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]

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]

[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 static behaviour of notched PPS/GF specimens was investigated. • V-shaped notched specimens were manufactured and tested. • Different notch root radii and manufacturing processes were considered. • Different approaches for the static strength assessment were compared. In this paper the static behaviour of polyphenylenesulfide reinforced by 40% wt. short glass fibre net-shaped plain and notched specimens was investigated. The specimen geometries were obtained by injection moulding and the experimental results were compared with data obtained from machined specimens with the same material and geometries. All data were reanalysed according to several models available in the literature for orthotropic materials, to find a rapid and efficient assessment tool for predicting the strength of short glass fibre reinforced materials in the early design stages. To this end, approaches based on orthotropic linear elastic stress analysis were considered, namely the linear elastic peak stress criterion, the nominal net-stress criterion, the point stress criterion, the average stress criterion, the strain energy density criterion, the generalized stress intensity factor-based approach, the inherent flaw model, the damaged zone criterion and the Hitchen criterion. Among the models, the average stress criterion and the generalized stress intensity factor-based approach provided the most accurate predictions of the static strength, ranging from −10% to +9% and from −19% to +2%, respectively, compared to the experimental data. [ABSTRACT FROM AUTHOR]

• The full Stokes parameters can be obtained from a single image instantaneously using a camera equipped with microreaders. • The distributions of the isochromatic and isoclinic parameters as well as their time variations can be measure by the proposed instantaneous phase-stepping photoelasticity. • The crack tip stress fields are obtained by analyzing the stress intensity factors and T-stresses from the measured principal stress difference. • Time-variations of the stress intensity factors and the T-stress explain the complicated oscillating crack growth behavior. A method for analyzing the phase of photoelastic fringes by polarization image analysis using the camera equipped with a pixelated microretarder array is described. Unlike the conventional phase-stepping method, this method does not require multiple images to be acquired and can analyze problems that vary from moment to moment. Therefore, this method can be applied to viscoelastic problems, crack propagation problems, and other problems involving variation with time. [ABSTRACT FROM AUTHOR]

Fretting fatigue pertains to the behaviour of engineering components undergoing cyclic loading while in contact with each other. This intricate contact-related phenomenon often results in premature failure compared to conventional fatigue issues. Moreover, when these components operate in high-temperature atmospheres and experience high wear conditions, such as the heat transfer tubes in the nuclear reactor, the application of Functionally Graded Material (FGM) coatings becomes essential. Consequently, it is imperative to investigate how FGM coatings influence the initiation and propagation behaviour of fretting fatigue cracks. This paper employs the Critical Plane (CP) method to calculate the damage parameter. Additionally, Linear Elastic Fracture Mechanics (LEFM), specifically the Extended Maximum Tangential Stress (E-MTS) criterion, is utilized to examine how FGM coatings affect the paths of fatigue crack propagation in the presence of fretting conditions. Meanwhile, due to the unavailability of material properties of FGM coatings, the damage parameter and stress intensity factors are utilized to indirectly assess the effect of FGM coatings on crack initiation and propagation lifetimes. The FGM coating significantly influences tangential stress, thereby affecting the length of the stick zone, while having minimal impact on the distribution of normal stress along the contact surface. Furthermore, it is observed that adjusting the variation in composition of FGM coatings and the elastic modulus of the first FGM coating layer provides a potential technique for enhancing both crack initiation and propagation lifetimes. [ABSTRACT FROM AUTHOR]

• The FEA was performed on orthotropic CTS specimens to evaluate SIFs and compliance. • Impacts of three commonly used boundary conditions of CTS models were evaluated. • Coupled effects of crack length, loading angle, and material orthotropy on fracture parameters were revealed. • CTS tests of composite were conducted to measure mixed-mode fracture toughness. • The results will aid in standardizing orthotropic CTS fracture toughness test. Conducting Compact-Tension-Shear (CTS) tests emerges as a promising research methodology to determine the fracture toughness of orthotropic materials in mixed-mode I&II. However, the absence of pertinent fracture parameter solutions incorporating material orthotropy impedes the further application and standardization of CTS testing. Therefore, this study performed a systematic two-dimensional finite element analysis (FEA) on orthotropic CTS specimens to evaluate critical fracture parameters, including the normalized stress intensity factors (Y I , Y II) and compliance (u). First, the impacts of three commonly cited boundary conditions (BCs) of CTS models were investigated, revealing that the simplified or equivalent methods developed for isotropic CTS models are no longer applicable. Subsequently, the suitable CTS models were used to analysis the coupling effects of material orthotropy (λ , ρ), crack length ratios (a / W), and loading angles (β). Findings indicated that Y I or u no longer exhibit a monotonic relationship with respect to a / W or β under strong orthotropy. The impact of λ and ρ on fracture parameters is equally significant across different geometries and loading conditions. Further, the impact of orthotropy on Y II is relatively small, while the more affected Y I may have a difference compared to isotropic results of over 80%. Finally, CTS tests were carried out on the unidirectional carbon fiber-reinforced epoxy resin composite measuring the fracture toughness in mixed-modes I&II. The obtained fracture parameter solutions were applied and validated during the process. The acquired results are poised to contribute to the advancement of fracture toughness testing standardization for orthotropic materials under mixed-mode loading. [ABSTRACT FROM AUTHOR]

• Deriving/estimating plain strain fracture toughness for ASTM A322 material. • Developing flaw tolerance limit plots for ASTM A322 and ASTM A722 material. • Estimating remaining service life of existing post-tension grouted anchors. Brittle failure of grouted post-tensioned anchors used in trunnion girders at dams has given rise to concerns and questions surrounding their continued use and remaining service life. This paper reviews the brittle failure of five grouted post-tensioned anchor rods due to stress corrosion cracking at dams in California. To provide an early warning system to dam owners and expand on available resources for practicing engineers, this study derives plain strain fracture toughness from the failed grouted post-tension anchors using cross sectional photos. Using derived and available fracture toughness values, flaw tolerance limit plots, which can quickly illuminate the severity of a defect for various anchor diameters, were developed for semicircular and straight fronted flaw types using linear elastic fracture mechanics and stress intensity factors for both ASTM A322 and ASTM A722 materials. To help demonstrate the use of flaw tolerance limit plots and estimate the remaining service life of an in-situ anchor, an example problem was developed. [ABSTRACT FROM AUTHOR]

Hydrogen-induced cracking or embrittlement can have a substantial and severe impact on the fatigue life of large austenitic stainless steel hydrogen storage pressure vessels. In this study, a dynamic model for the plastic zone in the crack tip considering the hydrogen diffusion was established and a correction factor for the stress intensity factor of the hydrogen storage pressure vessel was proposed for 316L stainless steel, which is commonly used pressure vessel material. The crack propagation characteristics and fatigue life of the stainless steel vessel were investigated. The results indicated that the shortest fatigue life under hydrogen pressure occurs at the intersection of the vent nozzle and the vessel head. The hydrogen environment not only reduces vessel service life but also makes the influence of pressure on cracks propagation more pronounced. It leads to a significant reduction in the fatigue life of pressure vessels when overpressure happens during operation. These research findings are valuable for the accurate assessment of the vessel fatigue life and improving the quality of large hydrogen storage vessel structures. • A revised stress intensify factor for hydrogen storage pressure vessel was proposed. • The influence of vessel's working pressure and structure on its service life was studied. • Cracks with fatigue life most affected by the pressure in the hydrogen environment were found. • The vessel's fatigue life considering the influence of hydrogen diffusion was obtained. [ABSTRACT FROM AUTHOR]

Weibull stress-based methods for failure probability assessment have been developed and analyzed to assess the integrity of tristructural isotropic (TRISO) fuel particles during fuel life cycles and accident operating conditions. While simple, these methods entail a number of drawbacks when stress concentrates near crack tips, including finite element mesh size dependency when the Weibull stress is averaged over the finite element domain. Fracture mechanics approaches involving the use of interaction integrals eliminate this lack of mesh convergence and produce consistent fracture predictions. In this work, we use an interaction integral approach to computing stress intensity factors for a crack in the inner pyrolytic carbon layer perpendicular to the silicon carbide layer, which is simplified representation of a failure mode in TRISO particles. The interface between these two TRISO layers has been shown to become porous, which we simulate by considering a transition of mechanical properties over such porous length, i.e. the layers are modeled as a functionally graded material. Aspects such as porosity and thermal and irradiation eigenstrains are considered in computing the stress intensity factor from a fracture mechanics approach and compared with the known Weibull stress failure approach. The methodology introduced in this paper enables a more general fracture probability assessment in TRISO particles and eliminates the need to identify best suited parameters when using local or averaged stress-based failure criterion. Finally, the numerical sensitivity studies show how parameters such as the porous transition zone length, the material stiffness, and creep affect the probability of TRISO fuel particle failure. [ABSTRACT FROM AUTHOR]

Rib-to-deck welded joints are among the most susceptible to fatigue in orthotropic bridge decks (OSDs). Prior research has primarily examined the stress intensity factor (SIF) and propagation morphology of a solitary fracture at these joints, allocating limited attention to the investigation of the propagation of multiple cracks. This paper presents a methodology for simulating and computing the weld toe magnification factor and the SIF of semi-elliptical surface cracks in innovative double-sided welded rib-to-deck (DWRTD) joints. The intention was to simplify the calculation of the SIF for this fatigue detail. The SIF obtained from the calculation model in combination with a multiple crack coalescence approach resulted in a series of fatigue life prediction models of multiple co-planar semi-elliptical cracks. Compared with the results of fatigue tests on the DWRTD joints, the calculated fatigue life and propagation morphology of multiple cracks from the model showed good agreement. Finally, the parameters were analysed to investigate the effects of crack number, bridge deck thickness, residual stress, and penetration rate. Compared to a single crack, multiple cracks reduced the service life of the bridge deck by approximately 30%. When the bridge deck thickness increases from 12 mm to 20 mm, the nominal stress amplitude near the weld ∆ σ decreases by 2.2 times, resulting in a 7-fold increase in crack propagation time. Compared to penetration rate and residual stress, ∆ σ is the most crucial factor affecting fatigue propagation life. Therefore, it is suggested to increase the thickness of the bridge deck during design. • A fatigue propagation life prediction model is developed for multiple cracks in rib-to-deck joints. • Clarified the effects of multi-crack propagation on fatigue life and experimental validation. • Parametric analysis is carried out to propose suitable dimensions for rib-to-deck joints of the OSDs. [ABSTRACT FROM AUTHOR]

This study presents normalized three-dimensional mixed-mode stress intensity factor (SIF) distributions for inclined surface cracks in finite-thickness plates under uniaxial tension. Inclination angle, aspect ratio and ratio of crack depth to plate thickness were chosen as variable parameters affecting the problem. Mixed-mode SIFs distributions are given comparatively with independent graphs for different combinations of parameters and their effects are also examined separately. The results indicate that at a constant ratio of a/c , magnitude of the normalized mode-I SIF increases with increasing ratio of a/t and decreases with increasing inclination angle, while mode-II and mode-III SIFs increase up to a specific value of inclination angle and decrease afterwards. Having compiled an extensive solution library of mixed-mode SIFs, as functions of the aforementioned parameters, regression-based equations are also generated for the crack front's free surface and deepest penetration points. It is also presented, using the principle of superposition, that the given solutions can be used for inclined surface cracks in thin-walled plate structures, such as thin-walled cylindrical pressure vessels, ship and other marine structures subjected to biaxial uniform tensile loading. • Main parameters included are; crack inclination angle, crack aspect ratio and ratio of crack depth to plate thickness. • Equations are developed for normalized mixed-mode SIFs in terms of parameters defining the problem. • Results from equations show excellent agreement with those from independent validation analyses. • Assessments of stress intensity factors for arbitrary values of parameters can accurately be made. [ABSTRACT FROM AUTHOR]

• A unified SIF range is proposed to include stress ratio effects, with physical significance and experimental validation. • It is found that Paris exponents could be related to dislocation nucleation, glide velocity and crack tip shielding. • The relationship between coefficient C and exponent m in Paris law emerges naturally from our simulations. The Paris law has been broadly employed to describe fatigue crack growth (FCG) at steady state. It establishes the relationship between FCG rate and stress intensity factor (SIF) range. However, its physical insight remains an issue of controversy. The study aims to employ dislocation dynamics to explore two aspects associated with the Paris law: how does the stress-ratio affect the application of the Paris law? What is the microcosmic mechanism behind the Paris exponent in Paris law? We limit our exploration on the scenarios that dislocation nucleation and dislocation glide dominate FCG in an ideally isotropic single crystallite. Our exploration revealed that (1) a unified SIF range without empirical parameters could be adopted to account for the stress ratio effect, and this observation is in line with existing experiments, and (2) SIF affects FCG by influencing the nucleation of dislocation sources and activity of dislocations before crack tips. The stress-dependent dislocation nucleation time is correlated with the exponent of the Paris law. [ABSTRACT FROM AUTHOR]

Slow crack growth (SCG) plays an important role in the fracture of ceramics and glasses. A full understanding of the long term reliability of ceramic components therefore requires knowledge not only of fracture toughness (K c) but also characteristics of SCG such as the threshold stress intensity factor (K 0) of individual microstructural features. Previous investigations have been limited by the small scale of the microstructure and low crack growth rates involved. Here, the stress intensity factors for crack propagation K p in sapphire were measured continuously under stable crack growth using chevron-notched microcantilevers, in air and in vacuum. K p in vacuum was considered close to the fracture toughness K c , with a value of 2.8 ± 0.1 MPa m1/2 for the a-plane of sapphire. K p in air at 54 % relative humidity was reduced substantially by moisture-assisted SCG to around 1.7 MPa m1/2 and, with crack velocities of ∼20 nm/s, was considered to be close to K 0. Cyclic loading in vacuum enabled quantitative measurements to be made during repeated crack growth and healing for the first time. Cracks healed up along their full length when unloaded but exhibited severe degradation of toughness on reloading. The toughness fell from 2.8 MPa m1/2 on the a -plane of pristine sapphire to 1.6 MPa m1/2 after one healing cycle and to successively lower values after further cycles. This technique offers a powerful method of investigating SCG and crack healing at the microstructural scale in different environments, with greater accuracy and on shorter timescales than can be achieved in macroscopic tests. [Display omitted] [ABSTRACT FROM AUTHOR]

Based on the theory of elastic fracture and using direct modeling method, a numerical model was developed for solving the composite stress intensity factor of semi-elliptical cracks on exchanger outer walls with inclined angles. The model exchanger had an outer diameter of φ50 mm, inner diameter of φ44 mm and length of 300 mm. The values of crack plane inclination β (0°, 10°, 20°, 30°, 40° and 45°), crack depth a (0.5 mm, 0.75 mm, 1 mm and 1.25 mm), and crack shape ratio a / b (0.4, 0.5, 0.55, 0.6, 0.7, 0.8, 0.9 and 1.0) were obtained and 3D surface crack model was established. The results were significance for the evaluation of the remaining life of exchanger components. [ABSTRACT FROM AUTHOR]

[Display omitted] • Dissimilar joints of aluminum to steel exhibited high static and fatigue properties. • A method was developed to compare fatigue properties of various dissimilar joints. • Static fracture energy was promising to predict the dissimilar joint fatigue property. • Stress intensity factors were used to explain the transition in fatigue failure mode. • High cycle fatigue was not strongly affected by brittle Fe-Al intermetallic layer. Lightweight structures made of aluminum alloys and high strength steels are increasingly used for improving vehicle fuel efficiency. One barrier for joining aluminum and steel is the formation of brittle Fe-Al intermetallics that can have deleterious effects on joint ductility and strength under static loading conditions. However, it is unclear how the intermetallics affect the joint fatigue properties. In this study, the effect of intermetallics on fatigue properties of dissimilar metal joints between a 6xxx aluminum alloy and a high-strength steel is investigated on welds created by ultrasonic interlayered resistance spot welding (Ulti-RSW). Joint efficiency calculations are used to normalize the peak load so the fatigue properties of Ulti-RSW are compared with a wide range of joining processes in the literature. During fatigue testing the failure mode transitions from interfacial or button pull-out failure during low cycle fatigue loading (below 100,000 cycles) to through-thickness failure during high cycle (above 100,000 cycles). Based on the stress intensity factors calculated using a simple 2D fracture mechanics model, the transition in failure mode is attributed to the plastic deformation near the notch tip. Overall, this study shows that the intermetallics have little effect on the high-cycle fatigue properties of dissimilar spot joints. [ABSTRACT FROM AUTHOR]

• Closed-form solutions for SIFs of DECBD specimens were derived considering crack surface friction. • Load distribution angle affecting the SIFs was proved to be negligible when α ≥ 0.60. • Mode II SIF decreases with increasing friction coefficient for DECBD specimens. The weight function method was employed to derive the closed-form solutions of stress intensity factors (SIFs) for double-edge cracked Brazilian disk (DECBD) specimens subjected to parabolic distribution loads, taking into account the influence of crack surface friction. Additionally, the accuracy and validity of these solutions were discussed in comparison with previous numerical results. Furthermore, the impact of friction coefficient and load distribution angle on SIFs was further investigated. The results indicate that the effect degree of load distribution angle on SIFs is closely correlated with both the loading angle θ and crack length α. Both the mode I and mode II SIFs increase with increasing load distribution angle γ for θ = 15° and α < 0.4. However, when α ≥0.60, the impact of load distribution angle γ on SIFs becomes negligible. Furthermore, the friction between crack surfaces of DECBD specimens significantly affects the dimensionless mode II SIF Y II , leading to a decrease in dimensionless mode II SIF Y II as the friction coefficient μ increases. Moreover, it further demonstrates that both the relative crack length α and friction coefficient μ play important roles in determining the critical loading angle θ IIc for crack sticking. The critical loading angle θ IIc for crack sticking increases with an increasing relative crack length; however, an increase in the friction coefficient leads to a reduction of this critical loading angle θ IIc. [ABSTRACT FROM AUTHOR]

This paper introduces a novel method for assessing fracture mechanics parameters such as Stress Intensity Factor (SIF), Energy Release Rate (J) and Crack Tip Opening Displacement (CTOD). An electromagnetic–mechanical coupling (EMC) approach is employed to evaluate and to measure these fracture parameters by monitoring the variation of impedance using eddy currents. This approach relies on the eddy current signal obtained from a sensor, which calculates and verifies SIF parameters along with the J-integral and CTOD through changing the sensor impedance. To ensure theoretical consistency, the magnetic field is theoretically used, formulated and verified. Additionally, a numerical simulation method employing the finite element method is used to analyze and identify cracks in structures and assess their propagation. The quantification of SIF and J-integral parameters is demonstrated using two sensors based on a differential probe. This research paper demonstrates that the proposed method is the most efficient approach for exploring and detecting cracks in materials, as well as understanding their propagation behavior. [ABSTRACT FROM AUTHOR]

One of the goals of fracture mechanics in the analysis of problems involving cracks is to investigate crack growth and propagation. Each crack grows and propagates in the environment based on its geometry and loading conditions, which can occur under pure mode or a combination of modes. The growth and propagation pattern of the crack in these conditions aligns with the fracture mode. In the presence of multiple cracks in the environment, the growth and propagation paths of these cracks differ from the isolated crack case, where they can either grow independently under certain conditions or merge together. Nowadays, extensive research has been conducted on cracks and their mathematical relationships with respect to the geometry and loading conditions of various components. Since in many cases, a large number of cracks may occur in proximity to each other, the intensification and protective effects of each crack on others and their impact on the overall behaviour of components are of great importance. This study focuses on investigating the behaviour of interaction and the stress intensity factor for an infinite plate with parallel adjacent cracks. Remote stress boundary conditions in the form of tensile and compressive stresses have been applied to this plate, and using the J-integral and the finite element method with the Abaqus finite element analysis software, this subject has been examined. The obtained results indicate that depending on the type of vertical and horizontal distances and the angle of their placement between the adjacent crack and the main crack in the first, second, and mixed modes, the adjacent crack can have intensifying, protective, or neutral effects. Furthermore, a good estimation of the secondary crack's influence on the main crack has been provided using a neural network method (MLP), which creates an appropriate weight function for the upcoming sample. [ABSTRACT FROM AUTHOR]

[Display omitted] • Mixed-mode I&II FCG tests are conducted on 16MND5 steel using CTS specimens. • Crack driving force and crack closure both have significant impacts on the FCG curves. • Fatigue fractography reveals similar microscopic features in the Paris region for all CTS tests. • A unified method for characterizing FCG rates is developed. Although numerous fatigue crack growth (FCG) tests have been conducted, the conclusions drawn regarding the mixed-mode FCG rate are inconsistent and even contradictory. A reasonable conjecture is that crack driving force and crack closure effects may play a crucial role in causing this situation. In this paper, the 16MND5 steel, commonly used reactor pressure vessel (RPV) steel, was employed to investigate the mixed-mode I&II FCG behaviors through the compact-tension-shear (CTS) experiments. The influence of crack driving force and crack closure effect was analyzed and discussed. The results show that the crack propagation path tends to maximize the tangential stress component at the crack tip, and the effect of Δ K II can be negligible once the Paris region is reached. Moreover, when considering the crack closure corrected Δ K I , named Δ K I eff , all the FCG rate data under different loading conditions can be collapsed into a narrower band of distribution. The premise for arriving at this result is to use the stress intensity factors solution that are applicable to specimens with real slanted propagating cracks, rather than applying equivalent methods based on single-edge straight crack assumptions. Finally, the fatigue fractography further confirms that the FCG mechanism during the Paris region all follow a similar quasi-mode I behavior. [ABSTRACT FROM AUTHOR]

The study focuses on the stress intensity correction factor (M k) for internal surface cracks located at the girth pipe root toe. To assess the impact of various parameters on M k , three-dimensional finite element models are developed. These models take different types of misalignment, a range of variable-wall-thickness ratios, and initial crack depths into account. The findings reveal that the stress intensity correction factor M k tends to increase with the rise in misalignment and variable-wall-thickness ratio. Conversely, an increase in the initial crack depth leads to a decrease in M k. The study demonstrates that the M k values, when accounting for different geometric factors, are significantly higher than those calculated using BS 7910. This suggests that the BS 7910 standard may provide overly optimistic predictions. As a result, a revised M k formula is proposed, which generally maintains an error margin of less than 10 %. This modified formula offers a significant enhancement to prevailing codes and standards, furnishing a more dependable benchmark for the assessment of structural integrity in pipeline laying procedures. • Sophisticated models of the root toe considering different geometric parameters are established to study the K. • Different geometric parameters exert distinct impacts on the stress intensity factor K. • An enhanced M k formula is derived and the conservative property of the existing M k formula is proved. [ABSTRACT FROM AUTHOR]

The existence of crack groups in structures is objective and inevitable during the process of manufacture and service. In this paper, the interactions between penetrating parallel double cracks are systematically investigated through finite element methods, experimental studies and theoretical analyses, where both the brittle dominant and ductile materials are taken as the research objects. The interactions between cracks are discussed through the interference factors C based on stress intensity factor K , which is related with the relative distance between crack tips. It is found that the fracture behaviors of multiple cracks are associated with all the interference factors at four crack tips. For the alignment double crack, shielding effects at all the crack tips cause the mutually exclusive crack propagations, and then strengthen the critical load of the specimen. For offset double cracks, the inner crack extension directions are attracted to each other, the outer crack extension directions are repelling each other, the critical loads depend on the degree of the attraction or the repelling effect. There exists a relationship between the comprehensive interference factor with all the crack tips included and the loading capacity. For the specimen with multiple surface cracks, the interference effects are also related with the relative distance between crack tips, through which it can be preliminary obtained that the regulations and the effect to the fracture behaviors are similar to those of penetrating cracked specimen, which will be discussed in detail in our next findings. The interference behaviors and critical loads of multiple cracks discussed above also provide an important basis on the coalescence and evaluation of multiple cracks. • Interferences factor based on K is proposed to describe the interference effects at crack tips, which is mainly dependent on the relative distance between crack tips, for specimens with both penetrating cracks and surface cracks. • Cracks' repelling propagations strengthen the critical loading of the specimen, while the cracks' attraction propagations weaken the critical loading, which role in dominant is the main factor determining the final loading capacity of the cracked specimen. • Relationships between the comprehensive interference factor with all the crack tips included and the loading capacity is proposed. [ABSTRACT FROM AUTHOR]

• Equivalent stress intensity factors were obtained at 25 ℃. • Plastic dissipated energy, elastic storage energy and surface energy were obtained. • Effect of temperature and underlying layer type on bonding was investigated. • The crack initiation and propagation were analyzed based on energy parameters. Layer bonding performance is essential for ensuring the longevity of open-graded friction course (OGFC) pavements. This study examined the interlayer bonding efficacy between OGFC and the underlying layer, considering variations in underlying layer types and the quantity of tack coat applied. To assess the bonding characteristics, three-point bending tests were performed at temperatures of 0 ℃ and 25 ℃. Parameters such as bonding stiffness, stress intensity factor, equivalent stress intensity factor, and energy parameters were determined to elucidate the fracture behavior between OGFC layers and their supporting layers. The total fracture energy (G F) was segmented into three components: plastic dissipation energy (U d), elastic stored energy (U e), and surface energy (U p), providing a comprehensive analysis of the energy dynamics during fracture. Results showed that at 0 ℃, the maximum bonding stiffnesses of OGFC-A and OGFC-B were obtained when the coat application contents were 1.0 kg/m2 and 0.5 kg/m2, respectively. With the increase of temperature, the bonding stiffness decreased significantly. At 0 ℃, the maximum value of K IC of OGFC-A was higher than that of OGFC-B by 7.1 %, which was attributed to the rougher surface of mixture A in terms of texture depth, average roughness and fractal dimension. At 0 ℃ and 25 ℃, the optimal tack coat application contents for fracture energy were 1.0 kg/m2 and 0.5 kg/m2 for OGFC-A and OGFC-B, respectively. At 0 ℃, the maximum value of G F of OGFC-B was higher than that of OGFC-A by 54.0 %; while at 25 ℃, the maximum value of G F of OGFC-B was lower than that of OGFC-A by 16.7 %. At both 0 ℃ and 25 ℃, the maximum values of U d + U e of OGFC-B were larger than that of OGFC-A, indicating that at both 0 ℃ and 25 ℃, the rougher interface of the underlying layer (mixture A) would not require more energy to initiate a crack. At 0 ℃, then energy required for crack propagation of OGFC-B was larger than that of OGFC-A; while at 25 ℃, opposite results were obtained, indicating a rougher interface (mixture A) helped delay the crack propagation. Temperature, underlying layer type, and tack coat affected the proportions of U d , U e and U p. [ABSTRACT FROM AUTHOR]

In the companion report (Telpande et al., n.d.), we discussed the impact of a weak external magnetic field (up to 0.4 T) on the electric current-induced fracture of pre-notched thin metallic conductors, revealing a linear decrease in critical current density, j c , necessary for crack propagation. This study extends the investigation to explore the effects of stronger external magnetic fields (0.6–1 T) on the fracture of pre-notched, current-carrying metallic foils. The experimental analysis reveals a substantial, albeit linear, drop (up to 40 %) in j c under stronger magnetic fields. Interestingly, calculations of the dynamic stress intensity factor, K IE,t , which assesses the interplay between applied current density and external magnetic field, indicate crack growth under a strong magnetic field even when K IE,t is below the plane stress critical stress intensity factor, K IC. A remarkable phenomenon emerges: the application of electric current pulses combined with strong external magnetic fields induces observable surface undulations near the notch tip. A comprehensive 3D finite element model, integrating linear and nonlinear buckling analyses under multiphysics stimuli, attributes these undulations to localized buckling near the notch tip. This buckling-induced stress redistribution near the crack tip contributes to an overall reduction in fracture toughness due to mode mixity, leading to the fracture of the Al foil below K IC. This investigation, along with the companion report (Telpande et al., n.d.), significantly advances our understanding of the effects of magnetic fields on the fracture of current-carrying conductors. [ABSTRACT FROM AUTHOR]

• A convenient calculation method for SIF in orthotropic cylindrical shell is proposed. • The relation between SIF and FEM stress has been found. • It is found that the SIFs for different loadings can be expressed in the same way. • Simplified equations of SIF components of orthotropic and isotropic shells are the same. • The validity of present method is clarified by comparing to the conventional method. A convenient and universal calculation method for stress intensity factor (SIF) in cracked orthotropic cylindrical shell under diverse loadings is described. The present expressions are derived from traditional classical numerical method and simplified by extracting and eliminating the complex but regular parameters. A simple relation between SIF and crack tip stress from finite element method (FEM) is constructed by means of reference problem and unknown problem, then a simple SIF formulation can be realized and the impact of material orthotropy is considered. The feasibility and advantages of present study are proved to be analyzed by comparing against published results. [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]

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]

• 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]

• A coupled oscillatory element is proposed for interface planar crack. • A general numerical method for solving interface planar crack is established. • It is proved that all K 1 , K 2 and K 3 are related to two parameters ε and γ. • K 1 , K 2 and K 3 are given for interface elliptical crack under uniform tension. This paper studies the stress intensity factors and their correlations with bimaterial parameters for the interface planar cracks by hypersingular integral equations. A new bimaterial parameter γ is defined, and the correlations of the stress intensity factors of interface planar crack with two parameters ε and γ are proved. The relative displacement fundamental function is proposed based on the crack's peripheral equation, thus one kind of element with coupled oscillatory characteristic of mode-1 and mode-2 is established for the interface planar crack. For the interface elliptical cracks with b/a = 0.2, 0.4, 0.6, 0.8, 1.0, the stress intensity factors along the crack front are calculated by solving the hypersingular integral equations. Comparison with the existing exact solutions show that the numerical results have a high accuracy. For the interface planar cracks under tensile load, there exist K 1 , K 2 and K 3 at the same time. The numerical results show that K 1 is very weakly related to ε and γ, K 2 strongly to ε and weakly to γ, and K 3 shows a significant correlation with both parameters ε and γ. K 3 is much smaller than K 1 and K 2 and can be ignored in fracture analysis of problems with remote mode-1 loading. [ABSTRACT FROM AUTHOR]

• The inclined or circular arc cracks in both upper and lower parts of bonded dissimilar materials are formulated. • The modified complex potential methods are used to formulate the hypersingular integral equations. • This hypersingular integral equations is solve numerically using the appropriate quadrature formula. • The stress intensity factors at the crack tips depend on the elastic constants ratio and cracks geometries. The new hypersingular integral equations (HSIEs) for the multiple cracks problems in both upper and lower parts of the bonded dissimilar materials are formulated using the modified complex potential method, and with the help of the continuity conditions of the resultant force function and displacement. The crack opening displacement is the unknown and the traction along the crack as the right term of the equations. The appropriate quadrature formulas are used in solving the obtained HSIEs for the unknown coefficients. Numerical results for the multiple inclined or circular arc cracks subjected to the remote shear stress are presented. [ABSTRACT FROM AUTHOR]

• Low temperature fracture behaviors of cement emulsified mortar were investigated. • Fracture behaviors for tensile, shear and mixed tensile-shear were measured. • D-Optimal Mixture Design Method was employed. • Regression models based on the experimental results were developed. • Dependence of fracture mode I, II, and I/II on mix design ratios was demonstrated. • Tensile-shear and shear modes revealed lowest and highest fracture toughness. • Optimum designs for maximizing fracture toughness of all three modes was delimited. Cement emulsified asphalt mortar (CEAM) is a key component of ballastless rail track systems which is tasked with damping the train movement energy and transferring loads to the concrete roadbed. This mortar consists of asphalt emulsion, sand, cement, and water and enjoys better toughness and flexibility properties than cement mortar thanks to the combined effect of cement and asphalt emulsion. One of the primary causes of failure in this mortar is cracking at low temperatures. This study investigated the fracture toughness of CEAM (CRTS- II) with different volume percentages of mortar constituents, namely cement, sand, water, and asphalt emulsion, at low temperature in the linear elastic fracture mechanics (LEFM) framework. The critical stress intensity factors of the mortar for pure tensile (mode I), pure shear (mode II), and mixed tensile-shear (mixed mode I/II) fractures with M e values of respectively 1.0, 0, and 0. 67 were obtained. Considering the necessity of examining the effect of mix design ratios and their interactions and the need to limit these ratios to ensure acceptable rheological and mechanical properties, the experiments were designed using the D-Optimal mixture design method at 5% significance level. By assuming a quadratic model between the critical stress intensity factors of each fracture mode and the volume percentages of mortar constituents, a total of 20 randomized mix designs were obtained. For each mix design, the semi-circular bending (SCB) test was performed with at least 3 replications. The regression models based on the experimental results were developed. The findings demonstrated the dependence of mode I, mode II, and mixed mode I/II critical stress intensity factors on the mix design ratios. The lowest and highest fracture toughness estimates were related to the mixed tensile-shear and pure shear modes, respectively. Finally, the mixture design method was used to delimit the optimum mix design region for maximizing the fracture toughness of all three modes. [ABSTRACT FROM AUTHOR]

In order to determine the threshold stress intensity factor and critical hydride length for delayed hydride cracking in Zr-2.5Nb pressure tube alloy, the distribution of normal stress in the plastic zone of crack tip by the developed method that combines theory calculation with extended finite element method (XFEM) was improved. The fracture process of two-phase composites containing Zr-2.5Nb and hydride precipitate was simulated by XFEM. Based on that, critical hydride length L C corresponding to the theoretical model for K 1H was estimated. Meanwhile, to illustrate the validity of theoretical and numerical methods, recent theoretical models and experimental measurements were utilized to verify the results of this paper. The theoretical model of DHC was improved to estimate the critical hydride length corresponding to threshold stress intensity factor. The predicted value of critical hydride length is close to the experimental values. • Distribution of the normal stress in plastic zone is improved by valid estimation of σ 0. • The theoretical model combining XFEM is used to calculate the K 1H and L C. • The influence of hydride size on the instability fracture point is revealed by XFEM. [ABSTRACT FROM AUTHOR]

Gradient nano-grained (GNG) materials, in which grain size changes from nano-scale in the surface to micro-scale in the core, have shown superior fatigue property, good strength and ductility. However, crack growth behaviors of GNG materials are studied hardly. In this work, the effect of grain size gradient on crack growth is investigated to reveal the inhibition mechanism of crack growth in GNG materials. The developed model employs a distributed dislocation method to model the evolution of plastic zone. The influence of grain size gradient on the distribution of dislocations in grains and the local stress intensity factor is analyzed. The results show that the sizes of dislocation zone and dislocation-free zone in grains become larger as the gradient of grain size increases. The number of dislocations emitted from the crack tip increases with the grain size gradient increasing, so the shielding effect of emitted dislocations on the crack growth increases and crack blunting becomes more serious. This means that a sharper grain size gradient inhibits the crack growth more effectively. The results in this paper are important for understanding the fracture behaviors of materials with grain size gradient and are helpful for material design and structural optimization. [ABSTRACT FROM AUTHOR]

The paper underscores the difficulty in characterizing crack growth in shape memory alloys with conventional stress intensity approaches even when anisotropy is accounted for. The local displacements deviate significantly from the presumed K solutions because of transformation localization at macro scales extending from the crack tip. Modifications in stress intensity due to variant induced tractions are derived providing an explanation of the extrinsic behavior. Precise displacement and strain measurements are provided to highlight the complexity of deformation and the need for better fracture mechanics models, including crack tip opening displacements, to characterize fatigue crack growth in shape memory alloys. Unlabelled Image [ABSTRACT FROM AUTHOR]

• The √ area parameter model is applicable to defects with a maximum size of ∼100 µm. • The long-crack threshold, Δ K th,lc , is applicable to defects larger than ∼100 µm. • Models based on the relative stress gradient can be used for blunt defects. • An equation to predict the critical size of detrimental defects is introduced. • The critical defect size increases with increasing load ratio. The defect tolerance of three different martensitic stainless steels (17-4PH, X20Cr13 and AISI403) under cyclic loading was investigated. Fatigue tests were performed with specimens containing diverse artificial defects (corrosion pits, single and multiple drilled holes, sharp circumferential notches and pre-cracked holes). The measured cyclic strengths are compared to predictions based on the area parameter model proposed by Murakami and Endo. This model is well applicable to small sharp defects if the threshold condition for crack propagation determines the fatigue limit. The transition size from small to large defects, area t r a n s , – above which the threshold stress intensity factor range, Δ K th , becomes a constant value – is between 80 and 166 µm for the investigated steels. For larger defects, the threshold for long cracks, Δ K th,lc , serves well to predict the fatigue strength under fully reversed loading, i.e. at a load ratio of R = −1. Comprehensive tests were performed to study the influence of mean stress, and threshold conditions were determined that enable to predict the fatigue limit at different load ratios. A simple equation is introduced to estimate the critical defect size, area c r i t i c a l , which is the size above which defects become detrimental under cyclic loading. It has been found that area c r i t i c a l increases with increasing load ratio while area t r a n s is independent of R. Furthermore, higher values of the threshold stress intensity factor range were determined for large defects (with sizes larger than area t r a n s ) compared to long cracks if the load ratio is higher than R = −1. This could be explained by the plane stress condition at the material surface which is prevalent for surface defects, while the condition for long cracks can be assumed as plane strain. It is further demonstrated that the effect of small defects on the fatigue strength of stainless steels is highly sensitive to the notch root radius, ρ. Small holes with diameters of 100 µm (ρ = 50 µm) or larger are less detrimental for the fatigue strength than defects with high stress concentrations – such as corrosion pits. [ABSTRACT FROM AUTHOR]

This study focused on the numerical analysis of a cracked fuselage panel of an airplane on the basis of new nonlinear fracture mechanics parameters and concepts. Through finite element analysis (FEA) of the fragment of the fuselage panel with central crack, the governing parameters of the elastic–plastic crack-tip stress field (i.e., I n -integral and the plastic stress intensity factor) were determined as a function of the crack length and biaxial loading conditions. Elastic–plastic FEAs of the cracked fuselage panel were performed by considering the accumulated damages in the fracture process zone at the crack tip via special cohesive elements. The curvilinear crack path in the fuselage panel under biaxial loading was predicted on the basis of strain energy density and cohesive zone concepts. • This study focused on the numerical analysis of a cracked fuselage panel of an airplane on the basis of new nonlinear fracture mechanic parameters and concepts. • The governing parameters of the elastic–plastic crack-tip stress field were determined as a function of the crack length and biaxial loading conditions. • Elastic–plastic FEAs of the cracked fuselage panel were performed by considering the accumulated damage in the fracture process zone at the crack tip via special cohesive elements. • The curvilinear crack path in the fuselage panel under biaxial loading was predicted on the basis of strain energy density and cohesive zone concepts. [ABSTRACT FROM AUTHOR]

A new enriched finite element technique, named the Discontinuity-Enriched Finite Element Method (DE-FEM), was introduced recently for solving problems with both weak and strong discontinuities in 2-D. In this mesh-independent procedure, enriched degrees of freedom are added to new nodes collocated at the intersections between discontinuities and the sides of finite elements of the background mesh. In this work we extend DE-FEM to 3-D and describe in detail the implementation of a geometric engine capable of handling interactions between discontinuities and the background mesh. Several numerical examples in linear elastic fracture mechanics demonstrate the capability and performance of DE-FEM in handling discontinuities in a fully mesh-independent manner. We compare convergence properties and the ability to extract stress intensity factors with standard FEM. Most importantly, we show DE-FEM provides a stable formulation with regard to the condition number of the resulting system stiffness matrix. • The Discontinuity-Enriched Finite Element Method is introduced to solve 3-D problems; • A geometric engine is proposed to handle arbitrary (intersecting) discontinuities; • Intersecting discontinuities are resolved by hierarchical enrichment functions; • We show the methodology's convergence and ability to extract stress intensity factors; • We demonstrate the method's stability with the use of a simple preconditioner. [ABSTRACT FROM AUTHOR]

• Three-dimensional preset depth crack fatigue propagation models were established. • The propagation of the crack tip section was monitored through the probe. • The fatigue propagation of crack tip inside the semi-rigid base was investigated. Nowadays, it is of non-negligible importance to extend the service life of in-service pavements. As the base form, shrinkage fractures and plate faults are the main reasons for the failure of semi-rigid base and it is of practical significance to study the cracking mechanism of the fracture damage from the microscopic point of view. In order to obtain the fatigue propagation law of the cracks inside the semi-rigid base, a three-dimensional preset depth crack fatigue propagation model was established based on the finite element quasi-static method and ground-penetrating radar detection data, and monitors the propagation of the crack tip section through the probe, obtaining the number of load actions and the crack propagation depth during the destabilization. Subsequently, this paper investigates the stress field distribution and fatigue propagation failure law of crack tip section inside the semi-rigid base based on the ensemble analysis method of stress intensity factor, combined with the macroscopic modulus change of the base structure. The propagation form of single-crack cracks within the base layer is mainly dominated by type I (opening type) cracks, but there are also the remaining two crack propagation trends at the tip. The analysis shows that the smaller the modulus of the semi-rigid base, the less likely the crack is to undergo an initial tip change. In the case of four preset depths, the preset depth of 50 mm is the most vulnerable to crack tip change. Relatively speaking, and the 200 mm preset depth cracks expand the maximum depth when the structure fails in all preset depths. It can be seen from the experiments that the strain field at the crack tip of 50 mm presetting depth is stronger. The strength of stress and strain fields near the crack tip at 200 mm and 150 mm preset depths is mainly related to the modulus of the base layer. The larger the modulus, the stronger the stress and strain fields. The distribution of the field strength at the crack tip of 100 mm and 50 mm presetting depth is less affected by the base layer modulus. In this study, the three-dimensional simulation of the fatigue action of the internal cracks in the semi-rigid base is innovatively proposed, which helps to clarify the distribution of the stress field and the fatigue failure of the internal crack tip of the semi-rigid base, and provides a new way of thinking for the assessment of the service performance of the long-life pavements and the failure mechanism of the microscopic damages. [ABSTRACT FROM AUTHOR]

• Positive and negative oscillations of K II under compression are the reason for zigzag crack propagation paths modeled by the traditional fracture criterion. • GMTS criterion considering T -stress can effectively eliminate K II oscillations but requires complicated parameter calculations. • SLMS criterion proposed in this study can conveniently and efficiently model the propagation of both tensile and shear cracks. • The effects of flaw inclination, friction coefficient, loading level, and flaw surface contact status on the crack propagation paths were studied. The traditional fracture criterion performs well when calculating crack propagation under tensile conditions, but a zigzag crack propagation path was obtained under compression, which is inconsistent with experimental results. This study indicates that the positive and negative oscillations of the mode-II stress intensity factor (K II) under compressive loading during crack propagation is the reason for the zigzag trajectory of crack propagation. Such oscillation of K II can be effectively eliminated when the non-singular stress (T -stress) at the flaw tips is considered, and thus, the path of crack propagation can also be smoothed. However, due to the complicated calculations of the stress intensity factors and T -stress at each step of crack propagation, it is not suitable for simulation in fast, complex environments and multi-flaws. Also, the lack of a shear fracture criterion in traditional fracture methods leads to difficulty in studying shear crack propagation in rock. Therefore, a strength-based localized maximum stress (SLMS) criterion was proposed in this study to model both tensile and shear crack propagations in rock more efficiently, conveniently, and accurately. Then, the crack propagation processes in both plate and Brazilian disc specimens with a single flaw under uniaxial and biaxial compression were modeled to investigate the effects of the flaw inclination angle, friction coefficient, and loading level on the crack propagation path. The influence of the contact friction between the flaw surfaces on the contact status and the crack propagation path during the crack propagation process was also analyzed. Also, the crack propagation in a plate with a single flaw under biaxial tension was modeled, which shows bifurcation crack propagation when the lateral tension is several times larger than the axial tension. All the modeled results indicated that the proposed SLMS criterion can get better results when modeling crack propagations for open or closed flaws under tension or compression conditions. [ABSTRACT FROM AUTHOR]

This work utilized computer vision and machine learning techniques to predict both qualitative characteristics and quantitative values, from SEM images of Ti–6Al–4V fracture surfaces from compact tension specimen fatigue crack growth tests. This work found that Convolutional Neural Networks (CNNs) focused on different features in images based on the length scale of the image. This study determined a lower limit field of view related to the number of grains imaged, and confirmed that transfer learning of a pre-trained CNN can distinguish between two forging direction and two different load ratios, and predict crack length, a , and repurposed for Δ K , and d a d N. • A pre-trained CNN classified forging direction based on fatigue fracture surfaces. • The same CNN modified for regression predicted crack length from only fracture images. • Longer length scale features capturing multiple grains are better for models. • Models can predict crack growth rate stress intensity factor range, and load ratio. [ABSTRACT FROM AUTHOR]

• Dynamic compression tests of saturated reef limestone concrete under biaxial constraints is carried out. • The strain rate effect of dynamic mechanical properties of water-saturated reef limestone concrete is analyzed. • The strengthening effect of lateral stress constraint on the dynamic stress of reef limestone concrete is discussed. • The enhancement mechanism of water-saturated state on the dynamic strength of reef limestone concrete is revealed. On the basis of not destroying the island's ecological environment, concrete mixed with reef limestone aggregates in situ is beneficial to solve the problem of shortage of terrestrial rock resources in the island area. Considering the influence of water-saturated state, lateral stress constraint and strain rate, the dynamic mechanical properties and failure characteristics of reef limestone concrete under biaxial stress constraint are studied by using true triaxial Hopkinson bar test technology. The dynamic failure behavior of reef limestone concrete is analyzed from macro-meso level by means of SEM test method, and the stress intensity factor theory of crack tip is cited to reveal the enhancement effect of dynamic strength of water-saturated reef limestone concrete under the coupling effect of biaxial stress constraint and impact load. The results show that the dynamic compressive strength of reef limestone concrete increases with the strain rate in a power function, and the growth rate decreases gradually. Under the same impact load, the compressive strength of reef limestone concrete in water-saturated state increases more significantly than that in dry state. The lateral stress constraint has a significant enhancement effect on the dynamic strength of reef limestone concrete samples, and changes the Poisson's ratio of reef limestone concrete samples. In addition, based on the equivalent crack model theory, it is verified that under the combined action of biaxial stress constraint and high strain rate, the dynamic stress intensity factor of the crack tip of the reef limestone concrete sample in water-saturated state is larger than that in dry state. [ABSTRACT FROM AUTHOR]