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Interconnected cracks are prefabricated on plexiglass plates (polymethyl methacrylate, PMMA) to study the effect of crack length on the initiation and propagation of interconnected cracks under impact loads. A new dynamic caustics test system was constructed to analyze the specimen's initiation process; the fractal method was used to quantify crack propagation; and the numerical simulation was used to monitor the specimen's full-field stress change. The results show that, with the direction of the impact loads as the axis of symmetry, interconnected cracks with different lengths and symmetrical angles, only the longer cracks initiate under the action of impact loads. With the increase in the length of one side of the interconnected crack, the crack initiation time is delayed, the trajectory of crack propagation becomes more irregular, and the peak propagation velocity of the crack increases first and then decreases. After the analysis, it was concluded that there is a certain competitive relationship in the crack tip propagation law between interconnected cracks with different lengths. In the energy storage stage, the tip of the longer crack is more likely to accumulate energy than that of the shorter crack, and it also has a suppressive effect on the energy storage of the latter. In the initiation and propagation stages, the energy at the tip of the uninitiated shorter crack will transfer to the tip of the longer crack, promoting its propagation. The research provides a basis for analyzing the initiation and propagation laws of interconnected cracks in practical engineering applications. [ABSTRACT FROM AUTHOR]

This paper presents an extension of the recently developed smoothed floating node method (SFNM) with cohesive zone approach to model crack growth in elastic materials under thermo-elastic loading conditions. The SFNM utilizes floating nodes to accurately model the crack by activating dormant nodes at intersection points of crack path and the corresponding element edges. Through the activation of floating nodes, the cracked element transforms into sub-elements, facilitating separate integration of each sub-element. A smoothing cell-based integration technique is employed to convert the area integral to line integral which mitigates the element distortion issues. The temperature distribution is initially determined across the entire domain, and then imposed as thermal loads in the 2D domain. The thermal stress intensity factor is calculated for both homogeneous and bi-material specimens using the interaction energy integral approach, and the crack propagation is predicted using circumferential stress criterion. The accuracy of the proposed framework is demonstrated with several benchmark problems of fracture mechanics. The develop framework yields comparable results with the available literature with less modeling complexity. [ABSTRACT FROM AUTHOR]

This article aims to investigate the effect of elevated temperature on the fatigue performance of CFRP-reinforced cracked steel plates and optimize the design parameters for their reinforcement. Based on the self-developed adhesive GY34, a finite element model of the CFRP-reinforced central cracked steel plate is established by the ABAQUS software. Parametric analysis is carried out on different bonding methods of CFRP plates and different thicknesses of adhesive layers for CFRP-reinforced cracked steel plates. The effect of elevated temperature on the reinforcement is also studied to verify the excellent performance of GY34 adhesive. Furthermore, the enhancement of fatigue life for cracked steel plates reinforced with CFRP plates at different temperatures is investigated using the Paris model and modified Newman model. The results show that double-sided reinforcement with CFRP is more effective than single-sided reinforcement. All of the different bonding methods could reduce effectively the stress intensity factor of cracked steel plates and improve significantly the bearing capacity of the steel plates. Among them, increasing the number of CFRP layers and their elastic modulus yield the most significant improvement on the reinforcing effect. Elevated temperatures effect greatly on the mechanical properties of adhesively bonded CFRP-reinforced steel plates. The effective bonding length and the stress intensity factor amplitude at the crack tip of the steel plate increases with temperature rises, which may accelerate the growth rate of fatigue crack and reduce the reinforcing effect on fatigue life. [ABSTRACT FROM AUTHOR]

Studies have shown that fractional derivatives have important memory effect on the thermal shock fracture of structures. In the present work, four generalized fractional models are applied to investigate the thermal fracture problem of cracked plates. Laplace transform and finite sine transform are employed to obtain transient temperature and thermal stresses. Stress intensity factors around the crack tips are evaluated through the weight function method for edge and center cracks. Numerical results show that memory effects on the thermoelastic fields are different with different fractional derivative definition and fractional orders, and the effects will vary accordingly with crack geometry parameters. [ABSTRACT FROM AUTHOR]

The basis of describing stress intensity factor and predicting residual life of structure is the right numerical model of dynamic crack propagation. 'FEM+M integral' and 'XFEM+M integral' methods were, respectively, adopted. Difficulties of 'FEM+M integral' method were solved, such as the singularity of crack tip, nodal uncoincidence of rubber layer unit and plate unit during mesh repartition and calculation convergence. In addition, difficulties of 'XFEM+M integral' method were overcome, such as difficult crack tip coordinates, difficult cutting point of crack and element and crack deflection in the element. On this basis, the effective calculation of stress intensity factor was realised. Through simulation and calculation, it is found that the error value is within 5%. The model reliability is further verified within the allowable error range. [ABSTRACT FROM AUTHOR]

The very high‐cycle fatigue (VHCF) fractographies of high‐strength steel AISI 4340 with tensile strength ranging from 1285 to 2363 MPa fabricated by tempering were systematically observed and quantitatively analyzed. It is found that the fatigue crack initiation sites were gradually transferred from the specimen surface to the interior with increasing the tensile strength or decreasing the stress amplitude. Such phenomenon has become common rule in the high‐cycle fatigue (HCF) or VHCF regimes of high‐strength steels. Based on the fracture mechanics, a simplified transition mechanism for fatigue crack initiation sites is established in terms of the influence of applied stress amplitude and microstructure, which is beneficial to enhance our understanding on the variation of fatigue strength increasing the tensile strength. Highlights: The effects of tempering temperature on fatigue crack initiation are studied.The sites of fatigue crack initiation is counted, and influence mechanism is discussed.A model is proposed to explain the relationship between tensile and fatigue strength. [ABSTRACT FROM AUTHOR]

Prolonged rolling contact fatigue between wheels and rails results in the formation of surface cracks on the rail and accurately analyzing the crack expansion behavior is essential to ensuring the safe operation of the train. Drawing upon the principles of fracture mechanics and finite element theory, this study establishes a finite element model of wheel–rail rolling contact that incorporates the presence of cracks. The method utilizes an interaction integral to calculate the stress intensity factors at the leading edge of the crack; then, the Paris formula is used to solve the crack spreading rate. It systematically examines the effects of the initial crack angle, the coefficient of friction of wheels to rails, and crack size on the behavior of fatigue crack propagation. The results indicate that the cracks primarily extend in the depth direction of the rail, transforming the semi-circular surface cracks into elliptical cracks with the major axis oriented along the rail's width. Crack propagation is primarily driven by model II and III composite crack propagation, with their expansion rates influenced by operating conditions. In contrast, mode-I expansion is less sensitive to these conditions. Under single-variable loading conditions, a smaller initial crack angle results in a faster crack growth rate. Increasing crack length accelerates crack growth, while a higher friction coefficient inhibits it. [ABSTRACT FROM AUTHOR]

Combined the phase field model with the wavelet dummy node-virtual crack closure technique (WDN-VCCT) used for stress intensity factors (SIFs) calculation. Calculated the node displacement using an improved brittle fracture phase field method, established the relationship between node displacement and node force using WDN-VCCT, and calculated the SIFs at the crack tip. The correctness and accuracy of the proposed method were verified through functional gradient material (FGM) tensile experiment. The influence of crack inclination angle, crack position and gradient index on mechanical response, and SIFs values at the crack tip was discussed. This study provides important computational tools for estimating the service life of FGMs and important references for structural optimization design methods. [ABSTRACT FROM AUTHOR]

AbstractThis study analyzes the initial subsurface crack propagation in bearing steel by utilizing a 3D Voronoi finite element model to simulate the bearing steel’s grain structure. Subsurface stress calculations validate the model. Stress intensity factors were computed to determine crack propagation as a function of initial crack orientation, length, and depth. A novel aspect of this study is the integration of FE analysis with an Artificial Neural Network for predictive modeling. A grid search method was employed for hyperparameter tuning, and ten-fold cross-validation was used to evaluate the ANN’s performance, ensuring robust and accurate predictions. This hybrid approach enables the prediction of SIFs based on various load and crack parameters, facilitating a rapid assessment of crack propagation risk. The results provide valuable insights into the reliability and lifespan of bearing steel, contributing significantly to the field of bearing failure analysis. [ABSTRACT FROM AUTHOR]

The method of pull-out test has been used to identify the mechanical performance of hybrid and fiber-reinforced composite materials. This paper investigates the elastic phase preceding the pull-out of a rigid line inclusion from the polymer matrix with fixed top and bottom surfaces. The mode-III problem is investigated such that the pull-out force is applied from the out-of-plane direction and it can be either transient or static. By applying the singular integral equation technique, the semi-analytical elastic field expressions are obtained. Under the static pull-out force, the stress intensity factor (SIF) near the inclusion tip shows a monotonic increase as the length and height of the matrix increase, whereas for the transient pull-out force, the SIF displays an initial increasing and followed by a decline. The maximum SIF is obtained for (1) the matrix length is 2 to 2.5 times of the inclusion length, and (2) the matrix height is 1 to 2 times of the inclusion length. Moreover, this paper provides a solution approach that incorporates the elasticity of the inclusion, showing that there is an optimal shear stiffness that minimizes the stress singularity of system. The conclusions of this study hold significance for the design and performance evaluation of fiber-reinforced composite materials. [ABSTRACT FROM AUTHOR]

A theoretical model was established to investigate the interaction between hydrogen clusters and edge dislocations emitted from a semi-elliptical surface crack tip in deformed nanometallic materials. The model's solution was obtained by using the complex method, and the influence of the concentration and location of hydrogen clusters, temperature, crack shape, material constants, and the dislocation emission angle on the critical stress intensity factor (SIFs) corresponding to the first dislocation emission from crack tips was investigated through numerical analysis. The results show that dislocations are easily emitted from the crack tip at high hydrogen concentration, and hydrogen clusters close to the crack tip will hinder the emission of dislocations from its crack tip. When considering the influence of hydrogen cluster, an increase in temperature, an extension of crack length or an increase in crack tip curvature radius can all make the emission of dislocations at the crack tip difficult, thereby reducing the toughness of the material caused by dislocation emission. [ABSTRACT FROM AUTHOR]

Modified Green–Lindsay generalized thermoelasticity theory was established by Yu et al. (Meccanica 53(10):2543–2554, 2018). On the basis of this theory, transient motions remove discontinuities in displacement fields. The goal of this article is to address a dynamical problem involving finite linear mode-I cracks in an isotropic and homogeneous elastic medium in a two-dimensional infinite space using the innovative framework of modified Green–Lindsay generalized thermoelasticity theory. There is a specified temperature and stress distribution on the crack's boundary. The integral transform techniques are used to obtain the numerical values of temperature, stress, displacement and stress intensity factor for copper material. These non-dimensional physical fields are explained graphically. Specifically, the present undertaking demonstrates its utility in addressing challenges related to fracture mechanics, geophysics and mining particularly in the context of coupling thermal and mechanical fields. This concerted effort proves valuable in exploring and resolving issues within these fields. [ABSTRACT FROM AUTHOR]

The present study is dedicated to analyzing Griffith crack transference within finitely thick and infinitely extending transversely isotropic strip. This strip is bounded by two parallel punches exerting a constant load distribution through Dirac delta functions, which are a consequence of plane waves propagating due to mechanical point loading. Moreover, the developed model employs coupled singular integral equations and Cauchy-type singularities. It is utilized to analyze the point load at the advancing crack tip, while leveraging Hilbert transformation properties to derive the stress intensity factor (SIF) under constant point loading in a closed analytical form. The investigation incorporates numerical computations and graphical representations to scrutinize the impact of various parameters, including crack length and speed, punch pressure, and different positions of the point load, on the SIF. These analyses are conducted for both transversely isotropic and isotropic material strips. [ABSTRACT FROM AUTHOR]

The interactions between multiple cracks significantly influence fracture mechanics parameters, necessitating their consideration in crack assessments. Codes such as ASME Section XI, API 579, BS 7910, and British Energy R6 provide guidelines for crack growth and coalescence, taking crack interactions into account. However, these guidelines often employ idealized crack models, which lead to overly conservative assessments. This study proposes a new criterion for multiple crack coalescence, based on the plastic zone size, to better model the growth and merging of natural cracks. This criterion was implemented using the Advanced Iterative Finite Element Method (AI-FEM), an automated crack-growth simulation program utilizing re-meshing. Fatigue crack growth (FCG) simulations using AI-FEM validated the proposed criterion by comparing it with experimental data. Additionally, the AI-FEM results were compared with those obtained through code-based procedures to evaluate the conservatism of current codes. The findings demonstrate that the proposed criterion closely matches experimental results, providing a more realistic simulation of crack growth and reducing the conservatism of existing codes. [ABSTRACT FROM AUTHOR]

This research work studies a problem associated with an axisymmetric torsion of an orthotropic layer by a circular rigid disc at the midplane. The orthotropic layer is sandwiched by two identical orthotropic half-spaces with two interfaced cracks. The layer and half-spaces are dissimilar in nature. The mixed boundary value problem is reduced to a system of dual integral equations by Hankel transformation, which are converted to Fredholm integral equations of the second kind. The integral equations are solved numerically by the quadrature rule. The stress intensity factors for crack and disc have been derived and are presented graphically for different thicknesses of orthotropic layer. [ABSTRACT FROM AUTHOR]

In linear elastic fracture mechanics, the stress intensity factor describes the magnitude of the stress singularity near a crack tip caused by remote stress and is related to the rate of fatigue crack growth. The literature lacks SIF solutions for cracks emanating from a three-dimensional semi-ellipsoidal pit. This study undertakes a comprehensive parametric investigation of the Mode I stress intensity factor (K I) concerning cracks originating from a semi-ellipsoidal pit in a plate. This work utilizes finite element analysis, controlled by Python scripts, to conduct an extensive study on the effect of various pit dimensions and crack lengths on K I . Two cracks in the shape of a circular arc are introduced at the pit mouth perpendicular to the loading direction. The K I values are calculated using the displacement extrapolation method. The effect of normalized geometric parameters pit-depth-to-pit-width (a / 2 c ), pit-depth-to-plate-thickness (a / t) , and crack-radius-to-pit-depth (R / a) are investigated. The crack-radius-to-pit-depth (R / a) is found to be the dominating parameter based on correlation analysis. The data obtained from 216 FEA simulations are incorporated into a predictive model using a k-dimensional (k-d) tree and k-Nearest Neighbour (k-NN) algorithm. [ABSTRACT FROM AUTHOR]

We derive a series-form analytical solution to the thermoelastic problem of an insulated and traction-free crack in a confocal elliptical isotropic elastic inhomogeneity embedded in an infinite isotropic elastic matrix subjected to uniform remote heat flux. Using complex variable techniques such as conformal mapping, analytic continuation and Laurent series expansions, the original thermoelastic problem is reduced to an infinite system of linear algebraic equations, the solution of which will yield the mode I and mode II stress intensity factors at the crack tip. An exact closed-form solution is derived when the inhomogeneity and the matrix have identical shear moduli. Detailed numerical results are presented to demonstrate the series-form and closed-form solutions with an emphasis on the particular case of a vanishingly thin inhomogeneity. [ABSTRACT FROM AUTHOR]

The present work investigates the motion of a semi-infinite moving crack inside a semi-infinite half-space of orthotropic medium subjected to anti-plane shear wave. The crack is located at a finite depth from the surface of semi-infinite orthotropic medium. Our aim is to examine how such anisotropy and geometric parameters can be adjusted to reduce the magnitude of stress intensity factor (SIF) to control the crack propagation near the crack tip region. As mathematical tools, Fourier transformation and inverse Fourier transformation techniques are employed to convert the governing mixed boundary value problem to the well-known Weiner-Hopf equation with suitable boundary conditions. Some physical quantities such as SIF at the crack tip and crack opening displacement (COD) around the crack tip have been derived. Graphical exhibition has been carried out to show the impact of relevant parameters such as crack velocity, layer depth from the surface to crack and orthotropic material properties on SIF and COD. The numerical results show that SIF decay with crack depth from the layer. It is also observed that SIF decreases with an increase in crack velocity and finally tends to zero as crack velocity approches near SH-wave velocity. Also, the value of COD decays as we move along the damage near the crack tip along negative x-axis and finally tends to zero at the crack tip. This behavior of COD is consistent with the physical nature of the semi-infinite crack of the problem. The results are validated for isotropic material with some reported work and are well in agreement. The study of these physical quantities (SIF, COD) ensures the arrest of onset of crack expansion by monitoring geometric parameters and wave velocity to avoid fracture. [ABSTRACT FROM AUTHOR]

High-speed railway tunnels in various countries have continuously reported accidents of vault falling concrete blocks. Once the concrete block falling occurs, serious consequences follow, and traffic safety may be endangered. The aerodynamic shockwave evolves from the initial compression wave may be an important inducement causing the tunnel lining cracks to grow and form falling concrete blocks. A joint calculation framework is established based on ANSYS Fluent, ABAQUS, and FRANC3D for calculating the crack tip field under the aerodynamic shockwave. The intensification effect of aerodynamic shockwaves in the crack is revealed, and the evolution characteristics of the crack tip field and the influence factors of stress intensity factor (SIF) are analyzed. Results show that (1) the aerodynamic shockwave intensifies after entering the crack, resulting in more significant pressure in the crack than the input pressure. The maximum pressure of the inclined and longitudinal cracks is higher than the corresponding values of the circumferential crack, respectively. (2) The maximum SIF of the circumferential, inclined, and longitudinal crack appears at 0.5, 0.68, and 0.78 times the crack front length. The maximum SIF of the circumferential crack is higher than that of the inclined and longitudinal crack. The possibility of crack growth of the circumferential crack is the highest under aerodynamic shockwaves. (3) The influence of train speed on the SIF of the circumferential crack is more than 40%. When the train speed, crack depth, and crack length change, the change of pressure in the crack is the direct cause of the change of SIF. [ABSTRACT FROM AUTHOR]

Fatigue is a common issue in steel elements, leading to microstructural fractures and causing failure below the yield point of the material due to cyclic loading. High fatigue loads in steel building structures can cause brittle failure at the joints and supports, potentially leading to partial or total damage. The present study deals with accurate prediction of the fatigue life and stress intensity factor (SIF) of pre-cracked steel beams, which is crucial for ensuring their structural integrity and durability under cyclic loading. A computationally efficient adaptive meshing tool, known as Separative Morphing Adaptive Remeshing Technology (SMART), in ANSYS APDL is employed to create a reliable three-dimensional finite element model (FEM) that simulates fatigue crack growth with a stress ratio of "R = 0". The objective of this research is to examine the feasibility of using a non-linear FE model with an adaptive meshing technique, SMART, to predict the crack growth, fatigue life, and SIF on pre-cracked steel beams strengthened with FRP. Through a comprehensive parametric analysis, the effects of different types of FRPs (carbon and glass) and fiber orientations (θ = 0° to 90°) on both the SIF and fatigue life are evaluated. The results reveal that the use of longitudinally oriented FRP (θ = 0°) significantly reduces the SIF, resulting in substantial improvements in the fatigue life of up to 15 times with CFRP and 4.5 times with GFRP. The results of this study demonstrate that FRP strengthening significantly extends the fatigue life of pre-cracked steel beams, and the developed FE model is a reliable tool for predicting crack growth, SIF, and fatigue life. [ABSTRACT FROM AUTHOR]

To investigate the propagation behavior of thermal cracks on the wheel tread under the conditions of long downhill ramps, a three-dimensional finite element model of a 1/16 wheel, including an initial thermal crack, was developed using the finite element software ANSYS 17.0. The loading scenarios considered include mechanical wheel–rail loads, both with and without the superposition of thermal wheel–brake shoe friction loads. The virtual crack closure method (VCCM) is employed to analyze the variations in stress intensity factors (SIFs) for Modes I, II, and III (KI, KII, and KIII) at the 0°, mid, and 90° positions along the crack tip. The simulation results show that temperature is a critical factor for the propagation of thermal cracks. Among the SIFs, KII (Mode II) is larger than KI (Mode I) and KIII (Mode III). Specifically, the thermal load on the wheel tread during braking contributes up to 23.83% to KII when the wheel tread reaches the martensitic phase transition temperature due to brake failure. These results are consistent with the observed radial propagation of thermal cracks in wheel treads under operational conditions. [ABSTRACT FROM AUTHOR]

Epoxy asphalt pavement cracking caused by subgrade settlement is detrimental to the long-term safe service of roads. A threedimensional finite element model of epoxy asphalt pavement is established to investigate the effects of subgrade settlement on the propagation of top-down cracking (TDC). The contour integral method is utilized to calculate the stress intensity factor (SIF) at the crack tip, and then the extended finite element method (XFEM) is used to analyze the propagation behavior of TDC under combined subgrade settlement and traffic loading. The results of these analyses indicate that increased subgrade settlement, stiffer surface layers, and softer bases will increase the SIF, resulting in a faster crack propagation rate. It is suggested that the use of epoxy asphalt materials in pavement structures can allow more subgrade settlement than conventional asphalt mixtures. However, when the base layer modulus is higher than 12500 MPa, the increase in surface modulus can decrease crack propagation length. Sensitivity analysis results demonstrate that subgrade settlement has the most significant impact on TDC propagation. The conclusions of this study are expected to provide a theoretical basis for crack prevention in the design and maintenance of pavement structures. [ABSTRACT FROM AUTHOR]

Active repair systems employing piezoelectric (PZT) patches have emerged as promising solutions for mitigating crack propagation and enhancing structural integrity in various engineering applications. However, the existing literature predominantly focuses on the application of PZT patches for repairing structures under mechanical loading. In this study, a finite element analysis (FEA) is employed to investigate the repair of a centre-cracked aluminium plate under both mechanical and thermo-mechanical loading conditions. This study explores the influence of key parameters, including temperature, PZT patch thickness, type of PZT material, adhesive material, and adhesive thickness, on the structural integrity and crack propagation behaviour. The results reveal significant differences in stress distribution and crack propagation tendencies under varying loading conditions and parameter settings. These findings emphasize the necessity of considering thermo-mechanical loading conditions and parameter variations when designing effective active repair systems. In conclusion, this study provides valuable insights into optimizing PZT patch-based repair strategies for improved structural integrity and crack mitigation in aerospace and other engineering applications under diverse loading scenarios. [ABSTRACT FROM AUTHOR]

Abstract Combined the phase field model with the wavelet dummy node-virtual crack closure technique (WDN-VCCT) used for stress intensity factors (SIFs) calculation. Calculated the node displacement using an improved brittle fracture phase field method, established the relationship between node displacement and node force using WDN-VCCT, and calculated the SIFs at the crack tip. The correctness and accuracy of the proposed method were verified through functional gradient material (FGM) tensile experiment. The influence of crack inclination angle, crack position and gradient index on mechanical response, and SIFs values at the crack tip was discussed. This study provides important computational tools for estimating the service life of FGMs and important references for structural optimization design methods.

For decades, resistance spot welding (RSW) between aluminum and copper has encountered difficulties; however, it remains essential for modern applications. Additionally, crack propagation and the stress intensity factor (SIF) of dissimilar RSW have not been extensively investigated. The welding parameters used for Al-Al joints were as follows: welding current, time, and electrode force were set at 14,000 Amps, 0.8 seconds, and 7,000 N, respectively. Conversely, for Al-Cu joints, 14,000 Amps, 1 second, and 8,800 N were determined. The similar joints exhibited an average weld nugget size of 6 mm, whereas the dissimilar joints had a nugget size of 5.2 mm. The tensile shear force was 690 N and 780 N for dissimilar and similar joints, respectively. Accordingly, the fatigue load, as a percentage of the tensile force, was utilized at 414 N and 468 N for Al-Cu and Al-Al, respectively. Finite Element Analysis (FEA) was employed to determine the SIF. The initial crack length was determined to be 0.1 mm. The numerical solution was then compared with theoretical solutions for the opening SIF-KI, such as the equations proposed by Pook and Zhang. The FEA results showed higher values of SIF compared to those from theoretical solutions. Additionally, crack propagation was investigated for both dissimilar and similar joints at a determined failure load. Cracks tended to develop close to the heat-affected zone (HAZ) around the weld nugget diameter (dn). SIF and crack path have been verified.

The present paper provides an analytical solution for a periodic array of two collinear and symmetric cracks (P-TCSC) under remote tension. This is achieved by representing the multiple collinear cracks problem as the contact problem with discrete ligament regions, and the governing equations are obtained as integral equations with Cauchy-type kernel. Closed-form expressions are derived for the crack opening profile, normal stress distribution and mode I stress intensity factors (SIFs), which can reduce to the classical solutions of two collinear and symmetric cracks (TCSC) or a periodic row of collinear cracks with equal length and equal spacing (PCEE) under special conditions. Finite element analysis is also performed to validate the analytical solutions obtained. Different from the TCSC case, results show that crack initiation for P-TCSC seems more complicated depending on a combination of two nondimensional parameters, and a SIFs map for P-TCSC is further constructed to give a more precise evaluation. The proposed method relies solely on solving the integral equations with Cauchy-type kernel combined with the corresponding boundary conditions without a prior knowledge of the complex potential function in traditional complex variable method of plane elasticity, and it may find application in plastic zone evaluation and fracture criteria of collinear cracks. [ABSTRACT FROM AUTHOR]

This paper considers the problem of symmetrical three-point bending of a prismatic beam with an edge crack. The solution is obtained by the mixed finite element method within the simplified Toupin–Mindlin strain gradient elasticity theory. A mixed variational formulation of the boundary value problem for displacements–strains–stresses and their gradients is applied, simplifying the choice of approximating functions. The concept of energy balance is adopted to calculate the energy release rate with a virtual increase in crack length. The increment of the potential energy of an elastic body is determined by accounting for the strain and stress gradient contribution. Numerical calculations were performed using a quasi-uniform triangular mesh of the cross-type. The mesh refinement was applied in the vicinity of the crack tip, at the concentrated support, and the point of application of the transverse force, and uniform mesh partitioning was utilized in the rest of the beam. The fine-mesh analysis was carried out on the successively condensed meshes in the stress concentration domain for different values of the length scale parameter. The crack opening displacements and the distribution of strains and Cauchy stresses for various values of the length scale parameter are presented. An increase in this parameter increases the stiffness of the crack, which leads to a decrease in the crack opening displacements and a smooth closure of its faces at the crack tip. In addition, accounting for the scale parameter reduces the calculated values of strains and stresses near the crack tip. Based on the energy balance criterion, local fracture parameters such as the release rate of elastic energy at the crack tip and the stress intensity factor are determined for different values of the mesh step. The numerical calculations indicate the convergence of the obtained approximations. The main feature of solutions, which includes the strain gradient contribution, is the decrease in the values of the calculated parameters associated with the fracture energy compared to the classical elasticity theory. [ABSTRACT FROM AUTHOR]

The huge impact of kinetic energy released by the breaking of hard roof is one of the important factors that induces dynamic disasters in coal mines. The key to preventing and controlling coal and rock dynamic disasters is the directional fracture of strata at a specific position and reducing the length of hard roof suspension. The multi-hole sleeve fracturing technology has the advantages of simple operation and wide application conditions and has a wide research prospect in the field of hard roof weakening. In order to understand the mechanism of multi-hole sleeve fracturing, the mechanical mechanism of multi-hole sleeve fracturing was studied using theoretical analysis and numerical simulation. The variation law of inter-hole stress under different influencing factors was revealed, and the crack propagation law and force chain distribution characteristics in the fracturing process were obtained. The pre-cracking effect of sleeve fracturing can be improved by changing the drilling structure through grooving. In order to determine the reasonable hole arrangement parameters, a mechanical model of the multi-hole sleeve fracturing with prefabricated cracks was established based on linear elastic fracture mechanics. The calculation equations of stress intensity factor, critical expansion pressure, and critical crack initiation angle of cracks were given, and the variation rules of stress intensity factor, critical expansion pressure, and critical crack initiation angle of cracks under different influencing factors were obtained. The results show that: ① The lateral pressure coefficient k has a significant effect on the minimum crack initiation stress of the borehole. With the lateral pressure coefficient k > 1, the minimum crack initiation stress decreases with the increase of the hole angle. With the lateral pressure coefficient k < 1, the minimum crack initiation stress decreases with the increase of the hole angle. ② The numerical simulation results show that there is a stress superposition effect between the sleeves, and the contact force chain is a 'radial' distribution. The fracturing process of the sleeve is mainly a tensile failure, and the deformation and failure at the connection of the hole center is the most severe, forming a 'banded' fracture surface along the direction of the hole. ③ The stress distribution near the slot end is changed by the slot, and the circumferential tensile stress is larger than that of the seamless slot model. When the slot length is 0.5 times the radius of the hole, the critical expansion pressure is the smallest, and the crack is most likely to expand. ④ The critical initiation angle is determined by KI and KII, which is less than 70.53°. Under the condition that the pump pressure and in-situ stress conditions cannot be changed, the directional fracturing of the rock can be realized by adjusting the hole angle and the length of the prefabricated slot.

Purpose – This paper comprehensively addresses the influence of chopped strand mat glass fiber-reinforced polymer (GFRP) patch configurations such as geometry, dimensions, position and the number of layers of patches, whether a single or double patch is used and how well debonding the area under the patch improves the strength of the cracked aluminum plates with different crack lengths. Design/methodology/approach – Single-edge cracked aluminum specimens of 150 mm in length and 50 mm in width were tested using the tensile test. The cracked aluminum specimens were then repaired using GFRP patches with various configurations. A three-dimensional (3D) finite element method (FEM) was adopted to simulate the repaired cracked aluminum plates using composite patches to obtain the stress intensity factor (SIF). The numerical modeling and validation of ABAQUS software and the contour integral method for SIF calculations provide a valuable tool for further investigation and design optimization. Findings – The width of the GFRP patches affected the efficiency of the rehabilitated cracked aluminum plate. Increasing patch width WP from 5 mm to 15 mm increases the peak load by 9.7 and 17.5%, respectively, if compared with the specimen without the patch. The efficiency of the GFRP patch in reducing the SIF increased as the number of layers increased, i.e. the maximum load was enhanced by 5%. Originality/value – This study assessed repairing metallic structures using the chopped strand mat GFRP. Furthermore, it demonstrated the superiority of rectangular patches over semicircular ones, along with the benefit of using double patches for out-of-plane bending prevention and it emphasizes the detrimental effect of defects in the bonding area between the patch and the cracked component. This underlines the importance of proper surface preparation and bonding techniques for successful repair. Graphical abstract –

Most techniques of measuring the stress intensity factor (SIF) in the cracking process assume a crack in a planar medium. Currently, there is no effective approach for curved brittle shells, particularly for non-developable cases, i.e., shapes with non-vanishing Gaussian curvature. This paper introduces a novel approach to obtaining material properties related to fracture by experimentally observing weakly curved surfaces. Based on the DIC record of the displacement field around the crack tip, the truncated Williams expansion is fitted to the data adjusted according to the shallow shell equations. The convergence properties of the method are investigated by comparing experimental data of PMMA cylinders to theoretical and numerical predictions. The applicability of the technique to non-developable surfaces is verified. It is demonstrated that robust convergence requires the number of terms in the Williams expansion exceeding 6. For different geometries, the ratio of the data selection radius and the length of the crack should exceed 0.3.

AbstractThe fracture problem has been modeled using Radial Point Interpolation Method (RPIM) to examine the effects of support domain size and shape parameter value on the calculation of Stress Intensity Factor (SIF). The study focuses on an edge crack problem subjected to normal load and shear loads, determining that the support domain size of ‘α≥3.5 and shape parameter value between ‘n=1.9-2.1’ yield results of accuracy with error %≤3%. Additionally, research extended by varying the problem domain size and crack location to verify consistency. The findings indicate that selecting the optimal shape parameter value will ensure better accuracy over the enrichment techniques with lesser computational cost. [ABSTRACT FROM AUTHOR]

The aim of this study is to provide a solution for the plastic limit pressure and stress intensity factor of the elbows containing a part-through axial semi-elliptical crack by considering various crack sizes. The supporting system and loading conditions of the pipeline are described. The critical part of the observed pipeline was isolated for analysis and subjected to various sizes of semi-elliptical cracks. By performing numerical analysis, results were obtained for crack dimension ratios of c/a, and depth/thickness ratios of a/t. The obtained results include plastic limit pressure and stress intensity factor. The results were analyzed with a symbolic regression algorithm, and closed-form solutions for the limit pressure and stress intensity factor were proposed. To validate pipeline integrity, the Structural Integrity Assessment Procedure (SINTAP) was applied, and the FAD (Failure Assessment Diagram) was generated for cracks below the FAD function. The failure pressure was calculated by determining the points where the loading paths intersect the FAD function. [ABSTRACT FROM AUTHOR]

An unresolved question in fracture mechanics is whether the variations in the size or aspect-ratio of cracked plates or structures have a significant effect on the stress intensity factor (SIF) at the crack tip. Indeed, there are significant numerical data showing the effect of specimen aspect-ratio on SIF. There is also experimental evidence supporting the existence of the size effect on fatigue and fracture behavior. However, there is no analytical formula to capture such a size effect on the stress intensity factor for standard fracture mechanics crack configurations. In this study, a novel net-section-based approach is used to develop simple and approximate SIF expressions for center and edge cracks in tension plates of various aspect ratios. Expressions have been derived for both uniform stress as well as uniform displacement boundary conditions. Comparisons are made with the available numerical stress intensity factor data. A remarkable agreement of the net-section-based SIF expressions with the numerical data (complex potential, finite element, and variational approaches) is found. For the clamped-end condition, the net-section approach leads to Rice's limiting SIF for a semi-infinite crack in an infinitely wide strip, validating the analysis. Additionally, the SIF expressions developed here also highlight some discrepancies in numerical data. The study provides simple SIF expressions that can be readily used to analyze specimen size or aspect-ratio effects on critical values of stress intensity factors for cracks in materials and structures under tension loading. [ABSTRACT FROM AUTHOR]

This study focuses on the failure analysis of a hypocycloid-type crack within a thermo-elastic material. Employing the conformal mapping method, analytical continuation theorem, and principle of superposition, the explicit general solution for stress intensity factors (SIFs) associated with an arbitrary-edged hypocycloid-type crack is determined analytically under the influence of remote homogeneous heat flux and mechanical load. The superposition method combines stress functions and SIFs for two distinct loading conditions. The outcomes of the normalized SIFs are affected by the magnitude and orientation of the heat flux and mechanical load. A full-field stress distribution is provided to account for variations in SIFs. Certain combinations of loads lead to maximum SIF values, rendering the system highly vulnerable to damage, while two specific scenarios inhibit crack propagation, thereby reducing the risk of structural failure. [ABSTRACT FROM AUTHOR]

Reinforcing crack-damaged concrete structures with ultra-high-performance concrete (UHPC) proves to be more time-, labor-, and cost-efficient than demolishing and rebuilding under the dual-carbon strategy. In this study, the extended finite element method (XFEM) in ABAQUS was first employed to develop a numerical model of UHPC-reinforced single-notched concrete (U+SNC) beams, analyze their crack extension behavior, and obtain the parameters necessary for calculating fracture toughness. Subsequently, the fracture toughness and instability toughness of U+SNC were calculated using the improved double K fracture criterion. The effects of varying crack height ratios (a/h) of SNC, layer thicknesses (d) of UHPC reinforcement, and fiber contents in UHPC (VSF) on the fracture properties of U+SNC beams were comprehensively investigated. The results indicate that (1) the UHPC reinforcement layer significantly enhances the load-carrying capacity and crack resistance of the U+SNC beams. Crack extension in the reinforced beams occurs more slowly than in the unreinforced beams; |(2) the fracture performance of the U+BNC beams increases exponentially with d. Considering both the reinforcement effect benefit and beam deadweight, the optimal cost-effective performance is achieved when d is 20 mm; (3) with constant d, increasing a/h favors the reinforcement effect of UHPC on the beams; (4) as VSF increases, the crack extension stage in the U+BNC beam becomes more gradual, with higher toughness and flexural properties; therefore, the best mechanical properties are achieved at a VSF of 3%. [ABSTRACT FROM AUTHOR]

In high-cold regions, the instability of precarious rock masses in open-pit mines is often exacerbated by the effects of freeze-thaw cycles, posing a significant threat to the continuous production of open-pit mining operations. To address this issue effectively, we conducted an in-depth study on the precarious rock masses in the near-slope of a mining area in a high-cold region using a fracture mechanics-based stability analysis method. We analyzed the impact of freezethaw cycles on the engineering stability. Introducing a novel approach, we established the temperature field at different time points to determine whether the freeze-thaw depth influences the generation of freeze-thaw forces on the controlling structural surfaces. Employing the maximum circumferential stress criterion, we conducted a comprehensive analysis of tension cracks in the slope and derived corresponding safety factor expressions. Focusing on retrogressive rock slopes, we divided the slope's precarious rock masses into n potentially unstable approximate rectangular rock bodies. Based on this, we developed a fracture mechanics-based slope stability calculation method considering the combined effects of freeze-thaw forces, crack water pressure, and gravity. Through relevant numerical examples, we successfully calculated the safety factors of the segmented rock bodies, revealing the varying influence of freezethaw forces on rock mass stability. By integrating the calculation results with practical engineering considerations, we validated the feasibility of our proposed method. Lastly, aligning with pertinent precarious rock stability assessment criteria, we provided corresponding remediation measures based on the distinct stability conditions of the rock masses. Through comprehensive research and an effective computational approach, we offer a scientifically viable solution for the stability of precarious rock masses in open-pit mines in high-cold regions, thereby providing robust technical support for the sustainable production of mining enterprises. [ABSTRACT FROM AUTHOR]

AbstractIn this study, the progress of surface crack and high cycle fatigue of the surface piercing propellers (SPPs) are investigated numerically using the finite element method. The cyclic load is calculated from the hydrodynamic pressure on the blade by simulating the fluid around the blade using the computational fluid dynamics software STAR-CCM+. The initial cracks are assumed to be created near the blade root. The fatigue life is calculated from the Paris-Erdogan equation. The results show that the crack close to the root has a shorter life and the stresses at the crack front depend on the blade-water interaction duration. [ABSTRACT FROM AUTHOR]

Steel hollow structure section (HSS) chord-to-branch joints in Vierendeel trusses are concerned for their proneness to fracture due to imperfection in fabrication. In this paper, the stress intensity factors (SIFs) for HSS chord-to-branch joints are examined based on fracture mechanics and finite element modelling. Through a well-prepared sub-modelling strategy, the influences of geometric parameters related to the crack propagation behaviour are analysed and discussed. The crack front of the HSS chord-to-branch joint without the axial stress of the branch is shown to have notably high SIFs at the deepest point and the surface point. Alternatively, the concentration of highest SIFs at the deepest point of the elliptical arc of the crack becomes significant with the increase of the axial stress of the branch. The increase of the chord wall thickness is shown to be beneficial in the reduction of the SIFs for HSS chord-to-branch joints, especially for lower chord width ratio normalized by thickness. Conversely, the influence of the crack shape indicated by larger aspect ratio on the reduced SIFs becomes obvious and consistent for greater chord width ratio normalized by thickness. The SIFs for HSS chord-to-branch joints are decreased with the increase of the normalized crack depth with respect to the chord wall thickness, particular for shallow surface cracks. Such a trend becomes obvious for the joints with lower fillet weld leg length of equal leg fillet welds with respect to the chord wall thickness or with lower weld leg length along the HSS branch with respect to that along the chord. [ABSTRACT FROM AUTHOR]

This study deals with the propagation of semi-infinite crack impacted by SH-wave propagation in a pre-stressed magnetoelastic orthotropic strip (PMOS). The proposed analytical model makes use of the Wiener-Hopf (WH) approach and two-sided Fourier integral transforms (FIT). The exact formulation of the stress intensity factor (SIF) for constant concentrated force (CCF) has been established in closed form. The effect of influencing factors, including the crack length, crack speed, magnetoelastic parameter, horizontal compressive pre-stress (HCP)/horizontal tensile pre-stress (HTP), vertical compressive pre-stress (VCP)/vertical tensile pre-stress (VTP), and anisotropy parameter on the SIF in the considered strip has been unraveled. The proposed model is compared with the case of a pre-stressed magnetoelastic isotropic strip (PMIS) and some peculiarities, along with the influence of orthotropy have been reported. The significant results reported in the present manuscript reveal that magnetoelasticity and pre-stress is a prominent factor impacting crack propagation in elastic material with orthotropy configuration properties and has a significant impact on the SIF, which has not been taken into account in the existing literature on the subject of fracture mechanics. The present investigation helps with structural and reliability analysis, fracture propagation, material durability and failure of engineering structures. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new approach for numerically simulating the growth of cracks in unidirectional composite materials, termed extended isogeometric analysis, evaluating the maximum stress intensity factor and T-stress. To validate our approach, we used a small anisotropic plate with two edge cracks, beginning with formulating the governing equations based on the energy integral method, Stroh's Formula, and the Elastic Law describing the behaviour of anisotropic materials, while considering boundary conditions and initial states. A MATLAB code was developed to solve these equations numerically and to post-process the tensile stress and the stress intensity factor (SIF) in the first mode. The results for the SIF closely match those obtained using the extended finite element method (X-FEM), with a discrepancy of only 0.0021 Pa·m0.5. This finding underscores the credibility of our approach. The extended finite element method has demonstrated robustness in predicting crack propagation in composite materials in recent years, leading to its adoption by several widely used software packages in various industries. [ABSTRACT FROM AUTHOR]

The problem of a semi-infinite moving crack at the interface of two bonded dissimilar strips of finite width has been solved. The crack is subjected to two constant normal displacements applied on the boundaries. The problem has been converted to one that is suitable for applying the Wiener–Hopf technique. Fourier transform technique has been used to reduce the mixed boundary value problem to the standard form of the Wiener–Hopf equation which has been solved in asymptotic form to obtain the analytical expressions of stress intensity factor and crack opening displacement. Finally the numerical values of stress intensity factor and crack opening displacement have been plotted graphically against various parameters to show the effects of these parameters on stress intensity factor and crack opening displacement. [ABSTRACT FROM AUTHOR]

The advent of digital image and volume correlation has attracted wide use in fracture mechanics. The full‐field nature of digital image and volume correlation allows for the integration of computational fracture mechanics to analyse cracked samples quantitatively. This review provides a comprehensive overview of current methods used to extract fracture properties from full‐field displacement data. The term full‐field fracture mechanics is introduced to highlight the uniqueness of using inherently noisy experiential data to extract fracture properties. The review focuses on post‐processing‐based approaches rather than integrated approaches, as these have less limitations and are more commonly employed. There are four approaches that are discussed in extracting fracture properties from experimentally computed displacement data: field‐fitting, integral, crack‐opening and cohesive zone modelling approaches. This is further developed to discuss problems associated with using digital image and volume correlation to extract properties, including application examples. [ABSTRACT FROM AUTHOR]

Based on numerical simulation and fatigue tests, different types of crack were simulated and local full-scale specimens of typical fatigue details in steel bridge deck were designed for drilling. The relationship between the reasonable hole diameter, stress intensity factor K at the crack tip and yield strength σys of the base metal was explored. The result demonstrates that the reasonable hole diameter is linearly related to $K^ 2/\sigma _{ys}^ 2$ K 2 / σ ys 2 . The larger the ratio of KIII/KI, the smaller the reasonable diameter required. Considering that KIII cannot be measured in real bridges, taking KI2/σys as the basis for diameter selection can ensure a large surplus. The method of determining the hole diameter by K and σys is applicable when the crack length is relatively short compared with the boundary size. In addition, the stress intensity factor measured by the two-strain-gage method is slightly higher than that calculated by extended finite element method, with an average error of about 10%, which has the accuracy required for real-bridge application. [ABSTRACT FROM AUTHOR]