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In this study, pre-cracked cubic specimens of concrete materials were especially prepared in a concrete laboratory to study the breaking process of brittle solids. Then, the linear elastic fracture mechanics concept of the stress intensity factor and the experimental methods were used to investigate the failure mechanism of pre-cracked concrete specimens under compression. The crack propagation mechanism and the ultimate strengths of these specimens were obtained in the laboratory. Several numerical analyses were also carried out on the pre-cracked specimens, using the finite element method and ABAQUS software package. The damage location and convergence diagram of the differential evolutionary algorithm under mode I, II, III or IV loading conditions were investigated for the cubic pre-cracked concrete specimens containing a single center crack with different inclination angles. The crack propagation mechanisms obtained numerically were compared with the corresponding experimental ones proving the proposed method's feasibility. [ABSTRACT FROM AUTHOR]

To analyze the stress of functionally graded materials (FGMs) through an experiment, transparent homogeneous FGMs (THFGMs) with similar theoretical and physical properties need to be created. This study developed such THFGMs and proposed a method for determining their stress intensity factors (SIFs) and T-stresses via photoelastic experiments. The Young's modulus and Poisson's ratio of these THFGMs linearly change along the physical variation direction, and the shear modulus varies almost linearly. The SIFs and T-stresses were obtained for the central and edge cracks in finite rectangular FGM plates with linear variations in the shear modulus under constant density along the direction of the crack under mode I loading. The SIFs and T-stresses can be obtained using the exponential and linear variation in the stress fields, even if the physical properties of FGM plates show linear variation in the shear modulus. The characteristics of the experimental SIFs obtained in this study generally agree with those of theoretical SIFs reported in previous research. For center crack tips, the SIFs at the hard right crack tip were greater than those at the soft left crack tip. For edge crack tips, when a/W < 0.35, the SIFs were lower than the homogeneous materials. By contrast, when a/W > 0.35, the SIFs were greater than the homogeneous materials. The experimental T-stresses for the center crack agreed well with the numerical T-stresses reported in previous research. For the edge crack, when a/W ≤ 0.3, the experimental T-stresses agreed with the numerical T-stress, but when a/W ≥ 0.4, considerable differences were observed between the experimental and numerical T-stresses. Where a(a) denotes the crack length for edge cracks or half the crack length for center cracks, and W is the width of the specimen. Experimental results coincide well with those reported in the literature, except for the T-stresses for edge crack when a/W > 0.3. Therefore, the THFGMs, which are new FGMs developed in this study, can be effectively used in experimental fracture analysis. [ABSTRACT FROM AUTHOR]

The temperature dependence of the fatigue crack propagation rate in stage IIb in bimodal Ti6Al4V was investigated at different stress ratios R. Fatigue tests were conducted between room temperature and 550K at R of 0.1, 0.7, 0.8, and 0.9, and two phenomena were elucidated consequently. First, the fatigue crack growth rates were nearly temperature independent for R = 0.1, 0.7, and 0.8 while it is temperature dependent at R = 0.9. This difference in the temperature dependence can be explained by the assumptions that the fatigue crack growth is controlled by the dislocation activities associated with work-hardening for R = 0.8 while it is controlled by dislocation glide at R = 0.9. Second, the fatigue crack growth rates at R = 0.9 was higher than those at R = 0.1, 0.7, and 0.8. This increase in the fatigue crack growth rate at R = 0.9 can be explained by the change in the stress intensity factor of crack opening. Both the controlling mechanisms emanated from the change in the dislocation structure in front of the crack tip. [ABSTRACT FROM AUTHOR]

This study proposes two alternative approaches to complement existing integration strategies used in the weight function method for linear elastic crack problems. The first approach is based on an interpolation type integration scheme and the second approach is based on Gauss quadrature. The proposed approaches enable a computationally efficient numerical integration for computing stress intensity factors in 2D fracture problems. The efficiency is gained through a comparatively low number of integration points facilitated by higher-order approximation. The integration weights only need to be computed once for a given crack length-to-width ratio and can be applied to arbitrary continuous and smooth stress distributions. The proposed approaches show excellent accuracy. In particular, the Gauss quadrature approach exhibits several orders of magnitude more accuracy compared to the most commonly used trapezoidal integration. [ABSTRACT FROM AUTHOR]

In the present work, the effect of various discontinuities like voids, soft inclusions and hard inclusions of the mixed-mode stress intensity factor (MMSIF), crack growth and energy release rate (ERR) of an edge crack isotropic plate under different loading like tensile, shear, combine and exponential by various numerical examples is investigated. The basic formulation is based on the extended finite element method (XFEM) through the M interaction approach using the level set method. The effect of single and multi voids and inclusions with position variation on MMSIF and crack growth are also investigated. The presented results would be applicable to enhancing the better fracture resistance of cracked structures and various loading conditions. [ABSTRACT FROM AUTHOR]

Fatigue is one of the main failure modes in marine structures, and it is caused by the strong cyclic characteristics of the loads they support. This failure mode is amplified in areas of high stress concentration, such as at the intersection of primary and secondary elements. In this paper, a two-phase study is proposed that compares numerical and experimental results using a digital image correlation technique. The described procedure establishes selection, design, and scantling criteria and provides recommendations for the design of the transverse structure using specimens with different geometries. These geometries correspond to different designs for the transverse primary structure that use a longitudinal secondary stiffener with variable thickness and longitudinal spacing to transverse in a dynamic and quasi-static regime. The stress state for this regime is calculated based on the biaxiality indication concept, which uses the fatigue phenomenon (safety factor and sensitivity curves) and fracture mechanics (parameters of the Paris crack propagation law, correlation value, and law of variation of the stress intensity factor). [ABSTRACT FROM AUTHOR]

There are a large number of non-penetrating collinear cracks in the rock slope of an open-pit mine. The timeliness of cracks in the rock mass is a problem that cannot be ignored in terms of slope engineering safety. Based on the superposition principle and fracture mechanics, the stress intensity factor of the rock mass crack tip with collinear fractures under biaxial compression was calculated in this study. A mechanical model of rock mass crack propagation with collinear fractures under constant load was established according to the Charles equation. The effects of loading time, crack penetration rate, and crack dip angle on crack propagation along the direction of the rock bridge were analyzed theoretically. The variations in crack propagation with time in the rock mass were examined using a LS-DYNA creep numerical model. The results show that the fracture growth rate changes in three stages over time, progressing through a stable stage, a decreasing stage, and an abrupt stage. A higher crack penetration rate and a larger crack inclination angle cause a higher rock bridge penetration rate in the rock mass. When the crack penetration rate exceeds 74% or the fracture inclination angle is about 60°, the crack expansion directly enters the abrupt stage, and the rock bridge is penetrated. The theoretical analysis results are in close agreement with the numerical results of this work, which validates the proposed age expansion mechanical model for rock masses with non-penetrating collinear fractures. [ABSTRACT FROM AUTHOR]

When estimating fossil fuel carbon dioxide (FFCO 2) emissions from observed CO 2 concentrations, the accuracy can be hampered by biogenic carbon exchanges during the growing season, even for urban areas where strong fossil fuel emissions are found. While biogenic carbon fluxes have been studied extensively across natural vegetation types, biogenic carbon fluxes within an urban area have been challenging to quantify due to limited observations and differences between urban and rural regions. Here we developed a simple model representation, i.e., Solar-Induced Fluorescence (SIF) for Modeling Urban biogenic Fluxes ("SMUrF"), that estimates the gross primary production (GPP) and ecosystem respiration (Reco) over cities around the globe. Specifically, we leveraged space-based SIF, machine learning, eddy-covariance (EC) flux data, and ancillary remote-sensing-based products, and we developed algorithms to gap-fill fluxes for urban areas. Grid-level hourly mean net ecosystem exchange (NEE) fluxes are extracted from SMUrF and evaluated against (1) non-gap-filled measurements at 67 EC sites from FLUXNET during 2010–2014 (r>0.7 for most data-rich biomes), (2) independent observations at two urban vegetation and two crop EC sites over Indianapolis from August 2017 to December 2018 (r=0.75), and (3) an urban biospheric model based on fine-grained land cover classification in Los Angeles (r=0.83). Moreover, we compared SMUrF-based NEE with inventory-based FFCO 2 emissions over 40 cities and addressed the urban–rural contrast in both the magnitude and timing of CO 2 fluxes. To illustrate the application of SMUrF, we used it to interpret a few summertime satellite tracks over four cities and compared the urban–rural gradient in column CO 2 (XCO 2) anomalies due to NEE against XCO 2 enhancements due to FFCO 2 emissions. With rapid advances in space-based measurements and increased sampling of SIF and CO 2 measurements over urban areas, SMUrF can be useful to inform the biogenic CO 2 fluxes over highly vegetated regions during the growing season. [ABSTRACT FROM AUTHOR]

Purpose: According to the structural parameters of an actual turbofan aeroengine, the dynamics modeling and vibration analysis of multi-stage blade-disk-shaft integrated structure with three-dimensional crack are conducted. Methods: Based on the theory of fracture mechanics, the stress intensity factor is considered as a fracture criterion. This paper proposes a three-dimensional (3-d) equivalent notch model which is simpler and more convenient than the traditional crack simulation model. Moreover, its validity is analyzed. Aiming at the harsh working environment of the blades, the penetration crack is considered at the edge and the middle of a blade root, respectively. Results: The influence of the crack on the strength failure of the rotor system is studied. Results show that the appropriate small angle equivalent notch model can be convenient and effective to simulate the fracture cracks, in which 5° is proved to be the best angle. Conclusions: The crack aggravates the vibration of blades obviously. A parametric study is conducted, with a particular focus on the effects of pressure load and centrifugal load on the stress intensity factors and displacement fields. [ABSTRACT FROM AUTHOR]

The wedge-splitting test is widely used in the testing of fracture mechanical parameters of concrete or concrete-like materials. This test provides a stable crack propagation, which was analysed on a cube specimen. Another interesting application for measuring fracture mechanical properties combines wedge-splitting test with a three-point bending test. In this contribution, we analyse the stress fields in such a nontraditional geometry of wedge-splitting test by employing a linear elastic fracture mechanics [ABSTRACT FROM AUTHOR]

In this study, the stress intensity factor (SIF) of an interface kinked crack is analyzed by the singular integral equation of the body force method. The problem can be expressed by distributing the body force doublets of the tension and shear types along all the boundaries of the kinked and interface crack parts. The SIFs can be obtained directly from the densities of the body force doublets at the crack tips. Although the problem has already been calculated using the crack connection model, the accuracy of the analysis has not been clarified. From the analysis results in this study, it can be seen that the SIFs calculated by the crack connection model have a nonnegligible error, and the present method gives more accurate results. The advantage of the present method is that the SIFs of the kinked and the interface crack tips can be obtained at the same time with high accuracy. [ABSTRACT FROM AUTHOR]

In this paper, the stress intensity factor (SIF) formula F ISE along the crack front of a semi-elliptical surface crack is studied. The exact SIF solution F ISE is used by solving the hypersingular integral equation of the body force method discussed in the previous paper. To obtain the accurate formula, the SIF ratio F ISE / F IE is focused considering the exact solution F IE of an elliptical crack. By applying the least squares method to the ratio F ISE / F IE , accurate and convenient formula is proposed. The proposed formulas may provide the accurate SIF distributions for the aspect ratio a / b = 1 –4 better than 0.2% accuracy. [ABSTRACT FROM AUTHOR]

The paper presents the numerically evaluated dependence of the stress intensity factor (SIF) on crack velocity ( K I - a ˙ dependence) in Homalite-100 specimens subjected to pulse loading. Experiments on crack propagation (Ravi-Chandar and Knauss in Int J Fract 25:247–262, 1984. https://doi.org/10.1007/BF00963460; Int J Fract 26:65–80, 1984. https://doi.org/10.1007/BF01152313; Int J Fract 26:141–154, 1984. https://doi.org/10.1007/BF01157550; Int J Fract 26:189–200, 1984. https://doi.org/10.1007/bf01140627) were simulated using the finite element method and incubation time fracture criterion. According to (Ravi-Chandar and Knauss in Int J Fract 26:141–154, 1984. https://doi.org/10.1007/BF01157550), experimental data on the SIF–crack velocity dependence exhibit unstable behavior, i.e. considerable scattering of the SIF values: a broad range of SIF values corresponds to a single crack velocity. This way, the conventional approach based on a K I - a ˙ dependence being a material property is not applicable in this case. Such a phenomenon is also observed in a numerically obtained K I - a ˙ dependence, meaning that the developed approach makes it possible to evade the known ambiguity of the K I - a ˙ relation to predict the crack propagation. [ABSTRACT FROM AUTHOR]

The earth's crustal stress determination is a crucial item in civil, petroleum, and mining engineering and also in energy development fields. The hydraulic fracturing (HF) is one of the standard methods for estimating in situ stress, which is often analyzed with classical approach for stress estimations. The classical approach neglects the presence of pre-existing cracks in rock mass; however, the hydraulic fracturing is a phenomenon of fracture propagation in which the fracture mechanics approach is more appropriate to consider more complex items in stress estimations. In this study, the in situ stress tests are conducted in Azad Pumped Storage Power Plant (Azad PSPP) in the west of Iran and then the classical approach and four available analytical fracture mechanics methods are applied to determine the in situ stresses. Moreover, numerical modeling based on the displacement discontinuity method (DDM) is used to model hydraulic fracturing process and the results are compared with analytical methods. A comprehensive analysis on the length of pre-existing crack is done as an influential parameter on stress magnitudes. The results indicate that the magnitudes of in situ stresses calculated by the fracture mechanics approach are often greater than the stress magnitudes calculated by the classical approach. Also, the effect of crack inclination angle and pre-existing crack length on the magnitudes of σH is studied. In addition, the distribution of fluid pressure along the cracks and its influence on the stress intensity factor in the crack tip are analyzed, and consequently, the estimation of in situ stress is investigated. [ABSTRACT FROM AUTHOR]

In this work, a mathematical model is developed based on Griffith's crack theory while incorporating couple stress and surface elasticity in order to examine the performance and operability of cracked vibrating beam micro/nanogyroscopes. A size dependent crack severity factor is used to represent increased local flexibility due to surface crack. The gyroscope size is decreased from micro- to nano-scale to analyze the effects of a driving side surface crack on the sensitivity of micro/nanogyroscopes. The static pull-in, natural frequencies, nonlinear frequency response, and gyroscope sensitivity that are calculated using the size dependent crack severity are compared to the results obtained using the classical crack severity factor. This allows for the determination of the length scale, in which size dependency must be considered in the crack severity. It is found that size dependent effects significantly increase the crack severity in nanogyroscopes leading to significant changes in the sensor's sensitivity in comparison with the classical crack severity. [ABSTRACT FROM AUTHOR]

A part of the multilayer pavement structure containing top‐down crack in the hot mix asphalt (HMA) layer and subjected to loading of a moving vehicle is simulated using the finite element method. Aggregate distribution and packing algorithm was used for modeling the HMA layer around the top‐down crack as a heterogeneous two‐phase (aggregate/fine aggregate matrix [FAM]) medium. By considering the heterogeneity aspects of the asphalt mixture, the influence of traffic loading location, aggregate distribution, crack length, thickness layer, and mechanical properties of layers and components were investigated on the fracture parameters. The results showed that for different locations of vehicle wheels relative to the top‐down crack, the magnitude and sign of the fracture parameters in heterogeneous modeling were significantly different from the similar values of the homogeneous simulation. The stress intensity factors and especially the T‐stress were significantly sensitive to the crack tip location that can be placed either inside the stiffer aggregate or the softer FAM part. [ABSTRACT FROM AUTHOR]

A dynamic caustics test system was used, and different moving cracks were analysed to study the interaction between the crack growth rate, stress intensity factor, and curvature of the elliptical end of a moving crack under impact loading. Based on the linear elastic fracture mechanics theory, linearly fitting of the crack tip stress intensity factor and the elliptical curvature were employed to obtain the specific functional expressions. ABAQUS software was used to numerically simulate the moving crack fracture process passing through different elliptical curvatures. The crack tip stress intensity factor was calculated by the stress extrapolation method. The stress intensity factor obtained from the numerical calculation and the caustics test was consistent. The test and numerical simulation results showed that the direction of moving cracks entering and passing through the elliptical defects shows a certain regularity. As the ellipse curvature increased, the moving crack stress intensity factor passing through the ellipse gradually decreased, and the moving crack also passed easily through oval defects. [ABSTRACT FROM AUTHOR]

Measuring and calculating methods of critical stress intensity factors (SIFs) have become hot topics which attracted large attention recently. In this work, anti-symmetrical four-point bending tests of cracked fine-grained concrete specimens were conducted experimentally and numerically by using a computer-controlled universal testing machine and ABAQUS code. A comparative study of the calculation method of pure mode II stress intensity factor of a fine-grained concrete was performed by utilizing the conventional finite element method (FEM) in two and three dimensions as well as the extended finite element method (XFEM) in three dimensions. The results show that in three-dimensional models, the crack mode is closest to the pure mode II at the center of specimen thickness. Pure mode II stress intensity factors obtained by SEAM2D and XFEM3D are 1.013 and 1.0617 times that by SEAM3D, respectively. Pure mode II stress intensity factors of the fine-grained concrete obtained by the conventional FEM are more stable than that by XFEM. The number of mesh circles has slight influence on the calculation results of pure mode II stress intensity factor. [ABSTRACT FROM AUTHOR]

Deep underground surrounding rock is often in the true triaxial stress state. Therefore, it is of great practical importance to recognize the short-term stress-strain relationship of progressive failure and the long-term characteristics of creep failure for the design, construction and maintenance of underground engineering in the true triaxial stress state. This paper aims to propose a feasible theoretical model to solve the problem of the constitutive relation and creep characteristics of rocks under true triaxial compression. Starting from the stress intensity factor, an angular parameter on the crack surface is introduced to characterize the true triaxial stress state. Then, the relationship between microcrack length and macroscopic strain is derived by various representations of rock damage, and then the constitutive relation during rock fracture is derived by combining it with the rock strength factor formula. Finally, the creep failure law of rocks is derived by introducing the relationship between the length of subcritical crack growth and time. The rationality of the theoretical model is verified by comparing theories and experiments. The effects of minimum principal stress, intermediate principal stress, and the crack inclination angle on the stress-strain relationship are analyzed, providing an important basis for selecting the stress state for long-term creep behavior. The analysis examines the relationship between creep failure time and principal stress, and discusses the effect of the crack angle on creep failure time and steady-state creep strain rate. [ABSTRACT FROM AUTHOR]

• The CRTS Ⅲ slab track model with prefabricated cracks is established by extended finite element method. • The stress intensity factors (SIFs) at the tips of cracks on the track slab under train load are solved. • The effects of the crack length and depth on the SIFs of three types of cracks are discussed. • The variations of crack growth rate calculated by Paris' semi-empirical during service are analyzed. Microcracks may occur in Chinese Railway Track System type III (CRTS III) ballastless track slabs during service, and it is necessary to investigate their potential propagation under train load, which could lead to slab deterioration and affect the durability of the track structure. In this paper, based on the fracture mechanics theory, the stress intensity factors (SIFs) at the tips of transverse crack, longitudinal crack and vertical crack on the CRTS III track slabs under train load are solved by the extended finite element method (XFEM) in Abaqus software. The changes of SIFs at the crack tips during the passage of the train are analyzed, and the effects of the crack length and depth on the SIFs of the three types of cracks are discussed under train load. Crack growth rate is calculated using Paris' semi-empirical law to estimate slab life. The results show that the train load contributes to the propagation of transverse and vertical cracks in the vertical direction and inhibits the longitudinal cracks. When the middle of the sixth vehicle is above the crack, the SIFs at the tips of the crack reach their maximum values. The SIF of vertical cracks exceeds the fracture toughness at a certain depth. The fatigue load cycles calculated by Paris' semi-empirical law suggest that maintenance will not be required due to insufficient propagation under train load during service. [ABSTRACT FROM AUTHOR]

Steel Catenary Riser (SCR), as a pipeline type transmittal structure connecting seabed exploitation system and surface platform, has been widely used in the exploitation of offshore oil and gas resources. However, the initial crack defects inside the riser wall, which could be caused by manufacturing, installation and environment, may create server threats to the riser's safe operation. The current practice does not consider the impact of Welding Residual Stress (WRS) on defect evaluation of the cracked riser. The Finite Element Analysis (FEA) carried out by a simulation module embedded in ABAQUS was applied to simulate the distribution of WRS in the area near the welding center, and the results were extracted and added to the crack surface as secondary stress. The variation of Stress Intensity Factors (SIFs) and the plastic factors were analyzed through Interaction Integral Method (IIM). The results showed that the IIM could effectively solve the SCR's crack SIF. The SIF of axial crack is greater than that of circumferential crack. Compared to BS7910, the WRS is more accurately evaluated because it considers the variation of WRS with crack thickness. The results of this article provide engineering reference for analyzing welded SCRs. • The residual stress have been calculated according to FEM and the results have been compared to BS7910 specifications. • Stress intensity factor of cracks under the influence of residual stress has been calculated too. • The fracture ratio of different crack sizes have been calculated through SIFs and ultimately evaluated the riser. [ABSTRACT FROM AUTHOR]

[Display omitted] This paper investigates the role of compositional complexity in the fracture behavior of a model quinary high entropy FCC alloy. The simulations are based on a multi-scale technique bridging continuum fracture mechanics with massively parallel molecular dynamics techniques at the atomistic level to study the deformation mechanisms. The atomistic part is based on empirical interatomic potentials and study the crack tip plasticity response for increasingly higher stress intensity factors. Crack blunting/propagation tests were performed and the material response analyzed using various techniques, focusing on the role that the local composition in the random alloy plays in the deformation mechanisms and the competition between dislocation emission from the crack tip and cleavage. Crack tip plasticity is studied in the complex alloy and in a corresponding "average atom" single component interatomic potential tailored to have the same average properties as the complex alloy but no local compositional complexity. Five different crystallographic orientations are studied and the complex high entropy alloy presents a higher fracture resistance than the average atom material for three of these orientations. The additional fracture resistance is shown to be due to enhanced dislocation emission from the crack tip and crack arrest in certain locations in the complex alloy system. [ABSTRACT FROM AUTHOR]

• The crack-inclusion interaction in one-dimensional orthorhombic and two-dimensional quasicrystal matrixes was studied based on the Eshelby's equivalent inclusion and phase transformation toughening theories. • The circular inclusions have shielding or amplification effects on cracks in the quasicrystal matrix. • The stress intensity factors and J-integrals at the crack tip are affected by inclusions, boundary conditions, and nonlocal parameters. • The existence of phason elasticity and coupling elasticity in the quasicrystal matrix can inhibit crack propagation, and the former has a greater effect on crack propagation than the latter. Quasicrystal (QC) materials are a type of innovative materials with long-range quasiperiodic translational symmetry and amorphous rotational symmetry. During the manufacturing process, various defects inevitably occur in QC materials. Therefore, studying the interaction between multiple defects and central cracks in QC materials can help reveal the fracture characteristics of defective materials. This study explores the interaction between a crack and a symmetrical-shaped inclusion in a QC medium with the nonlocal effect under the remote stress. Based on the transformation toughening and Eshelby's inclusion theories, we propose formulas for calculating the stress intensity factor caused by inclusions near the crack tip in QC materials. The finite element method is applied to verify these formulas where a crack occurs near a circular inclusion. The comprehensive numerical results show the remarkable shielding or amplification effect of inclusions on the crack tips in the QC matrix. In addition, the boundary conditions, size and shape of the inclusions, and the nonlocal effect all influence the stress intensity factor and J -integral. This study provides a reference for the design and evaluation of the QC composites with crack–inclusion interactions. [ABSTRACT FROM AUTHOR]

Structural integrity analysis for reactor pressure vessel (RPV) nozzles has been a vital issue due to the irradiation embrittlement and especially the discontinuity of geometry in RPV nozzles, which may cause a higher stress concentration and influence the structural integrity of RPV nozzles. For the linear elastic fracture mechanics (LEFM) analysis of the RPV nozzle, a postulated crack with a specific crack depth is presumed to evaluate the stress intensity factors (SIFs) whose crack depth does not grow during LEFM analysis. Thus, this paper would discuss the crack propagation for the postulated crack with a specific crack depth under the different reference temperature of nil-ductility transition (R T N D T ), and the SIFs on the specific crack depth are also calculated. In recent research, the extended finite element method (XFEM) was developed, which is based on the enrichment solution space to simplify the computational fracture mechanics with the crack propagation of various discontinuities, and can be used to evaluate the crack propagation of RPV nozzle with a specific crack depth under R T N D T of −23.89, −10.89, 0.89, 2.69, and 2.89 °C. To investigate the crack propagation and structural integrity of RPV nozzles, the finite element analysis of Taiwan domestic boiling water reactor (BWR) nozzles containing the postulated circular corner crack with depths of one-fourth and one-tenth thickness along the 45° path from the tip of the nozzle corner is engaged. The present result shows that the crack was growing when the R T N D T was 0.89 °C and. In addition, the XFEM calculation of the SIFs for the specific crack depth is similar to the LEFM results. • The RPV nozzles with postulated cracks were established to investigate crack propagation through XFEM. • The differences in RT NDT were used to evaluate the fracture toughness and discuss the crack propagation for RPV nozzles. • The stress intensity factors (SIFs) obtained by XFEM, LEFM, and the ASME BPVC were compared. • The XFEM analysis would overestimate SIFs more than the ASME BPVC and the LEFM. [ABSTRACT FROM AUTHOR]

This study proposes an effective method to determine the stress intensity factors (SIFs) of the interface crack considering the viscoelasticities of the bilateral materials and verifies the feasibility of the initial fracture toughness-based fracture criterion for the concrete-rock interface under sustained loading. Firstly, low-level sustained loading tests were conducted on the composite concrete-rock specimens with respect to two interface roughness degrees and two sustained load levels less than the initial cracking load. Then, an implicit creep equation was employed to characterise the viscoelasticities of bilateral materials and then calculate the mechanical responses of the concrete-rock interface in the low-level sustained loading test. The SIFs of the interface crack under sustained loading were determined by using the elastic strain energy density ahead of the crack tip. By averaging the SIFs over the radius of the core region of the crack tip, the representative SIFs under sustained loading were obtained. The test results indicated that the SIFs showed decreasing tendencies under sustained loading, and the initial fracture toughness can be considered as a material property of the concrete-rock interface. The initial fracture toughness-based fracture criterion was verified to be feasible to determine the initial cracking status of the concrete-rock interface under sustained loading. In addition, due to the reductions of the SIFs under sustained loading, additional loads were required to compensate the losses of the SIFs, leading to the enhancement of the initial cracking loads after experiencing the sustained loading. [ABSTRACT FROM AUTHOR]

One of the mechanisms of destruction of a solid is the formation and growth of "micro" and "macro" cracks. This task is especially acute for space objects. A microcrack in the body of the spacecraft practically does not affect its mechanical strength, but it can lead to depressurization of the body, which can lead to the loss of life support for the crew. Cracks can have different causes of their occurrence, but the mechanism of their growth in modern fracture mechanics is associated with the chosen criterion. For example, in the force criterion, crack growth begins when the stress intensity factors also reach a certain threshold critical value characteristic of a given material. This paper presents the results of calculating stress intensity factors for spatial branching cracks. The calculations were carried out on the basis of the original author's program, which makes it possible to determine the stress and displacement fields in a three-dimensional elastic body weakened by a system of arbitrarily oriented cracks. The program is based on the method of discontinuous displacements, implemented for three-dimensional problems of fracture mechanics in an elastic medium, implemented in C ++ codes. The main purpose of the work is to demonstrate the possibility of determining the stress intensity factors for a spatial branching crack and their dependence on the geometric parameters of the problem. • The propagation of branching cracks in structures is investigated. • The method allows determining the most probable branching angles. • Numerically developed stress intensity factors are in good agreement with analytical solutions. • Stress intensity factor depends on the nature of the applied load. [ABSTRACT FROM AUTHOR]

The present problem aims to study the scattering behavior of SH-waves by a circular cavity near two symmetrically permeable interface cracks in the piezoelectric bi-material half-space. The steady-state response of the problem is obtained, with the aid of the Green's function method and the complex function method. Above all, the essential expression of Green's function is constructed by the mirror method. This expression satisfies the conditions of being stress-free and electric insulation on the horizontal boundary of the orthogonal space where the circular cavity is located, and the condition of bearing a harmonic out-plane line source force on the vertical boundary. Next, on the basis of dividing the bi-material medium into two parts along the vertical boundary, the first kind of Fredholm integral equation with uncertain anti-plane forces is established by using the conjunction method and the crack-division technology. Then, the solution is obtained by solving an algebraic equation with finite terms, which is an effective truncation of the integral equation. Finally, the dynamic stress concentration factor around the edge of the circular cavity and the dynamic stress intensity factor at the crack tip are calculated numerically. On this basis, the effects of incident wave frequency, crack length, crack location and circular cavity position on the dynamic stress concentration factor and dynamic stress intensity factor are discussed. [ABSTRACT FROM AUTHOR]

The cutterhead of a tunnel-boring machine (TBM) is the main weighted part in the process of tunneling and bears loadings in different directions. A fatigue failure of a cutterhead would severely affect the construction progress and safety. Therefore, it is of great importance to study the fatigue reliability of its cracks. In this study, the area of the cutterhead with a higher stress was found using static strength analysis and we analyzed the dynamic stress characteristics. In addition, the stress intensity factor of a cutterhead crack was calculated using the submodeling technique, and the crack propagation mechanism and damage characteristics of a cutterhead crack were also analyzed. Then, combined with crack fatigue theory, we proposed a fatigue reliability evaluation method based on the Joint Committee on Structure Safety method (known as the JC method), and the effects of different factors on the reliability were discussed for different geological conditions. The results show that the crack propagation was of the open and tear types in the deepest part of the crack tip, but there are three kinds of propagation modes at both ends. As the initial crack depth increased, the fatigue reliability of the cutterhead decreased significantly. The reliability was positively correlated with the crack shape ratio. However, there were no significant relationships between the reliability and the depth of the critical crack. [ABSTRACT FROM AUTHOR]

Determining the stress intensity factor (SIF) for cracked engineering structures under different loading conditions is one of the core issues of fracture analysis. A slender fin-shaped shell possesses both shell and beam characteristics, in the cross section of which some complex cracks, such as the circumferential and T-shaped cracks, may arise. There will be different singular stress fields next to crack tips for a cracked fin-shaped shell under bending. Based on the conservation law and elementary mechanics, a technique to determine SIFs is proposed in this article, which is simple and easy to understand. The SIFs calculated using the present method agree well with FEM results even if elementary mechanics is used. [ABSTRACT FROM AUTHOR]

This paper introduces an analytical expression for the stress intensity factors at the crack tips of a row of periodic and collinear cracks between infinite dissimilar orthotropic materials. The analytical Jk‐integrals of these traction‐free cracks have been presented for different material combinations, 'crack length'/'interval width' ratios (λ) and various in‐plane loading conditions. Some of the analytical Jk‐integrals have been compared with the numerical values computed using the boundary element crack shape sensitivities which are in good agreement. For any in‐plane loading condition of a bimaterial plate with periodic and collinear interface cracks, the normalised J1‐integral is almost independent of λ, but there is a slight variation in the normalised J2‐integral with respect to λ. This is provided that the normalising factor is the strain energy release rate of a homogeneous plate made from one of the materials with the same ratio of λ and subject to the same loading condition. [ABSTRACT FROM AUTHOR]

Rolling contact fatigue failure is one of the main fatigue damages in railway wheels caused by cyclic rolling contact with rails. This fatigue failure is caused by internal defects such as nonmetallic inclusions or voids and may occur in heavy haul freight car wheels. The subsurface crack propagation behaviors caused by the internal defects are evaluated by twin-disc-type rolling contact fatigue tests using test specimens with artificial defects. Finite element analyses involving simulated rolling contact fatigue tests are also conducted. The subsurface cracks are more likely to propagate in the test specimens with larger artificial defects. Moreover, cracks initiating from the trailing side of the defects propagate faster than those from the leading side. Shear mode equivalent stress intensity factors obtained from the finite element analyses correspond well to the results of the rolling contact fatigue tests. The test specimen models with larger defects have larger equivalent stress intensity factor ranges than the test specimen models with smaller defects in both the leading and trailing sides. The results of the finite element analyses also suggest that the crack propagations are affected by the deformation of the artificial defects, which leads to higher resistance to crack propagation in test specimens with smaller internal defects. [ABSTRACT FROM AUTHOR]

During blasting construction in tunnel engineering, an inclined fissure near the blast hole produces the "Z" type of over-excavation and subsequently affects the overall blasting effect and stability of the tunnel. In this work, dynamic caustics testing was used to study the burst propagation mode and penetration form of explosive cracks at different positions between holes under double-hole blasting conditions. Results showed that the existence of gently inclined cracks changed the propagation law of explosive stress wave. The dominant fracture surface was formed in the vertical direction between the borehole and the fracture. Finally, the crack penetrates to form "Z"-type over-excavation, which was analyzed by the dynamic caustics test. The expansion velocity of the burst crack reached the maximum under the reflection of the explosion stress wave and then decreased with the attenuation of the stress wave intensity. The peak propagation velocity decreased with the increasing vertical distance between the prefabricated fracture and the borehole, and the stress intensity factor at the crack tip immediately reached its peak value after detonation, and the oscillation then decreased. These research results can serve a basis for reducing tunnel blasting over-excavation under this condition and optimizing blasting parameters. [ABSTRACT FROM AUTHOR]

An isolated ellipsoidal inclusion and an elliptical crack in a homogeneous elastic medium with ellipsoidal anisotropy are considered. For constant external stress (strain) fields applied to the medium, the solutions of these problems are reduced to calculation of 2D-regular integrals. For materials with ellipsoidal anisotropy, the integrand functions in these integrals can be presented in explicit analytical forms that simplifies substantially construction of the numerical solutions of the problems. The stress intensity factors at the crack edge are expressed in the forms of 1D-integrals which integrand functions have also explicit analytical forms for media with ellipsoidal anisotropy. [ABSTRACT FROM AUTHOR]

The problem of electric and stress state in a piezoelectric space with an arbitrary orientated elliptical crack under homogeneous force and electric loading is considered. The solution to this problem is obtained on the basis of the triple Fourier transformation and the Fourier transform of Green?s function for an infinite electroelastic space. Testing the approach against particular cases confirms its effectiveness. The numerical study is carried out, and the stress intensity factors along the elliptical crack front are studied for different crack orientations in the orthotropic electroelastic space under tension. [ABSTRACT FROM AUTHOR]

This review article briefly compiles data available in the literature on cases of stress corrosion cracking on carbon steels in the presence of environments containing CO2 from a corrosion point of view, seeking to clarify which main factors influence the crack nucleation and propagation. The aspects related to the stress intensity factor and fracture mechanics approach will not be discussed, as well as residual stresses, which are known to be determinant factors in the study of stress corrosion cracking and therefore deserve individual reviews. It will discuss stress corrosion cracking in high strength carbon steels with a brief description of this systems corrosion mechanisms under study and the main variables involved. Methods for assessing the susceptibility of materials to SCC will also be addressed in the form of results obtained by other authors. Also, it seeks to warn about the care in dealing with the subject, given the variation of parameters in the environment that are influential in the outbreak and spread of the phenomenon. Finally, tests will be commented on to verify the susceptibility to the phenomenon and a brief description of the known cracking mechanisms. [ABSTRACT FROM AUTHOR]

• Influence of plastic material properties on fracture resistance parameter is analyzed. • Mechanism-based strain-gradient plasticity theory, Taylor dislocation model are used. • Amplitude and stress intensity factors for strain gradient plasticity are formulated. Behavior of strain gradient plasticity SIFs differs significantly from HRR solution. The crack tip mechanics of strain gradient plasticity solids is investigated analytically and numerically. A first-order mechanism-based strain gradient (MSG) plasticity theory based on Taylor's dislocation model is adopted and implemented in the commercial finite element package ANSYS by means of a user subroutine. Two boundary value problems are considered, a single edge tension specimen and a biaxially loaded plate. First, crack tip fields are characterized. Strain gradient effects associated with dislocation hardening mechanisms elevate crack tip stresses relative to conventional plasticity. A parametric study is conducted and differences with conventional plasticity predictions are quantified. Moreover, the asymptotic nature of the crack tip solution is investigated. The numerical results reveal that the singularity order predicted by the first-order MSG theory is equal or higher to that of linear elastic solids. Also, the crack tip field appears not to have a separable solution. Moreover, contrarily to what has been shown in the higher order version of MSG plasticity, the singularity order exhibits sensitivity to the plastic material properties. Secondly, analytical and numerical approaches are employed to formulate novel amplitude factors for strain gradient plasticity. A generalized J -integral is derived and used to characterize a nonlinear amplitude factor. A closed-form equation for the analytical stress intensity factor is obtained. Amplitude factors are also derived by decomposing the numerical solution for the crack tip stress field. Nonlinear amplitude factor solutions are determined across a wide range of values for the material length scale l and the strain hardening exponent N. The domains of strain gradient relevance are identified, setting the basis for the application of first-order MSG plasticity for fracture and damage assessment. [ABSTRACT FROM AUTHOR]

These pressure vessels are made by different type of heads. One of them is hemi-spherical head. The area of geometrical discontinuity, like the connection of the cylinder to its hemi-spherical head, are the most susceptible areas for crack initiation along their welds. So it is worthwhile to consider cracks located at this connection. The purpose of this article is to investigate the effect of variation of stress field and geometry of problem on distribution of Stress Intensity Factor (SIF) for a semi-elliptical surface crack which is located at the connection of cylinder to its hemispherical head. The three dimensional finite element analysis is performed by employing singular elements along the crack front. The ratio of crack depth to crack length (a/c) ranged from 0.3 to 1.2; the ratio of crack depth to wall thickness (a/t) ranged from 0.2 to 0.8; and the cylinder geometry parameter of vessel γ = R0/Ri ranged from 1.2 to 2. For better comparison the results are normalized and reported in non-dimensional formats. The results show that the crack configuration, vessel thickness and radius have significant influence on the stress intensity factor distribution along the crack front. Also For a fixed R0 / Ri1.5 and a/t = 0.4 the maximum value of SIF occur in the cylindrical part and approximately near the deepest point of crack; not on the deepest point of crack depth and this may be due to changing stress field in this connection. The stress intensity factors are presented in suitable curves for various geometrical configurations providing useful tool for the fracture mechanics design of cracked pressure vessels. [ABSTRACT FROM AUTHOR]

This paper introduces an approximation method developed for calculating stress intensity factor for pressure vessels in nuclear power plants. The method is based on weight functions, which has high accuracy among the methods based on crack-free stress calculations. Besides it has the advantage over the weight functions method, it corresponds to the approximation methods can be found in nuclear codes like ASME BPVC [1]. Numerical test calculations are performed to experimentally show the differences of several possible approximation methods. The results show the weighted least squares method using stress intensity factor weight functions, do have the above-mentioned advantages. [ABSTRACT FROM AUTHOR]

The Timoshenko interdependent interpolation element, based on the assumption of cubic interpolation for the transverse displacement and quadratic interpolation for the rotation, is developed for both the static and the dynamic problems. Next, the different behavior of a beam due to the presence of a damaged zone is investigated and the problem of identifying diffused crack affecting a portion of the beam using natural frequencies is studied. The damaged zone can be completely taken into account by introducing only three parameters, and for the inverse problem, numerical optimization is applied to define their values. [ABSTRACT FROM AUTHOR]

This paper is focused on the interaction of surface cracks of an egg-shaped pressure shell of manned deep-sea submersibles. The surface cracks of the egg-shaped shell were subjected to the combined action of uniform external pressure and welding residual stress. The stress intensity factors were calculated using the M-integral method as an important parameter to characterize the stress and displacement fields in the vicinity of crack tips. The study is to evaluate the influence degree of the disturbing crack on the main crack and investigate the interaction between multiple cracks. The results provide references for optimizing the design and manufacture of egg-shaped pressure shells. [ABSTRACT FROM AUTHOR]

The linear amplitude sweep (LAS) test has been widely accepted for estimating the fatigue resistance of asphalt binders in the last 10 years. This paper proposes a fracture mechanics–based analytical approach for crack initiation and propagation characterization in the LAS test, aiming to more precisely explore the binder crack growth and failure mechanism. Seven unmodified neat asphalt binders and one styrene-butadiene-styrene (SBS) polymer-modified binder are selected in this study. The crack length (a), rate of cracking (da/dN), stress intensity factor (K), and energy release rate (G) are the fundamental parameters for the data interpretation approach proposed in this paper. Experimental and analysis results demonstrate that the energy-based failure definition (either from continuum damage mechanics or fracture mechanics) should be utilized to detect the material-dependent failure occurrence in LAS test. The fracture behavior of asphalt binder in the LAS test follows the two-phase crack growth (TPCG) model in terms of the crack initiation and crack propagation. The crack propagation phase further consists of stable crack growth and unstable crack growth. It is found that the fatigue performance of asphalt binder is intrinsically governed and dominated by its resistance to the crack propagation. The SBS binder in this study clearly displays slower crack propagation behavior than other neat binders. Additionally, the traditional fatigue life can also be divided into the crack initiation life and crack propagation life, which is promising to clarify the specific modification contribution to binder fatigue resistance. The two critical crack lengths of initiated crack and propagated crack for a given asphalt binder are found to be correlated to each other, indicating the potential links between the binder crack initiation and propagation behaviors. [ABSTRACT FROM AUTHOR]

Many studies exist on carbon fiber-reinforced polymer (CFRP) strengthening of cracked steel details (e.g., cracks in riveted or welded bridge connections). The majority of these studies used CFRP sheets without prestressing. The efficiency of such systems for fatigue strengthening is often limited because the high strength of CFRP materials is not utilized under service loads. However, prestressing small CFRP sheets is very difficult and requires hydraulic jacks and mechanical clamps, which makes the strengthening process very complicated or even impossible. Therefore, in this study, NiTi shape memory alloy (NiTi-SMA) wires and CFRP sheets were used to produce a heat activated prestressed SMA-CFRP composite patch. This composite patch offers both the benefits of the prestress of SMA and the high elastic modulus of CFRP. The proposed patch is relatively small (300 × 45 mm) and can be prestressed, which makes it a good solution for the strengthening of cracked bridge connections, for example, welded connections. In this study, the composite patch is used to enhance the fatigue performance of central cracked steel plates. Because the SMA wires were small (1 mm in diameter), firstly 45 SMA wires were converted into a sheet of SMA strands and then embedded into multiple CFRP layers, forming an SMA-CFRP composite patch, which offers an easy manufacturing process. Eight central cracked steel plates were tested under cyclic loading. For the specimens strengthened by prestressed SMA-CFRP composites, the fatigue lives were extended to 2.7 times (with normal modulus CFRP) and 6 times (with high modulus CFRP), respectively. A finite element (FE) simulation was employed to better understand and interpret the test results. The decreased effective stress intensity factor (SIF) range was the reason for the prolonged fatigue life of the cracked specimens. [ABSTRACT FROM AUTHOR]

Purpose: The aim of the proposed research is to create a calculation model of surface fatigue crack growth at the axle of railway wheelset working under operational loads. Design/methodology/approach: The energy approach of the fracture mechanics was used to formulate the calculation model of fatigue crack propagation at the wheelset axle surface. The method of least squares was used to determine the investigated material mechanical constants that the kinetic equations of the calculation model contain. The system of differential equations of crack growth kinetics was solved numerically using the Runge-Kutta method. Findings: On the basis of the energy approach of the fracture mechanics the calculation model of fatigue macrocrack growth in three-dimensional elastic-plastic body in case of a mixed-mode I+II+III macromechanism of fracture has been built. On the basis of the created calculation model, the kinetics of the growth of fatigue cracks was investigated both in the middle part of the wheelset axle and in the axle journal. Research limitations/implications: The results obtained on laboratory specimens should be tested during a real railway wheelset axle investigation. Practical implications: The created calculation model can be used in practice to formulate method of residual lifetime estimation of railway wheelset axle. Originality/value: It was shown, that surface crack kinetics depends not only on the crack initial area but also significantly depends on the crack edge geometry and comparatively small crack-like defects at the wheelset axle surface can reach critical sizes in comparatively short run. It has been found that mechanical shear stresses caused by the weight of the loaded railway wagon in the cross section of the wheelset axle journal can significantly accelerate the growth of the transverse fatigue crack at the axle surface, reducing the period of crack subcritical growth by about 20%. [ABSTRACT FROM AUTHOR]

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A new method for increasing the interface resistance between geopolymer coating and concrete lining structure without applying the organic binder was suggested in this study. Parallel grooves with different depths and orientations were milled on the top surface of concrete block, and well-blended geopolymer mixture (Na-PSS type geopolymer: Sodium poly-sialate-siloxo) was coated upon the grooved interface. The wedge splitting (WS) experiments were conducted to compare the interface adhesion capacity of specimens with different groove width/depth ratios and groove orientations. The average energy release rate (ERR) was calculated by integrating the Pv-CMOD diagram to quantify the interfacial fracture toughness. To understand the interface strength mechanisms and the fracture mode at the front crack mouth, franc 3D simulation was carried out to segregate the mixed fracture mode to determine the initial pure stress intensity factors K I , K II , K III at the crack mouth. Both the experiments and simulation results indicated that the highest interface fracture toughness was reached by the double diagonal parallel grooves with 0.375 width/depth ratio. These findings put forward a promising attaching method for efficient and reliable passive fire protection coating, with the aim of decreasing the risk of layer delamination in highway tunnels. [ABSTRACT FROM AUTHOR]

Solid solution strengthening plays a key role in the strength increasing of alloying metals, due to that a solid solution of alloying element causes lattice distortion to a certain extent. In the paper, the effect of solid solution magnesium additions on the edge dislocation emission from a blunted crack tip in aluminum alloys is investigated. The critical stress intensity factor for the dislocation emission considering different magnesium solute concentrations is analyzed under the mode I and mode II loading conditions. The results show that within a certain concentration range the magnesium solute concentration does affect dislocation emission, although the influence appears not very strong. The critical stress intensity factor for the dislocation emission decreases with the increment of solute concentration. This means that relatively increasing the solute concentration can promote the dislocation emission, cause effective blunting of cracks and thus improve the fracture toughness of materials. [ABSTRACT FROM AUTHOR]

The accuracy measurement of rock fracture toughness is one of the basic tasks of rock fracture mechanics. In order to study the influence of the width of the prefabricated crack on the fracture toughness of rock, the failure process of notched semi-circular bend (NSCB) specimens with four sizes and five different width of the prefabricated crack was studied by experimental and numerical methods. The influence of the width of the prefabricated crack on the peak load, crack initiation position, dimensionless stress intensity factor and fracture toughness is analyzed and discussed. The results show that the peak load and fracture toughness of NSCB increase with the increase of the width of the prefabricated crack, and the smaller the specimen size is, the larger the increase is. When the width of the prefabricated crack is less than 1.3 mm, the crack initiates at the dichotomy of the prefabricated crack tip; when the width of the prefabricated crack is greater than or equal to 1.3 mm, the crack initiates near the corner of the prefabricated crack tip. If NSCB specimen is adopted to determine the fracture toughness of limestone, it is recommended that the width of prefabricated crack should be less than 1.3 mm. The conclusions provide a reference for the fabrication of NSCB specimens and the accurate measurement of limestone fracture toughness. [ABSTRACT FROM AUTHOR]