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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 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]

• 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]

• A model of non-slipping adhesive contact between dissimilar solids is proposed. • J -integral gives energy release rates at adhesive contact edges. • Rolling resistance is linearly related to the adhesion hysteresis. In the present work, a mechanical model for two-dimensional non-slipping adhesive contact between dissimilar elastic solids under general loading, namely, normal forces, tangential forces and moments is proposed. The general solutions are obtained analytically with the stresses at the contact edges exhibiting oscillatory singularity, similar to those at a bimaterial interface crack. The well-known J -integral under the current context is analyzed. Its application under the selected integration contour readily gives the relationship between the stress intensity factors and energy release rates at the contact edges. With the results rolling adhesion between two solids with parabolic profiles is considered further. The applied moment can be directly determined by the difference in energy release rates at the trailing and leading edges and hence the rolling resistance even for adhesive contact with cohesive zones. These results provide the foundation for understanding some tribological phenomena associated with adhesion. [ABSTRACT FROM AUTHOR]

In this paper, fracture toughness (K J) was measured for high strength rail steels and AL2024-T351 via chamfered cylindrical flat-end indentation. The indentation loading focused on applying the J-integral approach to curves of load versus indentation depth up to the crack initiation point based on a modified limit load via multiple indenter sizes. To promote single indenter size for practical use, virtual indenter sizes were proposed based on geometrical similarities, where the stress intensity factors according to J-integral approach were extrapolated to minimize the contribution of the plastic component of J-integral (J P). However, when the indentation method for K J is applied to high strength rail steels, a consideration for the modification of the J-integral approach is suggested with the inclusion of stress triaxiality effect to accommodate the pressure sensitivity experienced in compression-based testing for some materials. The K J values were seen to agree well with fracture toughness from conventional testing (K IC) for all materials in the study showing a relative difference below 5% except the JP rail steel, which showed only a relative difference of 16%. This is based on the condition that pressure sensitivity effect is present for the rail steels and not for AL2024-T351. The study also compares different indenter sizes, which show similar pressure and normalized depth profiles consequently offering the potential for a non-destructive means to measure mechanical properties and fracture toughness via micro-sized indenters. This opens an opportunity for further studies in material characterization capabilities across a wide range of industries in the future. [ABSTRACT FROM AUTHOR]

The concept of debonding entropy provides insight into the physical mechanisms of fracture. It sheds light on how the fracture phenomenon is more intimately related to degradation and entropy. This paper aims to investigate the relationships between debonding entropy and fundamental concepts in fracture mechanics. A direct, simple relationship between debonding entropy and the J-integral value at fracture is developed and validated. The validation of this relation displays the connection between fracture mechanics and entropic degradation. [ABSTRACT FROM AUTHOR]

• Arcan fixture and stereo DIC used to study mixed-mode fracture in PMMA. • Displacement field decomposed into mode I-II-III stress intensity factors. • Intrinsic and extrinsic sources of additional load modes compromises tests' reliability. • Best fit fracture toughness equalled 1.82 ± 0.32 MPa m0.5. To characterise mixed-mode fracture, including mode I I I , a combination of Arcan fixture, that offers both in-plane and out-of-plane loading, and stereo digital image correlation (DIC) has proven valuable for measuring in-plane and out-of-plane surface displacement and deformation fields while allowing for direct stress intensity factor (SIF) extraction throughout the tests, but it comes with many caveats. Using stereo DIC, the mixed mode fracture behaviour of PMMA is analysed using a novel mode decomposition technique that combines experimental and analytical approaches. This technique divides the measured displacement field from digital image correlation into three distinct components: a symmetric field (u I), an in-plane anti-symmetric field (u II), and an out-of-plane antisymmetric field (u III), decomposed by a difference operation on the reflected and non-reflected fields about the crack plane. Then, the strain energy release rate of the crack is calculated for each loading mode using finite elements without knowledge of the sample geometry or nominal loading condition. Our work revealed parasitic loading modes induced by the Archan fixture plus other intrinsic sources related to load accommodation. Nevertheless, the calculated SIFs measured during stable crack growth were normalised using different fracture toughness (K IC) values with K IC of 1.82 ± 0.32 MPa m0.5, providing the best fit to the fracture loci with an R2 of 0.95. This value agrees well with the ASTM-obtained value of 1.7 MPa m0.5. [ABSTRACT FROM AUTHOR]

The presence of cracks on pipelines poses a potential threat to their operational status, and it is critical to assess the permissibility of pipelines containing cracks. The dimensional analysis combined with the finite element method is applied to investigate the fracture behavior of circumferential crack on the internal surface of pipe under internal pressure and large axial deformation. Dimensionless parameters are determined to represent the effects of crack size, pipe geometry, pipe material, and external load on the crack front driving force, and a strain-based J-integral formulation is obtained by a stepwise coefficient fitting approach rather than a polynomial fitting method. This J-integral formula can be used to quickly assess the crack front driving force of a pipe in service condition and subjected to axial displacement. The diameter-to-thickness ratio of the pipe and the dimensionless pressure of the pipe are found to act together in a combined form on the crack front driving force. Increases in dimensionless crack depth, dimensionless crack length, the ratio of circumferential stress to yield strength of the pipe, and strain hardening exponent cause an increase in the crack front driving force. The effect of dimensionless crack depth on crack front driving force is more significant than other dimensionless parameters. Changes in the other dimensionless parameters do not significantly change the crack front driving force when the dimensionless crack depth is small. Other dimensionless parameters have a progressively greater influence on the crack front driving force as the crack dimensionless crack depth increases. Large deformations in the ligament zone and increasing axial stress are the main reasons for the high crack front driving force. The J-integral formula has a similar form to that of the J-integral in the Electric Power Research Institute (EPRI) method when the effect of internal pressure is not considered. It can be reduced to predict the crack front driving force of a surface cracked plate subjected to uniaxial tensile loading. For the interaction between an internal surface crack and an embedded crack, re-characterizing the crack size using BS 7910 will overestimate the equivalent crack depth, and a more accurate equivalent crack size can be obtained using the J-integral formula proposed. • A strain-based J-integral formula is proposed by using dimensional analysis. • The effect of ligament deformation and axial stress on the J-integral is analyzed. • The J-integral formula can be used to predict the crack front driving force. • The formula can be simplified as a surface cracked plate under uniaxial tension. • The size of interacting cracks is re-characterized by using the J-integral formula. [ABSTRACT FROM AUTHOR]

[Display omitted] • Mode I/II fracture is characterized for CFRP-AA7050-T6 interface. • DIC is used to determine crack length and CTOD/CTSD. • J-integral method determines TSLs and bridging law. • New CZM is proposed for mode I fracture at composite-metal interface. • The length of cohesive zone is determined using DIC. The fracture behavior of AA 7050-T6/CFRP adhesive joints was investigated under mode I and II loading. Digital Image Correlation (DIC) provided precise measurements of crack length and crack tip opening/shear displacement (CTOD/CTSD), while the Extended Global Method (EGM) was used to determine the Energy Release Rate (ERR) and resistance curves (R-curves) for each fracture mode. The direct method was applied to establish the traction-separation law (TSL) and bridging law. Based on observed failure mechanisms, a novel cohesive law with five linear components was proposed, with parameters derived from experimentally obtained TSL and bridging law. Experimental determination of cohesive zone lengths for both fracture modes was achieved using the DIC technique, which was then compared with analytical predictions. Finally, the five-linear and trapezoidal cohesive zone model (CZM) was used to simulate the mode I and mode II fracture processes, respectively, within a finite element framework. [ABSTRACT FROM AUTHOR]

• Viscoelastic fracture mechanics approach is necessary for fracture analysis of propellants. • Mechanically aged samples show lower fracture resistance due to debonded particles. • Thermally aged samples exhibit better fracture response due to higher crosslinking density. • Ozone aged samples show worse fracture performance due to lower crosslinking density. • Cohesive stress is an appropriate parameter to describe propellant fracture, being related to a dewetting mechanism. Structural integrity of composite solid propellants (CSPs) is one of the main concerns when considering the performance of CSP motors. The development of cracks in the propellant's grain, caused by aging during the service life of the motor, is the main reason for its catastrophic failure. In addition, the fracture characterization of these viscoelastic and highly filled materials is not fully solved yet and hardly addressed for aged CSP. This manuscript presents a broad and comprehensive study on the fracture behavior of aged CSPs, where Schapery's viscoelastic fracture mechanics (VEFM) methodology is used to effectively characterize the fracture behavior of a composite solid propellant with carboxyl-terminated polybutadiene (CTPB) binder. For that, stress relaxation, fracture and tensile tests have been performed on non-aged and aged CSP. Three different accelerated aging methods were employed (mechanical, thermal and ozone) that are related to the phenomena that deteriorate the material during the lifespan of the motor. Two main contributions are derived from this work. The first one is the understanding of the fracture processes developed in aged CSP, under different types of aging. The second most relevant contribution is that the cohesive stress, as the fracture parameter inferred from the VEFM approach, is observed to be correlated to the dewetting stress, a material measurable parameter. The results have potential implications for the design and longevity of future solid rocket propellants. [ABSTRACT FROM AUTHOR]

• Crack initiation was detected using a strain gauge. • Calculation methods of the modified J-integral and modified fracture energy were proposed. • Fracture energy was divided in three parts: plastic energy, elastic energy, and surface energy. Crack initiation detection is of crucial significance for comprehending the entire fracture process behaviors, encompassing crack initiation and propagation. In the present study, strain gauges were utilized to detect crack initiation at a temperature of 25 °C, and the data related to crack initiation were employed for the calculations of the modified J-integral and modified fracture energy. Fracture energy was classified into three components: elastic energy, plastic energy, and surface energy. The improved fracture energy is the difference between the traditional fracture energy and the plastic energy. Semi-circular bending (SCB) tests were carried out on two types of asphalt mixtures, namely AC10 and AC16, with two distinct notch lengths of 15 mm and 30 mm. Crack mouth opening displacement (CMOD) was also recorded during the SCB tests. In addition, load-line-displacement (LLD) was also recorded. The results demonstrated that the peak of strain occurred earlier than that of the load, suggesting that specimens could endure further loads after the onset of a macro-crack. With the augmentation of notch length, the elastic energy, plastic energy, and surface energy decreased significantly for both AC10 and AC16. For both AC10 and AC16, approximately 70 % of the total energy was surface energy, which was utilized for crack propagation, and the proportion of plastic energy was lower than that of elastic energy. Plastic energy is predominantly employed for the plastic deformation of the asphalt binder. When the plastic energy was excluded from the total fracture energy, the disparity in fracture energy between specimens with different notch lengths was narrowed, indicating that the plastic energy was regarded as a key factor leading to the reduction in fracture due to the increased notch depth. When calculating the J-integrals using the data corresponding to crack initiation instead of the peak load data, the J-integrals decreased considerably, signifying that the surface energy within the range from crack initiation to the peak load point results in a significant increase in the J-integral. In comparison to AC16, AC10 exhibited higher J-integral, elastic energy, plastic energy, and surface energy, suggesting that AC10 demonstrated superior fracture resistance to crack initiation and propagation, which was mainly attributed to the porosity difference between AC10 and AC16 specimens. The load-LLD curves and load-CMOD curves generally exhibited a similar trend in energy parameters, while the load-CMOD curves manifested flatter curves within the descending phase. [ABSTRACT FROM AUTHOR]

[Display omitted] • Fatigue J-integral approach for hybrid DCB specimen successfully developed. • Beam rotation tracked by applying a repetitive pattern and image processing. • Slope of the beam was affected by the rigid loading blocks. • Compliance-based LEFM and J-integral data were in agreement for Al/epoxy laminates. • Drop of fatigue threshold and change in failure mode at glass transition of epoxy. A fatigue fracture mechanics methodology was developed and established, employing a slope-based J-integral approach combined with advanced image processing techniques. Adhesively bonded double cantilever beam (DCB) specimens were tested under constant displacement amplitude loading. The beam rotation was tracked by affixing a repetitive pattern on the DCB specimens and capturing images at the maximum displacement amplitude. Using a custom-developed image processing procedure, the beam rotation was deduced. To validate the methodology, DCB fatigue experiments were conducted at 23, 60 and 75 °C on aluminum adherends bonded with a structural 2-K epoxy adhesive. The J-based approach was compared with a conventional, compliance-based linear elastic fracture mechanics (LEFM) method. The epoxy was a rather brittle, high-modulus adhesive with a bond line thickness of 0.25 mm, resulting in predominantly linear elastic material behavior. By analyzing the images taken during fatigue testing, a stiffening effect of the steel load blocks was observed. Excluding pattern elements directly below the load block yielded the best agreement between J-integral and LEFM data. Both approaches were in excellent agreement within the investigated temperature range. The investigated adhesive exhibited a highly temperature-dependent behavior, which was associated with higher crack propagation rates and a lower fatigue threshold at 60 and 75 °C. [ABSTRACT FROM AUTHOR]

This study investigates the mechanical performance of 2024-T3 aluminum plates repaired with metallic and composite patches under accelerated aging in water immersion. The adhesive and composite patch properties were experimentally characterized for various immersion durations and integrated into numerical models. Results revealed a substantial decline in stress transfer efficiency with aging, particularly for composite patches, which become less effective in absorbing stresses under humid conditions. Key factors, including loading type, crack length, immersion duration, and patch material, were analyzed. Stress analysis highlights the degradation of both the adhesive and the composite patch, leading to reduced load transfer from the damaged area. These findings show the critical impact of environmental conditions on the durability of bonded repairs and provide insights to optimize repair strategies for long-term performance. This work uniquely compares the performance of metallic and composite patch repairs on aluminum plates under aging conditions, highlighting the superior long-term durability of metallic patches in humid environments due to their resistance to water-induced degradation. • An experimental analysis under fatigue test and a numerical analysis under tensile loading of the plates repaired by metal and composite patches was done. • A comparison of the fatigue test results in terms of crack length as a function of number of cycles is presented taking into account the immersion time. • The metal patch becomes more efficient than the composite patch if the repaired structure is exposed to humidity. • The analysis of the J-integral value showed that the repair whether metal patch or composite provides a good reduction. • If the adhesive and the patch absorb water, the metal patch becomes more efficient than the composite patch. [ABSTRACT FROM AUTHOR]

• The critical fracture toughness index of girth weld material in high-strength steel pipeline has been established. • The calculation method for the structural stress and fracture toughness of high-strength steel pipeline with crack in girth weld subjected to complex internal and external loads have been established and validated. • The prediction model for calculating the maximum J-integral value of pipeline with crack in girth weld subjected to complex loads has been established by integrating particle swarm optimization(PSO) and Long Short-Term Memory (LSTM). • A bicompetitive failure assessment method based on pipe body strain and fracture toughness J-integral of girth weld has been presented. • The fracture failure mechanism diagram of pipeline has been constructed based on three kinds of characteristic parameters. High-strength steel pipeline with crack in girth weld is susceptible to failure subjected to complex loads. Therefore, the critical fracture toughness index of girth weld of high-strength steel is determined through the three-point bending test in the paper. A quantitative investigation was conducted on the influence of pipeline, crack, and landslide characteristic parameters on J-integral using the established calculation method for the structural stress and fracture toughness of high-strength steel pipelines with crack in girth weld subjected to complex internal and external loads. To predict the maximum J-integral value of pipeline with crack in girth weld subjected to complex loads, the Particle Swarm Optimization(PSO) and Long Short-Term Memory(LSTM) hybrid model (PSO-LSTM) was employed. Based on pipe body strain and fracture toughness J-integral of girth weld, a bicompetitive failure assessment method was proposed; furthermore, the fracture failure mechanism diagram of pipeline are developed considering three kinds of characteristic parameters. The findings demonstrate that the J-integral serves as a more appropriate assessment index for assessing weld fracture toughness, with a critical value of 156.13 kJ/m2. Moreover, a positive correlation exists between the J-integral and crack size, landslide width, and cross-sectional area; conversely, a negative correlation is observed between the J-integral and pipe diameter and wall thickness. The maximum J-integral prediction model exhibits a high level of accuracy, with a maximum relative error of 9.59%. The fracture failure mechanism diagram of pipeline enables the identification of different failure modes and delineation of safety areas under various working conditions. The effectiveness of this methodology in assessing the safety of pipelines with crack in girth weld under landslide action has been demonstrated through its successful application to the cross-slope laying pipe on ZM pipeline. [ABSTRACT FROM AUTHOR]

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]

This research work is focused on the study of the fracture behaviour of a silica-filled NBR. The Mullins effect and its thermally-induced recovery are initially studied performing tensile tests: comparing the material's response in uniaxial tension and pure shear deformation conditions, a lower recovery is observed in the pure shear configuration. A similar study is then performed considering the fracture behaviour of the material. Tests are performed in quasi-static loading conditions and by applying a fracture mechanics approach. The fracture toughness is evaluated as J-integral at the crack onset and at the unstable fracture initiation; further, the crack propagation is analysed and the resistance curve is obtained. The dependence of the overall fracture behaviour of the material on the applied thermal history is evaluated. Even though the crosslinking degree seems not to be affected by the thermal treatment, the fracture behaviour is modified. A correlation of these results with a change in the material's propensity to form cavities under stretching is proposed. • Mullins effect in a silica filled NBR is recovered in uniaxial tension by applying a thermal treatment. • The same thermal treatment induces a lower recovery of Mullins effect in pure shear deformation conditions. • Fracture toughness is reduced by stretch induced softening and this effect is not thermally recovered. • The more severe thermal history, the lower fracture toughness measured at unstable fracture initiation. • The applied thermal history affects the material's propensity to form cavities under stretching. [ABSTRACT FROM AUTHOR]

• A method to determine the fracture parameters for the propellant/liner interface affect zone is proposed. • For the first time, Tensile tests of rectangular specimens with different prefabricated crack lengths were carried out at different temperatures and loading rates. • The change law of the crack length of the rectangular specimen with time was extracted by programming batch processing. • The fracture toughness of NEPE propellant/liner interface under different loading conditions was obtained based on J-integral theory. The debonding of propellant/liner interface is one of the primary failure modes that impact the structural integrity of solid rocket motors. In order to study the mechanical properties of propellant/liner interface, tensile tests on rectangular specimens with various prefabricated crack lengths were conducted at different temperatures and loading rates, as well as uniaxial tensile tests on the propellant. Utilizing the digital image correlation(DIC) method, the strain field including the whole rectangular specimen and the propellant part was analyzed, and the change law of the crack length of the rectangular specimen with time was extracted by programming batch processing at different temperatures. Meanwhile, the fracture toughness of the NEPE propellant/liner interface under different loading conditions was obtained using J-integral theory. The results show that the area near the propellant/liner interface forms an interface affect zone (IAZ), where cracks grow steadily in a continuous and smooth way without significant fluctuations. The effect of temperature and loading rate on J-integral is interactive. The lower the temperature, the greater the fracture toughness of the interface and the lower the crack propagation rate. Finally, based on the bi-linear cohesive model, the numerical simulation of the interface affect zone (IAZ) in the rectangular specimen is carried out, which shows that the J-integral can effectively represent the energy required for the interface affect zone failure. A method to determine the fracture parameters for the propellant/liner interface affect zone is proposed. [ABSTRACT FROM AUTHOR]

Dielectric Functionally Graded Materials (FGMs) exhibit superior flexoelectric properties. Gradual changes in material properties lead to large strain gradients and excellent flexoelectric responses. Cracks behave in a complex manner inside piezoelectric-flexoelectric FGMs subjected to electromechanical loading. An extended isogeometric analysis (XIGA)-based formulation is developed for flexoelectric FGMs with crack discontinuities. Ceramic-polymer FGMs of barium titanate (BTO) and polyvinylidene fluoride (PVDF) are selected for analysis since this material combination has shown better flexoelectric response solely due to gradation. A higher-order electromechanical J-integral is used to study the behavior of cracks. The fracture behavior of different crack geometries at various grading indices and levels of flexoelectricity is investigated. A crack interaction study is conducted with varying crack parameters. The length-scale effect on the energy release rate is also shown. A significant reduction in the energy release rate is observed in FGMs due to the flexoelectric effect. [ABSTRACT FROM AUTHOR]

The mode-III fracture behavior of structural adhesive joints is examined using a modification of the SLB specimen. Tests were performed on the adhesive SikaPower ®-498. Crack growth resistance curves and traction separation laws in the context of cohesive zone modeling were obtained from the experimental data. Finally, data reduction schemes based on both simple beam theory and the J -integral are applied and discussed. To measure the crack-tip position (which cannot be easily detected with a simple camera since no practical line of sight exists in this particular test setup), both a digital image correlation (DIC) system and fiber-optic strain measurements were utilized for an indirect determination of the crack-tip position. Both systems allow multiple ways to evaluate the measured data, hence giving rise to a few different methods to locate the crack tip which were analyzed and compared regarding their benefits and disadvantages. • The four-point bend out-of-plane loaded single-leg bending (4-OSLB) test is proposed. • Only force measurements are required for G-analysis. • Backface strain measurements are used for the measurement of the crack length. • Evaluation methods based on DIC and fiber optical strain measurements are compared. [ABSTRACT FROM AUTHOR]

The fracture toughness and deformation behavior of Ti- x Al (x = 0, 2, 4 wt%) binary alloys were investigated. The non-thickness-dependent fracture toughness was measured based on the J -integral multiple-sample approach. Increased Al content induced reduced fracture toughness from 265 to 148 MPa·m1/2 of Ti- x Al alloys. The fracture toughness was discussed in this article by the mutual influence of the elastic component (J el) and the plastic component (J pl). The solid solution strengthening effect of Al was identified as the primary factor contributing to the increase in J el. Additionally, the evolution mechanism of J pl with varying Al content was elucidated by slip modes, twin activation, and dislocation configurations at the crack tip. Prismatic slip was found to be the predominant slip mode in Ti- x Al alloys. With the increase in Al content, the elevated critical resolved shear stress associated with prismatic slip hindered the alleviation of stress concentration, resulting in a decrease in J pl. The increase in content of Al in the Ti- x Al alloys inhibited the formation of {11 2 ¯ 2} twins. Compared to Ti-0Al and Ti-2Al alloys, a significant increase in < c > dislocations was observed in Ti-4Al alloy. The additional < c > dislocations impeded the movement of subsequent < a > dislocations, which potentially resulted in a reduction in J pl. Furthermore, a crack tip stress analysis method based on twin variant activation was proposed. In Ti-0Al and Ti-2Al alloys, twins activated by internal stress were more pronounced compared to the Ti-4Al alloy. The internal stress may be composed of back stresses, which are generated by twinning activation. • The contribution of elasticity and plasticity to fracture toughness in Ti- x Al alloys was discovered. • The deformation mechanisms at crack tip plastic zone of Ti- x Al alloys were scrutinized. • A stress analysis method based on twin variant activation at the crack tip was proposed. • The stress states at the crack tip of Ti-xAl alloys were analyzed. [ABSTRACT FROM AUTHOR]

This study investigates the fracture behavior of thick adhesive joints manufactured with composite adherends and bonded with an epoxy-based structural adhesive common to the wind turbine industry. For that purpose, double cantilever beam specimens with an adhesive thickness of approximately 10 mm and different pre-crack lengths are manufactured and tested under mode I loading. Analytical approaches are compared to assess the energy release rate, including the simple beam theory, modified beam theory, compliance calibration method, and beam on an elastic and elastic-plastic foundation. In order to evaluate the applicability of the analytical approaches, an in-situ measurement method based on Digital Image Correlation is also employed to determine the energy release rate of the thick adhesive joints. The crack propagation angle is determined theoretically using the second-order crack kinking theory. A good correlation is observed between the theoretical predictions and experimental results. Furthermore, it is demonstrated that due to the T-stress, the crack tends to deviate from the middle of the joint and propagate towards the interface. By comparing different data reduction methods to evaluate the energy release rate of thick adhesive joints, recommendations for their fracture analysis are made, pinpointing the beam on an elastic and elastic-plastic foundation as the most suitable model. • Pre-cracked thick adhesive joints in glass/epoxy composites have been examined under pure mode I loading conditions. • An in-situ measurement method based on DIC has been employed to analyze the crack tip parameters. • Experimental and analytical energy release rates derived from different approaches are compared. • The influence of the T-stress on the crack propagation angle is analyzed for thick adhesive joints. • The applicability of the J-integral based on a beam on an elastic-plastic foundation is examined for thick adhesive joints. [ABSTRACT FROM AUTHOR]

The Hydrogen Embrittlement (HE) appearance is the main reason for the desire to evaluate the burst pressure of pipes. Several existing models predict burst pressure of hydrogen-induced pre-cracking pipes with the fracture mechanics criterion (fracture toughness, J cr). Still, none of them has taken into account the model uncertainty. In this paper, we propose a surrogated model associated with molecular models. The discrete values of the dimensionless influence functions presented for elastic and plastic components of J are connected by machine learning (Random Forest Regression, RFR) and third-order polynomial functions with optimized factors to avoid the inconvenience of using the lookup table. The molecular empirical models are obtained by the up-to-date Balancing Composite Motion Optimization (BCMO) algorithm. Because samples of elastic and plastic databases are limited and the final output, P b , is not directly derived from molecular models, all databases are used for training without the conventional data splitting to train and test sets. Consequently, the proposed approaches (RFR model and Empirical model) are validated based on the experiments collected globally. The final models are accounted for the residual distribution as the unavoidable component. The efficiency of the Random Forest and empirical models is validated by experiments or simulations from the literature when the evaluation metrics (i.e., R -square, Mean Absolute Error) are (0.9666, 0.8695 MPa) and (0.9701, 0.7996 MPa), respectively. The drawbacks of the proposed models, heavily dependent on databases, are also illustrated and discussed for further development. Strict boundaries of input and output, especially the fracture toughness, which is commonly degraded due to the effect of HE, from the test set combined with the uncertainty of the models based on the analysis of model residuals are also proposed for validation. • RFR model used to determine burst pressure of hydrogen-assisted pre-cracking pipes. • Empirical model is coined in a compact form of third-order polynomial functions and BCMO algorithm. • Validation reveals the reliability of the semi-empirical approach with R 2 higher than 0.96 • Models' constraints set by ranges of database input taking into account the hydrogen embrittlement. • The distribution of residual on validation dataset is presented for model uncertainty. [ABSTRACT FROM AUTHOR]

• We present a DIC approach to measure J-R curve of M(T) specimens. • The proposed approach covers both monotonic and reversed loading conditions. • We validate the accuracy of the DIC approach in numerical and experimental studies. • We demonstrate the crack-tip re-sharpening caused by reversed loadings in DIC. This paper proposes a digital image correlation (DIC) based method to measure the fracture resistance curve and quantify the reversed loading effects in middle tension, M(T) specimens. The proposed method employs free-surface DIC measurement to derive J and utilizes the deformation profile to determine the crack size with enhanced accuracy than the conventional compliance-based approach. This study observes the re-sharpening of the crack-tip field during the reversed cycle through DIC, which facilitates the crack propagation and decreases the fracture resistance. The comparison between monotonic and reverse-loaded M(T) specimens demonstrates the decrease of the fracture resistance under reversed loadings. [ABSTRACT FROM AUTHOR]

• DIC setup with high-speed camera can capture crack propagation in brittle ceramics. • Accurate method to determine R-curves for ceramics is experimentally from DIC images. • Reaction-bonded SiC–B 4 C has higher crack resistance compared to monolithic SiC. • Increase thickness of β-SiC rim around α-SiC grains offers higher crack resistance. • Decrease Si amount between main α-SiC grains to nm level increases SiC–B 4 C toughness. The current research uses the Digital Image Correlation (DIC) approach to study the fracture behaviour of Reaction-Bonded Silicon Carbide-Boron Carbide (SiC–B 4 C) ceramic (RBSBC). A Photron camera with 137,500 fps was used to capture the crack propagation at an interframe time frame of 2.6 ms before final fracture. The purpose was to capture the rapid brittle behaviour of the ceramic during the onset of crack propagation. The RBSBC failed in a transgranular manner like most monolithic SiC-based materials as Hexoloy-SA. The presence of randomly dispersed coarse B 4 C grains helps in deflecting the crack path which increases the overall crack length. The material's resistance to crack propagation (R-curve) was measured using the crack tip opening displacement, the stress intensity at the crack tip K I , and the J -integral against crack extension. Two methods were used to determine the K I : experimentally based on the displacement values at the crack tip as obtained from the DIC images, and quasistatic based on the fracture load and the geometrical dimension of the crack. The experimentally-determined K I and J resulted in higher values compared to the quasistatic ones. However, they reflect the actual conditions at the crack tip, while the quasistatic conditions underestimate the resistance-plot. The RBSBC has higher R-curve compared to commercially available SiC-only materials as Hexoloy-SA and ABC-SiC. To improve the crack-resistance of RBSBC, the Si amount should decrease to a nm level, while the percentage of B 4 C grains should increase and be evenly dispersed across the material. [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]

• The fracture process zone has been experimentally examined. • The results assess the impact of the damage process on the cracking process. • Identification of a fracture process zone (FPZ) during the cracking process. • The FPZ is accompanied by a softening of the material located downstream of the crack propagation front. The study presents a novel method for identifying and monitoring the fracture process zone and its impact on cracking parameters, such as damage rate and fracture energy. Concrete samples subjected to a Wedge Splitting Test were investigated. Digital Image Correlation, a full-field measurement technique, was utilized to measure the experimental displacement fields at various scales. The experimental measurements, optimized through a Newton-Raphson iterative adjustment procedure, revealed the presence of a damaged zone accompanying the cracking process. This analysis also enabled the estimation of the material damage rate and provided a more realistic assessment of cracking parameters by integrating the entire process of damage and macro-cracking into the calculation of fracture energy. The results suggest that the appearance of a fracture process zone correlates with a reduction in the material's hardness downstream of the crack propagation front. [ABSTRACT FROM AUTHOR]

A novel Automated Crack Extension Measurement (ACEM) method based on combining decorrelation in strain field and a threshold near maximum of full-field strain obtained from digital image correlation, is developed in this work. A manual method for measuring crack extension from images of the specimen surface and ImageJ, was utilized to validate the accuracy of the proposed method. Initially, ACEM method was validated for crack extension under mode-I fracture of single edge notch specimens with different initial notch sizes. A satisfactory agreement was obtained from this analysis along with limits on the different parameter values used in ACEM. The method was then applied to low-cycle fatigue specimens with different initial notch lengths. Comparison of crack extension between ACEM and manual method reveals satisfactory agreement reinforcing the fidelity of the developed method for fracture and fatigue analysis. Fracture resistance and fatigue crack growth rate curves were also obtained for the different specimens. • The method is developed using full-field strain obtained from Digital Image Correlation • Sensitivity analysis is performed to find the optimal parameters of the method • The method is validated for fracture and low cycle fatigue • Accurate crack growth measurements obtained for monotonic and cyclic loading [ABSTRACT FROM AUTHOR]

• The plastic influence term on crack driving force is quantitatively described by the plastic wake height. • The relation between separation displacement and the crack driving force gives an extra constraint on how to choose a proper traction-separation law. • The plastic influence term on crack driving force is found to be independent of in-plane geometry as long as the crack tip plastic zone does not reach the outer boundary or merge with the plastic zone of the outer boundary. This paper has transferred the influence of plastic dissipation on the crack driving force into the crack growth resistance curve based on a displacement quantity defined at the current crack tip. Such a displacement is the crack-tip-opening displacement of the corresponding stationary crack for an elastic–plastic growing crack and represents the plastic wake height. Then, this displacement-based resistance curve provides a quantitative description of the plastic deformation influences during crack growth. This paper has three novel points: 1) the crack-tip-opening displacement for an imaginary stationary crack is divided into the separation displacement and the plastic wake height, in which the separation displacement is related to the crack driving force and the plastic wake height is correlated with the plastic influence term. 2) A unified constraint of the traction-separation law (TSL) for the cohesive zone is provided by the relation between separation displacement and the crack driving force, which can shed further light on how to choose a proper TSL. 3) According to the relation between the plastic wake height and the plastic dissipation term, the influence of plastic deformation on the crack driving force is found to be independent of initial crack length, specimen width and geometrical type as long as the crack tip plastic zone does not reach the outer boundary or merge with the plastic zone of the outer boundary. [ABSTRACT FROM AUTHOR]

The Newton-Raphson iterative scheme is a widely used technique for modeling the non-linear problems, but it is well known that the scheme is unstable and the convergence may be difficult to obtain in case of snap-back or bifurcation. The sequentially linear approach, which sets a critical integration point and uses a saw-tooth softening approximation, is an alternative approach to address these issues. However, the sequentially linear approach cannot fully solve some drawbacks such as mesh dependency of crack patterns, which is main shortcomings of smeared crack approach. In this paper, the saw-tooth curve based on exponential softening is newly developed and an approach combined it with local crack tracking algorithm is proposed. The crack tip point is chosen by crack tracking algorithm and the fracture behavior is analyzed by sequentially reducing the stiffness and strength in elements within crack path. Several benchmark examples are numerically solved to check the accuracy of crack path, ultimate load and capture of snap-back predicted by the proposed approach and the results are compared with those by traditional sequentially linear approach and experiments. • A saw-tooth curve is improved based on exponential softening. • The updated Young's modulus and strength can be easily obtained without iterations. • The sequentially linear approach is combined with the tracking procedure. • The accuracy of the predicted crack path is improved in smeared crack approach. • The snapbacks were correctly captured in three examples. [ABSTRACT FROM AUTHOR]

Universal slope-based J- integral methods have been developed for the determination of the energy release rate for adhesively bonded joints under mode I, mode II and mixed-mode (I/II) loading conditions. The individual J components corresponding to the mode I and mode II loading were separated based on the J -integral decomposition theory. The proposed methods use the slopes of the substrates at various locations to characterize the energy release rate and thus avoid the measurement of crack lengths, which are especially suitable for characterizing the tough interfaces associated with large fracture process zones ahead of crack tips. Under linear elastic deformation, the slope-based J equations were found to be equivalent to classical G equations based on linear elastic fracture mechanics (LEFM). Both experimental and numerical testing of adhesively bonded joints were undertaken to validate the slope-based J equations. The universal slope-based J -integral methods provide a reliable alternative to the measurement of G for adhesive joints or laminated composites undergoing nonlinear or inelastic deformations where conventional LEFM is not valid. It is shown that LEFM, even when coupled with an effective crack length approach, can be inaccurate when damage occurs in a test specimen away from the fracture process zone, as was seen here in mode II. Slope-based J equations can avoid these inaccuracies with a careful selection of contour paths. Slope based methods are therefore strong candidates for selection in future test standards for mode II fracture characterisation of structural adhesive joints. [Display omitted] [ABSTRACT FROM AUTHOR]

• A mechanistic model for quantitative analysis and prediction of the fatigue crack growth rate of paving materials is proposed. • The derived J-integral serves as the driving force for crack growth and it is a function of the horizontal tensile stress, initial resilient modulus, damage density, specimen size, and surface energy of the paving materials. • The fatigue life of cement-treated aggregates is primarily influenced by the crack initiation stage, while for asphalt mixtures, the crack growth stage plays a more significant role. • The Paris' law coefficients exhibit minimal variation across different stress levels and loading frequencies, and can be utilized to evaluate the fatigue crack resistance of paving materials. Fatigue crack growth rate (FCGR) is a critical indicator that reflects the rate at which material deterioration occurs under cyclic loads. However, there is currently a lack of a mechanistic quantitative analysis and prediction of the FCGR of paving materials under external indirect tensile (IDT) cyclic loads. To address this issue, this study aims to develop a mechanistic model for quantitative analysis and prediction of the FCGR in paving materials subjected to external IDT cyclic loads based on the J-integral based Paris' law. Two types of paving materials, namely cement-treated aggregates and asphalt mixtures, were selected to demonstrate the results and model of the FCGR. The results indicate that the derived J-integral serves as the driving force for crack growth and is influenced by horizontal tensile stress, initial resilient modulus, damage density, specimen size, and surface energy of the paving materials. The fatigue life of cement-treated aggregates is primarily influenced by the crack initiation stage, while for asphalt mixtures, the crack growth stage plays a more significant role. The application of Paris' law is found to be effective in predicting the FCGR at stable crack growth stage. The coefficients of Paris' law exhibit minimal variation across different stress levels and loading frequencies, and can be utilized to evaluate the fatigue crack resistance of different paving materials. [ABSTRACT FROM AUTHOR]

The whole process of pipeline–soil interactions between a landslide and a gas pipeline was simulated using the strength reduction method. The main purpose is to investigate how pipeline internal pressure, landslide displacement, crack depth ratio (the ratio of crack depth to wall thickness), crack aspect ratio (the ratio of crack depth to crack half-length), and reinforcement with anti-slide piles influence the J-integral of a circumferential crack in the pipeline under landslide impact. The simulation showed that increases in the landslide displacement, crack depth ratio, and pipeline internal pressure led to an increase in the maximum value of the J-integral at the crack leading edge. An increase in the crack aspect ratio reduced the maximum value of the J-integral. In addition, in the process in which the crack shape changed from semi-elliptical to semicircular, there was a critical crack aspect ratio at which the J-integral at the deepest point of the crack was equal to the J-integral at a point on the surface. The study also found that an increase in the number of anti-slide piles affected the location and distribution of the zone of maximum slippage and effectively reduced the maximum von mises stress and the J-integral at the crack tip. However, when the number and cross-sectional size of anti-slide piles exceed a certain threshold, further increasing or enlarging them barely affects the J-integral. • The strength reduction method simulates the full process of pipe-soil interaction. • The effect of crack depth ratio and crack aspect ratio on J integral is analyzed. • Beyond a threshold, adding or enlarging anti-slide piles barely affects J integral. [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]

Carbon steel is one of the most commonly used engineering materials. However, the mechanical properties of steel deteriorates due to exposure to harsh environments like corrosive surroundings and high temperatures. Extensive studies have been done to understand the exclusive effect of corrosion and high temperatures on tensile and fracture properties, although their combined effect has not been addressed. The present work aims to experimentally investigate this by conducting tensile and fracture tests at elevated temperatures on pre-corroded ductile steel. Pre-corroded steel was considered with corrosion levels up to 55%. Empirical relationships were established to quantify the degradation in tensile and fracture properties. An unloading compliance approach using a single specimen was utilized to determine the J -integral fracture toughness and also establish traction separation relation for mode I. The results reveal that the combined influence increases the degradation in fracture toughness, but it restricts the degradation in tensile properties. • Prior studies analyzed the individual impacts of corrosion and high temperatures. • Combined effect of corrosion and high temperatures is investigated here. • Combined action restricts the degradation in tensile properties. • Combined action increases the degradation in fracture toughness. [ABSTRACT FROM AUTHOR]

In this study, the mechanical properties of composite bituminous structures with geogrid products, used as an interlayer between different types of bituminous mixtures, at a constant temperature, were examined. A twofold experimental program based on new approaches was selected. A new configuration of the 3-Point Bending Test (3-PBT) was adopted to capture the J-integral and crack resistance property defined by crack resistance index (CRI) at the interface against bottom-up crack propagation. The bonding quality at the interface was also defined through a new index named coefficient of interface bonding (CIB), which was measured via a modified version of the slant shear device. The results derived from this research revealed that reinforcement of the interface, with varying degree of surface texture, by geogrid products significantly enhances the fracture toughness of the whole system in terms of the J-integral, which could be properly connected to the combined functions of bonding quality and crack resistance indices defined at the interface. • Study of fracture toughness of rehabilitated bituminous pavements. • Study the influential factors dictating the development of reflective cracking in bi-layer structures. • Investigate the interconnection between the fracture toughness and interfacial mechanical parameters. [ABSTRACT FROM AUTHOR]

• 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]

This work introduces a novel phase-field solution for simulating and predicting fractures in elastic solids. In this phase-field fracture model, the crack growth is driven by the material energy–momentum flux, or the configurational force, inspired by a null divergence conservation law and its variational theory, as opposed to employing the commonly-used strain energy degradation-based crack-driving force. By doing so, the crack growth or material configuration change is solely determined by the physics-based Eshelby energy–momentum tensor density or the Rice J-integral flux, which aligns with the energy release criterion of the celebrated Griffith–Eshelby–Rice (GER) theory. The proposed method not only preserves the integrity of the balance of linear momentum principle at the crack tip region but also provides a correct stress asymptotic field in front of the crack tip, while accurately capturing the crack growth. The key idea of this approach is to use the monotonically increasing and irreversible phase field as the marker of the configurational change and form a phase field variational principle that couples the strain energy density with the configurational strain energy density. By doing so, we only damage the displacement field as a form of diffused crack, as opposed to damaging the stress field in the existing phase-field method. Moreover, from numerical simulations, we discovered two different forms of energy release rates: one drives crack growth by enforcing the crack-tip traction loading condition, and one drives crack growth by enforcing the crack-tip deformation condition, demonstrating the ability of the proposed method to naturally capture two distinct modes of fractures due to two different near-crack tip loading conditions. These advancements and contributions reveal previously unknown insights into fracture mechanics. [Display omitted] • We developed a phase-field fracture model that uses energy–momentum flux to drive crack growth. • We use the phase field variable as the configuration change marker to calculate the crack-driving force. • The proposed phase-field fracture model preserves the balance of linear momentum at the crack tip. • The novel phase-field fracture model captures the asymptotic stress field in front of a crack tip. • The phase-field fracture model captures failure modes due to both the stress and deformation loads. • We reveal differences between a two different fracture modes due to traction and displacement loads. • The novel phase-field fracture model is variationally and thermodynamically consistent. [ABSTRACT FROM AUTHOR]

• A deep neural network-based method is proposed to predict the J -integral for surface cracked plates under biaxial loading. • Various crack geometries, material properties and loading parameters are considered for developing a FE J -integral datasets of surface cracked plates under biaxial loading. • When the biaxial ratio is negative, the resulting J -integral values along the crack front are significantly large. • The evaluation criteria for DNN models and grid search method are utilized to determine the optimal DNN model structure. • For the scope of the parameter matrix in this research, the determined DNN model shows accurate prediction performance. As surface cracks may cause potential failure for engineering structures, it is of vital significance to carry out the fracture assessment for cracked structures. The crack driving force in the form of J -integral is an important input parameter in fracture assessment. This paper focuses on the determination of J -integral for surface cracked plates under biaxial loading. A method for predicting the J -integral based on the deep neural network (DNN) is proposed to estimate J -integral efficiently and accurately. Firstly, extensive three-dimensional (3D) elastic–plastic finite element (FE) analysis is conducted to compute the J -integral along the crack front for developing a FE J -integral datasets containing 1600 cases. Various crack aspect ratios, crack depth ratios, strain hardening exponents, ratios of the loading perpendicular to the crack plane to yield stress, and biaxial ratios, are strategically considered. Secondly, DNN models for predicting the J -integral are constructed and trained according to the obtained datasets by FE analysis. Then, the evaluation criteria for DNN models and the grid search method are utilized to determine the optimal DNN model structure. Finally, test cases are employed to verify the feasibility and prediction accuracy of the determined DNN model. Based on validation results, the determined DNN model exhibits sufficiently accurate prediction performance. This research provides an idea for engineering applications, through building software based on continuously optimized DNN models, the J -integral for surface cracked plates under biaxial loading can be accurately and efficiently predicted for performing fracture assessments. [ABSTRACT FROM AUTHOR]

[Display omitted] • Adding fatigue failure analysis to existing data of thermal failure of rubber liners. • Experimental study of the impact of reinforcement types on crack growth properties. • Assessment of position and direction prone to crack growth by the J-integral method. • Comparative study of fatigue performance to loading and liner geometry types. • Giving a solid base to perform failure analysis by available crack growth analyses. A numerical crack growth analysis is here combined with the experimental fatigue and tearing data to fully characterize the crack growth performance of the rubber liners of downhole motors. Findings consistently revealed that the geometry of "uniform liner" has a more than three times higher J-integral than the "conventional liner" type and the crack growth in the former is remarkably affected by changing the material type, the crack length, and the loading conditions. By increasing the interference fit from 0.05 to 0.3 mm, the energy release rate changes in a range of 0.1–0.3 for the conventional liner, but it surprisingly reaches a value of 3.0 for the uniform liner. The significance of reinforcing rubber liners with either a particulate filler or a polymeric resin was identified. Very intensified fluctuations in the tearing force of samples containing the polymeric resin were observed. The fracture mechanics approach to fatigue was adapted to compare the performance of liners. Under similar conditions, it was observed that growth in crack length from 0.5 to 1.5 mm occurs in a span of 8.65 × 105 and 2.11 × 107 cycles, respectively for the uniform and conventional liners. [ABSTRACT FROM AUTHOR]

• A micromechanical model was first established to study crack and fibers. • The isotropic, anisotropic and microscopic models were compared. • The impacts of crack size and location, fiber content on stress field were revealed. • The variations of various mechanical properties were discussed. Accurately clarifying the influence of cracks on the mechanical behaviors of unidirectional fiber-reinforced composites (UD FRCs) is of great significance for the structural integrity evaluation of UD FRCs with defects. Although several experiments and numerical analyses have explored the impact of cracks on stress field, satisfactory quantitative characterizations of crack size, a / W and location, Δ , fiber content, V f have not yet been obtained. In this paper, the accurate and detailed microscopic models containing crack were first established and thoroughly validated. Then, a parametric study was conducted using three-dimensional micromechanical analysis to investigate how the crack size and location, fiber content affect the von Mises, stress triaxiality, Lode angle and J -integral of UD FRCs. Results showed that homogeneous models, whether isotropic or anisotropic, cannot accurately describe the mechanical behavior of cracked UD FRCs. The von Mises stress and J -integral are greatly influenced by the crack and fiber content, while stress triaxiality and Lode angle are not sensitive to changes in these factors. Further, the von Mises and J -integral increase with the decrease of V f and the increase of a / W , but show a more complex trend in the variation of Δ. These findings will help clarify the failure mechanism of cracked UD FRCs and can be used for reliability evaluation. [ABSTRACT FROM AUTHOR]

Due to the existence of microstructures involving characteristic length scales, micropolar materials such as bones, rocks and foam materials usually have complex fracture behaviors. The near-tip fields of an anti-plane crack in micropolar media and the local cracking modes, however, remain unclear. In this paper, the Williams asymptotic solutions of the near-tip fields of an anti-plane crack in micropolar elasticity are derived. A force stress intensity factor (FSIF) and two couple stress intensity factors (CSIFs) are the key fracture parameters characterizing the anti-plane crack-tip fields. And the energy release rate for an anti-plane crack is similar to the Rice's J-integral for classical continua. Then, six crack modes are introduced for a three-dimensional micropolar solid, i.e., three global modes controlled by the FSIFs and three local modes controlled by the CSIFs. Different from classical isotropic elasticity, a material constant appears in the singular terms of the crack-tip force stress and couple stress fields of isotropic micropolar materials. In addition, there are six constant terms in the asymptotic solutions of the crack-tip fields, i.e., three constant force stresses and tree constant couple stresses similar to the T-stress in classical fracture mechanics. Sequentially, the J-integral for three-dimensional micropolar solids is expressed concisely by the FSIFs and CSIFs. It can be observed that the CSIFs normalized by the torsion and bending characteristic lengths are dimensionally equivalent to the FSIFs. This work provides a theoretical basis for studying the fracture performance and crack propagation criterion of micropolar materials. • The asymptotic solutions of the near-tip fields of an anti-plane crack for micropolar elasticity are provided. • Three global and three local crack modes are deeply elucidated for micropolar elasticity. • The J-integral is expressed concisely by three force stress intensity factors and three couple stress intensity factors. [ABSTRACT FROM AUTHOR]

At the tissue-scale and above, there are now well-established structure-property relationships that provide good approximations of the biomechanical performance of bone through, for example, power-law relationships that relate tissue mineral density to elastic properties. However, below the tissue-level, the individual role of the constituents becomes prominent and these simple relationships tend to break down, with more detailed theoretical and computational models are required to describe the mechanical response. In this study, a two-dimensional micromechanics damage-based representative volume element (RVE) of lamellar bone was developed, which included a novel implementation of a phase-field damage model to describe the behaviour of non-collagenous proteins at mineral-mineral and mineral-fibril interface regions. It was found that, while the stiffness of the tissue was governed by the relative proportion of extra-fibrillar mineral and mineralised collagen fibrils, the strength and toughness of the tissue in transverse direction relied on the interactions occurring at mineral-mineral and mineral-fibril interfaces, highlighting the prominence of non-collagenous proteins in determine fracture-based processes at this scale. While fractures tended to initiate in mineral rich areas of the extra-fibrillar mineral matrix, it was found that the presence of mineralised collagen fibrils at low density did not provide a substantial contribution to crack propagation behaviour under transverse loading. However, at physiological volume fraction (V f MCF = 50 %), different scenarios could arise depending on the relative strength value of the interphase around the MCFs (σ f Interphase MCF ) to the interphase between individual minerals (σ f Interphase HA ): (i) When γ = σ f Interphase MCF σ f Interphase HA < 1 , MCFs appear to facilitate crack propagation with MCF-mineral debonding being the dominant failure mode; (ii) once γ > 1 , the MCFs hinder the microcracks, leading to inhibition of crack propagation, which can be regarded as an energy dissipation mechanism. The effective fracture properties of the tissue also experience a sudden increase in fracture work density (J-integral) once the crack is arrested by MCFs or severely deflected. Collectively, the predicted behaviour of the model compared well to those reported through experimental and computational methods, highlighting its potential to provide further understanding into the mechanistic response of bone ultrastructure alterations related to the structural and compositional changes resulting from disease and aging. [ABSTRACT FROM AUTHOR]

• Rigorous derivation of the redefined 3D J-integral is presented. • Weakly singular terms (WSTs) arise in the derivation. • Redefined J-integral is a total of the energy release rate and WSTs. • Significances of WSTs are clarified through the results of FE analyses. A rigorous three-dimensional J-integral in a domain integral representation is derived and applied to elastic–plastic crack propagation problems. It is called the "redefined J-integral" in this paper. The derivation is based on the power balance of a solid. The difference between the powers of external force and strain energy stored in the solid is the energy release rate at the crack tip while the crack propagates. In the process of deriving the redefined J-integral, weakly singular terms that are related to the change of deformation field in the vicinity of the crack front are found to arise. They play a key role in the elastic–plastic crack propagation phenomenon. However, the weakly singular terms have not been discussed in previous studies on the three-dimensional J-integral. The characteristics of the redefined three-dimensional J-integral are theoretically predicted and are verified through crack propagation problems, especially for the role of the weakly singular terms. At this point the present study is unique especially for the considerations on the weakly singular terms. It is found that the redefined three-dimensional J-integral measures the total of the energy release rate at and the change of deformation energy inside a small but finite volume surrounding the crack tip. Hence, the redefined three-dimensional J-integral can be used as the crack parameter for three-dimensional elastic–plastic solids. [ABSTRACT FROM AUTHOR]

In this paper, J -integral and T* -integral in elastic–plastic fracture are computed by the quadrature element method (QEM). Since high stress gradients exist in the immediate vicinity of the crack front, computing these integrals accurately is not a trivial task. The QEM facilitates the construction of arbitrarily high-order elements, which effectively capture the stress gradients, making it particularly suitable for this computation. After performing an elastoplastic stress–strain analysis of the fracture problem, the stress and deformation states are further formulated to compute the integrals. The integrals are formulated in several forms, including the contour and domain forms, as well as the incremental and total forms. Classical numerical examples are solved to demonstrate the effectiveness and high accuracy of the method. Overall, the equivalent domain integral (EDI) form outperforms the contour integral form because errors at the local contour have less effect on the integral. Moreover, the QEM yields more accurate solutions than the popular finite element method (FEM) that employs low-order finite elements and shares the same number of degrees of freedom. Additionally, it is found that the EDI form solution is not very sensitive to the specific type of the S function. Therefore, a linear function is suggested for convenience. [ABSTRACT FROM AUTHOR]

• A criterion of crack branching based on the energy release rate is proposed. • Theory of multidimensional space method for crack branching is established. • The formula of energy of the boundary shift is deduced. • The energy release rates of the crack branching in four quadrants are determined. In this paper, a criterion of crack branching based on the energy release rate is proposed. Theory of multidimensional space method for crack branching is established in the framework of the extended finite element method (XFEM), in which the formula of the boundary shift energy is deduced. The boundary cracking energy is obtained because the boundary shift model is abstracted into the boundary cracking model. The energy release rates of the crack branching in four quadrants are determined based on boundary cracking energy. Further, the energy release rate of the crack branching is introduced into multidimensional space method to determine the crack branching. If the crack tip branching, the criteria of crack branching are applied to determine the direction of the branching cracks, otherwise the criteria of maximum circumferential stress are applied to determine the direction of the cracks. Moreover, a classical numerical example is investigated to verify the correctness of the criterion of crack branching in the framework of the multidimensional space method. [ABSTRACT FROM AUTHOR]