Maximum Tensile Stress Criterion Research Articles

Investigation on directional rock fracture mechanism under instantaneous expansion from the perspective of damage mechanics: A 3-D simulation

With developments in geotechnical engineering, directional rock-breaking technology has been applied in large quantities. As a novel non-explosive rock-breaking technology, Instantaneous Expansion with a Single Crack (IESC) has been studied and applied to some extent in the past few years. IESC uses expansion gas to fracture rock mass in the predetermined direction by a special energy-gathering tube, which has the advantages of high safety, strong directional ability, and easy to operate. At present, there is a lack of in-depth investigation on the directional fracture mechanism of rock under the action of IESC. According to damage mechanics, the fundamental reason for rock fracture is due to the initiation, expansion, and penetration of internal cracks. In this study, a 3-D numerical model based on the theory of progressive failure is established to study the directional rock fracture mechanism of IESC, while a Conventional Expansion (CE) model without energy-gathering tube is established for comparative research. The maximum tensile stress criterion and unified strength criterion are used to identify damage failure of the element. The evolution processes of four key parameters are simulated, the types and degrees of tensile/compressive damage of the unit are analyzed, which aims to decipher the model's directional fracture mechanism under IESC loading. The established 3-D numerical models are validated by comparing with experimental results. The research results can contribute to further understanding the directional rock fracture mechanism of IESC and provide a theoretical basis for the application of IESC in the field.

Structural stability of China’s asteroid mission target 2016 HO3 and its possible structure

ABSTRACT Asteroid 2016 HO$_3$, a small asteroid (<60 m) in super fast rotation state ($\sim$28 min), and is the target of China’s Tianwen-2 asteroid sample-return mission. In this work, we investigate its structural stability using an advanced soft-sphere-discrete-element-model code, dembody, which is integrated with bonded-aggregate models to simulate highly irregular boulders. The asteroid body is numerically constructed by tens of thousands particles, and then is slowly spun up until structural failure. Rubble piles with different frictions, cohesions, morphologies, grain size distributions, and structures are investigated. We find a 2016 HO$_3$ shaped granular asteroid would undergo tensile failure at higher strengths as opposed to shear failure in lower strengths, regardless of its shape and constituent grain size ratio. In the tensile failure regime, the critical tensile strength is proportional to the square of the spin rate, but surprisingly, is independent of the internal friction angle. Such relations indicate that the Maximum Tensile Stress criterion emerges as superior paradigm for investigating the failure behaviour of fast-rotating asteroids. We predict that the high-spin rate of asteroid 2016 HO$_3$ requires a surface strength over $\sim$3 Pa and a bulk tensile strength over $\sim$10–30 Pa. Through comparing these strength conditions with the latest data from asteroid missions, we suggest a higher likelihood of a monolithic structure over a typical rubble pile structure. However, the possibility of the latter cannot be completely ruled out. In addition, the asteroid’s surface could retain a loose regolith layer globally or only near its poles, which could be the target for sampling of Tianwen-2 mission.

Influence of tectonic stress field on oil and gas migration in the Tahe Oilfield carbonate reservoir: Identification of areas favorable for reservoir formation

An understanding of the tectonic stress field distribution in the carbonate reservoirs of the Tahe Oilfield is essential for oil and gas migration and reservoir reconstruction. This study adopts a geological genesis perspective and integrates the unique attributes of the carbonate reservoirs in the Tahe Oilfield to simulate three-dimensional stress fields using the finite element method and Petrel software. The simulation, which takes pore pressure and boundary constraints into consideration, aligns with the findings of acoustic emission tests conducted by previous researchers and validates the model by corroborating the maximum horizontal principal stress direction with imaging logging interpretations. With subsequent utilization of the generalized Coulomb-Mohr shear failure criterion and the Griffith generalized maximum tensile stress criterion, the simulated stress enables the prediction of the total fracture intensity. To complement this analysis, we integrate seismic data and fault formation mechanisms to characterize variations in fracture intensity within distinct regions of the study area. Three key findings emerge from this investigation. First, due to the Hercynian thermal event, X-shaped conjugate faults display a disproportionately high degree of development compared to other primary fractures. Analyzing the mechanisms of formation and development of these X-shaped strike-slip faults reveals discernible differences in deformation characteristics between NW-trending and NE-trending faults, with the former exhibiting a greater propensity for fracture rupture and efficient oil-gas migration. Second, fault intersections are critical and efficient conduits for fluid accumulation and thereby contribute to reservoir formation. Lastly, exclusive of X-shaped conjugate faults, NE-trending faults exhibit the greatest propensity for oil and gas accumulation and migration. Collectively, these findings facilitate the identification of areas favorable for oil and gas migration and provide a crucial mechanical analysis that can inform the exploration and development of the Tahe Oilfield.

Study on Fracture Characteristics of Layered Sandstone under Asymmetric Loading.

In engineering practice, layered rock masses often display obvious anisotropy while deforming and failing, and the failure mode directly impacts the engineering construction stability. In this study, the fracture failure load, fracture toughness, crack deflection angle, and failure mode of a layered rock mass under different fracture modes were analyzed by utilizing improved asymmetric semi-circular disc specimens. According to the constitutive model of transversely isotropic materials, the maximum tensile stress (MTS), maximum energy release rate (MERR), and maximum strain energy density (MSED) calculation formulas were modified, and the calculation formulas of the three prediction criteria under anisotropic materials were derived. The calculation results were compared with the experimental results. The results show that the fracture toughness and crack deflection angle were significantly affected by the weak bedding plane. As a result of applying the MTS criterion, the results are closer to the experimental results, providing a solid foundation for engineering deformation, failure, and fracture analyses.

Analysis of fracture toughness deterioration and instability model of dangerous rock masses under freeze–thaw cycles

The instability of dangerous rock masses is primarily caused by the stress intensity factor at the primary structural plane exceeding the fracture toughness of the rock bridge section, which results in the propagation of fractures. Additionally, in cold regions, the fracture toughness of these rock masses gradually decreases due to freeze–thaw cycles. Initially, considering the deterioration of type I and type II fracture toughness in the rock bridge section and the frost heaving force between structural planes, an assessment model for the stability of dangerous rock mass under freeze–thaw cycles is established. Secondly, utilizing the theory of circular hole expansion, along with the Mohr-Coulomb yield criterion and maximum tensile stress criterion, a model is constructed to simulate the degradation of type I and type II fracture toughness in rock bridge segments under the influence of freeze–thaw cycles. The validity of this model was subsequently verified through experimental validation. Finally, through engineering case studies, the degradation pattern of the stability of dangerous rock formations under the action of freeze–thaw cycles was analyzed. The study reveals that the decreasing stability of dangerous rock mass under freeze–thaw conditions is intricately linked to the internal friction angle, elastic modulus, and initial tensile strength of the rocks. Notably, the long-term stability of hard and coarsely textured dangerous rock mass under such conditions generally improves. Conversely, the tensile strength of the rock bridge segment elevates, which is beneficial for the long-term stability of the rock mass. When the residual debris ratio exceeds 0.25, the instability of the rock mass deteriorates more modestly. To maintain long-term stability, managing debris loss or injecting fillers into the pores can be effective strategies.

Numerical study on dynamic cracking characteristic and mechanism of quasi-brittle materials under impulsive loading

This study focuses on investigating the dynamic cracking behaviors of quasi-brittle materials under impulsive loading using the extended non-ordinary state-based peridynamic (NOSB-PD) model. This extended model incorporates two stress-based failure criteria: Mohr-Coulomb and maximum tensile stress criteria, to represent shear and tensile fractures of quasi-brittle materials, respectively. By analyzing the evolution characteristics of the maximum principal stress obtained from the NOSB-PD model, the fracture mechanisms of quasi-brittle materials subjected to impulsive loading are explored. The research reveals that tensile failure predominantly governs the initiation and propagation processes of quasi-brittle materials under impulsive loading. The stress concentration effect, transfer effect, and dissipation effect observed in the maximum principal stress fields provide insights into the cracking mechanism during the failure processes of such materials. To validate the findings, the crack initiation modes and crack propagation paths obtained from the NOSB-PD model are compared with those obtained from the existing experimental and numerical approaches. The results demonstrate that the extended NOSB-PD model is effective in addressing fracture problems associated with quasi-brittle materials under impulsive loading conditions.

An adaptive extended finite element based crack propagation analysis method

In this paper, a method of crack propagation analysis based on adaptive extension finite element is proposed. This method combines adaptive mesh reconstruction technology with extended finite element method (XFEM). Firstly, the model of engineering structure is discretized with the help of mesh generation software, and the initial mesh is divided. Secondly, Construction of XFEM model, and the tip of crack strengthening function is introduced to describe the physical field properties of the crack tip. The integral equation is solved to obtain the crack tip parameters. Then, the adaptive mesh reconstruction technology is built to refine the mesh of crack tip area through the error estimation of crack tip. Finally, the SIFs at the crack tip were calculated using the interaction integral, and the path direction of crack growth was determined using the maximum circumferential tensile stress criterion. Thus, the propagation path can be well traced.

A coupled fluid-mechanical interaction model for controlled gas migration mechanism by dilatancy effect in saturated bentonite

A gas breakthrough in saturated bentonite is relevant to the safety of high-level radioactive waste repositories. The study of gas transport mechanisms in saturated bentonite is very important for the safety assessment of repositories. This paper proposed a coupled fluid-mechanical interaction model for predicting and simulating the path of gas transport and gas breakthrough in saturated Gaomiaozi bentonite. The model considered the effect of deformation and damage of bentonite on its permeability and introduced pore pressure into the deformation equation of bentonite. The damage coefficient was also introduced into the permeability evolution equation by combining the Mohr–Coulomb criterion, the maximum tensile stress criterion and the damage evolution. In addition, considering the heterogeneity of the soil, the Weibull distribution function was introduced to assign differential values to material parameters of the cells in the model. The numerical simulation of the bentonite stress field and seepage field was realized by the joint MATLAB and COMSOL secondary development, and the evolution law of the pore path in bentonite was explored under a flexible boundary. The gas breakthrough pressure and permeability pressures were calculated at various gas injection from a gas injection experiment into bentonite with flexible boundaries. Finally, the rationality and applicability of the model were verified by comparing the numerically calculated gas breakthrough pressure and permeability with experimental values.

Numerical investigation on fracture characteristic and failure mechanism of rock-like materials with intermittent flaws under compressive-shear loading

An extended non-ordinary state-based peridynamic (NOSB-PD) theory is utilized to investigate the fracture characteristics of rock-like materials containing intermittent flaws under compressive-shear loading. The stress-based failure criteria, i.e., the maximum tensile stress criterion and the Mohr-Coulomb criterion, are integrated into the NOSB-PD theory to respectively determine the tensile failure and shear failure of flawed rock-like materials. The distribution characteristics of maximum principal stress and shear stress acquired by the NOSB-PD theory are employed to analyze the fracture failure mechanism of flawed rock-like materials under compressive-shear loading. The effects of inclination angle of the central flaw on the initiation and coalescence modes of flawed rock-like specimens are investigated. The numerical results of flawed rock-like materials are in good agreement with the experimental results. The extended NOSB-PD has the ability to simulate the fracture processes under compressive-shear loading.

An XFEM-based simulation method for fracture grouting of expansible polymer grout in soil

To study the fracture propagation mechanism driven by expansible polymer grouting materials in soil, considering the characteristics of expansible polymer materials, a 2D elastoplastic model is established based on the extended finite element method (XFEM). In this method, the initiation location of fractures is judged by the maximum tensile stress criterion, and the propagation of fractures is controlled by fracture criteria applicable to the soil. The pressure on the fracture surface is solved iteratively by an experimentally derived relationship between expansion pressure and density of polymer grout. The correctness of the method is confirmed by contrasting the previous experimental results. On this basis, numerical computations with different grouting quantities are simulated to present the polymer grout's variation characteristics, including length, width, expansion pressure, and density. The method can reflect the interaction between the polymer and soil, which lays the foundation for the further study of the fracture propagation mechanism of expansive polymer grouting materials in soil.

Numerical study on cracking behavior and fracture failure mechanism of flawed rock materials under uniaxial compression

AbstractThe numerical approach is a vital means for evaluating the stability of flawed rocks. In this paper, the extended non‐ordinary state‐based peridynamics (NOSB‐PD) theory is employed to simulate the fracture process of rocks containing two pre‐existing flaws. Two stress criteria, including the maximum tensile stress criterion and the Mohr–Coulomb criterion, are implemented into the NOSB‐PD numerical method to respectively judge the tensile and shear failure of rock materials. The effects of inclination angles and ligament angles on the crack initiation and coalescence modes for flawed rocks are investigated based on the numerical results. The numerical results are in good agreement with the previous experimental results. The fracture mechanism of flawed rocks is revealed based on the evolutionary distribution characteristics of the maximum principal stress field and shear stress field obtained by the extended NOSB‐PD theory.

Numerical simulation the fracture of rock in the framework of plastic-bond-based SPH and its applications

In this paper, a two-dimensional numerical approach named plastic-bond-based smoothed particle hydrodynamics (PB-SPH) is proposed to simulate the fracture of rock with pre-existing flaws. Under the PB-SPH framework, interaction particles are interconnected through bonds. The Drucker–Prager criterion of a tensile zone cut-off coupled maximum tensile stress criterion is applied to judge shear failure and tensile failure. To verify the capability of the PB-SPH method in simulating rock fracture behavior, two-dimensional numerical simulations of a single flaw, two coplanar flaws, and multiple flaws of uniaxial compression are carried out. Compared with previous experimental and numerical results, the present numerical results show good agreements on crack initiation positions, crack morphology and crack patterns. The numerical simulation of the progressive failure process of rock slope with multiple flaws is carried out, which shows that the PB-SPH method can be well applied to rock mechanics engineering. The present results show that the PB-SPH method has a certain reference in the study of rock fracture mechanics and the application of rock mechanics engineering.

Prediction of Crack Propagation of Nano-Crystalline Coating Material Prepared from (SAM2X5): Experimentally and Numerically

The fracture and crack growth of materials can be practically and conveniently predicted through numerical analysis and linear elastics fracture mechanics. On this basis, the current study aims to present experimental work supported by a numerical technique for mimicking the crack propagation by Version 5.6 of COMSOL Multiphysics (version 5.6), used for the simulation of the coating made from Fe-based amorphous material with a thickness of 300 µm. The paper shows the effects of mixed-mode loading on cohesive zone parameters attained from load-crack mouth opening displacement (CMOD) curves. The microstructure dominates the fracture, which in mode I is altered from all-transgranular cleavage to nearly all-intergranular structure in mode II. Two common criteria for failure are linked to the mixed-mode results: Maximum energy release rate criterion (Maximum G) and maximum tensile stress criterion (Maximum S). However, distinguishing between the two criteria is made impossible by the large scatter in the data. The stress intensity factor is the basis for the. The stress intensity factor is the leading parameter facilitated by the singular element and should be estimated with accuracy. With the aim of comparing each criterion and illustrating the numerical schemes’ robustness, a number of examples are presented. It can be concluded that the Maximum G and Maximum S were successful and accurate in predicting the propagation of the Fe-based amorphous material prepared on mild steel.

Experimental and numerical research of the behavior of 3D internal cracks under uniaxial compression using 3D-ILC technology

Uniaxial compression tests are one of the classic tests of solid mechanics. However, there remain some unsolved problems involving the test methods and numerical simulation. In the present study, in view of the difficulties in the manufacture of real internal cracks, glass, a classical material whose brittleness is quite close to that of natural rock material, is selected to generate pure closed internal cracks using 3D Internal Laser-Engraved Crack (3D-ILC) technology. Through the uniaxial compression test, we observe that the failure of specimens originates from the pre-existing internal crack. First, wing cracks are generated around it, which then propagate. As the load reaches the maximum bearing capacity, the later tensile crack eventually leads to the failure of the specimen. This test method can be used to observe and study the crack propagation process, failure law, failure mode and characteristic load of brittle materials. In the numerical analysis, adaptive grid method is used for grid division and update. The distribution of KI, KII, and KIII at the crack tip is obtained by M-Integral, and the crack propagation is simulated in combination with the maximum tensile stress (MTS) criterion. In terms of numerical simulation, the mode I/II/III propagation simulation of 3D internal crack is successfully realized, which is of great significance. At present, the research of 3D crack propagation and internal crack propagation has encountered bottlenecks in theory, experiment and numerical simulation. It is hoped that the experimental and numerical simulation methods in this paper can provide some reference.

Research on the propagation mechanism of hydraulic fractures in infill horizontal wells

In recent years, infill horizontal well technology has been used to develop oil and gas in the remaining oil areas of unconventional low-permeability reservoirs. However, the initial fractures in parent wells will affect the hydraulic fractures formed by fracturing infilling horizontal wells. The interaction mechanisms between initial fractures and artificial fractures in infill horizontal wells are still unclear. Combined with the boundary element method and the maximum circumferential tensile stress criterion, a numerical model of hydraulic fracturing that can simulate the evolution of fracture trajectory and stress field was established. The analytical solution of the hydraulic fracture-induced stress field was used to verify the accuracy of the model. Using this model, propagation of hydraulic fractures in infill horizontal wells under different conditions was analyzed. Simulation results show that both the fracture spacing and well spacing have a significant impact on the propagation trajectory of hydraulic fractures in infill horizontal wells. The shorter the fracture spacing and well spacing is, the stronger the inter-fracture stress interference between the initial fractures and hydraulic fractures is. Reasonable fracture spacing and well spacing can enhance the induced stress field and form a complex fracture network in the reservoir. Too small well spacing may cause artificial fractures to communicate with initial fractures, thereby reducing hydraulic fracturing efficiency and limiting the stimulation volume of the reservoir.

Dynamic response and safety control of civil air defense tunnel group during the whole process of underpass tunnel blasting excavation

To ensure the safety and stability of adjacent underground structures is a key problem for the subway tunnel blasting construction. In this paper, there is a tunnel group (Sheshan civil air defense engineering) composed of several tunnel units right above a subway tunnel under blasting construction (Wuhan Metro Line 5). The vibration of the tunnel group induced by two blasting excavations of the subway tunnel was monitored. For further research, an effective 3D numerical model established by LS-DYNA, which was verified by field monitoring data, was used to analyze the dynamic response of the tunnel group in the whole process of the subway tunnel blasting. According to the numerical simulation results, the dynamic response characteristics of each tunnel unit were studied, and the most vulnerable area in each tunnel unit was determined. Then, the functional relationships between the maximum vibration velocities and the maximum tensile stresses of the vulnerable areas were established. Based on the maximum tensile stress criterion, the safety vibration velocity threshold of each vulnerable area was calculated using the relationship models. Furthermore, for convenient field monitoring during the subway construction, the safety vibration threshold at the floor of the tunnel group was also calculated. Lastly, to obtain the maximum charge per delay, five cut blasting with different charges were simulated. The maximum charge of the cut blasting in different stages of the subway tunnel blasting excavation was proposed. The research results of this paper have reference value for the blasting vibration safety control of similar tunnel excavation projects in the future.

Numerical Simulation of 3-D Internal Crack Propagation in Rock under Semi-circle Bending

Semi-circle bending (SCB) test is an important test in the field of rock fracture. In order to investigate the propagation process of 3-D internal cracks under semi-circular bending, numerical simulations of SCB specimens were carried out based on the finite element method and adaptive mesh technique. The results show that the numerical simulation results of this method are in good agreement with the previous laboratory test. The symmetrical loading model belongs to the pure I loading where the value of KI is positively related to the bottom load span S/R. The asymmetric loading model belongs to mix-mode loading. With the increase of unilateral load span S2/R, there is a decline and then a rise of the value of SIF at the same point at the crack tip. The S2/R is an important factor affecting the mechanical properties of rock specimens. The crack propagation path was obtained based on the maximum tensile stress (MTS) criterion. In-plane propagation of the internal crack in the symmetrically loading model leads to failure of the specimen. Wing propagation of the internal crack in the asymmetrically loading model causes the specimen to fracture into two asymmetrical parts. Quantitative analysis of the internal crack propagation of the symmetrical loading model shows that the growth rate of the lower end of the crack is the largest, and the upper end of the crack is the smallest. The above results can provide a reference for the research on the propagation of 3-D internal cracks of SCB specimens.

Experimental and Computational Investigations on Fretting Fatigue Crack Growth in Dovetail Joints

Fretting fatigue is a significant damage mode for turbine engine blade/disk components. In the present work, fretting fatigue crack growth of a nickel-based superalloy was experimentally and computationally investigated. Fretting fatigue experiments of dovetail joints were conducted under loading ratio , and the results revealed that the fretting fatigue cracks nucleated in multiple sites on the contact edge, which was accompanied by oxide wear debris and propagated with a single through-thickness crack. The crack growth rate was determined based on the variation of applied loading ratio in the experiments. With the help of the maximum tensile stress criterion, the friction coefficient of the fretting pair was determined from simulations of the fretting fatigue crack propagation. With the increasing friction coefficient, the kinking angle of the fretting crack approaches a stable value. The stress was verified to have significant effects on the short crack kinking and implemented in the maximum tensile stress criterion. A methodology based on fracture mechanics was proposed to identify the friction coefficient on the fretting surfaces.

Experimental and Numerical Study on the Failure Characteristics of Brittle Solids with a Circular Hole and Internal Cracks.

A stress analysis of a circular hole is one of the classical problems in mechanics. Internal cracks are inherent properties of materials, and they are mostly three-dimensional in form. However, studies on hole problems with three-dimensional internal cracks are still lacking. In this paper, internal cracks were generated in brittle materials containing circular holes based on 3D internal laser-engraved crack technology. Then, uniaxial compression tests were performed. The experimental results were compared with the existing literature, and theoretical and numerical simulation studies were carried out. The results show that: (1) The main crack shapes are the primary cracks and remote cracks. (2) The dynamic fracture characteristics existed in the formation of primary cracks and the surface of remote cracks. The tips of primary cracks were arc-shaped, and the surfaces of the remote cracks were curved. Remote cracks were tangential to the orifice where type III spear-like characteristics appeared. (3) The stress birefringence technology can be combined with 3D internal laser-engraved crack technology for internal crack stress information monitoring, the moire around the orifice was “flamboyant”, and the moire at the tip of the prefabricated crack was “petallike”. (4) The existence of internal cracks reduced the cracking and breaking load of the specimen, and compared with the intact orifice specimen, the upper primary crack, the lower primary crack, the remote crack and the failure load were reduced by 41.2%, 31.7%, 15.9%, and 32.3%, respectively. (5) The results of qualitative stress analysis of the orifice specimen were consistent with the initiation law of primary cracks and remote cracks. The K distribution based on M integral and the numerical simulation of crack propagation process based on the maximum tensile stress criterion were consistent with the law of primary crack growth. Compared with the current mainstream method of transparent rock research, 3D internal laser-engraved crack technology has certain advantages in terms of brittleness, crack authenticity, stress field visualization, and fracture characteristics, and the result will provide experimental and theoretical references for research on three-dimensional problems and internal cracks in fracture mechanics.

Fracture of brittle solid with an internal penny-shaped crack: Semi-circular bending test and numerical simulation

Semi-circular bending (SCB) tests are usually performed on samples with a bottom notch to investigate the mechanical properties of certain materials. Few studies have been conducted on the propagation of internal cracks in SCB tests despite the fact that the existence of internal defects is inevitable in most materials. When using the three-dimensional internal laser-engraved crack method, internal cracks are generated without causing any damage to the surfaces of the sample. Here, SCB tests are performed on samples with internal cracks at different depths. The crack growth process, failure mode, and macro- and micro-fractography are analyzed. Numerical simulations are carried out, revealing the distribution of the stress intensity factors around the crack tip and the internal crack growth path. The simulation results are consistent with those of the SCB tests. The results show that: (1) The propagation mode of internal cracks is mixed in the SCB tests; (2) The existence of internal cracks significantly reduces the failure load of the samples; (3) Dynamic fracture occurs in the intact samples of groups A and B1 (depth: 30 mm), while the failure of the samples of groups B2–B5 is due to the internal crack propagation. (4) Based on the J-integral and the maximum tensile stress criterion, the distribution of the stress intensity factors around the crack tip and the fracture path are in agreement with the test results.