Search

In the high-temperature environment, a larger thermal expansion mismatch of a bimaterial leads to pronounced thermal stresses and interface crack growth. In this paper, a generalized fractional heat conduction model is used to determine the instantaneous thermal fracture behaviors of a bimaterial interface crack. An axisymmetric thermoelastic problem is solved with the aid of Goodier's thermoelastic displacement potential and Love's potential functions. A mixed initial-boundary value problem is then converted to a singular integral equation of second kind by using the Hankel and Laplace integral transforms. Numerical results of the intensity factors of heat flux and thermal stresses are evaluated using Stehfest's Laplace inversion scheme. The influence of fractional kernel functions with power and exponential law are analyzed, respectively, for aluminum-steel and steel-epoxy, respectively. The thermal stress intensity factors exhibit more wave-like behaviors based on Riemann-Liouville and Atangana-Baleanu models which is different from Caputo-Fabrizio and the complete diffusion model. • An interface crack between dissimilar materials is analyzed. • Goodier's and Love's potential functions are utilized for solving the problem. • Transient heat flux and thermal stress intensity factors are investigated. • Characteristics for various fractional heat flux kernel are considered. [ABSTRACT FROM AUTHOR]

We extend the applicability of the embedded unit cell (EUC) method to three-dimensional (3D) fracture problems, which are modeled by the extended finite element method (XFEM). The EUC method is a concurrent multiscale method based on the computational homogenization theory for nonperiodic domains. Herein, we show that this method can accurately estimate fracture parameters and, in particular, stress intensity factors using the J-integral method. Additionally, the method is shown to capture crack propagation within the microscale domain, as well as cracks initiating at the microscale and propagating outwards onto the macroscale through the internal subdomain boundaries. To demonstrate the accuracy, robustness, and computational efficiency of the proposed method, several 3D numerical benchmark examples, including planar cracks with single and mixed-mode fractures, are considered. In particular, we analyze horizontal, inclined, square, and penny-shaped cracks embedded in a homogeneous material. The results are verified against full FEM models and known analytical solutions if available. Practical Applications: The insights of this research offer practical application for engineers and scientists in designing more resilient and durable structures. By extending the EUC method to 3D fracture problems, the study addresses the ability to forecast and access fracture phenomena in materials. This method is shown to be an effective approach for exploring the interaction between local microscopic discontinuities and cross-scale crack propagation, crucial for evaluating the durability of engineering structures. The EUC approach, integrated with XFEM, provides a comprehensive methodology for analyzing different fracture scenarios, including stationary mixed-mode cracks and crack-propagation examples. Its ability to accurately transition from microscale to macroscale analysis without remeshing introduces a valuable computational advantage, making it a more cost-efficient solution in fracture analysis. This research's application offers tangible benefits in industrial context, especially in aerospace, automotive, and construction industries, where precise evaluation of structure and material failure can lead to more cost-efficient and safer designs by reducing the maintenance costs and failure risks. [ABSTRACT FROM AUTHOR]

Crack growth tests of 316LN stainless steel under load‐controlled and strain‐controlled thermo‐mechanical fatigue (TMF) loadings at the temperature range of 350°C ~ 550°C were conducted. Moreover, the isothermal fatigue (IF) crack growth tests at the maximum temperature of 550°C were performed for comparison. The differences in IF and TMF crack propagation behavior under different loading conditions were thoroughly discussed, and the underlying mechanisms were revealed by a comprehensive characterization of the deformation state of the crack tip region using digital image correlation (DIC) and electron backscatter diffraction (EBSD) methods. Furthermore, it was found that the EBSD characterization was simply based on a single plane made it difficult to evaluate the complex crack growth behavior. In addition, the limitations of the classical parameter of stress intensity factor under TMF loading were presented. Highlights: TMF crack growth behavior of 316LN steel under load‐ and strain‐controlled modes were studied.TMF crack growth rate was higher than that in the isothermal fatigue test at the maximum temperature.The crack growth rate under load‐controlled tests was lower than that in the strain‐controlled tests.Plastic deformation at the crack tip was characterized by DIC and multi‐layer EBSD methods. [ABSTRACT FROM AUTHOR]

Copyright of Atomic Energy Science & Technology is the property of Editorial Board of Atomic Energy Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We first study an arbitrary number of identical parallel screw dislocations evenly distributed along a concentric circle within a nanowire of radius R. Two equilibrium positions, one stable and the other unstable, co-exist for each screw dislocation. As the number of screw dislocations approaches infinity, each will find a stable equilibrium configuration at a distance 0.7071R from the centerline. Next, we investigate a mode III Zener–Stroh central crack in a nanowire. The crack is simulated by a continuous distribution of screw dislocations which leads to a Cauchy-type singular integral equation whose numerical solution results in the stress intensity factor at the crack tip as well as the Eshelby twist of the rod induced by the imaginary screw dislocations comprising the Zener–Stroh crack. The Eshelby twist will significantly reduce the magnitude of the stress intensity factor at the crack tip. [ABSTRACT FROM AUTHOR]

This study deals with the propagation of a semi-infinite crack influenced by SH-wave propagation in an initially stressed dry sandy (ISDS) strip. The Fourier integral transforms (FIT) and Wiener–Hopf (WH) approach are used to solve the model analytically. For the cases of concentrated force of constant intensity (CF) and constant load (CL), the stress intensity factor (SIF) is calculated. The effects of sandiness, crack speed/length, and initial stress on the SIF in ISDS strip are numerically elucidated and graphically demonstrated. Comparison of the SIF analysed for differently configured strips influenced by distinct cases of initial stresses is one of the novel features of this study. [ABSTRACT FROM AUTHOR]

This study developed a procedure for rapidly reconstructing a crack profile for calculating the parameters of fracture mechanics such as stress intensity factor with energy release rate (J) and displacement opening crack tip using data from the eddy current sensor. The inverse problem focused on adopting genetic algorithms to solve the direct problem iteratively. The use of the differential probe allows a rapid and precise resolution of the direct problem. The incident field produced by the two coils is determined using the 3D finite element results and the variation of impedance in each coil due to the crack. For the inverse problem, the crack's surface is considered regular shape in terms of dimensions, and the sensor's impedance expresses the objective function in terms of the width and length of the crack. The evaluation of the shape function and mesh matrix is made dependent on the iterative process, which makes the reversal procedure computationally lightweight when using genetic algorithms. [ABSTRACT FROM AUTHOR]

This paper explores the thermal behavior of multiple interface cracks situated between a half-plane and a thermal coating layer when subjected to transient thermal loading. The temperature distribution is analyzed using the hyperbolic heat conduction theory. In this model, cracks are represented as arrays of thermal dislocations, with densities calculated via Fourier and Laplace transformations. The methodology involves determining the temperature gradient within the uncracked region, and these calculations contribute to formulating a singular integral equation specific to the crack problem. This equation is subsequently utilized to ascertain the dislocation densities at the crack surface, which facilitates the estimation of temperature gradient intensity factors for the interface cracks experiencing transient thermal loading. This paper further explores how the relaxation time, loading parameters, and crack dimensions impact the temperature gradient intensity factors. The results can be used in fracture analysis of structures operating at high temperatures and can also assist in the selection and design of coating materials for specific applications, to minimize the damage caused by temperature loading. [ABSTRACT FROM AUTHOR]

Based on the numerical results on the non‐linear correlation between volume of plastic zone and global loading level represented by stress intensity factor, the dependence of cleavage fracture toughness of ferritic steels on specimen size and temperature is evaluated based on an empirical statistical model. The statistical correlation is supported by two sets of toughness data measured from different sized compact tension specimens at different temperatures. To further improve the accuracy of the statistical model, future work is identified to quantify the variation of volume of plastic deformation zone with loading level and measure the average volume for each microcrack at different temperature. Highlights: A non‐Weibull statistical model of cleavage toughness is proposed.Dependence of cleavage toughness on temperature and specimen size is studied.The model is validated by two sets of cleavage toughness data.Two research topics are identified for model improvement. [ABSTRACT FROM AUTHOR]

The stress intensity factor (SIF) distribution of a semi‐elliptical surface crack is often used for evaluating the fatigue strength of structures. Virtually exact distributions of SIFs FISE,FIISE,FIIISE can be provided along the crack front by solving the hypersingular integral equation of the body force method. In this paper, to create a very accurate SIF variation formula, the elliptical crack SIF solutions FIE, FIIE, FIIIE are used and the SIF ratios FISE/FIE, FIISE/FIIE, FIIISE/FIIIE are mainly focused. Paying attention to the corner point singularity, by applying the least squares method to the ratio FISE/FIE, FIISE/FIIE in the whole range of parametric angle β, FISE and FIISE formulas can be proposed. Instead, FIIISE formula can be proposed by applying the method of least squares to the ratio of FIIISE/FIIIE in the range β≥15° but applying directly to FIIISE in the range β≤15°. In this way, all of formulas proposed in this paper provide the SIFs with better than 1.0% accuracy. Highlights: Accurate SIF formulas for semi‐elliptical surface cracks were created within 1% error.Similar to solving the HIEM, closed form solutions of an elliptical crack were utilized.This formula assume the crack front intersects the free surface at an angle θS≅100.5°.Using singularity r‐0.5 along the crack front, the shape FISE(β)≈const. was investigated. [ABSTRACT FROM AUTHOR]

The high- and very-high-cycle-fatigue properties of IN718 Ni-based superalloy manufactured by selective laser melting (SLM) were investigated by axially loaded fatigue tests at room temperature (25 °C) and elevated temperature (650 °C) with a stress ratio of R = −1. Due to the high energy density and rapid cooling rate of the SLM process, the grains grew as dendrites surrounded by chain and dotted Laves phases. Subsequently, the results of monotonic tensile tests show that the SLMed IN718 has good resistance to elevated temperature. The stress–life characteristic curves revealed a continuous decline with no conventional fatigue limit. The fracture observation illustrated that surface flaw-induced failure is predominant at 25 °C, while internal failure, caused by crystallographic facets cracking, is prevalent at 650 °C under lower stress. Furthermore, the internal failure mechanism related with microstructure was summarized. Based on the evaluation of stress intensity factor ranges, the threshold values of long and small crack growth can be obtained, as well as the transition lengths from small to long cracks can also be calculated. Finally, a model based on fatigue indicator parameter was proposed to predict the fatigue life, and the predicted results were acceptable. [ABSTRACT FROM AUTHOR]

Hastelloy C-276 alloy is the preferred substrate for YBa 2 Cu 3 O 7-δ (YBCO) coated conductors prepared by Ion-beam-assisted deposition (IBAD) route, but its surface is too rough to meet application requirements. Y(CH 3 COO) 3 ·4H 2 O precursor solution has a low flattening efficiency, and its film edges are prone to crack formations. In this paper, a model for the stress intensity factor was established to study the effect of the presence of cracks on film stress. The simulation results showed that increasing the coating thickness reduced the overall stress, but increased the stress concentration at the crack. The larger bottom layer defects also made it easier for cracks to be generated. Then, 10-m long Hastelloy C-276/Y 2 O 3 strips were prepared by colloidal-solution deposition planarization (CSDP), with an average surface roughness Rq of 0.427 and only 10 coating layers. This improved the flattening efficiency by 40 %, and a CeO 2 layer with a good biaxial texture was finally prepared. [ABSTRACT FROM AUTHOR]

Strength prediction under the action of pores is crucial for the safety of ceramics. Here, a quantitative prediction model of pore-strength response under mode-I loading was developed based on the new mapping relationship between stress intensity factor and tip radius. The new model was proved to have great application after comparison and analysis of the pore-strength test data of three typical ceramics as well as the pertinent data as-reported in the literature. Results indicated that when the tip radius of pore (ρ) exceeds the critical value (ρ c = K Ic 2/(π σ 0 2)), the stress intensity factor increases as a power function with increasing ρ , at which point the strength decay is significantly weakened, and when the ρ is lower than the ρ c , the pore can be equated to a crack problem. This work can not only forecast and assess the failure strength of ceramics containing pores, but also provide guidance for the design of extremely dependable ceramics. [ABSTRACT FROM AUTHOR]

Lug is one of the most important lap joints in many engineering structures, especially airframes. Through‐thickness and part‐through cracks emanating from pin‐loaded lug hole are frequently encountered due to stress concentration. Stress intensity factors for various crack geometries are the prerequisite for damage tolerance design of attachment lug. In this paper, analytical 2D weight functions for through‐thickness crack in lug are derived considering the contact condition between the pin and lug. With the derived 2D weight function, a highly efficient 3D slice synthesis weight function method (SSWFM) is then developed to determine 3D SIFs of hole‐edge corner/surface crack in straight and tapered lugs under various pin loadings. The resulting 3D SIFs are verified by comparisons with the numerical FEM/Franc3D solutions and literature data. The SSWFM is about 1800 times faster than the numerical FEM/Franc3D and therefore will significantly enhance damage tolerance analysis capability for attachment lugs. Highlights: Accurate and wide‐range weight functions of pin‐loaded cracked lug are derived considering the contact constraint.A 3D weight function method for corner and surface cracks of lug is established.It is accurate and much faster than FEM for SIF calculation. [ABSTRACT FROM AUTHOR]

This study investigated the high cycle fatigue crack initiation and propagation behaviors in coarse‐grained FeCrAl alloys, with a focus on the relationship between the path of small cracks and the local microstructure. The results show that the small cracks initiate along the {100} slip plane due to the synthetical influence of local microstructure and shear stress. The initiation zone forms inclined areas with layered fine‐grain areas caused by cyclic shear stress. Quantitative analysis of the stress intensity factor (SIF) indicates that in the realm of mixed‐mode loading, the SIF of Mode I takes the lead in determining the intensity of stress and strain fields at the crack tip. As the crack propagates further, the SIF steadily increases. Once it reaches a specific threshold, the propagation mode within a coarse grain shifts from Mode II to Mode I. Moreover, fatigue life increases with a tendency for decreased SIF during crack deflection. Highlights: The influence of microstructure on crack initiation and early propagation behavior was studied.The cyclic shear stress leads to the formation of layered fine‐grain areas.The quantitative analysis elucidates the reason for the deviation of crack direction within a coarse grain. [ABSTRACT FROM AUTHOR]

[Display omitted] The Bouligand structure has been observed in a variety of biological materials, such as lamellar bone and exoskeleton of lobsters. It is a hierarchical and non-homogeneous architecture that exhibits excellent damage-resistant performance. This paper presents a multiscale fracture model considering the material inhomogeneity, the multiscale property, and the anisotropy to reveal the toughening mechanisms in the Bouligand structure. Firstly, the macro and micro constitutive properties of this composite are derived. Then, a multiscale fracture model is developed to characterize the local stress intensity factors and the energy release rates at the crack front of twisted cracks. Our results demonstrate that the decrease in the local energy release rate can be attributed to two-step mechanisms. The first mechanism is that the multiscale structure and the material inhomogeneity cause a release of stress near the initial crack tip. The second mechanism is that the twisted crack leads to the transformation from single-mode loading to mixed-mode loading, which enhances the fracture toughness. These results can not only reveal the toughening mechanism of the Bouligand structure but also provide guidelines for the design of high-performance composites. Biological materials in nature often possess excellent mechanical properties that have not been achieved by synthetic materials. Bioinspired Bouligand structures provide prototypes for designing high-performance materials. In this study, we propose a multiscale theoretical fracture model to investigate the fracture properties of Bouligand structures with twisted cracks. We systematically consider the roles of material inhomogeneity, anisotropy, and multiscale properties. Our analysis demonstrates that the remarkable toughness of Bouligand structures results from the combined effects of material inhomogeneity and twisted cracks. This research contributes to unveiling the secret behind the outstanding toughness of Bouligand structures and provides inspiration for the development of novel designs for man-made composites. [ABSTRACT FROM AUTHOR]

The coupled seepage–stress action has a significant deterioration effect on the structural face of the hydraulic tunnel enclosure, which intensifies the shear rupture tendency of the deteriorated structural face of the rock mass. The plastic deformation of a typical I–II composite fissure was taken as the research object, the characteristics of the tip plastic zone of the composite fissure seepage rock were explored, and the influence law of osmotic pressure and fissure rock parameters (fissure dip angle, Poisson's ratio, and fissure length) on the radius of the tip plastic zone was analyzed. Based on the Drucker–Prager yield criterion and the stress intensity factor of the composite fracture, the theoretical analytical formula of the fracture plastic zone radius under the action of high and low osmotic pressure was established, and the fracture rock plastic zone radius was significantly correlated with the fracture parameters. The radius of the plastic zone of fracture under low osmotic pressure evolves in a trend of decreasing–increasing–decreasing with the increase in fracture dip angle, and the peak radius of the plastic zone appears at 45°. Poisson's ratio and fracture length have less influence on the radius of the plastic zone. The radius of the plastic zone of fracture under high osmotic pressure grows in an incremental nonlinear curve, and the peak radius of the plastic zone appears at 90°, being positively correlated with the length of fracture. This study can provide theoretical reference for the analysis of the stability of the surrounding rock in hydraulic tunnels. [ABSTRACT FROM AUTHOR]

Fracture mechanics is fundamental in various fields, such as mechanical engineering, civil engineering, hydraulics, and medicine. In addition, thanks to this field, we can estimate the age of the components of a structure, and the inspection and maintenance intervals can be precise. Thus, fracture mechanics is a science that studies numerical tools to characterize various parameters, such as the contour integral (J), stress intensity factors, and internal energy. However, in this paper, comparing the two types of elements (CPS3) and (CPS4R) gives comparable and proportional results; logically, a good correlation was obtained between them. In this article, those parameters were simulated and analyzed numerically by the finite element method (FEM) of a two-dimensional model consisting of a steel material with elastic properties. The analysis of the crack parameters was evaluated by the two models of elements CPS3 and CPS4R. On the other hand, the crack parameters between the two elements were compared. In addition, the numerical simulation was carried out using the computer code ABAQUS 16.3.1. [ABSTRACT FROM AUTHOR]

The stress distribution and fracture parameter calibration of ice–rock models are important aspects of studying rock properties at high altitudes and latitudes. However, progress in ice–rock modeling has been slow and singular, and it is limited due to the discrete nature of rocks and the applicability of fracture mechanics. In this study, a circular inhomogeneous ice–rock model is proposed for the first time, and a method is provided for calculating the stress field of the model under biaxial loading. A method for calculating the single-crack stress intensity factor of the model subjected to biaxial compressive loading is also provided. The novelty of this work is that the inhomogeneous ice–rock model is treated as a superposition of two models, namely, a circular pore plate and circular ice, according to the superposition principle. The key is that the stress field distribution law of the ice–rock model is obtained based on the basis of the displacement continuity of the ice–rock interface. The analytical and approximate solutions of the stress intensity factor of a single crack were also obtained by considering the normal phase effect of the crack surface and combining the stress distribution law of the ice–rock model. Comparison with the CAE method was made to verify the correctness of the stress field and stress intensity factor calculation methods. The evolution laws of lateral pressure coefficients, the elastic modulus ratio of ice and rock on the stress field, and the stress intensity factor were analyzed. The effects of lateral pressure coefficients, elastic modulus ratios, and crack distributions on the failure modes were investigated using the extended finite element method (XFEM). This study can provide a theoretical basis for the evaluation of mechanical properties and prediction of the failure modes of frozen rock bodies. [ABSTRACT FROM AUTHOR]

Influence of the depth and location of perforation, direction and magnitudes of in situ stresses, wellbore angle, and pumping pressure is investigated numerically for the hydraulic fracture. 3D models of rock formation with vertical, inclined or horizontal wells containing semi‐circular crack are analyzed to obtain both KI and the minimum pumping pressure. By computing the magnitude and sign of the T‐stress it is demonstrated that hydraulic fracture path is generally stable except for a very limited situations in which the vertical well is subjected to the lowest in situ stresses. The minimum horizontal in situ stress has the most dominant role in controlling the hydraulic fracture. A direct relationship between KI and T was obtained for different ranges of in situ stresses and some relations were presented for estimating the critical stress intensity factor at the onset of hydraulic fracture and minimum injection pressure in terms of the applied in situ stresses. Highlights: Influence of in situ stresses, well orientation and perforation size on KI and T values.Determining the minimum pumping pressure in terms of in situ stresses and well type.Stability analysis of hydraulic fracture path for vertical‐oblique‐horizontal wellbores.Obtaining direct relationships between KI and T by changing in situ stresses. [ABSTRACT FROM AUTHOR]

The aim of this study is to solve a practical problem encountered in the automotive industry, especially the failure of a cracked lower control arm made of al 6062 T6 material during static and crash physical tests, and to characterize the behavior of cracked parts made of aluminum materials using the fracture mechanics parameters. As a first step, we carried out a numerical study and simulation using Abaqus/CAE 2020 software and the finite element method to determine the stress concentration and load limit capacity for different car weight cases. The von Mises stress variation shows crack initiation and propagation to be in the area of the lower control arm's attachment to the vehicle platform, where stress is concentrated. These numerical results are consistent with the experimental test results found by automotive manufacturers. Also, we find that the mechanical load that can support this part is below 4900 N for good performance. In the second step, we use the results of the first section to simulate the failure of a lower control arm with a crack defect. This paper investigates the stress intensity factor KI in mode I for different lengths (L) and depths (a) of the crack in the lower control arm using the extended finite element method (XFEM) under Abaqus/CAE. For crack failure initiation and progression, we relied on the traction separation law, specifically the maximum principal stress (MAXPS) criterion. The KI factor was evaluated for the materials steel and Al 6062 T6. The results obtained from the variation of the KI coefficient as a function of crack depth (a) and the thickness (t) show that the crack remains stable even when a depth ratio (a/t = 0.8) is reached for the steel material. However, the crack in the Aluminum 6062 T6 material becomes unstable at depth (a/t = 0.6), with a high risk of total failure of the lower control arm. [ABSTRACT FROM AUTHOR]

In the shipbuilding, construction, automotive, and aerospace industries, welding is still a crucial manufacturing process because it can be utilized to create massive, intricate structures with exact dimensional specifications. These kinds of structures are essential for urbanization considering they are used in applications such as tanks, ships, and bridges. However, one of the most important types of structural damage in welding continues to be fatigue. Therefore, it is necessary to take this phenomenon into account when designing and to assess it while a structure is in use. Although traditional methodologies including strain life, linear elastic fracture mechanics, and stress-based procedures are useful for diagnosing fatigue failures, these techniques are typically geometry restricted, require a lot of computing time, are not self-improving, and have limited automation capabilities. Meanwhile, following the conception of machine learning, which can swiftly discover failure trends, cut costs, and time while also paving the way for automation, many damage problems have shown promise in receiving exceptional solutions. This study seeks to provide a thorough overview of how algorithms of machine learning are utilized to forecast the life span of structures joined with welding. It will also go through their drawbacks and advantages. Specifically, the perspectives examined are from the views of the material type, application, welding method, input parameters, and output parameters. It is seen that input parameters such as arc voltage, welding speed, stress intensity factor range, crack growth parameters, stress histories, thickness, and nugget size influence output parameters in the manner of residual stress, number of cycles to failure, impact strength, and stress concentration factors, amongst others. Steel (including high strength steel and stainless steel) accounted for the highest frequency of material usage, while bridges were the most desired area of application. Meanwhile, the predominant taxonomy of machine learning was the random/hybrid-based type. Thus, the selection of the most appropriate and reliable algorithm for any requisite matter in this area could ultimately be determined, opening new research and development opportunities for automation, testing, structural integrity, structural health monitoring, and damage-tolerant design of welded structures. [ABSTRACT FROM AUTHOR]

The stress intensity factor and stress field expression for long cracks near an infinite-length plate bore are calculated using the Muskhelishvili Complex Function Approach. It applies to engineered bore edge cracks, especially under the condition in which the elliptical bore is subjected to internal pressure or only the surface of the crack is subjected to internal pressure. The formula is validated by numerical simulation and applies both to elliptical and circular holes. The variation of stress intensity factor with crack length is analyzed when the special round hole is only subjected to internal pressure. It has practical application value in fracture engineering. [ABSTRACT FROM AUTHOR]

Calculation of the stress intensity factor K is a crucial and difficult task in linear elastic fracture mechanics. With the capacity to solve complex input-output problems of an underlying system, machine learning is especially useful in the calculation of K. However, when faced with complex systems, such as the firtree groove structure of a turbine disk, the data--consuming issue has always been a thorny problem in K-solutions combined with machine learning studies for a long time. In this paper, a novel K-solution method called PA-GPR (Pool-based Active learning with Gaussian Process Regression) for the calculation of the stress intensity factor for surface cracks in the firtree groove structure of a turbine disk is proposed. Using the pool-based active learning strategy, the proposed K-solution method could make the GPR model have a great regression performance with a few samples required. In the pool-based active learning strategy analysis, the learning function based on greedy sampling is proposed to select samples with a high contribution to the training of the GPR model. The calculation of K for a semi-elliptical surface crack in the firtree groove structure is evaluated to verify the accuracy and effectiveness of the proposed method. The results show that this novel method is accurate, time-saving and effective. [ABSTRACT FROM AUTHOR]

The basic aspects of the J-A concept of elastoplastic two-parameter fracture mechanics based on a three-term asymptotic description of the stress field at the crack tip are presented. It is noted that the field of elastoplastic stresses at the crack tip is controlled by two parameters of fracture mechanics, namely, J-integral and parameter A. Parameter A is a measure of the deviation of the stress field from the HRR stress field and can be considered a parameter of elastoplastic constraint at the crack tip under conditions of both small- and large-scale yielding. The results of studying the influence of the exponent of the strain hardening of the material, crack aspect ratio, and the thickness of standard specimens with a crack on the elastoplastic stress intensity factor and parameter A are presented. A two-parameter elastoplastic J-A fracture criterion based on the relationship between J-integral and strain (stress) on the surface of the crack-notch and the principle of linear summation of damage is formulated. To reflect the crack-tip constraint, the parameter A is introduced into the criterion equation as a function of applied failure stresses. The elastoplastic fracture toughness as a function of the crack-tip constraint in the fracture criterion is interpreted as the corrected elastoplastic fracture toughness of a specimen with the corresponding constraint parameters A. The results of studying the normalized corrected fracture toughness as a function of failure stresses, crack aspect ratio, and strain hardening exponent of the material are presented. [ABSTRACT FROM AUTHOR]

The majority of classical methods which analyze the stability of existing cracks are based on theorems which calculate the forces in a state of limit equilibrium and do not take into consideration the deformation of the structure and the internal constraints thereof. This is not entirely consistent with what exactly happens in reality. For this purpose, we have proposed this study which analyzes the stability of cracks by the stress intensity factor through the calculation of the J-Integral, which is used in the calculation of the stress intensity factor. The stress intensity factor is a mechanical parameter, its values play a very important role in predicting the cracked state of the structure, and when it takes a certain value which is equal to the toughness of the material, the crack will cause the rupture of the structure. There are several methods for calculating the stress intensity factor. We have chosen to calculate it using the energy method because the direct calculation of the latter poses a problem because of the secularity of the flow around the crack. In this paper, we used the J-Integral and the energy release time to calculate the stress intensity factor. We also calculated using the laws of country the growth rate and the necessary number of cycles for the propagation of a crack. [ABSTRACT FROM AUTHOR]

This paper focuses on life prediction models considering the variability of loads. It describes the fatigue strength and crack growth behavior of AISI 304L austenitic stainless steel at room temperature. The deformation behavior of the austenitic stainless steel was investigated via tensile and fatigue tests. Crack tests were performed on CT50 specimens for constant ΔP and ΔK under different cyclic loads before the specimen was severely cracked by a monotonically increasing load. The impact of loading sequence and the evolution of the dissipated energy ΔJ were investigated using constant charge ΔP and stress intensity ΔK. The dissipated energy per cycle is used to predict fatigue crack growth. Experimental results proved that the various parameters considered in terms of cyclic loading and the results obtained under monotonic loading up to unstable failure show that cracking at constant ΔP is significantly more damaging than at constant ΔK. Therefore, cyclic loading with a constant pressure drop will result in faster crack growth or shorter fatigue life than loading with a constant stress intensity factor ΔK. [ABSTRACT FROM AUTHOR]

Surface cracks are commonly observed in coatings and films. When structures with coatings are subject to stretching, opening mode cracks are likely to form on the surface, which may further lead to other forms of damage, such as interfacial delamination and substrate damage. Possible crack forms include cracks extending towards the interface and channeling across the film. In this paper, a two-dimensional numerical model is proposed to obtain the structural strain energy at arbitrary crack lengths for bilayer structures under uniaxial tension. The energy release rate and structural stress intensity factors can be obtained accordingly, and the effects of geometry and material features on fracture characteristics are investigated, with most crack patterns being confirmed as unstable. The proposed model can also facilitate the analysis of the stress distribution in periodic crack patterns of films. The results from the numerical model are compared with those obtained by the finite element method (FEM), and the accuracy of the theoretical results is demonstrated. [ABSTRACT FROM AUTHOR]

To improve the thermoelectric converting performance in applications such as power generation, reutilization of heat energy, refrigeration, and ultrasensitive sensors in scramjet engines, a thermoelectric film/substrate system is widely designed and applied, whose interfacial behavior dominates the strength and service life of thermoelectric devices. Herein, a theoretical model of a thermoelectric film bonded to a graded substrate is proposed. The interfacial shear stress, the normal stress in the thermoelectric film, and the stress intensity factors affected by various material and geometric parameters are comprehensively studied. It is found that adjusting the inhomogeneity parameter of the graded substrate, thermal conductivity, and current density of the thermoelectric film can reduce the risk of interfacial failure of the thermoelectric film/graded substrate system. Selecting a stiffer and thicker thermoelectric film is advantageous to the reliability of the thermoelectric film/graded substrate system. The results should be of great guiding significance for the present and upcoming applications of thermoelectric materials in various fields. [ABSTRACT FROM AUTHOR]

During pipeline operation, internal cracks may occur. The severity around the crack tip can be quantified by the stress intensity factor (KI), which is a linear–elastic fracture mechanics parameter. For pressurized pipes featuring infinitely long internal surface cracks, KI can be interpolated from a function considering pressure, geometry, and crack size, as presented in API 579-1/ASME FFS-1. To enhance KI prediction accuracy, an artificial neural network (ANN) model was developed for such pressurized pipes. Predictions from the ANN model and API 579-1/ASME FFS-1 were compared with precise finite element analysis (FEA). The ANN model with an eight-neuron sub-layer outperformed others, displaying the lowest mean squared error (MSE) and minimal validation discrepancies. Nonlinear validation data improved both MSE and testing performance compared to uniform validation. The ANN model accurately predicted normalized KI, with differences of 2.2% or lower when compared to FEA results. Conversely, API 579-1/ASME FFS-1′s bilinear interpolation predicted inaccurately, exhibiting disparities of up to 4.3% within the linear zone and 24% within the nonlinearity zone. Additionally, the ANN model effectively forecasted the critical crack size (aC), differing by 0.59% from FEA, while API 579-1/ASME FFS-1′s bilinear interpolation underestimated aC by 4.13%. In summary, the developed ANN model offers accurate forecasts of normalized KI and critical crack size for pressurized pipes, providing valuable insights for structural assessments in critical engineering applications. [ABSTRACT FROM AUTHOR]

The mechanical properties of magnetoelectroelastic (MEE) materials are brittle, which is easy to produce nano-defects (hole or crack). The micro-fields of nanoscale cracks and holes are size dependent significantly. Nanoscale cracks and holes interact with each other, and the interference effect is very obvious. In this paper, the Model III fracture behavior of nanoscale circular hole edge arbitrary position radial crack is studied under anti-plane mechanical load, in-plane electric displacement load and in-plane magnetic induction load. Based on the surface elasticity theory, the conformal mapping technique and the MEE elasticity theory, the MEE fields expressions of the nano-hole and nano-crack are obtained, and the analytical solution of generalized intensity factors (stress intensity factor, electric displacement intensity factor and magnetic induction intensity factor) at crack tip is given. The comparison between the present results and the existing research shows the correctness of the present method in this paper. The influences of the microstructure and coupling loads on the generalized intensity factors are discussed. [ABSTRACT FROM AUTHOR]

This article describes the influence of corrugated steel fiber on the mechanical properties and fracture energy of Ultra-High Performance Concretes (UHPC) of various strength levels. Three UHPC formulations with compressive strengths of 143, 152, and 177 MPa were tested. The following parameters for the formulations without fiber and those containing 2% steel fiber by volume were determined: compressive strength, splitting tensile strength, flexural strength, modulus of elasticity, Poisson's ratio and critical stress intensity factor. From the axial tensile test results, the following parameters were obtained: the cracking stress, tensile strength, and fracture energy of Ultra-High Performance Fiber Reinforced Concrete (UHPFRC) of different strength levels. With the introduction of steel fiber, an increase in all the investigated parameters is observed regardless of the strength of the concrete matrix. The most remarkable influence the fiber has on the splitting tensile strength, flexural strength and critical stress intensity coefficient, the increase is up to 1.6–3.2 times. There was a slight increase in compressive strength and elastic modulus—up to 5.0–7.4% depending on the composition. Poisson's ratio was equal to 0.2 regardless of the strength of the concrete matrix and the presence of steel fiber. Based on the test results, equations were proposed to predict the properties of UHPC and UHPFRC depending on the water–cement ratio, silica fume content, cement compressive strength and the volumetric content of corrugated steel fiber. The calculated and experimental values showed good convergence with a correlation coefficient in the range of 0.885–0.997. [ABSTRACT FROM AUTHOR]

In order to study the fatigue performance of the initial crack between the CFRP reinforced deck and the U-rib weld after considering the residual stress, the welding residual stress of the deck and the U-rib weld was analyzed by the welding subprogram of ABAQUS, and then the segment model of the deck and the U-rib of the steel bridge deck was established by using the interaction technology of FRANC 3D-ABAQUS, and the stress intensity factor of the crack between the deck and the U-rib weld under the vehicle-only, vehicle-residual stress combined loads, and CFRP-strengthened combined loads were analyzed. The growth analysis of cracks before and after reinforcement was carried out. The results show that the amplitude of the stress intensity factor of the crack tip is less than the threshold when only the vehicle is applied, and the crack will not spread. After considering the residual stress, the maximum KI value of the crack at the welding toe is increased by 6.9 times compared with the maximum value of the vehicle only, and the maximum KI value at the welding root is increased by 10.7 times; the reinforcement method of CFRP pasted on the lower surface has a reinforcement effect on the fatigue crack at the welding toe, but the fatigue crack at the welding root has no reinforcement effect; the reinforcement effect of the welded toe crack increases with the increase of the number of CFRP layers, length, and width. When the weld toe crack after reinforcement extends to half the thickness of the deck, the number of car-residual stress combined load cycles increases by 43% compared to when it is not reinforced. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to compare the fracture behavior of interfaces obtained using fourth-generation and universal dental adhesives. The study relies on optic and SEM to evaluate the dentin–adhesive–restoration material interface of the samples and also on FEA simulation of fracture behavior. Specimen fabrication relied on 20 extracted teeth, in which class I cavities were created according to a protocol established based on the rules of minimally invasive therapy. For the direct adhesive technique, the adhesives used were: three-step All Bond, three-batch A and one-step Clearfil Universal Bond Quick-batch B. The restoration was performed with the same composite for both adhesives: Gradia direct posterior. The simulation used a 3D reconstructed molar on which geometric operations were performed to obtain an assembly that replicated a physical specimen. Material properties were applied to each component based on the information found in the literature. A simplified model for crack propagation was constructed, and using the fracture mechanics tool in Ansys 2019, the stress intensity factors that act at the crack tip of the adhesive interface were obtained. Mechanical simulation and microscopic investigation showed us how the interface of the dentine–adhesive–filling material performed in cases of both dental adhesives and for a certain loading condition. Important differences were identified among the adhesives, the fourth generation being superior to the fourth generation especially due to the separate steps in which the tooth surface was prepared for adhesion. [ABSTRACT FROM AUTHOR]

This work presents a comprehensive analytical solution for the mixed‐mode I/II stress intensity factor of a biaxially loaded plate that has a centrally straight inclined crack with frictional surfaces. The solution addresses every possible combination of coefficient of friction, biaxial ratio, crack length, and angle. The present results agree with the available corresponding finite element solutions. For the tension‐compression and compression‐tension biaxial loading, crack angles are recognized to achieve pure mode I, pure mode II, and mixed‐mode crack tip deformation in terms of stress biaxiality and friction coefficient. In the compression‐compression biaxial loading, only mode II crack tip deformation is operative. The ranges of crack angles necessary to produce dormant cracks are determined for the biaxial loading patterns, where a compressive stress is involved, as a function of the biaxial ratio and friction coefficient. It is possible to apply the present solution to cracked plates with two‐dimensional stresses that include a shear stress. Highlights: This work evaluates modes I/II stress intensity factor of central inclined frictional cracks in plates under biaxial loading.The solution addresses every possible combination of friction, biaxiality, and crack angle and length.The solution covers the three biaxial loading patterns that include a compressive stress.The solution can be applied to cracks in plates under complex 2D stresses that include a shear stress. [ABSTRACT FROM AUTHOR]

This paper uses the displacement discontinuity method, one of the boundary element methods, to solve two major engineering problems. The first one addresses the safe design of underground excavations in fractured rock masses. The implemented method was used to control the slip of discontinuities passing through a circular opening at 45°. Special contact elements were used to simulate a possible slip on the cracks. At the same time, stress intensity factors (SIFs) were calculated using the gradient elasticity theory (special tip elements where numerical integrations are needed were excluded). The crack propagation due to shear slip occurrence was defined using the criterion of maximum tangential stress at an angle of 71° from the initial crack direction. The second one involved in the crack's propagation was solved by applying pressure to the circular opening, while a part of it was transferred to the cracks, approximating the mechanism of hydraulic fracture. Finally, the implementation of higher elasticity elements in the cracks provided an accurate estimation of SIFs, showing an error of about 4%, as confirmed by comparisons with existing type I loading solutions. [ABSTRACT FROM AUTHOR]

In this work, the Christopher–James–Patterson crack tip field model is used to infer and assess the effective stress intensity factor ranges measured from thermoelastic and digital image correlation data. The effective stress intensity factor range obtained via the Christopher–James–Patterson model, which provides an effective rationalization of fatigue crack growth rates, is separated into two components representing the elastic and retardation components to assess shielding phenomena on growing fatigue cracks. For this analysis, fatigue crack growth tests were performed on Compact-Tension specimens manufactured in pure grade 2 titanium for different stress ratio levels, and digital image correlation and thermoelastic measurements were made for different crack lengths. A good agreement (~2% average deviation) was found between the results obtained via thermoelastic stress analysis and digital image correlation indicating the validity of the Christopher–James–Patterson model to investigate phenomena in fracture mechanics where plasticity plays an important role. The results show the importance of considering crack-shielding effects using the Christopher–James–Patterson model beyond considering an exclusive crack closure influence. [ABSTRACT FROM AUTHOR]

The objective of this study is to examine the behavior of fatigue crack growth (FCG) in the mixed mode (I/II) of the AISI 316 austenitic stainless steel alloy, considering mode mixity angles of 30°, 45°, and 60°. This particular alloy is widely used in the marine industry and various structural components because of its exceptional properties, such as high corrosion resistance, good formability, weldability, and high-temperature strength. By investigating the crack growth behavior, the study seeks to provide insights into the material's durability and potential for long-term use in demanding applications. To analyze fatigue crack growth behavior using linear elastic fracture mechanics (LEFM), this study utilizes compact tension shear (CTS) specimens with varying loading angles. The CTS specimens provide an accurate simulation of real-world loading conditions by allowing for the application of various loading configurations, resulting in mixed-mode loading. The ANSYS Mechanical APDL 19.2 software, which includes advanced features such as separating, morphing, and adaptive remeshing technologies (SMART), was utilized in this study to precisely model the path of crack propagation, evaluate the associated fatigue life, and determine stress intensity factors. Through comparison with experimental data, it was confirmed that the loading angle had a significant impact on both the fatigue crack growth paths and the fatigue life cycles. The stress-intensity factor predictions from numerical models were compared to analytical data. Interestingly, it was observed that the maximum shear stress and von Mises stresses occurred when the loading angle was 45 degrees, which is considered a pure shear loading condition. The comparison shows consistent results, indicating that the simulation accurately captures the behavior of the AISI 316 austenitic stainless steel alloy under mixed-mode loading conditions. [ABSTRACT FROM AUTHOR]

To obtain the effect of fracture failure mechanics characteristics and behavior of brittle rock masses on the compound factors of fissure openings and inclination, uniaxial loading tests were performed on single-fissured rock-mass specimens with different openings using a rock mechanics test machine. The test results show that with the increase in fissure openings, the fissured rock-mass peak strength variation behavior with the increase in fissure inclination angle changes from first decreasing and then increasing to gradually increasing, and the angle at the minimum value of peak strength shifts from 45° to 0°. At the same fissure angle, the peak strength of the fissured rock mass decreases with the increase in the fissure opening size. The greater the opening size of the prefabricated fissure, the smaller the peak strength of the fissured rock mass and the greater the influence of changes in the fissure inclination angle. The elastic modulus of the fissured rock-mass specimen shows a positive correlation with the fissure inclination angle and a negative correlation with the fissure opening size. Combined with the neighborhood stress field analysis of the open fissure tip, the criterion of composite fracture under tension failure is established, and the linear relationship between the stress intensity factors KI and KII is verified. The criterion of composite fracture of open fissures under shear failure is also identified, which is based on the linear relationship between the stress intensity factors. [ABSTRACT FROM AUTHOR]

Crack defects in subsea pipelines may lead to pipe wall failure due to leak or rupture. Hence, crack analysis is essential to ensure pipeline integrity by assessing whether it is still fit for service. Cracks are evaluated using stress intensity factor (SIF) under certain loads by ensuring that this factor does not exceed the pipe material fracture toughness, at which point the crack initiates and propagates, leading to pipeline failure. A parametric study is performed to compute SIF values of circumferential semi-elliptical cracks on the external surface of a pipeline with a combination of crack depths of 4, 5, and 6 mm, and crack lengths of 20, 40, and 60 mm. An API 5L X65 grade pipeline with 254 mm outside diameter and 12.7 mm wall thickness is assessed by utilizing the extended finite element method. The models have been validated using theoretical SIF values calculated using API 579-1, with an average absolute deviation of 2.08%. It is concluded that for these cases, each millimeter increase in initial crack depth may reduce the pipeline pressure capacity up to 12 times compared to the initial crack length. [ABSTRACT FROM AUTHOR]

Studies have been carried out aimed at improving the corrosion resistance of concrete and its other characteristics for operation in harsh environmental conditions. The influence of a complex additive containing multilayer carbon nanotubes and hydrothermal SiO2 nanoparticles on the durability of concrete has been determined. Experiments were carried out to study water tightness, frost resistance, water absorption, and power parameters of concrete (stress intensity factors). It has been established that the introduction of nanoparticles into concrete improves the microstructure of its cement matrix, which leads to a decrease in the penetration of chloride ions into concrete and to an increase in its water permeability. [ABSTRACT FROM AUTHOR]

We consider the plane elasticity problem of two asymmetrical edge cracks emanating from an elliptical hole in two-dimensional decagonal quasicrystals (QCs) under remotely uniform tensile stress. A complex variation method of two-dimensional QCs is developed to solve the plane elasticity problem of two-dimensional decagonal QCs containing complex defects. The analytical solutions for the stress field and the stress intensity factors near the crack tip are expressed by using a conformal mapping technique and complex potential theory. Some special cases of the results are also obtained, such as the T-type crack, cross crack, and Griffith crack. The effects of geometrical parameters of crack configuration on the stress intensity factors are presented graphically. [ABSTRACT FROM AUTHOR]

This work presents a comprehensive study consisting of two aspects: a numerical analytical aspect and a laboratory experimental aspect. The numerical study was a three-dimensional finite element numerical analysis of performance of corroded and horizontally cracked aluminium plates, which were repaired by composite patching. The effect of the composite types on the variance of the damaged area of the adhesive (FM-73) and their efficiency on the stress intensity factor were studied. In the experimental study, corroded aluminium plates were prepared and repaired them using technology of the composite. The results showed that the panels that were repaired with composite (boron/epoxy) give values of stress intensity factor (KI) and damaged area ratio (DR) less than the other two studied composites (glass/epoxy and graphite/epoxy), and increase the ultimate strength of plates damage, and this leads to the conclusion that (Boron/epoxy) increases the performance and durability of (Al 2017-A) plates. [ABSTRACT FROM AUTHOR]

Bolted spherical joints, due to their prominent merits in installation, have been widely used in modern spatial structures. Despite significant research, there is a lack of understanding of their flexural fracture behaviour, which is important for the catastrophe prevention of the whole structure. Given the recent development to fill this knowledge gap, it is the objective of this paper to experimentally investigate the flexural bending capacity of the overall fracture section featured by a heightened neutral axis and fracture behaviour related to variable crack depth in screw threads. Accordingly, two full-scale bolted spherical joints with different bolt diameters were evaluated under three-point bending. The fracture behaviour of bolted spherical joints is first revealed with respect to typical stress distribution and fracture mode. A new theoretical flexural bending capacity expression for the fracture section with a heightened neutral axis is proposed and validated. A numerical model is then developed to estimate the stress amplification and stress intensity factors related to the crack opening (mode-I) fracture for the screw threads of these joints. The model is validated against the theoretical solutions of the thread-tooth-root model. The maximum stress of the screw thread is shown to take place at the same location as the test bolted sphere, while its magnitude can be greatly reduced with an increased thread root radius and flank angle. Finally, different design variants related to threads that have influences on the SIFs are compared, and the moderate steepness of the flank thread has been found to be efficient in reducing the joint fracture. The research findings could thus be beneficial for further improving the fracture resistance of bolted spherical joints. [ABSTRACT FROM AUTHOR]

The edge-cracked semi-circular bend (SCB) specimen subjected to three-point bending loading is used in many applications to measure the fracture behavior of quasi-brittle materials. The main objective of the present work was to study the effect of the crack length to SCB specimen radius ratio (a/R), span to specimen diameter ratio (S/D), and specimen size on its flexural and mode I crack growth behavior. The contour integral method was implemented using the 3-D finite element method to determine the mode I stress intensity factor. In addition, high-strength concrete specimens were experimentally studied to validate the numerical results. The results show that the maximum compression stress is not sensitive to the S/D value, while the tensile stress is very sensitive. The value of S/D is the main parameter controlling the crack driving force (i.e., the crack mouth opening displacement (CMOD) and the normalized stress intensity factor, YI). For the same S/D, the SCB specimen diameter value change has a marginal effect on CMOD and YI. The specimen with S/D = 0.8 showed that it is the most compatible specimen with three-point bending test conditions, regardless of the SCB specimen size. A good agreement between the numerical and experimental results was achieved. [ABSTRACT FROM AUTHOR]

Since each rock type represents different deformation characteristics, prediction of the damage beforehand is one of the most fundamental problems of industrial activities and rock engineering studies. Previous studies have predicted the stress–strain behaviors preceding rock failure; however, quantitative analyses of the progressive damage in different rocks under stress have not been accurately presented. This study aims to quantify pre-failure rock damage by investigating the stress-induced microscale cracking process in three different rock types, including diabase, ignimbrite, and marble, representing strong, medium-hard, and weak rock types, respectively. We demonstrate crack intensity at critical stress levels where cracking initiates (σci), propagates (σcd), and where failure occurs (σpeak) based on scanning electron microscope (SEM) images. Furthermore, the progression of rock damage was quantified for each rock type through the fractal analyses of crack patterns on these images. Our results show that the patterns in diabase have the highest fractal dimensions (DB) for all three stress levels. While marble produces the lowest DB value up to σci stress level, it presents greater DB values than those of ignimbrite, starting from the σcd level. This is because rock damage in ignimbrite is controlled by the groundmass, proceeding from such stress level. Rock texture controls the rock stiffness and, hence, the DB values of cracking. The mineral composition is effective on the rock strength, but the textural pattern of the minerals has a first-order control on the rock deformation behavior. Overall, our results provide a better understanding of progressive damage in different rock types, which is crucial in the design of engineering structures. [ABSTRACT FROM AUTHOR]

There is abundant shale oil in the ocean and on land. Due to the tight lithology of the reservoir, volume fracturing technology is needed to improve the oil and gas productivity. It is very important to study the expansion law of multiple natural fractures in rock masses and its influencing factors in the process of volume fracturing for the formation of fracture networks. Based on the theory of online elastic fracture mechanics, the calculation method of the stress intensity factor at the end of any I–II composite fracture is established by using effective shear stress and considering the influence of T-stress. The calculation model of the stress intensity factor of any fracture on the main fracture wall or the horizontal section of the main fracture wall is established according to the concrete stress conditions in the process of hydraulic fracturing. Based on the principle of stress superposition, the combined interference stress calculation model of fracture ends is established for the case of multiple penetrating cracks in infinite-plane rock masses. Based on the theory of shear failure and plane strain, a model of the initiation direction and condition of natural cracks on the horizontal section of the main fracture wall and both sides of the main fracture in brittle rock is established when there are many coaxial natural cracks under the action of remote site stress and water pressure on the fracture surface. According to the simulation results, on the main fracture wall, when σH > σv > σh or σH > σh > σv, when the crack angle (CA) is within a certain range and multiple natural cracks (MNC) exist, the required pressure for shear failure decreases. When the fracture angle exceeds a certain size, the required pressure increases. When there are MNC in the horizontal or perpendicular sections of the rock mass on both sides of the main fracture, the required net pressure for shear failure decreases within a certain CA range. When the CA exceeds a certain range, it increases or remains basically unchanged. On the whole, the presence of MNC reduces the net pressure for shear failure, which is conducive to the formation of fracture networks. [ABSTRACT FROM AUTHOR]

The maximum tangential stress (MTS) criterion is one of the most widely used criteria for predicting the direction of crack extension. The suitability of this criterion is examined under different loading conditions using the extended finite element method (XFEM). Experimental and numerical results reported in the literature are considered to evaluate the validity and accuracy of the criterion. The results demonstrate that the MTS criterion evaluated by stress intensity factors (SIFs) can accurately predict the direction of crack propagation in specimens under direct tensile loading. This criterion overestimates the angle of crack initiation in the specimen under indirect tensile loading but underestimates the angle in the specimen subjected to 3‐point bending. It is concluded that the MTS criterion based on SIFs could not accurately predict the direction of the crack initiation, which could, however, be determined properly based on the stress distribution around the crack tip obtained by the XFEM numerical models. HIGHLIGHTS: The suitability of the MTS criterion is examined under different loading conditions.Under indirect tensile loading, the MTS criterion overestimates crack initiation angle.The MTS criterion underestimates the angle in the specimen under 3‐point bending.Initiation angle can be predicted properly based on stress distribution around crack tip. [ABSTRACT FROM AUTHOR]