in the compression test, and the elastic bimodularity was due to the crack density. We developed a methodology to incorporate the initial microcracks using the FJ contact model to match the crack closure stress and bimodularity of a laboratory rock sample. By introducing microcracks and voids among the mineral grains, we automatically capture the crack initiation stress of Lac du Bonnet granite measured at approximately 40% of the UCS.

Defining Stress Thresholds of Granite Failure Process Based on Acoustic Emission Activity Parameters

In order to study the crack closure stress threshold σcc of hard rock, crack initiation stress threshold σci, stress threshold σcs of crack interaction, and damage stress threshold σc d, uniaxial compression test was carried out on granite samples. Stress sensor and dynamic strain gauge are used to measure the load, longitudinal, and lateral deformation of rock in real time. The acoustic emission characteristic parameters of rock fracture process are obtained by using the acoustic emission system. According to the change rule of the AE event rate, cumulative energy, energy rate, duration, and amplitude in the whole process of granite sample fracture, the stress threshold (σcc, σci, σcs, and σc d) of each loading stage in the process of rock sample fracture is obtained. The relationship between the stress threshold (σcc, σci, σcs, and σc d) of each stage and the uniaxial compressive strength σUCS of rock samples in the whole process of fracture is analyzed, which shows that the deformation characteristics and crack evolution law of the rock are unified. The research results can provide some reference for further understanding of rock damage evolution mechanism in engineering field.

Study on Crack Closure Considering Welding Residual Stress Under Constant Amplitude Loading and Overloading

Welding residual stress in the engineering structure has a non-negligible influence on crack propagation, and crack closure is a significant factor affecting the crack propagation. Based on the elastoplastic finite element method and crack closure theory, we studied crack closure and residual compressive stress field of butt-welded plates under constant amplitude loading and overloading regarding the stress ratio, maximum load, overload ratio, and number of overloads. The results show that the welding residual tensile stress can decrease the crack closure because of a decrease in the residual compressive stress in the wake zone, but the effect is gradually reduced with increased stress ratio or maximum load. And the combined effect of welding residual tensile stress and overload can produce a stronger retardation effect on crack propagation.

A Novel Method for Determining the Crack Closure Stress of Brittle Rocks Subjected to Compression

A Novel Method for Determining the Crack Closure Stress of Brittle Rocks Subjected to Compression

Effect of high temperature damage on triaxial mechanical failure behavior of sandstone specimens containing a single fissure

The quantitative temperature (T)-dependent relationships between the strength properties and elastic modulus of both intact and fissured sandstone are presented. Based on the experimental results, it can be concluded that tensile strength (TS) and mode I fracture toughness (KIC) decrease nonlinearly with increasing T. The elastic modulus (E) values of the intact and fissured sandstone specimens have different correlations with T and confining pressure (σ3), whereas the Poisson’s ratio does not depend on the temperature. As T increases, crack closure stress, crack initiation stress and crack damage threshold first increase and then decrease, however, these properties have linear correlations with σ3. The cohesion (C) of the intact specimen decreases nonlinearly with increasing T, whereas that of the fissured specimen first increases and then decreases. However, the internal friction angle (φ) of the intact and fissured specimens has nonlinear correlations with T. The permeability (k) of the intact sandstone decreases during the compaction-dominated stage and then increases at dilation-dominated stage under constant strain compression at σ3 = 30 MPa. Moreover, k decreases slightly as T increases to 250 °C but then increases with further increasing T. The crack types of intact and fissured specimens under different σ3 and temperature conditions are also discussed.

Experimental investigation on the crack propagation behaviors of sandstone under different loading and unloading conditions

A series of laboratory tests were conducted in order to investigate the effects on crack propagation characteristics of confining pressure, as well as the effect of the unloading rates of confining pressure. Under conventional compression conditions, with increases in confining pressure levels, decreases will occur in the initial crack volumetric strain and crack volumetric propagation strain. These decreases indicate that when a specimen is under higher confining pressure conditions, it tend to generate more cracks before failure occurs. The crack closure stress, crack initiation stress and crack damage stress of sandstone gradually increase with increasing confining pressure levels. The crack propagation velocity corresponding to peak stress of sandstone undergoing uniaxial compression is the largest. In addition, with increases in confining pressure, the crack propagation velocity decreases. At the same confining pressure level, the crack volumetric propagation velocity corresponding to peak stress is the largest, followed by the crack radial and crack axial propagation velocities. With increases in the unloading rates of the confining pressure, increases will occur in the crack volumetric propagation strain and crack propagation velocity of the sandstone. The crack propagation velocity corresponding to peak stress of sandstone is larger than it is under uniaxial and conventional triaxial compression. Therefore, the larger unloading rates may cause larger crack propagation velocities and as the burst liability increases, rock burst or coal bumps may be triggered.

Performance of rock crack stress thresholds determination criteria and investigating strength and confining pressure effects

Identifying crack stress thresholds of rocks under different loading conditions, e.g. long-term monotonic or cyclic loads, are crucial in the design of rock excavations and underground openings. The evaluation of the performance of damage thresholds, i.e. crack closure, crack initiation and crack damage stresses, for a variety of rocks, is crucial to assess the most suitable method to capture the stages of rock strength degradation for rock having different strengths subjected to different confining pressures expected to in the field. In this study, several uniaxial and triaxial tests on different rock specimens (Uniaxial compressive strengths from 5 to 278 MPa) were performed to investigate the application and performance of different criteria to determine damage threshold values, using their stress–strain response. It was found that the volumetric strain response of the rock is the most promising parameter to identify crack stress thresholds. For the rocks having different strength values and subjected to different confining pressures, on average, ratios of crack closure, crack initiation and crack damage to the peak strength are found to be 0.21, 0.33 and 0.80 respectively. Effect of rock strength on crack closure and crack initiation stress thresholds was found to be negligible. Crack damage threshold, however, increases with a rock strength increase. This was mainly attributed to the brittle failure behaviour of stronger rocks when compared to weaker rocks. In triaxial compressive testing, crack closure partially occurs during rock consolidation and therefore, crack closure stress decreases with confining pressure increase. Furthermore, a limiting effect on the generation and further growing of lateral cracks in the rocks did lead to an increase in the stress to induced crack damage with an increase in the confining pressure. On the other hand, the effect of confining pressure on the crack initiation stress was observed to be different in different rocks.

The effects of thermo-mechanical processing on fatigue crack propagation in commercially pure titanium with a harmonic structure

Commercially pure (CP) titanium having a bimodal harmonic structure, in which coarse grains are enveloped by a network consisting of fine grains, was obtained by consolidating mechanically milled powders to enhance both strength and ductility. We have examined the fatigue properties of materials having harmonic structures to achieve sufficient performance for practical applications in the engineering fields. In this study, thermo-mechanical processing (TMP) was performed for the CP titanium having a bimodal harmonic structure to improve its fatigue properties. Four-point bending fatigue tests and fatigue crack propagation tests were conducted under ambient conditions to investigate the fatigue crack initiation and propagation in CP titanium having a harmonic structure following TMP. Applying TMP to CP titanium having a harmonic structure increased its fatigue life due to greater resistance to the initiation of fatigue crack as a result of grain refinement. In contrast, CP titanium having a harmonic structure shows lower threshold stress intensity range, ΔKth, values following TMP as a result of reduced the degree of crack closure and lower effective threshold stress intensity range, ΔKeff,th, values due to grain refinement.

Generalized crack damage stress thresholds of hard rocks under true triaxial compression

The rock failure process can be characterized by several distinct stress thresholds: the crack closure stress σcc, crack initiation stress σci, crack damage stress σcd and peak stress σp. Seventy-one true triaxial compression tests were conducted to investigate the crack damage stress σcd, which is the stress at the onset of unstable crack development and dilation. Two empirical models are developed to predict the crack damage stress σcd using the intermediate principal stress σ2 and the minimum principal stress σ3. In addition, the proposed models are validated by ten results derived from the German Continental Deep Drilling Program (KTB) deep hole amphibolite. A comparison with other failure criteria also indicates the accuracy and simplicity of the proposed models. The proposed composite models show that the crack damage stress σcd gradually increases with increasing intermediate principal stress σ2 and minimum principal stress σ3. The physical meanings and ranges of six material parameters are analyzed and explained. Both the influence of the tangent Young’s modulus E and strain characteristics on the crack damage stress σcd and the inhomogeneity of the tested specimens are discussed in this paper.

Fatigue crack retardation associated with creep deformation induced by a tension hold in a single crystal Ni-base superalloy

Effect of creep deformation at crack tip on fatigue crack propagation in a single crystal Ni-base superalloy was investigated. Crack propagation test was conducted at 900 °C, introducing a single tension hold during fatigue loading. After the tension hold, nascent crack was immediately initiated when the fatigue loading was restarted. Subsequently, crack propagation rate significantly decreased and remained low for a certain distance, followed by its rapid acceleration and convergence on that under pure fatigue condition. This phenomenon was attributed to mechanisms based on two different concepts of crack closure and residual compressive stress.

Acoustic emission based mechanical behaviors of Beishan granite under conventional triaxial compression and hydro-mechanical coupling tests

Beishan area is now considered as a potential site of high-level radioactive waste (HLW) repository. In order to understand the mechanical behavior of Beishan granite, conventional triaxial compression (CTC) and hydro-mechanical (HM) coupling tests are conducted on Beishan granite. An acoustic emission (AE) monitoring system is employed to estimate the rock damage evolution during the tests. The testing results show that the compressibility of the rock specimens increases and expansibility decreases with increasing confining pressure under CTC tests, resulting in failure pattern transforms from splitting failure to shearing failure. Under HM coupling, the compressibility decreases and expansibility increases with increasing pore pressure, and the micro cracks can keep relatively equilibrium state due to the existence of fluid. Based on AE hit counts, the crack closure stress σcc, crack initiation stress σci and crack damage stress σcd are 12.3%, 48.7% and 81.1% of the peak stress σc under CTC tests, respectively. Under HM coupling, the crack closure stress σcc is vanished and the crack initiation stress σci is higher than that of CTC tests. In this sense, pore pressure can facilitate crack development once the crack damage stress σcd is reached. The fluctuation intensities of AE amplitude and frequency centroid (FC) increase during the loading process. The amplitude fluctuation range increases and FC decreases after peak during CTC tests. However, the amplitude fluctuation range reaches its maximum at peak stress under HM coupling tests, and FC decreases. Moreover, simplified models of failure process for crystalline rocks under compression and HM coupling are proposed.