•Stress-based failure criteria are implemented in NOSB-PD.•The effect of flaw length on the propagation of cracks is researched.•The effect of ligament angle on the coalescence of cracks is ...studied.•The effect of the confining stresses on the coalescence of flaws is investigated.
The maximum tensile stress criterion and the Mohr-Coulomb criterion are incorporated into the extended non-ordinary state-based peridynamics (NOSB-PD) to simulate the initiation, propagation and coalescence of the pre-existing flaws in rocks subjected to compressive loads. Wing cracks, oblique secondary cracks, quasi-coplanar secondary cracks and anti-wing cracks can be modeled and distinguished using the proposed numerical method. In the present study, a four-point beam in bending with two notches as a benchmark example is firstly conducted to verify the ability, accuracy and numerical convergence of the proposed numerical method. Then, the numerical samples of rock materials containing the one single pre-existing flaw with various lengths under uniaxial compression are modeled. Four significant factors, i.e. the axial stress versus axial strain curves, the peak strength, the ultimate failure mode and crack coalescence process, are obtained from the present numerical simulation. The effect of the flaw length on the propagation of cracks is investigated. Next, sandstone samples containing three pre-existing flaws with different ligament angles under uniaxial compression are also simulated. The effect of ligament angle on the propagation and coalescence of cracks is studied. Finally, rock-like samples containing two parallel pre-existing flaws subjected to biaxial compressive loads with confining stresses of 2.5, 5.0, 7.5 and 10.0MPa are simulated. The effect of the confining stresses on the initiation, propagation and coalescence of flaws is investigated. The present numerical results are in good agreement with the previous experimental ones.
To understand combined effects of water saturation and loading rate on the fracture behavior of rock materials, dynamic notched semi-circular bending (NSCB) tests were conducted on dry and saturated ...sandstone specimens under a wide range of loading rates using a modified split Hopkinson pressure bar (SHPB) setup. Test results revealed that, the dynamic fracture initiation, propagation toughness and crack propagation velocity of saturated specimen were apparently lower than that of dry ones at the same loading rate. The above parameters increased with the increase of loading rate. Compared with the dry specimen, the saturated specimen owned a higher rate dependency of the dynamic fracture initiation, propagation toughness and a lower rate dependency of crack propagation velocity. Moreover, dual effects of water on the fracture behavior under different loading rates were discussed. It is believed that the different rate dependencies of fracture behaviors between dry and saturated specimens was governed by the combined weakening and enhancing effects of water. A micro-mechanical model was further developed to explain the experimental results based on the duality of water and linear elastic fracture mechanics (LEFM).
Fracture coalescence, which plays an important role in the behavior of brittle materials, is investigated by loading rock-like specimens with two and three pre-existing flaws made by pulling out the ...embedded metal inserts in the pre-cured period. Different geometries are obtained by changing the angle of the flaws with respect to the direction of loading and the spacing. With reference to the experimental observation of crack initiation and propagation from pre-existing flaws, the influences of the third pre-existing flaw on the cracking processes was analyzed. It was found during the test that: with the increase of the angle of the rock bridge, the rock specimen takes a turn from wing crack propagation failure to crack coalescence failure, and it will be more obvious with the increase of the prefabricated crack angle. According to the different geometries of pre-existing cracks, seven types of coalescence have been identified based on the nature of the cracks for the specimen with two pre-existing flaws. The multi-crack interaction results in the continuous degradation of the macroscopic mechanical properties of the rock mass. On one hand, it weakens the trend of relative sliding of the coplanar cracks, and on the other hand, it changed the coalescence patterns of the fractured specimen. The research reported here provides increased understanding of the fundamental nature of rock mass failure in compression.
•Rock-like specimens containing two pre-existing flaws have been prepared and tested under uniaxial compression.•Seven types of coalescence have been identified for the specimen with two pre-existing flaws.•The crack interaction of the third pre-existing flaw on the cracking process was analyzed.•This research provides increased understanding of the fundamental nature of rock mass failure in compression.
•Coupling of peridynamics and finite element method for 3D analysis.•Governing equations with elements native to ANSYS.•Coupled degrees of freedom command to enforce coupling.•Crack propagation ...through broken elements and updating stiffness matrix.•Validation through simulating wedge splitting test.
This study presents an approach to couple peridynamic (PD) and finite element method (FEM) for 3D deformation and crack propagation in ANSYS framework. The stiffness matrix of the PD element is derived by using the peridynamic least squares minimization (PD LSM) method based on the small deformation assumption. The PD governing equations are constructed by using MATRIX 27 element native to ANSYS. The coupling between MATRIX 27 elements and traditional finite elements is achieved through the coupled degrees of freedom (DOF) command available in ANSYS. The crack propagation is implemented by monitoring the number of broken bonds and updating the stiffness matrix of the PD element. The accuracy of the coupled PD-FE approach is verified by comparison against the 3D FE displacement predictions. The validity of the coupled PD-FE approach is established by simulating the wedge splitting test.
•The Walker equation is employed to consider the mean stress effects.•Stocastic analysis is conducted to obtain fatigue crack growth rate with 95%, 97.7%, and 99% guarantee.•A user-defined fatigue ...crack propagation subroutine was developed using phantom nodes-based extended finite element method (PN-XFEM) and Virtual Crack Closure Technique (VCCT).
The assessment of fatigue crack propagation of steel structures is essential and important especially to improve the application of high strength steel in construction. The load ratio R, reflecting mean stress effects, will be changed with crack extension in the steel structures with complicated geometry. In this paper, the Walker equation is employed to fit the fatigue crack propagation rate of steel grades S355 and S690 based on experimental data in the literature to incorporate the mean stress effects. The material fatigue crack propagation parameters with 95%, 97.7%, and 99% guarantee of Walker equation were obtained by a stochastic analysis using the Monte Carlo method. The fatigue life was firstly predicted by the analytical method and was used as a baseline for numerical fatigue crack propagation simulation. A user-defined fatigue crack propagation subroutine based on the Walker equation was developed using phantom nodes-based extended finite element method (PN-XFEM) and Virtual Crack Closure Technique (VCCT) to consider the mean stress effects. The proposed three-dimensional fatigue crack propagation simulation subroutine is successfully validated of both steel grades, S355 and S690.
•Thermo-mechanical simulation of different zones within the HAZs for two steels.•Reproduction of the local microstructure in the real weldment.•Determination of monotonic and cyclic tensile, fracture ...and fatigue properties.•Application of the determined material parameters to the IBESS model.
Any fracture mechanics based determination of the fatigue strength of weldments requires different input information such as the local weld geometry and material data of the areas the crack is passing through during its propagation. The latter is so far not a trivial task as the fatigue crack is usually initiated at the weld toe at the transition from the weld metal to the heat affected zone. Furthermore, the crack propagates through the different microstructures of the weldment even into the base metal and causes final fracture. This paper describes how the material input information has been gained particularly for heat affected zone material by thermo-mechanically simulated material specimens for two steels of quite different static strength. The data comprise the cyclic stress-strain curve, the crack closure effect-corrected crack growth characteristics, fatigue threshold values for long cracks, the dependency of the parameter on the crack length and monotonic fracture resistance. The substantial experimental effort was necessary for the validation exercises of the IBESS approach, however, within the scope of practical application more easily applicable estimating methods are required. For that purpose, the paper provides a number of appropriate proposals in line with its check against the reference data from the elaborate analyses.
•We used ultra-fast time resolution method to recorded the entire fracture process of shale SCB samples, and the resolution capability of this method reached to 15 picoseconds.•We established lineral ...relationship between the energy-release rate and crack propagation rate. And the experimental results verified this relationship.•The fracture surface information was obtained by a laser three-dimensional scanning system, and it was utilized to categorize crack propagation behaviors.•We evaluated the influence of the bedding angle on total work done by the external load, dissipated energy, and absorbed energy.
The layer structures of shale greatly influence its crack propagation behavior. Nevertheless, the correlation between crack extension rates and mechanical parameters has not been well studied, especially, the relationship between the energy release rate and crack propagation rates. Consequently, there are unresolved issues regarding the effects of layer structure on the propagation of cracks in shale. In this paper, a series of three-point compressive loading tests were conducted on seven groups of shale semi-circular bend (SCB) samples with an inclination angle of 0°-90°. The entire fracture process was captured using the ultrafast time-resolution method with a resolution capability of up to 15 picoseconds. In addition, fracture surface information was obtained by a high-precision laser three-dimensional scanning system, and this information was utilized to categorize crack propagation behaviors, such as propagation along weak planes, intermittent penetration, and deflection penetration. Furthermore, a quantitative relationship was established between the energy-release rate and crack propagation rate, based on the first law of thermodynamics and the maximum energy release rate (MERR) criteria proposed by Griffith. The experimental results showed that there is a linear relationship between the energy-release rate and the propagation rate, which meets well with the established relationship. The experimental results indicated that symmetric loading does not result in significant angle localization during crack initiation. This suggests that crack propagation behavior in shale is a reflection of the interplay between energy-release rates and fracture resistance. Finally, this study evaluated the influence of the bedding angle on dissipated energy, and absorbed energy.
•Mechanical properties of the caprock are significantly changed under subsurface reservoir conditions and cyclic loading of hydrogen.•Hydrogen-brine multi-phase flow in the pore spaces of the caprock ...may increase capillary stress and fracture apertures in the rock resulting shrinkage cracking.•Stress-induced critical cracks and subcritical crack under the influence of geochemical reactions may cause significant impacts on carpock integrity during UHS.•Hydrogen diffusion and capillary trapping are amplified with the mechanical weakening and crack formation in the caprock.
This paper comprehensively reviews mechanical weakening and crack development in the caprock during underground hydrogen storage in depleted gas reservoirs. Hydrogen loss due to the geochemical interactions of hydrogen and caprock minerals critically impacts caprock integrity. As shown in the review, it is conspicuous that the mechanical properties of the caprock also change with the hydrogen injection, affecting its brittle-ductile behaviour. Furthermore, the stress–strain behaviour of the caprock is changed, and it undergoes irreversible deformations under the influence of confining pressure, cyclic loading, and changes in the mineral composition.
The fracturing of the caprock is another critical impact on the storage integrity, which may create new routes for the hydrogen permeation through the caprock. Cracks may form in the caprock in multiple ways, mainly 03 ways; 1) Highly pressurized hydrogen injection creates critical cracks in the caprock when the pore pressure exceeds the fracture toughness, called critical cracks, 2) The injected hydrogen accumulates under the caprock due to gravity segregation and, eventually, diffuses into the caprock, displacing its pore fluid (brine). Consequently, capillary stress on the caprock minerals and the pores may increase with developing cracks, called shrinkage cracks, and 3) Geomechanical interaction between hydron-pore fluid-rock minerals under the biotic environment (micro-organisms) available at underground storage sites can cause mechanical properties degradation in caprock, forming new cracks under low injection pressure conditions, called sub-critical cracks.
Although the critical or tensile crack formation process has been widely studied in the existing studies, minor attention has been given to other possible crack formation processes in the caprock, including the hydrogen-induced shrinkage cracking and the geomechanical reactions causing sub-critical cracking. In addition, the impact of this mechanical weakening of the caprock on its overall structure and flow characteristics hasn't been properly understood, adding extra uncertainty to the caprock's integrity during the underground hydrogen storage process.
PDF
