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The present work investigates the mode-I fracture of single-edge notched beams under symmetric three- and four-point bends through dual-horizon peridynamic simulations. Mode-I J-integral and crack opening displacement are computed for a wide range of initial crack length-beam width ratios. δ-Convergence is carried out. Results are discussed with analytical and finite element methods. Peridynamic simulations agree well with analytical results. [ABSTRACT FROM AUTHOR]

To estimate the fatigue life of lightweight automotive structures in compliance with top-down design principles, there is a need for an accurate adhesive joint fatigue life prediction method that is compatible with industrial finite element modeling practices. This paper proposes a method to split the analytical J-integral solution based on the fracture mode of joints. The split mode I and II J-integrals correspond to the opening mode and sliding mode of the bonded joint, respectively. By splitting the J-integral and introducing the concept of the mixed mode ratio, an improved approach for estimating adhesive joint fatigue life is presented, considering the influence of loading modes. The proposed fatigue life prediction method is validated through fatigue tests on a sub-component level bonded structure. The results of the validation demonstrate that the split J-integral analytical solution method, considering the mixed mode ratio, provides better predictions compared to its predecessor approach. [ABSTRACT FROM AUTHOR]

The present study develops the scaled boundary finite element method (SBFEM) to derive the J-integral directly based on defining the rectangular contour. To achieve this, firstly the J-integral is calculated for each element with different path integrals of radial direction in an arbitrary subdomain. Then, the computed values of elements are summed in the entire domain. Finally, to validate and displaying the efficiency of the SBFEM solution, three two-dimensional (2D) numerical examples are solved for different integration paths. The results indicate path-independent property and fast convergency of this semi-analytical method in the term of J-integral computation. [ABSTRACT FROM AUTHOR]

In the aeronautical construction several rivet holes are drilled, these holes constitute stress concentration zones which can be affects the fatigue life through cracks initiation at the edge of rivet holes. To remedy this problem and minimize stress level in these zones, the cold expansion technique is used to enhancing the fatigue life of rivet holes. The present work aims to investigate through finite element analysis the effect of three degree cold expansion (2%, 4.5% and 6%) on the reduction of stress level on the edge of rivet hole. The hole-crack interaction effect was thus analyzed. This effect is quantified by the values of JIntegral at the two tip of crack. The obtained results show that negative values of J-Integral was found which can be explained by the beneficial effect of residual compressive stresses induced by cold expansion on the crack closing. [ABSTRACT FROM AUTHOR]

Composite materials find extensive usage in industrial applications. However, they are susceptible to gradual damage over time. In this study, we explored the cracking processes in jute fiber-reinforced composite sheets subjected to uniaxial tension at varying displacement speeds (10, 20, and 30 mm/min) using Abaqus software. The composite plate dimensions are 25×35×10 mm³, with a 7 mm crack length. Our findings indicate that crack propagation in vehicle plates is influenced by mechanical properties relative to load, specifically through increased travel speed. We observed stress concentration around the crack, and the displacement speed significantly affects crack behavior. The cohesive J-integral was derived through finite element analysis, revealing a 90.90% relative error in the mean absolute value ΔJ across the five integral paths for the two sample types. Subsequently, five potential end conditions were assessed for further analysis, considering different boundary conditions: Simply supported (SSSS), two opposing sides clamped (SFSF), Clamped-Simply-Clamped-Simply (SCSC), two opposing sides clamped (CFCF), and all sides clamped (CCCC). Additionally, three different types of tensile actions in the y-direction were considered. [ABSTRACT FROM AUTHOR]

Due to the existence of structural and material property discontinuities in the ring-welded joints of large-diameter, high-steel-grade pipelines, which are prone to the risk of fracture. Therefore, in this paper, computer-aided engineering techniques, based on finite element analysis and numerical calculations, have been used to establish a model of pipeline containing internal surface crack defects for simulation, and J-integral algorithms have been applied to evaluate the effect of crack parameters on fracture behavior. This research highlights the critical role of computers in pipeline engineering and provides an important theoretical and methodological basis for further optimizing pipeline design and maintenance. [ABSTRACT FROM AUTHOR]

This work presents an analysis of the effect of ball indentation on fatigue crack growth. The main objective is to assess the effectiveness of indentation, particularly its influence on the J-integral, as a fracture criterion governing fracture toughness. Using the finite element method in Abaqus 6.14, we analyzed the residual stresses induced by indentation at different positions along the predicted line of crack propagation and calculated the J-integral. The results highlight that indentation at the crack tip position significantly reduces the J-integral compared to non-indented structures, demonstrating its potential to extend the lifespan of cracked components by delaying crack propagation. The findings underscore the practical application of ball indentation as a viable technique to retard crack growth, contributing to the longevity of cracked components and, consequently, structural integrity. This analysis revealed a crack propagation retardation gain of up to 56%. [ABSTRACT FROM AUTHOR]

Leak-before-break (LBB), as a part of the fitness-for-service (FFS) assessment, is a critical requirement to ensure pressure vessel structural integrity LBB generally means a leak will be detected before an in-service catastrophic failure occurs. Despite some established procedures in API 579-1/ASME FFS-1 or BS 7910 standards, performing a robust LBB assessment is not a regular and straightforward practice in the oil, gas, and petrochemical industries. A mix of different sources has been commonly used in case studies, which could lead to non-consistent results. This paper presents, firstly, a three-dimensional finite element analysis (FEA) within an LBB assessment framework for a cylindrical pressure vessel. The stress intensity factor (SIF) of a defective vessel with a through-thickness crack is numerically calculated using the J-integral method and based on linear elastic fracture mechanics (LEFM) approach. The accuracy of the numerical solutions is then compared with the analytical results proposed by the API 579-1/ASME FFS-1 standard. The maximum (limiting) through-thickness flaw size, which will not grow to an intolerable size during the vessel service life, is calculated analytically and numerically. Afterward, errors in measuring the exact length of the crack during inspections, the internal pressure fluctuations due to the vessel's operational conditions, and uncertainties in characterizing the mechanical properties of the base material, including its minimum yield strength and toughness, are quantified. A reliability analysis is finally evaluated to assess the probability of failure considering these uncertainties. [ABSTRACT FROM AUTHOR]

The presented work provides a detailed analysis of modern approaches to creating elastoplastic models of surface crack growth that take into account the influence of the type of biaxial loading on the development of stresses and strains at the crack tip and, accordingly, on the crack growth rate. The use of the plastic stress intensity factor as a characteristic of resistance to cyclic deformation and fracture for biaxial loading conditions is substantiated. Continuum plasticity models are proposed to simulate the elastoplastic behavior of metal using numerical methods and, in particular, the finite element method.

The J‐integral approach manifests itself in an efficient way to determine the crack growth and failure mechanism of tread and sidewall compounds used in tyres. Therefore, for a pure shear (PS) specimen of carbon black filled natural rubber, the J‐integral formula was vivisected, and the material parameters were defined using the concepts of solid mechanics considering the planar stress conditions. Theoretical calculations, experimental observations, and finite element analysis were executed to calculate the J value for different strain percentages. Different hyperelastic material models were used to understand the hyperelastic behavior of the test compound, but Yeoh model was found to be the best fit with the least error against the experimental test data. The frequency sweep dynamic mechanical analyzer test was done to observe the viscoelastic response of the material. It was observed that the J value decreased with decreasing contour radius and had exhibited stark difference with the global tearing energy values, indicating the effects of stress softening and the dependence of J value on the elastic characteristics of the material. Further, the J value attained from finite element methods for a random strain 22% was used to predict the crack growth rate of the pre‐notched PS specimen. Highlights: J‐integral formula for pure shear specimen using solid mechanics approach.J value comparison of theoretical, experimental, and finite element methods.Dependence of J value on the elastic characteristics of the material.Different hyperelastic models compared and Yeoh model chosen for analysis.Prediction of crack growth rate at a random strain percentage. [ABSTRACT FROM AUTHOR]

The state of pre-fracture of a thin adhesive layer of finite thickness in the vicinity of a crack-like defect is considered. It is proposed to take into account the hydrostatic pressure, which forms the volume deformation energy, in order to find the critical state. The critical value of the J-integral for the I+II loading mode is assumed to be dependent on the product of the volume strain energy and the layer thickness at the end face of the adhesive. The limiting value of the product of the volume energy and the layer thickness under loading in mode I, as well as the critical values of the J-integral for loading modes I and II, determine the value of the loosening parameter of a particular adhesive in the proposed failure criterion. [ABSTRACT FROM AUTHOR]

The fracture of structures under mixed‐mode loaded cracks is usually assessed using stress intensity factors (SIFs). Domain integrals, specially the J‐integral and the interaction integral, are widely used for SIF extraction and provide high accurate estimations with finite element methods, although the J‐integral does not allow the separation of the SIF components. However, interaction integral definition implies hypothesis that are not fulfilled in generic non‐planar cracks and therefore other methods can be an option to solve this problem. A different path‐independent integral, the neutral‐action integral, was introduced in 2010 by Kienzler et al. The application of the J‐integral and the neutral‐action integral allows the computation of the SIF in a mixed‐mode situation and separate the SIF components. The presented study considers the applicability of the neutral‐action integral and investigates its limitations. The research is performed using well‐known and basic problems that can be considered as a basis for other more complicated cases, in order to obtain an convergence analysis without introducing further errors. Highlights: Verification of Domain integral implementation for N‐integral.Comparison of N‐integral and interaction integral.Comparison of N‐integral with interaction integral in XFEM.Fatigue and fracture. [ABSTRACT FROM AUTHOR]

Natural defects such as nano inclusions and nanocracks are inevitable in dielectric materials. When materials are subjected to mechanical loading, the strain gradient around crack tips and inclusions would become large and induce significant flexoelectric fields. In contrast to classical crack-inclusion problems, the interactions between these flexoelectric fields may locally change the electromechanical behaviors of materials and result in some interesting phenomena. To better understand the crack-inclusion interactions in flexoelectric solids, in this work, we use a collocation mixed finite element method to model and analyze the flexoelectric fields around the crack tip and inclusion. On the basis of the J-integral, we analyze how the flexoelectric effect affect the interaction energy between nanocracks and nearby nano inclusions. This work proposes a new coupling mechanism in crack-inclusion problems and may inspire future experiments in flexoelectric solids. [ABSTRACT FROM AUTHOR]

The human body normally uses alternative materials such as implants to replace injured or damaged bone. Fatigue fracture is a common and serious type of damage in implant materials. Therefore, a deep understanding and estimation or prediction of such loading modes, which are influenced by many factors, is of great importance and attractiveness. In this study, the fracture toughness of Ti-27Nb, a well-known implant titanium alloy biomaterial, was simulated using an advanced finite element subroutine. Furthermore, a robust direct cyclic finite element fatigue model based on a fatigue failure criterion derived from Paris' law is used in conjunction with an advanced finite element model to estimate the initiation of fatigue crack growth in such materials under ambient conditions. The R-curve was fully predicted, yielding a minimum percent error of less than 2% for fracture toughness and less than 5% for fracture separation energy. This provides a valuable technique and data for fracture and fatigue performance of such bio-implant materials. Fatigue crack growth was predicted with a minimum percent difference of less than nine for compact tensile test standard specimens. The shape and mode of material behaviour have a significant effect on the Paris law constant. The fracture modes showed that the crack path is in two directions. The finite element direct cycle fatigue method was recommended to determine the fatigue crack growth of biomaterials. [ABSTRACT FROM AUTHOR]

Excellent tire wear resistance, wet grip resistance, and rolling resistance have made silica-filled green elastomeric composites suitable for an electric vehicle to lower fuel consumption. The study of damage mechanics of such materials has to be carried out in order to maximize safety during their usage. Accordingly, we aim to develop a damage model to characterize the effect of geometric configuration for such elastomeric composites. A 'VUSDFLD' damage subroutine is developed for the elastomeric composites, which is used in finite element analysis (FEA) and verified experimentally within 2% error. It is demonstrated that the change in geometric configuration can affect the fracture properties like J-integral and geometry factor. The J-R curve fits with a power-law equation with a correlation factor greater than 0.98. In contrast, using analytical modeling, an empirical relationship is proposed to trace CTOD-R curves of elastomeric composites with R2 greater than 0.88, which exhibits dependency of geometric configuration on fracture of elastomeric composites. We envisage that this fracture model can solve most of the fracture-related problems in elastomeric composites used in tires for EV and allied applications. [ABSTRACT FROM AUTHOR]

Nodal stresses are exploited in peridynamics to investigate the mode-I J-integral of single edge- and center-cracked plates with initial crack length-plate width ratios from 0.1 through 0.5. Computed values of the J-integral on six different contours differ from each other by about 1% and are compared and discussed with analytical methods, with finite element analysis as well as with previous peridynamic studies. Simulation results show that mode-I J-integral via peridynamic stresses are highly accurate. [ABSTRACT FROM AUTHOR]

The structural integrity of metallic structures/components depends on their fracture behaviour. These materials respond non-linearly in nature under applied service conditions. Therefore, the prediction of accurate fracture parameters under elasto-plastic conditions is cumbersome. This work consists of an accurate and robust computational approach to predict elasto-plastic fracture parameters for a 3-D cracked domain. A mesh-independent novel computational method known as the Extended Finite Element Method (XFEM) is employed to predict elasto-plastic fracture parameters (J-integral). Both material and geometrical non-linearity have been incorporated into the computational approach. The Ramberg-Osgood material model has been incorporated to characterise the non-linear relationship of stress-strain. The material non-linearity is modelled by von-Mises yield criteria along with isotropic strain hardening. Elastic predictor plastic corrector algorithm is used for modelling non-linear stress-strain behaviour. The geometric non-linearity is modelled by an updated Lagrangian approach. Few numerical cases are presented to show the efficacy of the proposed computational approach. To incorporate the proposed approach, an inhouse MATLAB code has been developed. The obtained numerical results are displayed in the form of convergence study, J-integral, and deformation contours. Additionally, a component-based problem, i.e. surface crack in a spur gear, has been analysed to show the robustness of the proposed methodology. [ABSTRACT FROM AUTHOR]

• J e is demonstrated to be equivalent to cohesive energy in elastic-plastic materials. • Cohesive energy can be obtained through standard fracture experiments. • Using J e as cohesive energy provides more accurate predictions than using J i. • Method is beneficial to standardize the determine procedure of cohesive parameters. The identification of cohesive parameters for elastic-plastic materials is an important topic in the field of fracture mechanics. A new method is proposed in this study to determine cohesive parameters based on the physical meaning of cohesive energy, which is equivalent to the elastic component of J -integral at crack initiation, J e. Through a comparative analysis of energy balance theory, the J -integral, and cohesive zone model, it is demonstrated that both the cohesive energy and J e are equivalent to the surface free energy, with a clear distinction from plastic dissipation energy. For a typical elastic-plastic material, 304 stainless steel, the cohesive energy and cohesive strength are determined through fracture tests on compact tensile (CT) specimens and the finite element inverse method. The obtained cohesive parameters are validated against the experimental data of the CT specimens and the single edge bend specimens. Results show that both the computed load–displacement curves and crack front shapes are in good agreement with the experimental data. Furthermore, the transferability of the present cohesive parameters is demonstrated by the accurate predictions for two different specimens. By distinguishing the surface free energy and plastic dissipation energy, the present method provides a reasonable and effective way to determine the cohesive parameters of elastic-plastic materials compared to previous methods. [ABSTRACT FROM AUTHOR]

The introduction of pressure piping increasingly requires the use of efficient materials which must withstand both high hydrostatic pressures, high mechanical loads and high thermal gradients. At nuclear power plants, piping systems are subjected to high pressures (up to 60 MPa). The occurrence of cracks and their possible spread is one of the serious risks in the industry. For this reason, elbows are considered critical components of a piping system. Therefore, in order to design and/or qualify a pipe structurally, it is useful to have a reliable evaluation of their structural behavior under different combined loads. The objective of this study is to determine analytical functions for the evaluation of the J integral as a function of crack size, elbow size, and the nature and intensity of loading. This assessment is derived from the numerical results obtained by the WARP3D calculation code exploiting the finite element method (FEM). [ABSTRACT FROM AUTHOR]

Defects like crack are common in engineering structures that are either material intrinsic or initiate during fabrication. The theory of fracture mechanics establishes a mechanistic relationship between the maximum allowable loads applied on a structural component to the size and location of an actual or assumed crack in the component. Linear‐elastic or complex elastic‐plastic, i. e., non‐linear models, are used to conduct the fracture analysis. Established studies show that methods of non‐linear fracture mechanics, in comparison to elastic methods, offer more accurate measures of the fracture behaviour in failed structures with high toughness and materials with low strength. In this work, an attempt is made to evaluate stress intensity factor‐KI and J‐integral of 40Ni2Cr1Mo28 alloy (structural application steel) for various crack length‐a to width ratio‐W (a/W = 0.25, 0.375, 0.5, 0.625 and 0.75) against the applied force in the form of load under plane stress condition by elasto‐plastic finite element analysis (compact tension specimen). Non‐linearity is modeled using the inverse Ramberg‐Osgood relation. Compact tension specimen is modeled in ANSYS software and analyzed by using Finite element analysis. It is found that there is a good agreement between both finite element analysis and theoretical value with an error deviation in the range of 0 % to 6 %. [ABSTRACT FROM AUTHOR]

Most human teeth have an exposed surface layer of calcified enamel, which is harder than the inner layer of dentin. The interface between the enamel and dentin is called the dentin–enamel junction (DEJ), which ensures that teeth do not collapse and fall off. The purpose of this study was to use finite element analysis software through the J -integral method and the extended finite element method (XFEM) to simulate three models of DEJ structures: (i) wavy DEJ with no thickness, (ii) rectangle DEJ with a thickness of 0.3 mm, and (iii) wavy DEJ with a thickness of 0.3 mm. This paper demonstrates that the layered structure of human teeth plays a positive role in enhancing the fracture strength and preventing the crack from spreading to the depths of teeth. At the same time, we also justify of the scalloped structure and concave orientation of the DEJ interface. The residual stresses in DEJ and its adjacent dentin region are also an important factor of tooth resistance to crack propagation. In addition, the configuration of the DEJ interface and residual stresses in DEJ and dentin areas are further justified by means of XFEM method. The findings in this study provide potential inspiration for the biomimetic design toward strengthening the dentin and dentin-like materials. [ABSTRACT FROM AUTHOR]

The adhesion/delamination characteristics at the stamp/film interface are critical for the efficiency of film microtransfer printing technology. To predict and regulate the interface mechanical behaviors, finite element models based on the J-integral, Virtual Crack Closure Technology (VCCT), and the cohesive zone method (CZM) were established and compared. Then, the effects of pulling speed and interface parameters on the pull-off force, which is used to characterize the interface adhesion strength, were investigated. Comparisons between the simulation results and previous experimental results demonstrated that the model based on the CZM was more applicable than the models based on the J-integral and VCCT in analyzing the adhesion/delamination behaviors of the stamp/film interface. Furthermore, the increase in pulling speed could enlarge the pull-off force for the viscoelastic stamp/film interface, while it had no influence on the pull-off force for the elastic stamp/film interface. In addition, a larger normal strength and normal fracture energy resulted in a larger pull-off force, which was beneficial to the realization of the picking-up process in microtransfer printing. [ABSTRACT FROM AUTHOR]

In this paper, stress intensity factor (SIF) solutions of eccentric annular external cracks in elliptical notched round bars under tension loading have been obtained from 3D finite element analysis, along with their relation to the energy release rate obtained with the J-integral contour. The analysis variables have been the ligament diameter, its eccentricity, and the elliptical notch aspect ratio. The maximum SIF increases with the ligament eccentricity, the presence of the notch (compared to when the bar is smooth), and the elliptical notch axial semi-axis (for the same notch depth); it decreases with the ligament diameter. For external cracks, eccentricity induces bending of the bar subjected to tensile loading, which can produce partial and full contact of the crack surface, relevant phenomena in terms of the SIF value at the different points of the crack front.

Interface cracks seriously affect the performance and service life of layered electronic devices. At nanoscale, the electric field concentration can be generated at the tip of insulating cracks by solely applying a uniform electric field loading, resulting in a large electric field gradient and thus inducing a significant converse flexoelectric effect. The deformation generated by the converse flexoelectric effect is expected to achieve crack shielding, however, its mechanism is still not clear. In this paper, the role of electric field gradients on interface crack behavior is studied by the collocation mixed finite element method (MFEM) and the J-integral. The result shows that the electric field gradient generated by a uniform electric displacement loading can reduce the J-integral of crack tips, achieving crack shielding. The result provides new ideas for the study of failure assessment, nanoscale fracture experiment and others. [Display omitted] • Electric field gradients are used to modulate fracture toughness and achieve crack shielding. • The path-independence of J-integral in interface cracks of flexoelectric solids is well verified. • A new idea for fracture property analysis, failure assessment and crack arrest is provided. [ABSTRACT FROM AUTHOR]

Based on the concept of configurational forces, the driving force of cracks in elastic–plastic, creeping materials is derived. In a numerical study, the variation of the crack driving force with increasing creep time is compared to the behaviors of different parameters that have been used in literature to describe the tendency to creep crack growth. This is performed for the assumption of stationary cracks in C(T)-specimens made of Waspaloy at 700 °C. The loading conditions are varied so that small-scale creep, transition creep, or extensive creep conditions prevail. Either the load or the load-point displacement are held constant. It is demonstrated that, for the considered cases, the conventional creep crack growth parameters do not reflect the crack driving force, but qualitatively follow a behavior similar to the (absolute value of the) time derivative of the crack driving force. [ABSTRACT FROM AUTHOR]

This article revisits the formulation of the J‐integral in the context of hydraulic fracture mechanics. We demonstrate that the use of the classical J‐integral in finite element models overestimates the length of hydraulic fractures in the viscosity‐dominated regime of propagation. A finite element analysis shows that the inaccurate numerical solution for fluid pressure is responsible for the loss in accuracy of the J‐integral. With this understanding, two novel contributions are presented. The first contribution consists of two variations of the J‐integral, termed the JHFM$J_{HFM}$ and JHFMA$J_{HFM}^A$‐integral, that demonstrate an enhanced ability to predict viscosity‐dominated propagation. In particular, such JHFM$J_{HFM}$‐integrals accurately extract stress intensity factors in both viscosity and toughness‐dominated regimes of propagation. The second contribution consists of a methodology to extract the propagation velocity from the energy release rate applicable throughout the toughness‐viscous propagation regimes. Both techniques are combined to form an implicit front‐tracking JHFM$J_{HFM}$‐algorithm capable of quickly converging on the location of the fracture front independently to the toughness‐viscous regime of propagation. The JHFM$J_{HFM}$‐algorithm represents an energy‐based alternative to the aperture‐based methods frequently used with the Implicit Level Set Algorithm to simulate hydraulic fracturing. Simulations conducted at various resolutions of the fracture suggest that the new approach is suitable for hydro‐mechanical finite element simulations at the reservoir scale. [ABSTRACT FROM AUTHOR]

The procedures of solving geometrically nonlinear deformation problems and computing fracture mechanics parameters developed by the authors became the basis for evaluation the geometrically nonlinear deformation effect on the design life of an initially cracked shutoff valve body under thermomechanical loading. For the initial crack located in the region of maximum tensile stresses, the equivalent stress intensity factor was defined for the case of combined fracture in terms of KI and KII. With the form changing effect, the equivalent stress intensity factor decreases by 2–4% on crack extension within its critical length, which will serve to increase the design life under cyclic loading by more than 12–13%. [ABSTRACT FROM AUTHOR]

Due to extensive applications of the thin film/substrate systems in engineering, the research on strength, ductility and reliability of these systems have attracted great deal of interest in recent years. The peel angle of debonded film on the ceramic substrate has a very important effect in the mechanical resistance of film/substrate bi-material. Among critical debonding parameters, peeling angle and thermal residual stresses can be a potential risk of brutal propagation causing the film/substrate composite failure under tensile loading. This study is carried out to analyze the peeling angle and residual thermal stresses effects with crack growth in the specimen. A two dimensional elastic-plastic finite element model is used to compute the J-integral and estimate the plastic zone size at the interfacial crack tip of film/substrate composite. Results show that the peeling phenomena is a fracture mixed mode where the dominance of either mode I or mode II is influenced by the peeling angle while delamination of thin film is greatly dependent on thermal residual stresses.

Fatigue lifetime of offshore pipelines with semi-elliptical circumferential surface cracks is often underestimated. An accurate prediction of the pipeline structural integrity is nevertheless important in order to prevent unnecessary and expensive downtime, failures leading to leakage or spillage of pipeline contents to the surrounding environment, and ultimately improve the reliability of the pipeline. The estimation of crack growth in pipelines under varying loads is highly dependent on the calculation of crack driving parameters, such as the stress intensity factor and the crack tip opening displacement (CTOD) using the 3D J-integral or its equivalent. This paper presents a numerical study to predict the fatigue lifetime of cracks in pipes, determining the J-integral that includes first and second derivatives of the displacement field for pipes containing a range of circumferential surface cracks. A pipe segment is structurally loaded and stress intensity factors (SIF) evaluated using the finite element method (FEM). Based on the results, a number-of-cycles to failure curve shows a longer lifetime than previously predicted by about 5% for a pipe with semi-elliptical external surface cracks. In addition, they indicate that the external short cracks are more dangerous than the internal long surface crack hereby requiring earlier assessment.

Crack orientation is a vital factor in the behavioral study of fractures, especially the study of crack propagation in structures that are under dynamic or fatigue loading. Indeed, many non-destructive testing (NDT) techniques have been developed recently for the detection of cracks such as the eddy current testing (ECT). However, the crack orientation has not been undertaken into consideration. In this paper, a NDT based on eddy current using 3D finite element modeling, is proposed for the determination of the crack orientation. The idea of this proposed technique benefits from the influences of crack orientation, which can be observed on the components of eddy current and the related magnetic flux density following the x, y axes, for the estimation of the crack angle orientation based on an interpolation criteria. The obtained results through the presented simulation prove the validity of the proposed technique for the detection of crack angle orientation. [ABSTRACT FROM AUTHOR]

Purpose: It has been usual to prefer an enrichment pattern independent of the mesh when applying singular functions in the Generalized/eXtended finite element method (G/XFEM). This choice, when modeling crack tip singularities through extrinsic enrichment, has been understood as the only way to surpass the typical poor convergence rate obtained with the finite element method (FEM), on uniform or quasi-uniform meshes conforming to the crack. Then, the purpose of this study is to revisit the topological enrichment strategy in the light of a higher-order continuity obtained with a smooth partition of unity (PoU). Aiming to verify the smoothness' impacts on the blending phenomenon, a series of numerical experiments is conceived to compare the two GFEM versions: the conventional one, based on piecewise continuous PoU's, and another which considers PoU's with high-regularity. Design/methodology/approach: The stress approximations right at the crack tip vicinity are qualified by focusing on crack severity parameters. For this purpose, the material forces method originated from the configurational mechanics is employed. Some attempts to improve solution using different polynomial enrichment schemes, besides the singular one, are discussed aiming to verify the transition/blending effects. A classical two-dimensional problem of the linear elastic fracture mechanics (LEFM) is solved, considering the pure mode I and the mixed-mode loadings. Findings: The results reveal that, in the presence of smooth PoU's, the topological enrichment can still be considered as a suitable strategy for extrinsic enrichment. First, because such an enrichment pattern still can treat the crack independently of the mesh and deliver some advantage in terms of convergence rates, under certain conditions, when compared to the conventional FEM. Second, because the topological pattern demands fewer degrees of freedom and impacts conditioning less than the geometrical strategy. Originality/value: Several outputs are presented, considering estimations for the J –integral and the angle of probable crack advance, this last computed from two different strategies to monitoring blending/transition effects, besides some comments about conditioning. Both h- and p-behaviors are displayed to allow a discussion from different points of view concerning the topological enrichment in smooth GFEM. [ABSTRACT FROM AUTHOR]

Cracks are one of the main problems that plague road workers. A correct understanding of the internal crack propagation mechanism of asphalt pavement will help road workers evaluate the road's working status more comprehensively and make more reasonable decisions in design, construction, and maintenance work. This paper established a three-dimensional asphalt pavement layered model using the software ABAQUS and fracture mechanics theory and the extended finite element method were used to explore the mechanical response of the pavement base layer's preset reflective cracks. This paper investigated the influence of the modulus of each layer, vehicle load on the principal stress, shear stress, J-integral, and two stress intensity factors (K1, K2) during the predetermined crack propagation process of the pavement base layer, and the entropy method was used to analyze the above-mentioned mechanical response. The results show that the main factor affecting the propagation of reflective cracks on asphalt pavements is the modulus of the bottom surface layer. However, from a modeling perspective, the effect of increasing load on crack growth is obvious. Therefore, in terms of technical feasibility, the prevention of reflective cracks should still be achieved by controlling the driving load and prohibiting overloading. [ABSTRACT FROM AUTHOR]

[Display omitted] • Propagation rates in J-controlled adhesive fatigue tests exhibit transients. • Procedure simulates fatigue test with J-controlled loading history. • CF22 fatigue model accounts for evolution of process zones and bridging. • Shifted Paris curve provides conservative characterization of adhesive fatigue. Fatigue analyses of adhesively bonded composite laminates were conducted to investigate discrepancies in experimentally measured rates of crack propagation in double cantilever beam specimens subjected to increasing or decreasing load histories. A cohesive fatigue damage model that accounts for the quasi-static traction-separation response and bridging was used in a finite element model of the test to identify transient effects caused by the evolution of the process zone in the adhesive, as well as the long-range, low-intensity bridging induced by the knit supporting carrier inside the adhesive. In addition to the quasi-static cohesive properties, the fatigue model requires two parameters that were obtained by fitting the rates of propagation at two experimental data points. The results indicate that the analyses accurately reproduce transient and steady-state rates of propagation observed in the experimental results, as well as the threshold of propagation. Transient rates of propagation consistently exceed those in steady state, which underscores the need to understand transients and account for them in fatigue characterization. The results also highlight that a Paris curve for steady-state propagation can be obtained most quickly using a decreasing load function, but that this curve is an unconservative bound to the rates of propagation. A lateral shift in the Paris curve is proposed for a conservative characterization that removes the effect of bridging and other R-curve effects. [ABSTRACT FROM AUTHOR]

Benchmark calculations were performed for steel plate subjected to tensile loading. Semi-circular and semi-elliptical cracks with various depths and aspect ratios were assumed. Elastic–plastic fracture analyses were carried out using finite element (FE) method. Two kinds of hardening laws were adopted and elastic–plastic fracture parameter, J-integral, was computed. The J-integral values from the FE analyses were compared with those of the reference stress method which is a simplified method to compute the elastic–plastic J-integral value. The outcomes of the benchmark analyses will contribute to the accuracy improvement of the J-integral computation by the reference stress method. • Benchmark study is conducted for reference stress method improvement. • Elastic–plastic fracture analysis is performed using FEM and J-integral is evaluated. • Steel plates subjected to tensile loading are studied with surface cracks. • J-integral values of FE computations and reference stress method are compared. [ABSTRACT FROM AUTHOR]

In this article, Mode‐I fracture and nanomechanical deformation of elastomeric composites are studied using nonlinear fracture mechanics implicating computer modeling techniques like finite element analysis, and the models developed are verified experimentally. The effect of low notch‐to‐width ratios (NWR) on failure properties like J‐integral, geometry factor, crack tip opening displacement (CTOD), crack advancement, and R‐curves is investigated. The geometry factor is found to be decreasing by 96% when NWR is increased from 0.06 to 0.34. An empirical relationship between CTOD and crack advancement for hybrid elastomeric composites depending on NWR is developed and has been verified analytically. Optimization of silica in 10 phr carbon black filled styrene butadiene rubber is performed, and several characterization techniques are used to justify the outcome. The applicability of mechanical properties like stress contours and factor of safety in fracture characterization of composites is explained briefly. A mesh sensitivity based finite element model has been developed for calibrating the nanoindentation test of elastomeric composites and verified experimentally. [ABSTRACT FROM AUTHOR]

This study experimentally and numerically investigated the crack propagation behavior of porous polymer membranes in order to identify the criterion for crack propagation. A notch was introduced into the membrane as an initial crack (pre-crack), and a uniaxial loading was applied to produce stable crack propagation. During the test, crack propagation was observed using a CCD camera and the digital image correlation (DIC) method. The strain around the pre-crack tip at the onset of crack propagation was measured experimentally using the DIC method. We found that large-scale yielding developed before crack propagation. Stable crack propagation was observed for all tensile tests. In parallel, a homogeneous model that mimicked the porous polymer membrane was created using the finite element method (FEM) to investigate the stress/strain distribution around the crack tip. This study adopted the yield criterion proposed by Deshpande and Fleck. The computed strain distribution was compared with the experimental results, and the distributions were found to be similar. The strain distribution obtained by the DIC method and FEM computation yielded a J-integral value, which could be used to investigate the criterion for crack propagation. Regardless of the initial crack length, the J-integral value at the onset of crack propagation was a constant value for all tests. We concluded that we successfully determined the criterion for crack propagation in the porous polymer membrane. Our comprehensive study using DIC experiments and FEM computations is useful for identifying the crack propagation behavior of a porous polymer membrane and for determining the criterion for crack propagation.

This paper presents and compares two combined experimental‐numerical techniques for the investigation of fracture properties of additively manufactured polymer parts using digital image correlation (DIC) measurements. The first method only uses measured kinematic fields, and the second is based on finite element simulations driven by measured boundary conditions. A mini single edge notched tensile sample manufactured by fused filament fabrication with ABS is studied. It is shown that both methods locally extract J‐integrals, and the crack tip is accurately located by the FE‐based method. By comparing computed displacements to those measured via DIC, it is possible to locally check the validity of the numerical model. The initiation and propagation stages are analyzed independently thanks to two different magnifications of acquired image series. [ABSTRACT FROM AUTHOR]

A pipe is a buried or aerial pipeline carrying goods, whether in liquid or gaseous form. Pipes are most often made from polymer tubes. These pipes prove to be subject to damage caused by a lack of material or crack thus calling for methods of repair or reinforcement. The objective of this study is to analyze by finite element analysis the presence of a horizontal crack in a high-density polyethylene pipe subjected to patch-corrected internal loading. Part of this study is devoted to analyzing the Von Misses stress distribution along a horizontal line, the applied loading type effect, the orientation of the fibers and the nature of the patch have been highlighted. The second part of our study is based on the calculation of the J-Integral where the same parameters of the first part were considered. The results clearly show that the mechanical characteristics of the composite must be optimized to provide an effective repair safely and allow relief of stress concentrations at the crack front. [ABSTRACT FROM AUTHOR]

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

Purpose: The purpose of this paper is to analyze the repair of a straight and angular crack in the structure using a piezoelectric material under thermo-mechanical loading by the extended finite element method (XFEM) approach. This provides a general and simple solution for the modeling of crack in the structure to analyze the repair. Design/methodology/approach: The extended finite element method is used to model crack geometry. The crack surface is modeled by Heaviside enrichment function while the crack front is modeled by branch enrichment functions. Findings: The effectiveness of the repair is measured in terms of stress intensity factor and J-integral. The critical voltage at which patch repair is most effective is evaluated and presented. Optimal patch shape, location of patch, adhesive thickness and adhesive modulus are obtained for effective repair under thermo-mechanical loading environment. Originality/value: The presented numerical modeling and simulation by the XFEM approach are of great benefit to analyze crack repair in two-dimensional and three-dimensional structures using piezoelectric patch material under thermo-mechanical loading. [ABSTRACT FROM AUTHOR]

The hypercomplex-variable finite element method, ZFEM, is extended to compute the mode I and mode II energy release rates (ERR) for functionally graded materials. The ERR is computed using an efficient local stiffness derivative approach, L-ZFEM, that computes the derivative of the stiffness matrix at the element level using the highly accurate complex-variable sensitivity method. Mode I and II values are computed using the appropriate perturbation of the surrounding crack tip elements, i.e., perturbations in the self-similar (mode I) and perpendicular (mode II) directions. The energy release rate values are as accurate as the J-integral results. The advantage of this approach is that the derivatives are only required for a small number of elements surrounding the crack tip and no energy conservation integrals are required. In addition, derivatives of the ERR with respect to the FGM material properties are computed by combining the local stiffness derivative approach with a global complex variable formulation, G-ZFEM. This methodology was implemented into the commercial finite element software Abaqus through a combination of Abaqus intrinsic elements and a complex variable user element subroutine (UEL). Numerical results are compared against analytical solutions and other numerical approaches and demonstrate excellent accuracy. [ABSTRACT FROM AUTHOR]

The steady-state energy release rate for tunneling cracks under mixed-mode loading is determined using finite element analyses. The balanced and symmetric laminate layup [ 0 / θ / 0 / - θ ] s is investigated, where the tunneling crack is located parallel to the fiber direction of the central off-axis oriented layer. It is found that for the steady-state situation, a simple energy balance calculation of the released energy of the separated crack surfaces for a fully developed crack gives the same value as the average value of a detailed J-integral analysis of the crack front. Furthermore, the crack front mode-mixity, obtained by the same energy balance calculation, was found to give a good prediction of the average mode-mixity found from a detailed stress intensity calculation along the crack-tip. Based on this simplified energy balance approach, the energy release rate is determined for all angles θ ∈ ] 0 ; 90 ] ∘ for orthotropic elastic properties ranging from typical low modulus glass fiber reinforced polymers to high modulus carbon fiber reinforced polymers. The predicted results can be used to investigate the influence of the layup angles on static and fatigue tunnel crack evolution in composite materials used within, e.g. automotive, aerospace, and wind energy applications. [ABSTRACT FROM AUTHOR]

This paper aims to analyze the multi-effects of the glass fiber reinforced polymer (GFRP) composite patch to repair the inclined cracked 2420-T3 aluminum plate. Three-dimensional finite element method (FEM) was used to study the effect of GFRP composite patch with different stacking composite laminate sequence, [0°]4, [90o]4, [45o]4, [0o/45o]2s, and [0°/90°]2s, on the crack driving force, J-integral, of inclined cracked 2420-T3 aluminum plate. Furthermore, the effects of patch geometry, number of layers, single or double side patch, and crack inclination angle are described. The present results show that the patch has a high effect in case of a crack in pure mode I. The effectiveness of the composite patch increases with increasing the crack length. Moreover, the efficiency of the composite patch has a high effect by changing the fiber orientation, the number of layers, and the single or double side patch. [ABSTRACT FROM AUTHOR]

The purpose of this study is to explore the hyperelastic effect on the energy release rate of a crack extension at the nanoscale. A molecular statics computation has been carried out to characterise the atomistic nature of fracturing. The concept of the J-integral is employed to measure the energy release rate for Ni and Si single crystals having a hyperelastic nature. The obtained J-integral is compared to the energy release rates predicted using the two-specimen method and the finite-element method. The results show that the effect of the highly-localized nonlinear zone in front of the crack tip potentially induces a breakdown of the linear elastic fracture mechanics model. [ABSTRACT FROM AUTHOR]

This paper presents a computational method to analyze 2D crack problems in magneto-electro-elastic solid described by the gradient theory with the direct flexoelectric effect. The finite-element method (FEM) is developed for these problems, where the constitutive equations for electric displacement and magnetic induction contain the strain-gradients. The coefficients staying at these terms are proportional to the scaling parameters. It expresses the size effect phenomenon in the considered advanced continuum model. The governing equations are derived by applying the variational principle. The FEM formulation is subsequently developed and implemented for the gradient theory of magneto-electro-elasticity. The path-independent J-integral is derived in the framework of considered theory. [ABSTRACT FROM AUTHOR]

The elastic-plastic behavior of the material is considered to analyze the effect of an external circumferential crack on a pipe with thickness transition and double slopes. Using the extended finite element method (XFEM), the J-integral of 3D cracks were investigated and compared between straight pipes and pipes with thickness transition and different slopes. Considering internal pressure, this work highlighted the investigation of a 3D crack problem in a thickness transition pipe with a double slope, In the extended finite element method (XFEM), the level sets and the enrichment zone were defined. A crack is easily modeled by enrichment functions. The comparison between the values of the Jintegral showed that the pipe containing thickness transition with double slopes is more sensitive to the considered cracks, more precisely, the parameters of the first thickness transition have more influence on the variation of J-integral than the parameters of the second thickness transition. The decreasing of the angle of the slopes and the increase of the ratio of the thicknesses is one effective method of reducing the J-integral. [ABSTRACT FROM AUTHOR]

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• The dynamic fracture analysis of plates using the Boundary Element Method is presented. • The J-Integral is used to evaluate the Dynamic Stress Resultant Intensity Factors. • Fractured plate is modeled using the Dual Boundary Element Method. • The Dual Reciprocity Boundary Element Method is used to treat domain integrals. • The time-domain solution is obtained through the Houbolt time-integration method. This work presents a Dual Boundary Element Method/Dual Reciprocity Boundary Element Method formulation for the dynamic analysis of fractured shear deformable plates. Equations for the Dual Boundary Element Method, including the direct boundary and the traction boundary equation for Reissner plates, were used for crack modeling. The Dual Reciprocity Boundary Element Method was used to treat both domain integrals related to distributed forces and inertial terms. Proposed formulation considers the rotary inertia of the plate. A general crack modeling strategy is presented. The J-Integral is used to evaluate the Dynamic Stress Resultant Intensity Factors. Test problems, including comparisons to Finite Element Method solutions, are presented. Results demonstrate, proposed formulation is a reliable method for dynamic analysis of shear deformable cracked plate bending problems. [ABSTRACT FROM AUTHOR]