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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]

Small punch test (SPT) is a conventional technique to determine material properties. Crack tip opening displacement (CTOD) and J-integral methods are two methods applied to pre-notched SPT specimens for fracture resistance estimation. In the CTOD method, the test is interrupted at certain forces less than the maximum force, and then, the specimen is put under microscopes to study the specimen notch status and measure the crack opening. This interruption leads to changes in deformations due to removing of forces. This study aims to remove the interruption problem. To this end, a new setup is introduced to embed an optical microscope under SPT specimens, thereby enabling online monitoring and real-time deformation measurement. This online deformation measurement where the specimen is under force can reduce the error in CTOD measurement. It helps to achieve more accurate results in fracture resistance estimation. To evaluate the method, a few SPT specimens were prepared from an aged compressor named Nevski. Mechanical properties were first conventionally determined by analyzing the SPT force-displacement curves according to standards. Then, prenotched SPT specimens with lateral notches and 4.5 mm and 5 mm notch lengths were employed for fracture energy estimation. Fracture energy was calculated according to the J-integral method that its accuracy is proven. Then, CTODs were measured at various forces using the images taken during the test, and the fracture energy was calculated from the CTOD method. There was a great agreement between the fracture energy calculated by the CTOD method and the proven J-integral method. The accuracy of online measurement was better than interruption measurement in previous studies, proving that the new approach is useful. [ABSTRACT FROM AUTHOR]

This paper utilizes the Wohler curve and the J-integral principle to predict the service life of purposely-damaged acrylonitrile butadiene styrene (ABS) specimens. The hardness of single- and double-notched specimens was measured using the J-integral, facilitating a comparison between two different types of defects. By analyzing the Wohler curve, we were able to examine the decline in the service life of the ABS specimens over various time intervals. According to the comparison, a hole with a single internal notch flaw is not as detrimental as one with two notch defects. [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]

A railway wheel flat occurs when the wheel locks and slides along the rail, forming a white etching layer (WEL) just under the flat surface where rolling contact fatigue cracks often form that can propagate into the wheel and spall during service. This study comprehensively investigated the influencing factors on wheel crack propagation that lead to spalling. Experiments were conducted to test wheel specimens with WELs of various dimensions, and simulations were performed to evaluate the stresses near the WELs as well as the rate and direction of crack propagation.

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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]

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]

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]

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]

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]

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]

Background: The elastic–plastic fracture toughness (Jc) is an important mechanical parameter for studying the failure behavior of air plasma-sprayed (APS) thermal barrier coatings (TBC) at high temperatures. Objective: This study aims to: (1) develop an effective test method to characterize the Jc of TBC at high temperatures; (2) acquire accurate Jc data for TBC at high temperatures; (3) analyze the influence of plasticity of top-coat on the Jc characterization. Methods: The elastic–plastic Ramberg–Osgood equation of the ceramic top-coat and the deformation fields of single edge notched tension (SENT) specimens were measured by high-temperature in-situ tension with digital image correlation (DIC) system. The Jc of TBC was calculated by the numerical J-integral with DIC-measured (DIC-J) deformation fields by adopting Ramberg–Osgood equation of the top-coat. The finite element analysis (FEA) method was adopted to analyze the influence of plasticity of top-coat on the Jc characterization. Results: The curves of Jc varying with crack propagation length (Δa) of TBC were obtained and were expressed as JR = 24.47 × [ 1 + 1.0446 × ( Δ a ~ )0.7624] J/m2 and JR = 16.52 × [ 1 + 1.4806 × ( Δ a ~ )0.6742] J/m2 at 800 and 1000 ℃, respectively. Conclusions: A high-temperature in-situ tensile test of SENT specimens combined with the DIC-J method was developed to characterize Jc of TBC. The Jc of TBC displays a rising resistance curve behavior, and FEA results indicated that Jc would be underestimated without considering the plasticity of the top-coat at 800 and 1000 ℃. [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]

High-density polyethylene (HDPE) has a higher strength-to-density ratio and stiffness but a low branching degree for the packed linear chains that restrict the ability to bond and resist cracking. This study conducts the role of inserting rigid nanoclay (NC) and soft acrylonitrile butadiene styrene (ABS) on the structural, nonlinear fracture toughness and crack resistance of a ternary HDPE/low-density polyethylene-grafted maleic anhydrite (LDPE-g-MA)/ABS blend. Varying additions of 1, 3, 5, and 7 % NC and 5, 10, 15 wt. % ABS were inserted into neat HDPE and HDPE90/LDPE-g-MA10. All materials were hand-mixed before feeding into a single screw extruder and directly melt-blended twice to achieve a good dispersion of nanofiller in the matrix. The structural characteristics and the fracture surfaces of NC/HDPE/LDPE-g-MA and NC/HDPE/LDPE-g-MA/ABS were investigated by TEM, XRD, SEM, and FTIR spectra. Tensile strength and the critical dissipated energy (JIc) determined by quasi-static J-integral fracture mechanic revealed a higher absorbing fracture energy of 75 KJ/m2 for the binary and 85 KJ/m2 for the ternary nanocomposites. The synergistic percolated role of the NC particles and ABS copolymer in front of the crack tip region hinders crack growth for the presence of micro-void coalescence and massive shear-yielding toughening mechanisms. [ABSTRACT FROM AUTHOR]

In this review, a highly pertinent and debatable issue in the maritime industry has been addressed. Although fracture mechanics theories have expanded substantially in recent decades, researchers of the present era in the marine industry still pay little attention in incorporating fracture characteristics into account while designing the structural components. Besides the fundamental strength characterization methodologies, which include establishing the ultimate strength, hardness and impact characteristics, the authors firmly advocate that the fracture parameters of the marine-grade materials must be carefully considered during structural design phase, decidedly for weldments of similar and distinct materials. Nonetheless, these types of paradigms are an inevitable part in prominent sectors, viz., nuclear reactors, pipeline industry and space missions. Owing to this, fracture mechanical investigations performed in marine fields incorporating the standard fracture parameters like stress intensity factor (K), J-integral (J), etc. are thoroughly discussed in this review. The application of different specimen types, viz., compact tension (CT) specimens, single edge notched bend (SENB) and single edge notched tension (SENT) specimens, is also succinctly summarized. The shortcomings of the experimental studies are suggested, and a thorough discussion is also done regarding the potential application of fracture mechanical characterization on marine grade materials and their weldments. [ABSTRACT FROM AUTHOR]

AbstractThis study investigates the effects of the material mechanical properties heterogeneity and strength mismatch variation on crack driving forces for cracks in a dissimilar metal welded joint (DMW) of a reactor pressure vessel inlet nozzle to the safe end. Linear elastic and elastic-plastic analyses are carried out to calculate the stress intensity factor (SIF) and J-integral for cracks in the DMW. The effects of crack locations, crack depths, and strength mismatch factors on the SIF and J-integral are studied. The SIF results obtained by finite element analysis are compared with those obtained by the influence function method adopted in the nuclear power code. Results show that the effect of crack location on the SIF can be ignored. The SIFs calculated by the influence function method for cracks in the DMW are basically reasonable, although its conservatism is slightly insufficient. Moreover, with moving the crack location from the nozzle through buttering and weld metal to the safe end, the J-integral increases. The effect of the crack location and strength mismatch factors on the J-integral is essentially caused by variation of the plastic zone and the material properties of the crack front. The crack sizes affect the level of influence of the crack location and the strength mismatch factors on the J-integral. The J-integral increases with decrease of the strength mismatch factor. [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]

Purpose: This study aims to investigate the reliability issues of microvoid cracks in solder joint packages exposed to thermal cycling fatigue. Design/methodology/approach: The specimens are subjected to JEDEC preconditioning level 1 (85 °C/85%RH/168 h) with five times reflow at 270°C. This is followed by thermal cycling from 0°C to 100°C, per IPC-7351B standards. The specimens' cross-sections are inspected for crack growth and propagation under backscattered scanning electronic microscopy. The decoupled thermomechanical simulation technique is applied to investigate the thermal fatigue behavior. The impacts of crack length on the stress and fatigue behavior of the package are investigated. Findings: Cracks are initiated from the ball grid array corner of the solder joint, propagating through the transverse section of the solder ball. The crack growth increases continuously up to 0.25-mm crack length, then slows down afterward. The J-integral and stress intensity factor (SIF) values at the crack tip decrease with increased crack length. Before 0.15-mm crack length, J-integral and SIF reduce slightly with crack length and are comparatively higher, resulting in a rapid increase in crack mouth opening displacement (CMOD). Beyond 0.25-mm crack length, the values significantly decline, that there is not much possibility of crack growth, resulting in a negligible change in CMOD value. This explains the crack growth arrest obtained after 0.25-mm crack length. Practical implications: This work's contribution is expected to reduce the additional manufacturing cost and lead time incurred in investigating reliability issues in solder joints. Originality/value: The work investigates crack propagation mechanisms of microvoid cracks in solder joints exposed to moisture and thermal fatigue, which is still limited in the literature. The parametric variation of the crack length on stress and fatigue characteristics of solder joints, which has never been conducted, is also studied. [ABSTRACT FROM AUTHOR]

The strength of backfill is greatly influenced by its inclination angle and interlayer concentration. in order to study the influence of inclination angle and interlayer mass concentration on the strength of backfill, a group of layered cemented backfill with cement-sand ratio of 1:4, interlayer mass concentration of 66%, 67% and 68% and inclination angles of 0°, 10°, 20° and 30° were prepared by using tailings as aggregate. The uniaxial compression test was carried out to analyse the effect of interlayer mass concentration and inclination angle on layered cemented backfill. The crack propagation and energy change law of the specimen during compression were analysed by J-integral and energy conservation law. The relationship between the crack initiation and propagation and strain energy of two representative threelayer backfill specimens was analysed by numerical modelling. The results show that the increase in the layer number and the inclination angle of the backfill can weaken the strength of the backfill. In a certain range of inclination angles, the weakening coefficient of the backfill caused by the inclination angle is very consistent with the cosine value of the corresponding angle. Due to the release of crack energy and the existence of interface J integral, the uniaxial compressive strength of different mass concentration backfill is different at various positions. When the displacement reaches a certain value, the crack and strain energy no longer increase. [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.

Abstract 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.

A global energy minimization criterion based on Griffith's theory is introduced for the node-splitting lattice spring model. The fracture criterion is computed by both direct numerical simulations of energy release rate G and through a J-integral formulation for comparison and validation. For mode I fractures, the standard implementation of J-integral formulation yields very good estimations of the energy release rate, but for mixed mode fracture the estimations deviates from the direct calculated energy release rate. The reasons for this discrepancy are elucidated and an approach to best approximate the J value is given. This method is compared with the more standard maximum tip stress threshold crack criterion, and shows a much better prediction of the energy release rate and is more robust under grid refinement. [ABSTRACT FROM AUTHOR]

Temperature has a great influence on the mechanical properties of ductile cast iron or nodular cast iron. A thermomechanical treatment was carried out at various elevated temperatures of 450 °C, 750 °C and 850 °C using a universal testing machine with a tub furnace. Specimens were held at these temperatures for 20 min to ensure a homogeneous temperature distribution along the entire length of the specimen, before a tensile load was applied. Specimens were deformed to various levels of uniform strain (0%, 25%, 50%, 75%, and 100%). These degrees of deformation were measured with a dial gauge attached to a movable cross plate. Three strain rates were used for each specimen and temperature: 1.8 × 10 − 4   s − 1 , 9 × 10 − 4   s − 1 and 4.5 × 10 − 3   s − 1 . A simple analytical model was extracted based on the CT tensile test geometry and yield stress and a 0.2% offset strain to measure the fracture toughness (JIC). To validate the analytical model, an extended finite element method (XFEM) was implemented for specimens tested at different temperatures, with a strain rate of 1.8 × 10 − 4   s − 1 . The model was then extended to include the tested specimens at other strain rates. The results show that increasing strain rates and temperature, especially at 850 °C, increased the ductility of the cast iron and thus its formability. The largest percentage strains were 1 and 1.5 at a temperature of 750 °C and a strain rate of 1.8 × 10 − 4   s − 1 and 9 × 10 − 4   s − 1 , respectively, and reached their maximum value of 1.7 and 2.2% at 850 °C and a strain rate of 9 × 10 − 4   s − 1 and 4.5 × 10 − 3   s − 1 , respectively. In addition, the simple and fast analytical model is useful in selecting materials for determining the fracture toughness (JIC) at various elevated temperatures and different strain rates. [ABSTRACT FROM AUTHOR]

A wide variety of additives are used to improve the performance of hot mix asphalt (HMA). Among these materials, styrene butadiene styrene (SBS) elastomer is one of the most commonly used additives. In this study, in addition to the SBS, the newly produced 711 and 601 elastomers were used as an alternative. Modified binders were prepared by adding three different elastomers in three different ratios (2%, 3%, and 4%) to pure bitumen. The HMA samples were prepared by mixing the modified binders and pure binder with the aggregate pile that is in a certain gradation. Subsequently, the mechanical and fracture properties of these mixture samples were investigated. Marshall stability, resistance to moisture damage (tensile ratio), indirect tensile stiffness modulus (ITSM), and indirect tensile fatigue test were performed on all the prepared mixture samples. In addition, semi-circular HMA samples with two different notch depths, 1 cm, and 2 cm, were obtained and their fracture properties were evaluated with different fracture mechanics approaches. The fracture performance test was evaluated with linear elastic fracture mechanics (LEFM) and elastic–plastic fracture mechanics (EPFM). As a result, fracture toughness and J-integral values were obtained. The results showed that all three elastomers exhibited higher mechanical performance compared to the pure mixture while the highest performances were observed in the mixtures containing 611. When the additives are evaluated among themselves, the ranking is 611, 701, and SBS, respectively. In addition, similar results were obtained according to their fracture performance and it was seen that 701 and 611 elastomers offered better results than SBS. [ABSTRACT FROM AUTHOR]

This study concerns several possible ways of computing the J-integral in the cases of laminated composite plate structures containing delamination. On the one hand, two special types of plate finite element families are provided for advanced fracture mechanical analyses. On the other hand, a numerical algorithm is introduced also that utilizes results derived from solid element models built in commercial finite element software. In order to create plate elements, the first-order (FSDT) and the third-order shear deformation theories (TSDT) are applied with two equivalent single layers. A subparametric element family is created by using the Hermite interpolation with the FSDT that grants the continuity of the derivatives at the element borders. Besides, an isoparametric family is created also with the TSDT employing the Lagrange interpolation scheme. This paper aims to present the compact formulations of calculating the J-integral around the delamination fronts for both plate element families. The calculation of the J-integral is implemented as a matrix multiplication by taking advantage of the properties of plate transition elements. The models yield improved fracture mechanical analyses for delaminated composite plates with linear elastic material behaviour. In addition, computing the J-integral is not available in most commercial finite element software for laminated orthotropic materials, therefore, an appropriate algorithm is presented here for this purpose. To conclude, the models and algorithms are applied to two case studies and subjected to a comprehensive comparison with analytical and formerly used finite element solutions. • A subparametric FSDT plate element family with granted continuity of the derivatives for delaminated plates. • An isoparametric TSDT plate element family that is appropriate for modelling curved delamination fronts. • A robust algorithm for computing the J-integral numerically in solid element models. [ABSTRACT FROM AUTHOR]

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]

This study aims to investigate the anisotropic fracture toughness of an α+β titanium alloy processed by β forging. A typical basket-weave microstructure is observed, including the primary α (αp) phase, micron-scaled secondary α (αs) phase and residual β phase. The tensile test results show that the anisotropic strength results from the fine grain strengthening as well as the texture strengthening, and the plasticity difference is determined by the normal stress acting on the main crack in the fracture process. The orientation of the specimen also has a significant impact on fracture toughness. The corresponding toughening models of underlying damage mechanism with different orientations are proposed and discussed. It is found that the internal toughening mechanism is dominant, and external toughening mechanism also plays an important role in fracture toughness, including delamination and crack deflection caused by elongated β grains arrangement. Finally, the differences of J-integral resistance curves with different orientations are investigated in detail. The strength and fracture toughness values, KJIC (crack-initiation toughness) and KSS (growth toughness), are both highest when loading along radial direction (RD), and the positive effects of β grain morphology and two-phase texture on anisotropy of KJIC are summarized.

The numerical study of crack propagation is a very complex and important problem for knowing the lifetime of a structure. Nowadays, the modelling of crack propagation by various numerical methods plays a beneficial part in solving problems in fracture mechanics. Significantly used in biomechanics, biomaterials and structural calculation, it also makes it possible to deal with certain problems of fatigue of materials. In this article, a numerical study based on the finite element method (FEM) was used for a two-dimensional model, of an elastoplastic material, containing a central crack. The article is also based on the study of different cracking factors, such as stress intensity factors KI and KII, J-integral and strain energy. On the other hand, the contrast of these parameters was precisely centred on the five contours of the crack front. In addition, Abaqus computer code was used to obtain different results, moreover, CPS4R elements were used for modelling.

This work aimed to investigate the fracture resistance of asphalt mixtures containing graphene oxide (GO) using fracture mechanics. Three dense-graded asphalt mixtures with 9.5, 13.2, and 16 mm nominal maximum aggregate size (NMAS) were modified with varying GO contents. Semi-circular bending (SCB) fracture tests were conducted to determine the fracture properties of the asphalt mixtures. Results showed that mode I fracture toughness (KIC) and fracture energy (Gf) at −20 °C, −10 °C, and 0 °C were significantly improved with the addition of GO. Likewise, increasing trends in J-integral were observed with increasing GO content at 0 °C, 10 °C, and 20 °C. The variations of the fracture mechanic parameters suggested that adding GO could help in enhancing the fracture performance at low and intermediate temperatures. The fracture properties showed a high dependency on test temperature. An increase in NMAS resulted in increased fracture strength of the mixtures. Additionally, a two-parameter Weibull distribution model was utilised to further investigate the fracture results. The fracture toughness of the asphalt mixtures was found to comply with the two-parameter Weibull distribution. Response surface methodology (RSM) was used to develop prediction models for the fracture properties. The proposed models exhibited a high degree of correlation. [ABSTRACT FROM AUTHOR]

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

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]

Comparative testing for crack resistance (fracture toughness) of weld metal specimens of a low-carbon steel welded joint in the as-supplied condition and after high-temperature exposure at a temperature of 1200 °C for 3.7 hours is conducted. A welded joint is obtained by automatic argon-arc welding with a consumable electrode in a hot-rolled 22K-type steel sheet of 60 mm thick using welding wire grade SV-08G2S. Tests for static crack resistance of specimens with a stress concentrator are carried out according to a three-point bending scheme. One of the energy criteria of nonlinear fracture mechanics, critical J-integral [J/m2], which takes into account plastic deformation at a crack tip, is used as a crack resistance characteristic. It is shown that high-temperature exposure leads to an increase in crack resistance (the J-integral value increases by two times) as a result of phase recrystallization and improving the coarse-grained overheated weld structure. [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]

This article describes a convenient method to quantify the dynamic J‐R curve through digital image correlation (DIC). The DIC approach, verified through numerical and experimental results for single edge notched bend (SE(B)) specimens, quantifies the dynamic J‐R curve during the drop‐weight tearing test (DWTT). The proposed method enables consistent measurement of the J‐integral and the amount of crack extension solely from the DIC measured displacement on the specimen surface, which facilitates direct comparison of fracture toughness under different strain rates. The results demonstrate enhanced Mode‐I fracture resistance of metallic materials under increased strain rates. Highlights: We present an approach to measure dynamic J‐R curve solely based on DIC data.We have validated the DIC J values from both numerical and experimental results.The measured crack size depends on the rotation center determined from DIC. [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]

Purpose: This study aims to contribute to the numerical modelling of drop impact on a flip-chip component assembled on printed circuit boards using solder micro-bumps. This contribution is based on the introduction of non-linear fracture mechanics in the numerical approach. Design/methodology/approach: The integration of non-linear fracture mechanics into the numerical approach requires the proposal and validation of several simplifying assumptions. Initially, a dynamic 3D model was simplified to a dynamic 2D model. Subsequently, the dynamic 2D model is replaced with an equivalent static 2D model. The equivalent static 2D model was used to perform calculations considering the non-linear fracture mechanics. A crack was modelled in the critical bump. The J-integral was used as a comparative parameter to study the effects of crack length, crack position and chip thickness on the fracture toughness of the solder bump. Findings: The different simplifying assumptions were validated by comparing the results obtained by the various models. Numerical results showed a high risk of failure at the critical solder bump in a zone close to the intermetallic layer. The obtained results were in agreement with the post-test observations using the "Dye and Pry" methods. Originality/value: The originality of this study lies in the introduction of non-linear fracture mechanics to model the mechanical response of solder bumps during drop impact. This study led to some interesting conclusions, highlighting the advantage of introducing non-linear fracture mechanics into the numerical simulations of microelectronic components during a drop impact. [ABSTRACT FROM AUTHOR]

A complex of comparative studies on static fracture toughness according to the three-point bending scheme was carried out for the 22K low-carbon steel (AISI 1022) after various heat treatment, namely after normalization, after prolonged heat treatment provoking temper brittleness (TO-1 regime included heating to 650 °C and slow stepwise cooling for 7 days), and after high-temperature heat treatment causing intensive grain growth (TO-2 regime included heating to 1200 °C with holding for 3.7 h). The criterion of non-linear fracture mechanics, namely the critical J-integral taking into account plastic deformation at the crack tip was used as a characteristic of fracture toughness. It is shown that, regardless of the type of structure formed by different heat treatment, the 22K steel is characterized by high fracture toughness. However, after heat treatment by the TO-1 and TO-2 regimes, the value of the critical J-integral decreases by 23 and 30%, respectively. [ABSTRACT FROM AUTHOR]

Cracking resulting from residual stress at the solid-tooth support interface frequently occurs in laser powder bed fusion (LPBF) metallic additive manufacturing, and thus it is critical to predict possible cracking and design the support to prevent it. This study employs a combination of computational methods and experiments to predict cracking at the interface and, for the first time, determine the relationship between the critical J-integral and the contact area of the solid-tooth support interface. In particular, the finite element method-based global-local approach is used to perform the modified inherent strain analysis with homogenized material for the entire part (global), which is followed by the fracture mechanics-based J-integral analysis at conjectured vulnerable locations (local). Both numerical and experimental validations are conducted, showing that the local-global approach is accurate and efficient in crack prediction at the interface between the solid and the tooth support in as-built LPBF printed metals. It is found that given the same basic tooth unit design in the support structure, the critical J-integral increases at an approximate linear slope of 2 with a local contact area percentage (∼20–40%) at the solid-support interface. These results will enable support designers the flexibility to design the support contact area to prevent solid-tooth support cracking while ensuring the ease of support removal.

In this work, the essential work of fracture (EWF) method is introduced for a peridynamic (PD) material model to characterize fracture toughness of ductile materials. First, an analytical derivation for the path-independence of the PD J-integral is provided. Thereafter, the classical J-integral and PD J-integral are computed on a number of analytical crack problems, for subsequent investigation on how it performs under large scale yielding of thin sheets. To represent a highly nonlinear elastic behavior, a new adaptive bond stiffness calibration and a modified bond-damage model with gradual softening are proposed. The model is employed for two different materials: a lower-ductility bainitic-martensitic steel and a higher-ductility bainitic steel. Up to the start of the softening phase, the PD model recovers the experimentally obtained stress–strain response of both materials. Due to the high failure sensitivity on the presence of defects for the lower-ductility material, the PD model could not recover the experimentally obtained EWF values. For the higher-ductility bainitic material, the PD model was able to match very well the experimentally obtained EWF values. Moreover, the J-integral value obtained from the PD model, at the absolute maximum specimen load, matched the corresponding EWF value. [ABSTRACT FROM AUTHOR]

The Mode I fracture behaviour of adhesive joints, bonded with two different epoxies, was evaluated applying the direct method to obtain the tensile cohesive law, together with Digital Image Correlation (DIC) analysis. The Double Cantilever Beam (DCB) test was performed, and the fracture toughness was attained by applying the J-integral. The DIC measurements were analysed resorting to a Python script, that was used as a post-processing tool, able to minimize the data noise stemming from the experimental results. This tool proved to be of utmost importance to guarantee acceptable results. Finally, the direct method could predict the main features of the cohesive law. Also, the law was used to simulate the fracture behaviour in a different test specimen, to evaluate the influence of the specimen geometry on the results. The obtained data indicates that the direct method is dependent on the joint geometry and the constraining condition of the adhesive. [ABSTRACT FROM AUTHOR]

In the past decade, bamboo scrimber has developed rapidly in the field of building materials due to its excellent mechanical properties, such as high toughness and high tensile strength. However, when the applied stress exceeds the ultimate strength limit of bamboo scrimber, cracks occur, which affects the performance of bamboo scrimber in structural applications. Due to the propensity of cracks to propagate, it reduces the load-bearing capacity of the bamboo scrimber material. Therefore, research on the fracture toughness of bamboo scrimber contributes to determining the material's load-bearing capacity and failure mechanisms, enabling its widespread application in engineering failure analysis. The fracture toughness of bamboo scrimber was studied via the single-edge notched beam (SENB) experiment and compact compression (CC) method. Nine groups of longitudinal and transverse samples were selected for experimental investigation. The fracture toughness of longitudinal bamboo scrimber under tensile and compressive loadings was 3.59 MPa·m1/2 and 2.39 MPa·m1/2, respectively. In addition, the fracture toughness of transverse bamboo scrimber under tensile and compressive conditions was 0.38 MPa·m1/2 and 1.79 MPa·m1/2, respectively. The results show that, for this material, there was a significant distinction between longitudinal and transverse. Subsequently, three-point bending tests and simulations were studied. The results show that the failure mode and the force–displacement curve of the numerical simulation were highly consistent compared with the experimental results. It could verify the correctness of the test parameters. Finally, the flexural strength of bamboo scrimber was calculated to be as high as 143.16 MPa. This paper provides data accumulation for the numerical simulation of bamboo scrimber, which can further promote the development of bamboo scrimber parameters in all aspects of the application. [ABSTRACT FROM AUTHOR]

Fracture mechanics, as a scientific discipline dealing with the study of cracks in welded structures, has defined parameters and introduced new test methods in order to better determine the tendency to crack growth, critical conditions for rapid fracture development, material resistance to rapid crack propagation and better definition of other parameters for assessing the behaviour of the material and the safety of the structure in the presence of cracks. In this paper, the focus is on determination of the parameter of elastic-plastic mechanics of J-integral, more precisely, on examination of the critical value of J-integral (JIc) of the welded joint of HSLA steel. The position of the tip of the fatigue crack and the properties of the region where fracture propagation occurs are main indicators of influence of the heterogeneity of the NN-70 welded structure and mechanical properties. Resistance to cracking in the welded joint shows that the heterogeneity has a major impact on the resistance to crack initiation and propagation, in elastic as well as in the plastic region.

ABSTRACTThe single-edged V-notch beam (SEVNB) method is considered as an effective method for evaluating the fracture toughness values of brittle materials. In this method, it is assumed that the V-notch is a natural crack. However, this assumption may cause an overestimation of the fracture toughness due to the “notch passivation effect”. To investigate the effects of the V-notch and groove tip angles on the fracture toughness testing of ceramic materials, three typical models were established in this work. The stress intensity factors of these models were calculated using a J-integral based on the linear finite element method (LFEM). The results indicated that the measured fracture toughness values could be overestimated by 0.5%- 13.7% when the angle of the V-notch tip increased from 10° to 60°. Increasing the angle formed by the V-notch and groove from 10° to 60°, fracture toughness was overevaluated by about 0% – 2.0%. When the angle formed by the V-notch and groove increased to 120°, the fracture toughness was overevaluated by about 31%. Finally, two equations were fitted to assess the angles effects on fracture toughness, and the results have been validated by experiments. An important reference for the SEVNB method can be found in this work.

Fatigue crack growth is a harmful physical phenomenon in engineering materials that can be intensified by the presence of tensile residual stresses. In the present study, the effect of tensile residual stresses on the fatigue crack growth in single-edge notched bending specimens of Ti-6Al-4V is studied. Mechanical residual stresses were created by applying a 4-point bending process. The residual stresses were evaluated utilizing the hole drilling approach under the ASTM E-837 standard. Fatigue crack propagation was measured by experimental test in specimens with and without initial residual stresses. A finite element analysis was conductedusing commercial finite element software to study the plastic zone at the crack tip and fracture mechanic parameters. It was observed that the residual stress field is redistributed after each step of crack propagation. The tensile residual stress in front of the crack tip decreased from near yield strength to approximately 30% of yield strength. The tensile residual stresses near the yield strength in Ti-6Al-4V increased the fatigue crack propagation rate by approximately 50%.

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]