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This paper presents a probabilistic method to predict fatigue crack growth for surface flaws in pipelines using a particle filtering method based on Bayes theorem. The random response of the fatigue behavior is updated continuously as measured data are accumulated by the particle filtering method. Fatigue crack growth is then predicted through an iterative process in which particles with a high probability are reproduced more during the update process, and particles with a lower probability are removed through a resampling procedure. The effectiveness of the particle filtering method was confirmed by controlling the depth and length direction of the cracks in the pipeline and predicting crack growth in one- and two-dimensional cases. In addition, the fatigue crack growth and remaining service life with a 90% confidence interval were predicted based on the findings of previous studies, and the relationship between the fatigue crack growth rate and the crack size was explained through the Paris' law, which represents fatigue crack growth. Finally, the applicability of the particle filtering method under different diameters, aspect ratios, and materials was investigated by considering the negative correlation between the Paris' law parameters. [ABSTRACT FROM AUTHOR]

In this paper, the fatigue crack growth rates of typical pressure vessel material 4130X under different corrosion conditions are investigated, and the effects of corrosion modes and loading frequency on the fatigue crack growth rate of 4130X are discussed. The results show that under the same loading conditions, the pre-corroded crack propagation rate is increased by 1.26 times compared with the uncorroded specimens. The plastic deformation mechanism of the crack tip in air is dominated by phase transformation but the hydrogen introduced by pre-corrosion causes a small number of dislocations at the crack tip. The crack growth rate obtained by corrosion fatigue is four times that of the uncorroded specimen, and the fracture surface shows a strong corrosion effect. The molecular dynamics simulation shows that the hydrogen atoms accumulated at the crack tip make the plastic deformation mechanism dominated by dislocation in the crack propagation process, and the coupling interaction between low frequency and the corrosion environment aggravates the hydrogen embrittlement of the crack tip. In the air condition, the loading frequency has no obvious effect on the crack growth rate: when the frequency decreases from 100 Hz to 0.01 Hz and other conditions remain unchanged, the fatigue crack growth rate increases by 1.5 times. The parameter n in the Paris expression is mainly influenced by frequency. The molecular dynamics simulation shows that low frequency promotes crack tip propagation. [ABSTRACT FROM AUTHOR]

Crack size prediction under variable amplitude loading is a very complex process, which is also important for life prediction in engineering. A crack growth model considering different stress ratio for fatigue remaining life prediction is proposed in this paper. The model utilizes stress ratio to describe the variable loading sequences, which makes the calculation greatly simplified. The rain-flow method is utilized to characterize the load sequence effects under variable amplitude loading. In addition, particle filter is utilized to estimate the model parameters describing the crack growth. Finally, case study indicates that the proposed approach is efficient in predicting crack growth and fatigue remaining life. [ABSTRACT FROM AUTHOR]

In this paper, the fracture kinetics and mechanisms in the low-cycle fatigue region were analyzed for different ultrafine-grained (UFG) materials with body-centered cubic (bcc), hexagonal close-packed (hcp) and face-centered cubic (fcc) lattices. Three-point bending principle fatigue tests were performed. The tests show that the UFG structure formation in the investigated materials has an ambiguous effect on the total number of cycles to failure (life) of the samples. The number of cycles to fatigue crack initiation (Nin) is about 20% of the total life of the samples, irrespective of the material state and the crystal lattice type. At the same value of the stress intensity coefficient range (∆K), for the majority of the investigated UFG materials, the fatigue crack propagation rate (dl/dN) is close to or lower than that of the initial coarse-grained (CG) materials. For the UFG materials, the coefficient n in the Paris equation is, in most cases, lower than that for the CG materials, which indicates that the UFG materials are less sensitive to cyclic overload. The fatigue fracture mechanisms of the investigated CG and UFG materials are rather similar, although the fracture of the UFG materials is accompanied by the formation of many secondary cracks, irrespective of the crystal lattice type. [ABSTRACT FROM AUTHOR]

Premature fracture of the bone plate caused by fatigue crack is the main failure mode in treating femoral shaft fracture. In order to improve the durability of the plate, this study proposed a crack attraction hole (CAH) to retard the crack propagation based on the fracture mechanics. In this paper, a numerical model of the femoral fracture internal fixation system was constructed, in which the femur was developed using a validated simplified model. First, the fatigue crack initiation location was defined at the stress concentration through static analysis. Next, with the joint simulation method of Franc3D and ABAQUS, the fatigue crack path in the bone plate was predicted. Meanwhile, the Paris parameters of Ti-6Al-4V obtained through experiments were encoded into Franc3D to calculate the crack propagation life. Finally, we considered the influence of CAH designs with different relative vertical distances (2.0, 3.0, and 4.0 mm) and diameters (1.5, 2.0, and 2.5 mm) on the crack propagation path and life of the bone plate. Additionally, the effects of all CAH configurations on the biomechanical performance of the bone plate fixation system were evaluated. The results indicated that the fatigue crack growth path in the bone plate is comparable to a straight line, and the crack growth rate significantly increases when the crack tip reaches the outer boundary of the plate. The findings suggest that the addition of CAH in the bone plate will lead to the deflection of the crack path and increase the fatigue life. Equally important, the improvement of the fatigue life was positively correlated with the diameter of CAH and negatively correlated with the relative vertical distance. In addition, the biomechanical properties of the bone plate system were slightly affected by CAH, substantiating the feasibility of this method. Finally, the comparative analysis verified that a CAH with a relative vertical distance of 3 mm and a diameter of 2 mm exhibited superior improvement in the comprehensive performance on the bone plate. [ABSTRACT FROM AUTHOR]

In this paper, the application requirement of the Residual Property Model based on the decrescent exponential function is reduced to only one mechanical test datum. For this, by using Creager and Paris's elastic stress field equation in front of the blunt elliptical hole, the theoretical radius was chosen for the tip curvative and the maximum stress in the load direction at the tip is ensured to be equal the fracture toughness. Thus, the workload of the model is reduced by making the u exponent in the e-u function dependent on the geometric correction factor and the crack length. It was applied to the laminated composite specimens with three-point bending and the specimens including circular hole, and critical fracture stress values close to actual values were achieved. [ABSTRACT FROM AUTHOR]

Tooth bending failure, one of the gear's most dangerous failure modes, is caused by alternating bending stress at the tooth root. The fatigue process is divided into crack initiation and crack propagation periods. In this paper, single tooth bending fatigue tests are conducted under a stress ratio of 0.05. Crack initiation life is predicted by the strain-life method. Material gradients and residual stresses are taken into account in the above process. The crack propagation life is predicted by linear elastic fracture mechanics. The Paris equation is used to simulate the fatigue crack growth. Finally, the total bending fatigue life can be estimated. Predicted fatigue life and failure locations show good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

In the past, fatigue cracks have appeared in the orthotropic steel decks of bridges shortly after they opened to traffic. Previous studies have shown that high tensile welding residual stress exists in welded joints of steel bridges, which significantly changes the average stress and stress ratio of the joints. However, traditional fatigue crack propagation (FCP) calculations based on the Paris equation do not consider the influence of the stress ratio. Steel Q345qD is a common material used in bridges. Therefore, it is meaningful to study the influence of the stress ratio on the FCP life of steel Q345qD. In this paper, an FCP equation based on the energy release rate considering the influence of the stress ratio is first derived and named the da/dN-ΔG-R equation. Next, three material parameters in the equation are determined based on the results from tests of steel Q345qD under different stress ratios. Then, a user subroutine based on the extended finite element method (XFEM) that considers the influence of the stress ratio is defined and the effects of mesh size are analyzed. Finally, the effects of the stress ratio on FCP are discussed and the adaptability of the da/dN-ΔG-R equation is verified by comparing the values obtained from the equation with experimental results. The results show that: with a 95% guarantee rate, three material parameters in the da/dN-ΔG-R equation are: log(C) = −10.71, m = 2.780, and γ = 0.957; in the numerical simulation, a mesh size of 1 mm is more appropriate than other mesh sizes as it shows better accuracy and efficiency; under the same energy release rate range, the crack growth rate decreases as the stress ratio increases; under the same loading amplitude and cycles, the fatigue life decreases as the stress ratio increases; and finally, the numerical results considering the influence of stress ratio based on the da/dN-ΔG-R equation are close to the test results, while the results without considering the stress ratio based on the Paris equation are inaccurate. [ABSTRACT FROM AUTHOR]

This paper evaluates the capabilities of the recently developed CF20 cohesive fatigue model, which can predict crack initiation as well as the rates of crack propagation by relying on intrinsic relationships between a stress‐life diagram and its corresponding Paris law. The model is validated here using a partially reinforced double cantilever beam (R‐DCB) benchmark proposed in literature. The two parameters needed for the CF20 cohesive fatigue model were obtained by performing preliminary analyses of a conventional DCB. The analysis results indicate that the CF20 cohesive fatigue model can accurately reproduce the complex evolution of the delamination observed in the R‐DCB. Highlights: A 3D benchmark is analyzed using the mixed‐mode CF20 cohesive fatigue formulation.The parameters of the model are obtained from experimental results of DCB specimens.The model predicts crack growth rate and delamination shape changes during propagation.A parametric study illustrates the precision needed to accurately predict the final delamination length. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the fatigue cracking evolution of cold recycled asphalt mixtures with asphalt emulsion (CRME) under different curing times. The fatigue cracking model of CRME based on damage mechanics and fracture mechanics was analyzed according to the fatigue loading curve. Firstly, the fatigue cracking evolution of CRME was studied through an SCB strength test and SCB fatigue test. Then, the fatigue damage mechanics were used to establish a nonlinear fatigue cracking model, and the damage degree of CRME at the initial cracking point was determined. The Paris formula was used to characterize the law of fatigue crack propagation. Finally, the microstructure of CRME was observed by scanning electron microscopy (SEM) with the backscattering method. The results indicate that the initial cracking point appears at around 60% of the fatigue life according to the SCB fatigue test by means of image analysis. The damage variable was obtained through the cracking model, and the value of the damage variable was determined as 0.06–0.17 at the initial cracking point. In addition, the Paris formula showed that the crack growth of CRME can be reflected by the stress intensity factor and correlative parameters. Moreover, cement hydration products were mixed with the asphalt membrane to form a denser spatial structure during the curing process, which may provide higher fatigue performance of CRME. This research may provide a theoretical reference for studying the fatigue cracking behavior of CRME. [ABSTRACT FROM AUTHOR]

Curling stresses in rigid pavements are the result of temperature gradient through the thickness of the concrete slab. These stresses have a periodic nature, and the induced cyclic flexural curling stresses lead to the cracking of the concrete slab. In a previous research by the authors, a phase change material (PCM)-rich concrete overlay was proposed as an effective method to control this failure mechanism. A PCM-rich concrete overlay is a concrete surface layer that contains a relatively high percentage of PCM. In the previous study, a phenomenological approach was employed, and it was demonstrated that the incorporation of PCM improves the curling fatigue performance of the concrete slab. Using fracture mechanics, this paper builds upon the findings of the previous study, and it serves as a mechanistic verification of the conclusions of the previous work. A modified Paris' Law was adopted to calculate the cumulative fatigue-fracture damage of the concrete slab due to cyclic thermally-induced curling stresses. The findings of this research demonstrated that the PCM-modified concrete slab undergoes a curling-induced fracture process that is less severe than the slab without the PCM. The impact of this reduction was quantified in terms of an improved fatigue-fracture performance of the pavement. [ABSTRACT FROM AUTHOR]

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Steel structures are frequently exposed to high‐cycle loading in which fatigue cracks initiate and propagate in the service life. The development of crack(s) will affect the structural integrity. In extreme cases, e.g., earthquakes and impacts, structures may be overloaded in several cycles or even a single loading cycle with the development of significant plastic deformation and macro cracks. Service loads, e.g., traffic and waves, will afterwards still be experienced in these damaged structures. The aforementioned two types of deformation are currently analyzed using damage and fracture mechanics methods, respectively. The cycle‐by‐cycle calculation and jump strategy relying on the Paris' equation, are employed for the low (including monotonic) and high‐cycle problems, using elastoplastic and linear‐elastic materials, respectively. The two calculation methods were developed independently, which presents a challenge in analyzing overloaded high‐cycle fatigue problems. This paper presents and executes a hybrid analysis using damage and fracture mechanics models for the single‐edge notch bend specimen. Either linear‐elastic or elasto‐plastic materials is employed in finite element simulations. The hybrid analysis with the combination of damage and linear‐elastic fracture mechanics shows the potential of a promising solution for assessing the fatigue behaviour of steel structures experiencing extreme loading and associated stepwise material damage. Some challenges are addressed in the combination of the ductile fracture followed by the high cycle fatigue calculation. [ABSTRACT FROM AUTHOR]

Corrosion and crack defects often exist at the same time in pipelines. The interaction impact between these defects could potentially affect the growth of the fatigue crack. In this paper, a crack propagation method is proposed for pipelines with interacting corrosion and crack defects. The finite element models are built to obtain the Stress Intensity Factors (SIFs) for fatigue crack. SIF interaction impact ratio is introduced to describe the interaction effect of corrosion on fatigue crack. Two approaches based on extreme gradient boosting (XGBoost) are proposed in this paper to predict the SIF interaction impact ratio at the deepest point of the crack defect for pipelines with interacting corrosion and crack defects. Crack size, corrosion size and the axial distance between these two defects are the factors that have an impact on the growth of the fatigue crack, and so they are considered as the input of XGBoost models. Based on the synthetic samples from finite element modeling, it has been proved that the proposed approaches can effectively predict the SIF interaction impact ratio with relatively high accuracy. The crack propagation models are built based on the proposed XGBoost models, Paris' law and corrosion growth model. Sensitivity analyses regarding corrosion initial depth and axial distance between defects are performed. The proposed method can support pipeline integrity management by linking the crack propagation model with corrosion size, crack size and the axial distance. The problem of how the interaction between corrosion and crack defects impacts crack defect growth is investigated. [ABSTRACT FROM AUTHOR]

In this paper, Composite Repair System (CRS) is applied to repair the circumferential internal surface cracked steel pipes subjected to bending. The Stress Intensity Factor (SIF) is quantitatively analysed by means of numerical simulations, and the crack growth rate is predicted by using the Paris' law. First, the three-dimensional finite element (FE) model is developed, and its reliability of evaluating SIF of internal surface crack in CRS reinforced pipe is validated. Then based on the FE method and combined with Paris' law, a case study is deployed to predict the internal surface crack growth in steel pipes reinforced with CRS. The results show that CRS have significantly reduced the SIF of the internal surface crack and decrease the crack growth rate, while unchanging the variation trend of the crack aspect ratio. Afterwards, a parametric study is performed in order to guide the optimisation design of CRS reinforcement. [ABSTRACT FROM AUTHOR]

Rolled steel plates and sections are often applied in structures in such a way that the principal load direction corresponds with the rolling direction. Examples are beams, arches, or pylons of bridges, supporting beams of ship decks, and the main elements of crane structures. However, some types of structure are subjected to a multiaxial stress state or are loaded with the main load direction perpendicular to rolling. The orientation may influence the mechanical properties. This paper studies the influence of anisotropy observed in the microstructure of rolled C–Mn steels on the tensile properties, Charpy impact values and particularly the fatigue crack growth rates. The influence of anisotropy is determined through tests performed at different orientations with respect to the rolling direction, namely, L‐T, T‐L and T‐S orientations. Samples were taken from structures that were constructed between 25 and 50 years ago from steel grades Fe510C or St52.3 (modern equivalences S355J2 or S355N). The orientation appears to have a statistically relevant influence on Charpy impact value and fatigue crack growth rate. The anisotropy ratio, defined as the ratio between the mechanical property in a certain orientation with that of the L‐T orientation, ranged between 0.30 and 0.53 for Charpy impact values. The anisotropy ratios appear correlated with the absolute Charpy value, with a correlation coefficient of ρ = −0.8. The anisotropy ratios of the crack growth in T‐L and T‐S orientations were 1.19 and 0.43, respectively. Anisotropy ratios for crack growth appear uncorrelated with anisotropy ratios for Charpy impact. The observed anisotropy may partially explain the difference between uniaxial and multiaxial fatigue crack growth as determined by others. [ABSTRACT FROM AUTHOR]

Fatigue damage of rail steel is an important issue affecting economic and human safety. In this paper, the effect of different quenching rates on the fatigue crack growth of hypereutectoid rail is analyzed. The material parameters C and m of the Paris formula are measured. The results show that an increase in cooling rate of rail decreases the value Paris law parameter C, increases the value m and decreases fatigue crack growth rate. This can be attributed to the decreased in the lamellar spacing and cluster diameter of the pearlite with an increase in cooling rate. More specifically, the smaller lamellar spacing and the cluster diameter make the crack pass easily through the cluster boundary of pearlite, which increases the number of zigzag crack growth paths and branching cracks that can help restrain fatigue crack growth. The fatigue fracture characteristic of hypereutectoid rail is that with an increase in cooling rate, the fatigue striation spacing and river pattern of the fracture surface become smaller, the crack growth path tends to zigzag, the tearing edges become deeper and the surface is relatively rougher. [ABSTRACT FROM AUTHOR]

This paper presents a study on the effect of microstructure on the fatigue crack growth (FCG) rate in advanced S355 marine steels in the Paris Region of the da/dN versus ΔK log–log plot. The environments of study were air and seawater (SW), under constant amplitude sinewave fatigue loading. Fundamentally, three phenomena (crack tip diversion, crack front bifurcation and metal crumb formation) were observed to influence the rate of FCG. These phenomena appear to be a function of the material microstructure, environment and crack tip loading conditions. The three factors retarded the crack growth by reducing or redistributing the effective driving force at the main active crack tip. A crack path containing extensively the three phenomena was observed to offer strong resistance to FCG. In SW, the degree of the electrochemical dissolution of the microplastic zone appears to be an additional primary factor influencing FCG in the steels. [ABSTRACT FROM AUTHOR]

Strength reduction in structures like aircraft could be resulted in cyclic loads over a period of time and is an important factor for structural life prediction. Service loads are emphasized at the regions of stress concentration, mostly at the connection of components. The initial flaw prompting the service life was expected by using the equivalent initial flaw size (EIFS) which has been recognized as a powerful design tool for life prediction of engineering structures. This method was introduced 30 years ago in an attempt to study the initial quality of structural details. In this paper, the prediction of life based on fracture mechanics in riveted joints has been addressed through the concept of EIFS. For estimation of initial crack length by EIFS, an extrapolation method has been used. The EIFS value is estimated using the coefficient of cyclic intensity (ΔK) and using the cyclic integral (ΔJ), and the results are compared with each other. The simulation results show that if the coefficient of tension has been used in the EIFS estimation, which is based on the Paris law, the EIFS value will be dependent on the loading domain, while the use of the J-cyclic integral in the EIFS decreases its dependence on the load domain dramatically. [ABSTRACT FROM AUTHOR]

Phase field models have been very successful in recent years and tend to become hegemonic in modelling the fracture of materials. This is primarily due to their ease of implementation to account for the entire fracture process including nucleation and propagation of cracks. In doing so, the cohesive force models have been somewhat neglected although they are based on better established physical bases and have at least as great a capacity to account for the main fracture phenomena. To confirm this claim, the paper will focus on the ability of the cohesive force models to correct the three main flaws of Griffith's law of brittle fracture concerning the nucleation of cracks, the size effects or fatigue. • The paper will focus on the ability of the cohesive force models to correct the three main flaws of Griffith's law of brittle fracture concerning the nucleation of cracks, the size effects or fatigue. Specifically, • one deduces from a stability condition a local yield stress criterion for the first occurence of a cohesive crack; • one shows how the introduction of a critical stress changes the non-physical size effect predicted by Griffith's theory at small scale; • after introducing an irreversibility condition into the cohesive force model, one constructs a Paris-type fatigue law governing behaviour under cyclic loading. [ABSTRACT FROM AUTHOR]

Hygrothermal ageing has detrimental effect of the fatigue delamination growth (FDG) in carbon fibre reinforced polymer laminates, and may increase the crack growth rate by a factor of ∼5. The paper examines, how this degradation for Mode I fatigue delamination is affected by the severity of the ageing conditions. Fatigue delamination tests for R = 0.1 and R = 0.5 are conducted after ageing (1) at 70 °C 85 % relative humidity (RH) and (2) immersion in 70 °C water bath (WB). Paris-type FDG characterisation is derived, in the form, which accounts for the effect of fibre bridging. It is demonstrated that parameters of FDG degradation do not differ for these two types of hygrothermal ageing. The physical reasons for this are examined using dynamic mechanical thermal analysis (DMTA) and fractographic analysis, which revealed similar irreversible degradation of the material near the fibre/matrix interface and in the matrix itself, and the similar damage mechanisms in fatigue delamination. Furthermore, this study can highlight the importance of obeying similitude principles in FDG characterisation, and provide extra information for the ISO standard development for mode I fatigue delamination in unidirectional carbon fibre reinforced polymer composites. [ABSTRACT FROM AUTHOR]

Featured Application: The new findings highlight the enhancement in corrosion-fatigue performance of steel bridges by using the uncoated weathering steel. Besides, an innovative approach has been established to simulate the corrosion-fatigue process in uncoated weathering steel bridges, providing deep insights into the service life of the bridges. The approaches suggested in the article can be used (not limited to) as a reference for the research and design of uncoated weathering steel bridges. Uncoated weathering steel (UWS) bridges have been extensively used to reduce the lifecycle cost since they are maintenance-free and eco-friendly. However, the fatigue issue becomes significant in UWS bridges due to the intended corrosion process utilized to form the corrodent-proof rust layer instead of the coating process. In this paper, an innovative model is proposed to simulate the corrosion-fatigue (C-F) process in UWS bridges. Generally, the C-F process could be considered as two relatively independent stages in a time series, including the pitting process of flaw-initiation and the fatigue crack propagation of the critical pitting flaw. In the proposed C-F model, Faraday's law has been employed at the critical flaw-initiation stage to describe the pitting process, in which the pitting current is applied to reflect the pitting rate in different corrosive environments. At the crack propagation stage, the influence of pitting corrosion is so small that it can be safely ignored. In simulating the crack propagation stage, the advanced NASGRO equation proposed by the NASA is employed instead of the classic Paris' law, in which a modified fatigue limit is adopted. The fatigue limit is then used to determine the critical size of pitting flaws, above which the fatigue effect joins as a parallel driving force in crack propagation. The model is then validated through the experimental data from published articles at the initiation stage as well as the whole C-F process. Two types of structural steel, i.e., HPS 70W and 14MnNbq steel, have been selected to carry out a case study. The result shows that the C-F life can be notably prolonged in the HPS 70W due to the enhancement in fatigue strength and corrosion resistance. Besides, a sensitivity analysis has been made on the crucial parameters, including the stress range, stress ratio, corrosive environment and average daily truck traffic (ADTT). The result has revealed the different influence of the above parameters on the initiation life and propagation life. [ABSTRACT FROM AUTHOR]

In this paper, fatigue life, crack growth trajectory, and stress intensity factors of top‐down and bottom‐up cracks have been investigated in a multilayered asphalt pavement using numerical method. Finite element models, Paris law, and maximum tangential stress criteria were used to determine the effects of vehicle position, thickness, and stiffness of layers on fatigue life of pavements. The results show that the minimum fatigue life of pavements with top‐down crack occurs when the wheels are symmetrically located relative to the crack plane. On the other side, in pavements with bottom‐up crack, it occurs when the front tire located on top of the crack. Moreover, the result reveals that the top‐down crack grows slower than bottom‐up crack. Also, the surface layer's stiffness has the most effect on fatigue life of pavement. [ABSTRACT FROM AUTHOR]

In this paper, a numerical crack growth analysis is conducted by using the Maximum Tangential Stress (MTS) criterion and its extension, which considers the contact stress between the crack surfaces. Moreover, fretting fatigue is a multiaxial non-proportional loading problem, and most components are subjected to asynchronous loads. Therefore, this paper mostly focuses on the influence of loading phase difference (Φ) on the crack propagation behavior. Meanwhile, for the fretting fatigue problem, as there is a relationship between the crack initiation and propagation, the effect of initiation characteristics, including crack initiation position and direction is studied under different loading phase differences using Linear Elastic Fracture Mechanics (LEFM) theory. It is observed that the predicted crack path and lifetime by using the extended MTS criterion and Paris' law is in good agreement with the experimental results in the literature. It is found that the phase difference has a strong effect on the crack propagation behavior. Furthermore, we found that the crack initiation position has a greater influence on crack propagation behavior than the crack initiation direction. [ABSTRACT FROM AUTHOR]

The experimental study of fatigue crack growth (FCG) behavior in Ti6Al4V alloy manufactured by selective laser melting (SLM) was carried out on an in situ fatigue testing machine. Two specimen orientations relative to the build direction (horizontal and vertical), two temperatures (room temperature, RT, and 400°C), and two stress ratios (0.1 and 0.5) were considered, and the FCG curves with the threshold values were determined. The results showed that the FCG properties were affected by the stress ratio due to different degree of crack closure and temperature with grain softening at 400°C in threshold and Paris region. The threshold value is highly dependent on the build direction of the alloy, which was caused by the anisotropic microstructure, while in the Paris region, the effect of material direction can be negligible and FCG rate tends to be consistent. The fracture mechanism at different stages was discussed and revealed by the fracture morphology observation using scanning electron microscopy. Highlights: The FCG resistance in threshold region is highly dependent on the material orientation.The FCG behaviors were examined and compared under different stress ratios and temperatures.Fatigue crack growth mechanism was revealed ranging from 3D small crack to 2D long crack. [ABSTRACT FROM AUTHOR]

• Mode II fatigue crack growth is characterized at the steel-to-composite interface. • Displacement and load controlled ENF and 4ENF test methods are compared. • Novel method is proposed to determine crack growth by shear strains from DIC. • Friction and geometrical non-linearity is considered by finite element models. In this paper, mode II fatigue crack growth properties of the composite-to-steel interface are characterised through different test configurations, namely ENF and 4ENF tests. Different loading types including force control and displacement control methods are compared. An innovative shear strain based method is proposed for monitoring the mode II crack growth at the bi-material interface through Digital Image Correlation (DIC). A 3D finite element model with Virtual Crack Closure Technique (VCCT) is built and used for obtaining the strain energy release rate (SERR) to investigate the effect of geometrical nonlinearity, friction at the interface and steel yielding, as well as to verify the mode mixity. The results show that the standard 3-point bending ENF specimen can be unstable under force control and sweeps narrow SERR range by a single test under displacement control. The 4-point bending 4ENF test shows stable crack propagation and clear SERR developing trend. More pronounced geometrical nonlinearity and friction effect exist for 4ENF test which can be considered when interpreting the Paris curves by a nonlinear finite element model. [ABSTRACT FROM AUTHOR]

Three-dimensional (3D) printing is one of the significant industrial manufacturing methods in the modern era. Many materials are used for 3D printing; however, as the most used material in fused deposition modelling (FDM) technology, acrylonitrile butadiene styrene (ABS) offers good mechanical properties. It is perfect for making structures for industrial applications in complex environments. Three-dimensional printing parameters, including building orientation, layers thickness, and nozzle size, critically affect the crack growth in FDM structures under complex loads. Therefore, this paper used the dynamic bending vibration test to investigate their influence on fatigue crack growth (FCG) rate under dynamic loads and the Paris power law constant C and m. The paper proposed an analytical solution to determine the stress intensity factor (SIF) at the crack tip based on the measurement of structural dynamic response. The experimental results show that the lower ambient temperature, as well as increased nozzle size and layer thickness, provide a lower FCG rate. The printing orientation, which is the same as loading, also slows the crack growth. The linear regression between these parameters and Paris Law's coefficient also proves the same conclusion. [ABSTRACT FROM AUTHOR]

Slow crack growth parameters for SiC-based filaments. τ is the lifetime, σ app the stress, n f the stress exponent and Ea τ the apparent activation energy describing the Arrhenius evolution of the environment constant A with temperature. [Display omitted] • Modified time to failure prediction expression applied to various SiC-based fibers. • Stress exponent subjected to a scale effect, induced by fiber misalignment. • Estimates for SCG parameters of SiC-based filaments. • Stress-probability time diagrams construction from simulation output. • Correlation between stress exponent and chemical composition (O and H content). The delayed failure of SiC fibrous reinforcement has continuously been investigated to warrant the long term performances of Ceramic Matrix Composite (CMC). Chiefly assessed on multifilament tow samples to alleviate some handling difficulties, subcritical crack growth (SCG) parameters are however ruled by structural artifacts which hinder the identification of intrinsic filament behavior. In this paper, we propose to estimate the true filament parameters for 5 fiber types from bundle behavior using a recently communicated Monte Carlo algorithm integrating flaw and stress distributions through a deterministic fracture mechanics law under Paris' formulation. So computed tow lifetime are broadly dispersed, encompassing raw data, and show a structure-dependent scale effect, revealed by n filament >n tow where n is the stress exponent. The relationship between SCG coefficient and chemical composition of the substrate is discussed and highlights the major effect of doping elements (Ti or Zr), oxygen or hydrogen content. [ABSTRACT FROM AUTHOR]

• The CRTS Ⅲ slab track model with prefabricated cracks is established by extended finite element method. • The stress intensity factors (SIFs) at the tips of cracks on the track slab under train load are solved. • The effects of the crack length and depth on the SIFs of three types of cracks are discussed. • The variations of crack growth rate calculated by Paris' semi-empirical during service are analyzed. Microcracks may occur in Chinese Railway Track System type III (CRTS III) ballastless track slabs during service, and it is necessary to investigate their potential propagation under train load, which could lead to slab deterioration and affect the durability of the track structure. In this paper, based on the fracture mechanics theory, the stress intensity factors (SIFs) at the tips of transverse crack, longitudinal crack and vertical crack on the CRTS III track slabs under train load are solved by the extended finite element method (XFEM) in Abaqus software. The changes of SIFs at the crack tips during the passage of the train are analyzed, and the effects of the crack length and depth on the SIFs of the three types of cracks are discussed under train load. Crack growth rate is calculated using Paris' semi-empirical law to estimate slab life. The results show that the train load contributes to the propagation of transverse and vertical cracks in the vertical direction and inhibits the longitudinal cracks. When the middle of the sixth vehicle is above the crack, the SIFs at the tips of the crack reach their maximum values. The SIF of vertical cracks exceeds the fracture toughness at a certain depth. The fatigue load cycles calculated by Paris' semi-empirical law suggest that maintenance will not be required due to insufficient propagation under train load during service. [ABSTRACT FROM AUTHOR]

Hybrid bi-material concepts in engineering structures where fibre-polymer composites are used together with steel structural members have potential to reduce material usage, extend fatigue life and improve structural reliability. The bond performance of the bi-material composite-to-steel interface is of crucial importance and highly relies on the surface preparation quality of the steel element. This paper investigates the influence of steel surface roughness on the mode II fracture toughness and fatigue crack growth behaviour of the bonded composite-to-steel joints. Glass fibre composite and mild structural steel material is considered directly bonded in a wet lay-up process. 4-point end notch flexure (4ENF) tests are conducted on specimens with the steel plates prepared with low, medium and high roughness, respectively. In addition, morphology of the fracture surfaces are characterised by a 3D profilemeter and the friction coefficient is measured by a tribometer for each roughness level. Results show that in quasi-static fracture, fibre bridging is dependent on the surface roughness. A roughness level with S q ≥ 22 µm of the steel surface can promote significant fibre bridging thus improved fracture toughness due to enlarged effective bonding area. Under cyclic loading, no fiber bridging is observed across all roughness levels tested. However, the Paris curve parameter C is significantly affected by the roughness level, which decreases by approximately 100 times as the steel surface roughness increases from the low level of S q = 5 µm to high level of S q = 22 µm. The m parameter of the Paris curve remains fairly constant across all the roughness levels tested. • Static and fatigue 4ENF tests are conducted on composite-to-steel bonded joints. • Steel roughness is correlated to fracture and fatigue resistance of the joints. • Friction effect is considered by FE models for more accurate SERR estimation. • Friction coefficient at the composite-to-steel interface is measured by tribometer. • Crack growth at the composite-to-steel interface is monitored by new DIC method. [ABSTRACT FROM AUTHOR]

Semiconductor advancements demand greater integrated circuit density, structural miniaturization, and complex material combinations, resulting in stress concentrations from property mismatches. This study investigates the failure in two types of interfaces found in chip packages: silicon–epoxy mold compound (EMC) and polyimide–EMC. These interfaces were subjected to quasi-static and fatigue loading conditions. Employing a compliance-based beam method, the tests determined interfacial critical fracture energy values, ( G I C ), of 0.051 N/mm and 0.037 N/mm for the silicon–EMC and polyimide–EMC interfaces, respectively. Fatigue testing on the polyimide–epoxy interface revealed a fatigue threshold strain energy, ( G t h ), of 0.042 N/mm. We also observed diverse failure modes and discuss potential mechanical failures in multi-layer chip packages. The findings of this study can contribute to the prediction and mitigation of failure modes in the analyzed chip packaging. The obtained threshold energy and crack growth rate provide insights for designing safe lives for bi-material interfaces in chip packaging under cyclic loads. These insights can guide future research directions, emphasizing the improvement of material properties and exploration of the influence of manufacturing parameters on delamination in multilayer semiconductors. [ABSTRACT FROM AUTHOR]

In this study, the cracks growth rate in the 13th row of the T56 compressor blades was studied to investigate their fatigue life. For this purpose, the centrifugal and aerodynamic forces on the blade were calculated and then the resulting stress field was obtained by using finite element method. Then, the critical points of stress were determined and the initial semi-elliptical cracks were modeled at these points. After modeling of the initial crack, the stress intensity factor on the crack front was calculated by ANSYS software. Furthermore, the number of required cycles for the crack growth and blade fracture were calculated by applying Paris law to a certain value. After crack growth at this stage, a crack with new length was also modeled at the same point and all the mentioned stages for its growth, were repeated. In this paper, the modal analysis of the blade was conducted and normal frequencies with possible stimulation on compressor velocity were determined by Campbell Diagram. After determining the stress field at resonant frequency, all stages of crack growth were repeated under these conditions to calculate the fatigue life. [ABSTRACT FROM AUTHOR]

The paper deals with an optimization problem related to axisymmetric membrane shells made of homogeneous, linear and isotropic materials and subject to a cyclic internal pressure. The optimization problem considers the possible crack growth in the shell as a structural constraint, which is accounted for by the well-known Paris law, and hence obeys the Linear Elastic Fracture Mechanics (LEFM) principles. The design variables are the meridian shape and the thickness distribution along the axis of the shell. After recalling the general background on the mechanics of thin-walled shells, the optimization problem is stated, formulated and solved in closed form by means of Pontryagin's Principle, showing two LEFM-based design criteria capable to help the designer in selecting the desired elastic performance through which the shell undergoes. It is shown that the derived optimal solutions are ellipsoids with variable thicknesses, whose distributions depend on the mass constraint and the applied pressure. Nevertheless, the optimal shapes guarantee the uniformity of either the meridian or the hoop stress, and such uniformity has been verified within a numerical example by an accurate finite element analysis. • The maximum volume problem for axisymmetric membrane shells is formulated. • The shells are subject to cyclic pressure and mass constraints. • The membrane theory of shells and Paris law are taken into consideration. • Optimal shapes are derived analytically by means of Pontryagin's Principle. • Two design criteria are given for uniform meridian and hoop membrane stresses. • The finite element method confirms the theoretical stress behavior. [ABSTRACT FROM AUTHOR]

• Implementation of slow growth design strategy for bonded joints/patch repairs for primary aircraft structures, consistent with FAA guidance. • Static and fatigue testing of a novel specimen configuration to identify the entire disbond crack growth process. • Indication of slow growth management approach feasible for bonded joints/patch repairs if the doubler/patch is designed to be sufficiently long. • Establishment of modified Paris law for predicting allowable fatigue life and determining inspection interval, in accordance with FAA guidance. • Potential solution for maintenance cost reduction for primary aircraft structures. The applicability of a damage slow growth management strategy to bonded joints/patch repairs of primary aircraft structures was evaluated through an experimental and computational study. Fatigue tests were conducted to investigate the entire process of disbond growth from initiation up to joint ultimate failure. The residual static strength of the joint as a function of disbond length was established using finite element modelling, in which the mesh size was calibrated using the static strength of the specimens measured in room temperature and dry (RD) and hot-wet (HW) conditions, based on the characteristic distance approach. A virtual crack close technique (VCCT) approach was utilised to assess the strain energy release rates (SERRs) as a function of disbond crack length. The measured disbond growth rates were correlated with the SERRs using a modified Paris law that enabled prediction of joint fatigue life. The fatigue test results indicated that for a joint having a sufficient static strength safety margin under a typical fatigue loading that would propagate disbond, the disbond growth would be stable in a particular length range. Thus, the slow growth approach would be feasible for a bonded joint/patch repairs if the patch is designed to be sufficiently large to allow extended damage propagation (whilst in the case when patch size must be limited, safe-life design for the patch termination region in critical repairs must be considered. Should disbond growth occur in this case, the joint must be repaired or replaced). The work presented in this paper validated the framework/procedure proposed previously by the authors (Tanulia et al., 2020) for managing damage slow growth in bonded joints/patch repairs. In the last part of this paper the planned follow-on research is briefly described. [ABSTRACT FROM AUTHOR]

Fatigue delamination damage is one of the most important fatigue failure modes for laminated composite structures. However, there are still many challenging problems in the development of the theoretical framework, mathematical/physical models, and numerical simulation of fatigue delamination. What is more, it is essential to establish a systematic classification of these methods and models. This article reviews the experimental phenomena of delamination onset and propagation under fatigue loading. The authors reviewed the commonly used phenomenological models for laminated composite structures. The research methods, general modeling formulas, and development prospects of phenomenological models were presented in detail. Based on the analysis of finite element models (FEMs) for laminated composite structures, several simulation methods for fatigue delamination damage models (FDDMs) were carefully classified. Then, the whole procedure, range of applications, capability assessment, and advantages and limitations of the models, which were based on four types of theoretical frameworks, were also discussed in detail. The theoretical frameworks include the strength theory model (SM), fracture mechanics model (FM), damage mechanics model (DM), and hybrid model (HM). To the best of the authors' knowledge, the FDDM based on the modified Paris law within the framework of hybrid fracture and damage mechanics is the most effective method so far. However, it is difficult for the traditional FDDM to solve the problem of the spatial delamination of complex structures. In addition, the balance between the cost of acquiring the model and the computational efficiency of the model is also critical. Therefore, several potential research directions, such as the extended finite element method (XFEM), isogeometric analysis (IGA), phase-field model (PFM), artificial intelligence algorithm, and higher-order deformation theory (HODT), have been presented in the conclusions. Through validation by investigators, these research directions have the ability to overcome the challenging technical issues in the fatigue delamination prediction of laminated composite structures. [ABSTRACT FROM AUTHOR]

Welding defects are known to cause crack propagation and reduce structural fatigue performance. Based on the Paris theory of fracture mechanics, research is conducted on evaluation methods for analyzing fatigue crack propagation by adopting random loads with long-term distribution that follows the Weibull distribution for the stress ranges of fatigue loads. This approach is combined with the corrective stress intensity factor (SIF) equation and the method for calculating the reference stress and failure criterion. A large container ship is selected for a simulation, and fatigue crack propagation analysis is conducted on typical critical locations. A detailed comparison of the forecasted fatigue life is carried out between fracture mechanics theory and the S-N curve. The results indicate that the fatigue life values obtained using the two methods are of the same magnitude. In general, for the welded structure, the fatigue life value obtained via the fracture mechanics method is shorter than that obtained via the S-N curve method, while, for the free edge of the structure and the unwelded structure, the predicted fatigue life value is closer than that predicted via the S-N curve method. Moreover, the influence of initial crack defects on the fatigue life is investigated, and the results show that the depth of the initial crack will greatly affect the fatigue life of the target ship in typical locations, but the influence of the shape ratio on the fatigue life is limited. Therefore, in the actual ship construction process, controlling the initial crack depth of components is effective for limiting crack propagation and improving fatigue life. The above conclusions and suggestions can serve as a reference for the structural design and fatigue life evaluation of large container ships. [ABSTRACT FROM AUTHOR]

• Shielding and its interactive effect with anti-shielding on crack tip field in multi-layered architectures. • Establishing a method to predict the fatigue crack life in layered architectures considering the shielding/anti-shielding effect. • In 4-layered architectures, the increase of first hard layer's thickness and the decrease of distance between first hard layer and the top surface will improve the fatigue performance. Previous research has indicated the potential effectiveness of adopting micro-scale layered architectures to improve the fatigue damage resistance of coatings. However, the optimisation of these coatings is difficult due to the existence of many different factors affecting fatigue performance in such micro-scale layered architectures. In particular, the interaction of successive shielding and anti-shielding processes on crack growth resistance is therefore addressed in this paper by numerical simulation analysis. The crack tip fields in a series of layered architectures were simulated based on varying assumed constitutive materials properties to reveal the interaction of shielding/anti-shielding characteristics in complex architectures in a simple exemplar system. The evolution of crack driving force (CDF) with crack length was calculated and linked to fatigue crack life under relatively simple conditions, including straight crack path and Paris law assumptions, to investigate the effect of the ordering of shielding/anti-shielding characteristics on the crack tip field and hence on fatigue crack life. Layered architectures with different numbers, ordering and placing of layers, were assessed and parametric studies of 4 layered architectures were carried out. This allows analysis of the effect of these individual factors on shielding and their interactive effect with anti-shielding in multi-layered architectures. Understanding the combined effect on crack growth performance and overall fatigue life controlled by crack propagation provides insight into the generic design of micro-scale layered architectures. [ABSTRACT FROM AUTHOR]

• Fatigue debonding is monitored via strain development from DIC and optical fibres. • Debonding retardation is found in fatigue experiments of wrapped composite joint. • Debonding retardation is explained by friction effect and Paris relationship. • Friction is implemented in VCCT to predict non-linear development of SERR. • Effects of friction coefficient, failure modes and Paris parameters are studied. Debonding crack propagation at the composite-to-steel interface has been found to be an important failure mechanism for wrapped composite joints under static and fatigue loads. Friction at the interface behind the crack tip may deviate fatigue debonding of the joints from the linear-fracture-mechanics behaviour. This paper presents static and fatigue tests of axial wrapped composite joints. 3D DIC and optical fiber system is employed to monitor displacements and crack propagation. A finite element model is established and validated against static and fatigue test results, where friction is considered at the cracked interface. Through FE modelling, it is proved that the friction at the interface significantly reduce the strain energy release rate (SERR) at the crack tip, leading to retardations of crack growth and stiffness degradation. Parametric study is conducted finally to investigate the influence of friction coefficient, failure modes as well as Paris relationship parameters on the predicted fatigue behaviour of wrapped composite joints. [ABSTRACT FROM AUTHOR]

• A new analytical model for microstructure-sensitive crack growth rate is developed, combining the latest physical understanding of short crack growth behaviour with the efficiency of classical fracture mechanics. • A stored energy fracture criterion is shown to capture microstructure-sensitivity of crack growth rates. Full-field implementation of the model is achieved using a new crystallographic criterion for crack path, showing strong agreement with experiment. • The potential for the model to be extended to make predictions in the Paris regime is also demonstrated in this paper. Short fatigue crack growth in engineering alloys is among the most prominent challenges in mechanics of materials. Owing to its microstructural sensitivity, advanced and computationally expensive numerical methods are required to solve for crack growth rate. A novel mechanistic analytical model is presented, which adopts a stored energy density fracture criterion. Full-field implementation of the model in polycrystalline materials is achieved using a crystallographic crack-path prediction method based on a local stress intensity factor term. The model is applied to a range of Zircaloy-4 microstructures and demonstrates strong agreement with experimental rates and crack paths. Growth rate fluctuations across individual grains and substantial texture sensitivity are captured using the model. More broadly, this work demonstrates the benefits of mechanistic analytical modelling over conventional fracture mechanics and recent numerical approaches for accurate material performance predictions and design. Additionally, it offers a significant computer processing time reduction compared with state-of-the-art numerical methods. [Display omitted] [ABSTRACT FROM AUTHOR]

• The effect of stress ratio on the fatigue crack growth behavior of steel Q345qC was investigated experimentally. • The microstructural characteristics of steel Q345qC were revealed. • The probabilistic fatigue crack growth rate equations of steel Q345qC were proposed. • The error between theoretically calculated and tested values of fatigue crack growth life is analyzed. The stress ratio effects and the scatter of the fatigue test results are the key issues in the design of steel fatigue performance. This paper reports an experimental and probabilistic investigation of the fatigue crack growth (FCG) behavior of steel Q345qC. Firstly, the microstructural characteristics and mechanical properties of steel Q345qC were examined via an optical microscope and tensile tests. Next, the FCG behavior of steel Q345qC was investigated under different stress ratios. The fatigue crack growth rate (FCGR) equations incorporating survival probabilities were proposed based on Paris and Walker laws. Finally, the theoretical FCG life under different survival probabilities in the crack stable growth region is calculated based on the integral formulas of Paris and Walker law and compared with the tested FCG life. The experimental results demonstrate that the larger the stress ratio, the shorter the length of stress intensity factor (SIF) amplitude experienced in the stable growth region and the smaller the SIF at the end of this region. Both probabilistic Paris and Walker equations can be used for FCGR calculations when the survival probability is set as 50%. The FCG life is calculated using the integral formula based on the Walker law with a high safety tolerance and a wide application interval of stress ratio when the survival probability is set as 90%. [ABSTRACT FROM AUTHOR]

In this paper, a new model for wirebond degradation during power cycling in IGBT power module is proposed. This model is based on experimental crack propagation analyses and on a plastic strain empirical law. For the experiments, two power cycling tests in switching mode under high voltage were carried out respectively with junction temperature swings of ∆ T j = 30 ° C and 40 ° C at a minimal temperature of T j , min = 55 ° C. The DUTs and the test conditions were chosen so that only degradations of chip top-side interconnections could occur. The on-state voltage (V CE) was measured online during the tests as an indicator of wire and metallization degradations, moreover, the samples were removed at different aging stages. The removed samples were cross-sectioned in order to observe the crack propagation evolution with cycling. Concerning the plastic strain law, we used results from literature giving the evolution of the plastic strain variation (∆ ε pl) with bond-wire contact crack growth. As results, this new lifetime prediction model based on a modified Paris's law for aluminium wire bonds fatigue of IGBTs shows a good fitting of the test results and is it can be used to predict the lifetime under other load conditions. Finally, the lifetime of tested IGBT modules are estimated and used to verify the effectiveness of the proposed model. • The work lies on a new crack propagation model of aluminium wire bonds in IGBT power modules. • An improved strain-based lifetime prediction model based on modified Paris's law for aluminium wire bonds is proposed. • Switching mode under high voltage tests were carried out under low junction temperature swings. • Cross-sections were performed in order to observe the crack propagation evolution with cycling. [ABSTRACT FROM AUTHOR]

In this paper, a possible extension of Griffith's fracture theory to describe fatigue-induced crack propagation is proposed. To this end, an energy-based model is presented, taking Griffith's model as the point of departure and employing the concept of state-dependent fracture toughness. Therein, fatigue degradation is achieved through a suitable history variable endowed with a functional form that is able to consider crucial aspects of fatigue, including the crack-tip singularity, the identification of fatigue-inducing loading conditions, and mean load effects. Simple paradigmatic examples indicate that the model provides a unified description of different fatigue responses and unveils peculiar regimes in the crack propagation process, always preserving the link to classical fracture mechanics. In this context, analytical results establish a clear relation between Griffith's fracture theory and Paris' law. The proposed modeling framework paves the way for future developments in modern fracture mechanics, e.g. , to derive a novel generation of variational fatigue phase-field fracture models suitably rooted in a Griffith-based theory. • Griffith's fracture theory extension to describe fatigue cracks. • Fatigue effects are described employing a state-dependent fracture toughness. • A clear link between Griffith's fracture theory and Paris' law is established. • The proposed model paves the way for novel fatigue phase-field models. [ABSTRACT FROM AUTHOR]

• Propagation rates of rolling contact fatigue cracks are measured experimentally. • FE model of the observed cracks is used to predict ΔK values during over-rolling. • Propagation rates of longer cracks follow Paris law of type dc dN ∝ Δ K eff 4 . • Mode II propagation (ΔK II) is the main driver of surface breaking RCF cracks. • These findings can aid predictions of remaining useful life of machine elements. Rolling contact fatigue (RCF) is a major life limiting factor for machine elements that employ non-conformal, rolling sliding, lubricated contacts such as rolling bearings and gears. This paper explores the application of linear elastic fracture mechanics (LEFM) principles, as commonly used in structural fatigue, for prediction of RCF crack propagation. A triple-disc contact fatigue machine is used to generate RCF cracks of varying lengths in AISI 52100 bearing steel roller specimens. Crack propagation rates across the surface are measured using optical inspection of test specimens and the final crack geometry is established through specimen sectioning. A numerical finite element model of surface breaking RCF cracks based on LEFM methods is devised to predict the evolution of stress intensity factors (SIFs) during over-rolling of the contact over the experimentally observed crack geometries. The model employs a suitable fracture mechanics mesh to resolve stresses at the crack tip and accounts for Hertzian contact stresses, contact friction and crack face friction. Potential effects of lubricant pressurisation within the crack are not modelled. The predicted SIFs are then related to the experimentally measured crack propagation rates to establish the applicability of the LEFM principles to RCF crack propagation. Results show that LEFM can be used to predict the growth of surface braking RCF cracks. For cracks longer than about 100 μm, a Paris law relationship with the stress intensity exponent of about 4 is derived. Mode II was seen to be the dominant mode of propagation for surface braking RCF cracks. Mode I SIFs are much smaller but can exhibit significant values when the contact is located just ahead of the crack mouth. Decreasing the crack face friction significantly increases mode II stress intensity suggesting that this is one important mechanism by which lubricant entry into the surface braking crack can accelerate its propagation. The findings can help in improving the reliability of mechanical systems by supporting the development of new tools for prediction of remaining useful life of machine components such as bearings and gears. [ABSTRACT FROM AUTHOR]

This paper presents a novel method to construct a plate element enveloping crack tip in the extended finite element method (XFEM) frame for crack growth simulation. The element enveloping a crack tip is sub-partitioned into several triangular quarter-point singular elements around the crack tip. The sub-triangular singular element cut by the crack, like the ordinary elements separated by the crack in other regions, is enriched with the Heaviside function. As the sub-partition scheme retains the original boundary of the crack tip element and the discontinuity of the entire crack is reproduced by the Heaviside enrichment, the proposed method can model cracks independent of the background mesh. Using the singular elements instead of analytical asymptotic functions employed in the conventional XFEM allows to reflect the crack tip singularity for more fracture scenarios. The additional nodes created by the sub-partition act as internal nodes of the crack tip element, thus the classical and enriched degrees of freedom (DOFs) on these nodes can be eliminated through an element-level condensation, which could reduce the condition number of the system matrix. Crack growth in plates and shells under fatigue loading is described by using Paris' law. The performance of the proposed method is investigated through stress intensity factors (SIFs) prediction, convergence study, and fatigue crack growth analysis in several examples of cracked plates and cylindrical shells. • A novel method for constructing crack tip element is developed based on XFEM. • The crack tip element is sub-partitioned into several triangular singular elements. • The sub-triangular singular element cut by crack is enriched with the Heaviside function. • All the DOFs on the sub-partition-induced nodes are eliminated through element-level condensation. • Several examples including fatigue crack growth in cylindrical shells show effectiveness and accuracy of the method. [ABSTRACT FROM AUTHOR]

It is sparse and inconclusive that research on the subject whether the fatigue life of the structure will be reduced by shot peening strengthening before shot peen forming (S + F), and this study investigates accordingly. First, the crack growth rate test of the machine-processing plate and shot peening strengthening before shot peen forming plate demonstrate that both plates' final crack growth rate and length are similar. However, the test shows the "fluctuation phenomenon" of crack growth rate and the "intersection phenomenon" in the Paris curve. This study is based on a self-developed simulation plugin for crack growth paths. The results verify that "fluctuation" causes the differential distribution of the overall stress intensity factor in the strengthened (4.5% increase compared to machine-processing) and formed (9.8% decrease compared to machine-processing) crater areas of the shot peening strengthening before shot peen forming plate. Comparing to the full coverage strengthening area, the forming area (only 30% coverage) in the early stage of growth as well as the gain amplitude of the residual stress in the late stage of growth gradually decrease and tend to be the same as that of the machine-processing, as validated by the "intersection phenomenon". [ABSTRACT FROM AUTHOR]

Mass concrete structures under long-term loads are susceptible to time-dependent fractures, which pose a threat to their structural integrity and safety. In order to study the crack growth rate of concrete materials under long-term constant load, the data were processed according to the calculation method of fatigue crack growth rate. The relationship between the crack growth rate and strength factor in the stable growth stage was obtained using the Paris formula. The experimental data and theoretical analysis show that the time-dependent fracture curve CMOR(t)-t of the standard three-point bending beam specimens could be divided into three stages. The relationship between the crack propagation rate da/dt(t) in the second stage and the intensity factor K(t) could be well described by the Paris formula. The life of crack growth of a standard three-point curved beam is inversely proportional to the level of constant load. These conclusions can provide data support for further studies on crack extension life under long-term constant load. [ABSTRACT FROM AUTHOR]

The 7075 aluminum alloy is a promising material for the aerospace industry due to its combination of light weight and high strength. This study proposed a method for predicting fatigue crack initiation of the 7075 aluminum alloy by crystal plasticity finite element analysis considering microstructures. In order to accurately predict the total fatigue life, it is necessary to calculate the number of cycles for fatigue crack initiation, small crack growth, and long crack growth. The long crack growth life can be estimated by the Paris law, but fatigue crack initiation and small crack growth are sensitive to the microstructures and have been difficult to predict. In this work, the microstructure of 7075 aluminum alloy was reconstructed based on experimental observations in the literature and crystal plasticity simulations were performed to calculate the elasto-plastic deformation behavior in the reconstructed polycrystalline model under cyclic deformation. The calculated local plastic strain was introduced into the crack initiation criterion (Tanaka and Mura, 1981) to predict fatigue crack initiation life. The predicted crack initiation life and crack morphology were in good agreement with the experimental results, indicating that the proposed method is effective in predicting fatigue crack initiation in aluminum alloys. From the obtained results, future issues regarding the prediction of fatigue crack initiation were discussed. [ABSTRACT FROM AUTHOR]

Disbond damage growth in honeycomb cored sandwich structures due to static and fatigue mixed mode loading is investigated numerically and experimentally. A two dimensional finite element model was generated using core homogenization and the Crack Surface Displacement Extrapolation mode separation method, integrated into a fracture mechanics based analysis sub-routine to predict face/core interface fatigue crack propagation. The Cycle Jump technique was furthermore applied to accelerate fatigue analysis. Mixed mode fatigue characterization testing was conducted using Double Cantilever Beam specimens loaded with Uneven Bending Moments, generating a relationship between crack propagation rates and energy release rate amplitudes as a modified Paris Law, measured at three mode-mixity phase angles. The measured Paris laws were subsequently used as input data for the numerical fatigue model. The numerical model was validated against CFRP/Nomex® Sandwich Tearing Test specimen tests with a propagating face/core interface crack yielding varying mode-mixities. The results from the validation showed good agreement between numerical predictions and experimental measurements. [ABSTRACT FROM AUTHOR]

The transverse cracking behavior of a carbon-fiber-reinforced plastic (CFRP) cross-ply laminate is investigated using a fatigue test and an entropy-based failure criterion in this study. The results of fatigue experiments show that the crack accumulation behavior depends on the cyclic number level and frequency, in which two obvious transverse cracks are observed after 104 cyclic loads and 37 transverse cracks occur after 105 cycles. The final numbers of transverse cracks decrease from 29 to 11 when the load frequency increases from 5 Hz to 10 Hz. An entropy-based failure criterion is proposed to predict the long-term lifetime of laminates under cyclic loadings. The transverse strength of 90° ply is approximated by the Weibull distribution for a realistic simulation. Progressive damage and transverse cracking behavior in CFRP ply can be reproduced due to entropy generation and strength degradation. The effects of stress level and load frequency on the transverse cracking behavior are investigated. It is discovered that, at the edge, the stress σ22 + σ33 that is a dominant factor for matrix tensile failure mode is greater than the interior at the first cycle load, and as stress levels rise, a transverse initial crack forms sooner. However, the initial transverse crack initiation is delayed as load frequencies increase. In addition, transverse crack density increases quickly after initial crack formation and then increases slowly with the number of load cycles. The proposed method's results agree well with those of the existing experimental method qualitatively. In addition, the proposed entropy-based failure criterion can account for the effect of load frequency on transverse crack growth rate, which cannot be addressed by the well-known Paris law. [ABSTRACT FROM AUTHOR]

In this paper, interactions of double parallel cracks were studied by performing experiments and numerical simulations. Fatigue crack propagation tests were carried out to measure crack growth rates in the specimens with double parallel cracks or a single crack. Finite element method was adopted to calculate stress intensity factors at the crack tips. Results show that the double parallel cracks at different positions present a shielding effect or enhancement effect on crack growth rates and stress intensity factors. When the double parallel cracks are offset, crack interactions mostly behave as enhancement effects. Empirical formulas were obtained to calculate the stress intensity factor at the "dangerous" crack tip of the double parallel cracks. By modifying the material parameters in Paris equation of the single crack, the double parallel cracks are simplified into a single crack with the same crack growth rates. [ABSTRACT FROM AUTHOR]