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Most fatigue-loading research has concentrated on constant-amplitude tests, which seldom represent actual service conditions. Because of the significant time and expense associated with variable-amplitude experiments, researchers often employ block/step-loading tests to evaluate the effects of variable-amplitude loading. These tests utilize various sequences of low-to-high and high-to-low loads to simulate real-world scenarios. Empirical investigations have shown inconsistencies in the damage accumulation under different load sequences. Although literature reviews exist for simulation and experimental methods, there is limited research examining the impact of step/variable-amplitude loading on adhesive joints in composite materials. This review aims to address this gap by comprehensively analyzing the effects of load sequence and block loading on fatigue damage progression in fiber-reinforced polymer composites. Additionally, the applicability of various step-loading fatigue damage accumulation models to adhesive materials is evaluated through numerical simulation to study its suitability in predicting fatigue failure. This review also explores recent theoretical advancements in this field over the past few years, examining more than 100 fatigue damage accumulation models categorized into seven subcategories: (i) linear damage rules, (ii) nonlinear damage curve and two-stage linearization models, (iii) life curve modification models, (iv) models based on crack growth concepts, (v) continuum damage mechanics-based models, (vi) material degradation models, and (vii) energy-based models. Finally, numerical simulations using the most common nonlinear cumulative fatigue damage accumulation models were conducted to predict fatigue failure in adhesively bonded joints under four step-loading tests, and the results were compared with the experimental data. Numerical simulations revealed the need and scope of further development of a fatigue failure model under step/variable loading. This comprehensive review offers valuable insights into the complex nature of fatigue failure in adhesive joints under variable loading conditions and highlights current state-of-the-art nonlinear fatigue damage accumulation models for adhesive materials. [ABSTRACT FROM AUTHOR]

This study investigates the fatigue behavior of AlSi10Mg alloy manufactured via laser powder bed fusion under variable amplitude loading conditions. Two material conditions were examined: as‐built and stress relief, with the later involving a lower temperature compared to the conventional heat treatments, aimed at preventing the Al‐Si network rupture. Fatigue tests were conducted using two distinct loading spectra: block loading and random loading. While the stress relief reduced the monotonic properties of the material, it resulted in increased fatigue performance due to the homogenization of residual stress throughout the depth. Fracture surface analysis revealed initiation points on subsurface defects, with both block and random loading cases exhibiting overload markings from loading transitions. The predictive model incorporating crack initiation and propagation periods yielded good results, with the equivalent stress range approach providing higher quality estimation compared to the real stress range approach. Highlights: Fatigue behavior under variable amplitude loadings of AlSi10Mg is investigated.Stress relief reduced the monotonic properties but enhanced fatigue resistance.Random spectrum exhibited higher fatigue performance due to lower mean stress influence.Crack initiation and propagation periods were predicted using a linear damage rule. [ABSTRACT FROM AUTHOR]

A reliable approach based on an entropy-damage model for assessing remaining useful fatigue life is presented. Two damage models are presented and evaluated to assess their effectiveness in predicting remaining useful life. The first model focuses on reduced toughness caused by fatigue degradation, while the second is based on accumulating entropy during fatigue loading. The entropy-based approach employs infrared thermography to anticipate entropy accumulation and damage status. Outcomes reveal that the entropy-driven technique offers enhanced precision. Moreover, its damage growth rate remains consistent, regardless of the number of cycles leading to failure, ensuring a more stable tracking of damage evolution. It successfully predicts the remaining useful life and can treat variable load sequencing without knowing the loading history. An extensive set of experimental results with carbon steel 1018 are presented to illustrate the utility of the approach. [ABSTRACT FROM AUTHOR]

A cyclic plasticity constitutive model was developed for materials with asymmetric cyclic behavior to explain the stabilized stress–strain response under variable amplitude loading. The proposed constitutive model incorporated the von Mises yield function with an adjustment to accommodate asymmetric yielding under tension and compression. A combined isotropic–kinematic hardening model was proposed to describe the evolution of the yield surface in the reference uniaxial frame and the actual frame. The history of plastic deformation is memorized by introducing internal variables, accumulated slip, and residual twins, which govern the cyclic flow behavior in the subsequent reversal. The additional conditions required to predict the stabilized hysteresis response of a material under variable amplitude loading were set out and incorporated into the constitutive model. The model was numerically implemented and programmed into a user material (UMAT) subroutine to run with the commercial finite element program, Abaqus/Standard 2019. The model was calibrated using the stabilized hysteresis response of ZEK100 and AZ31B sheets under constant amplitude strain-controlled cyclic loading for different strain amplitudes. To verify the model, constant amplitude and four different variable amplitude load spectra tests were performed and the stabilized stress–strain hysteresis response predicted by the model was compared with test results. It was demonstrated that the results are in very good agreement. [ABSTRACT FROM AUTHOR]

The assessment of fatigue is a crucial concern in welded components and structures. This study investigates the fatigue properties and models for predicting fatigue crack growth in Ti-6Al-4V titanium alloy when processed by vacuum brazing with TiCuNi filler. Fatigue properties and the impact of the stress ratio were determined through constant amplitude fatigue tests. By utilizing the results obtained from variable amplitude fatigue tests, various prediction models for fatigue crack growth were examined: modifications for load interaction, residual stress, and crack closure. The results indicate that the microstructures in the brazed zone consist of numerous fine, elongated needle-like Widmanstätten structures. In terms of cycle counting methods, the rainflow method outperforms the simple-range method. In the stable crack growth rate region, fatigue crack growth rate increases with the rise in stress ratio in a manner similar to high-strength steels. The Paris model without any modification obtains good predictions. For models modified with crack closure, the Elber model yields slightly better prediction results than the Schijve model. Among fatigue crack growth prediction models, the Willenborg model with residual stress modification produces the best results. Fracture surfaces within fatigued specimens' brazed zones exhibit ductile failure characteristics, where fatigue striations and secondary cracks were observed. [ABSTRACT FROM AUTHOR]

Heterogeneous brittle geomaterials are highly susceptible to cyclic loads. They contain inherent flaws and cracks that grow under fatigue loads and lead to failure. This study presents a numerical model for analyzing fatigue in these materials based on the two-dimensional (2D) boundary element method and linear elastic fracture mechanics. The process is formulated by coupling the displacement discontinuity method with the incorporation technique of dissimilar regions and the governing equations of fatigue. The heterogeneous media are assumed to consist of materials with different properties, and the interfaces are assumed to be completely bonded. In addition, the domains include multiple cracks exposed to constant and variable amplitude cyclic loads. The stress intensity factor is a crucial parameter in fatigue analysis, which is determined using the displacement field around crack tips. An incremental crack growth scheme is applied to calculating the fatigue life. The growth rate values are employed to estimate the length of crack extension when there are multiple cracks. The interaction between cracks is considered, which also includes the coalescence phenomenon. Finally, various structures under different cyclic loads are examined to evaluate the accuracy of this method. The results demonstrate the efficiency of the proposed approach in modeling fatigue crack growth and life estimation. The behavior of life curves for the heterogeneous domain was as expected. These curves illustrate the breakpoints caused by utilizing discrete incremental life equations. At these points, the trend of the curves changed with the material properties and fatigue characteristics of the new material around the crack tips.

An innovative critical plane determination approach with weight-averaged largest fatigue damage is proposed, in which the material failure modes can be considered. If material exhibits shear cracking behavior, a strain-based critical plane model with shear failure mode is selected to evaluate the weight function. Otherwise, other one with tensile failure mode is adopted. According to the proposed critical plane, a multiaxial fatigue lifetime estimation methodology is established for evaluating fatigue life. And, six kinds of materials are employed to validate the validity of presented methodology. The validation results reveal the presented methodology can estimate the orientation angles of failure plane accurately and supply satisfactory fatigue lifetime estimations for both shear and tensile failure mode materials. Furthermore, the proposed critical plane framework can be extended to be utilized with stress-based fatigue criteria, and prediction results show a good agreement with experimental data by another two materials.

Purpose: The purpose is to predict the distribution of the residual pretightening force of the bolt group under the action of any initial pretightening force, and to achieve the final residual pretightening force as the target to solve the initial pretightening force value to be applied. Design/methodology/approach: Based on the finite element method and the elastic interaction theory between bolt group, this paper establishes a prediction model for the residual pretightening force distribution of bolt group for one-step pretightening and multi-step pretightening of gasketless flange connection systems. In addition, using the general modeling method given in this paper, the prediction model of residual pretightening force of long plate bolt connection system is established, and compared with reference, which fully proves the effectiveness and universality of the general prediction model of residual pretightening force of bolt group. Findings: The appropriate pretightening sequence, increasing the number of pretightening steps and variable amplitude loading can effectively reduce the influence of elastic interaction and improve the uniformity of residual pretightening force of the bolt group. And the selection of material, number of bolts and connected thickness of bolt connection system also has a great influence on the distribution of residual pretightening force of bolt groups. Originality/value: The general prediction model for the residual pretightening force of bolt group of connecting structural components considering elastic interaction given in this paper can provide a reference for the design and optimization of the bolt assembly process of the rotor system and the casing system in aero-engine and the prediction of the performance of the connecting system. [ABSTRACT FROM AUTHOR]

The constant/variable amplitude loading fatigue test with interior inclusionfine granular area-fisheye induced failure under R=0 were carried out on carburized Cr-Ni steel. The results showed that the fatigue life under variable amplitude loading is longer than that under constant amplitude loading in very-high-cycle fatigue regime under same maximum stress level, and the surface morphology of fine granular area under variable amplitude loading is coarser than that under constant amplitude loading under same order of magnitude of fatigue life. Simultaneously, it can be determined that the formation micro-mechanism of fine granular area is caused by the continuous deboning due to stress concentration around interior micro-defects. Furthermore, the life prediction model based on double nonlinear fatigue damage, which considers the coupling effect of local equivalent stress (surface residual stress and local stress concentration effect), loading sequence, failure mechanism and nonlinear characteristics of fatigue damage under constant/variable amplitude loading is established, and predicted life has good accuracy within the factor-of-three lines. [ABSTRACT FROM AUTHOR]

In this paper, a fatigue crack growth (FCG) behavior under variable amplitude loadings and for mixed modes is analyzed in terms of residual compressive stress zone. For that, the Chaboche non-linear kinematic hardening model is used to evaluate the crack behavior on AA2024-T3. At first, a series of FCG simulation is performed for a single edge notched tension specimen to highlight the influences of the crack length, the overload ratio, the stress ratio, the mean stress, the mixed mode, and the load sequence on the crack tip residual -stress zone under variable amplitude loadings. Besides, the size and shape of crack tip residual-stress zone are simulated for low/high, high/low block loadings and with/without overloads. Moreover, and according to the findings, a FCG code using the Python script and the extended finite element method (XFEM) Is improved. The developed code processes FCG behavior under variable amplitude loadings using the shape of residual stress distribution near the crack tip. The predicted results show a good agreement in simulating fatigue crack path under variable amplitude loadings with those published in the literature. The originality of this study is to simulate the fatigue crack path of cracked structures under variable amplitude loadings with the compressive residual stress model coupled with the XFEM for mode I and different mixed mode. [ABSTRACT FROM AUTHOR]

A cyclic plasticity constitutive model was developed for materials with asymmetric cyclic behavior to explain the stabilized stress–strain response under variable amplitude loading. The proposed constitutive model incorporated the von Mises yield function with an adjustment to accommodate asymmetric yielding under tension and compression. A combined isotropic–kinematic hardening model was proposed to describe the evolution of the yield surface in the reference uniaxial frame and the actual frame. The history of plastic deformation is memorized by introducing internal variables, accumulated slip, and residual twins, which govern the cyclic flow behavior in the subsequent reversal. The additional conditions required to predict the stabilized hysteresis response of a material under variable amplitude loading were set out and incorporated into the constitutive model. The model was numerically implemented and programmed into a user material (UMAT) subroutine to run with the commercial finite element program, Abaqus/Standard 2019. The model was calibrated using the stabilized hysteresis response of ZEK100 and AZ31B sheets under constant amplitude strain-controlled cyclic loading for different strain amplitudes. To verify the model, constant amplitude and four different variable amplitude load spectra tests were performed and the stabilized stress–strain hysteresis response predicted by the model was compared with test results. It was demonstrated that the results are in very good agreement.

Metallic materials are widely employed in engineering constructions, and one of the most common failure mechanisms in metals is fatigue failure. Even though metal fatigue has been studied for almost 160 years, many problems remain unsolved. Fatigue in metal occurs when the metallic material is subjected to varying loads, resulting in failure due to damage accumulation. The fatigue process consists of a buildup of damage that leads to crack initiation, followed by a period of crack growth until the critical flaw size is reached. The sum of a start phase and a propagation phase represents the total life. To better understand the fatigue phenomenon at its different stages and predict the fatigue life, various types of prediction models have been developed and reported in the literature. This paper reviewed the different models that include microstructure scale parameters that can be used to predict how fatigue cracks start under variable amplitude loading, including the Modified Tanaka-Mura Model, Acoustic Second Harmonic Generation, and the Probability of Crack Initiation on Defects. For perfect life prediction under variable amplitude loading, a stress-based approach, a strain-based approach, and a continuum damage mechanics approach are reviewed. The purpose of this paper is to get overview of the current state of approaches to the life prediction of fatigue crack initiation with variable amplitude. Finally, gaps in knowledge about the prediction of fatigue crack initiation under variable loading at high temperatures are pointed out. [ABSTRACT FROM AUTHOR]

• Fatigue crack retardation and acceleration effects due to amplitude changes. • Analytical equations based on crack closure evolution obtained by strip-yield model. • Maximum crack closure after overload available by simple analytical equation. • Possibility of consideration of different material cyclic plastic properties. The paper presents an efficient methodology for computation of the evolution of the fatigue crack retardation and acceleration effects due to crack closure during variable amplitude loading. The presented approach can lead to a very effective tool for estimation of residual fatigue life of engineering structures. Conventionally, consideration of variable-amplitude loading is either computationally too demanding, such as in finite element modelling, or challenging to unify the strip-yield model with another computational code. The simple analytical formulae available in literature are based on residual stress, which does not describe correctly the delayed retardation effect and in some cases it can be non-conservative. This work presents simple analytical equations describing the development of the crack closure based on the results of the strip-yield model for amplitude changes at the load ratio R = 0.1. The parabolic function enables simple computation of the maximum crack closure occurring after an overload without running any simulation. The equations also enable computation of crack closure behaviour following amplitude changes with the consideration of various cyclic material properties reflected in the tuneable ratio between the monotonic and cyclic plastic zone sizes. [ABSTRACT FROM AUTHOR]

The assessment of fatigue is a crucial concern in welded components and structures. This study investigates the fatigue properties and models for predicting fatigue crack growth in Ti-6Al-4V titanium alloy when processed by vacuum brazing with TiCuNi filler. Fatigue properties and the impact of the stress ratio were determined through constant amplitude fatigue tests. By utilizing the results obtained from variable amplitude fatigue tests, various prediction models for fatigue crack growth were examined: modifications for load interaction, residual stress, and crack closure. The results indicate that the microstructures in the brazed zone consist of numerous fine, elongated needle-like Widmanstätten structures. In terms of cycle counting methods, the rainflow method outperforms the simple-range method. In the stable crack growth rate region, fatigue crack growth rate increases with the rise in stress ratio in a manner similar to high-strength steels. The Paris model without any modification obtains good predictions. For models modified with crack closure, the Elber model yields slightly better prediction results than the Schijve model. Among fatigue crack growth prediction models, the Willenborg model with residual stress modification produces the best results. Fracture surfaces within fatigued specimens’ brazed zones exhibit ductile failure characteristics, where fatigue striations and secondary cracks were observed.

The randomness of sea conditions and loading sequences are among the key contributing factors that affect our ability to accurately predict the fatigue crack growth in ships. Climate change may alter the long-term characteristics of these factors along the service life of existing or newly constructed ships. This paper presents a framework for quantifying the impact of climate change on crack propagation in ship hulls. A probabilistic fatigue crack propagation approach is developed to account for uncertainties associated with material properties and loading conditions; specifically, those affected by climate change. Global Climate Models (GCMs) are used to quantify the long-term effects of climate change on the sea conditions and the resulting ship loading time histories. The proposed approach is applied to a tanker ship operating within predefined routes in the Atlantic Ocean. The results show that the effect of climate change on the crack propagation depends on the navigation route. [ABSTRACT FROM AUTHOR]

A new path‐independent multiaxial fatigue damage parameter σn*, which is defined as the largest normal stress range between adjacent turning points of the maximum shear stress on the critical plane, is proposed to describe multiaxial fatigue damage. By combining the maximum normal stress σn,max or the largest normal stress range σn* with the maximum shear stress range on the critical plane, two axial equivalent stress modification factors, keqσ and keqσ*, are proposed, which can account for the influence of non‐proportional additional hardening. The sensitivity of the proposed axial equivalent stress modification factors to multiaxial variable amplitude loading sequences is analyzed. Furthermore, two new multiaxial fatigue damage models based on the axial equivalent stress modification factors are proposed to estimate fatigue life. The applicability of the presented methodology was verified by the experimental data of En15R steel and 7050‐T7451 aluminum alloy, and the results showed that the predicted fatigue lifetimes agree well with the experimental data under variable amplitude multiaxial loading. [ABSTRACT FROM AUTHOR]

This research estimates the high-cycle fatigue (HCF) life of integrated concrete bridge installed on water due to temperature changes. To this end, CATIA software was used to geometrically model of a real-scale bridge. Next, thermal–structural coupling analysis was performed by finite element (FE) simulation in ANSYS WORKBENCH software. The comparison technique with experimental data was used to validate the simulation. Afterward, thermal analysis was performed due to air temperature changes in different modes, including the average monthly temperature changes (large variations) as well as the maximum and minimum monthly temperature changes (small variations). The results showed that the most changes in deck length and subsequent maximum deviation in the upper part of steel piles were related to the three warm seasons in the presence of the water. Eventually, a probabilistic approach was employed to find variable amplitude fatigue lifetime of the component based on the number of annual loading blocks. To achieve the high-accuracy response, the effective parameters of the proposed probabilistic approach, including order of Fourier series and the stress range, were optimized automatically. In addition, to obtain HCF behavior of raw material, axial tension–compression fatigue tests were performed on the standard specimens fabricated from steel piles. The results revealed that considering small variations in the calculation of structural fatigue life led to a 550% reduction in life compared to structural analysis due to large variations. In addition, the obtained results were compared with the finite element results. [ABSTRACT FROM AUTHOR]

A modified fatigue damage model is proposed considering the loading sequence effect under variable amplitude loading conditions. The transition sequence is obtained from the counting sequence by an equivalent rainflow counting method and is used to provide the loading sequence information for fatigue damage accumulation prediction. Rainflow counting matrix and sequence transition matrix are formulated based on the rainflow counting sequence and the transition sequence. The relation between the two matrices and the original loading sequence is evaluated in detail. In the deterministic fatigue estimation, the rainflow counting matrix and the sequence transition matrix are integrated into the proposed modified damage model based on the linear damage rule. Mean stress transition is applied to the rainflow counting matrix for loading level effect. Existing experimental data are used to validate the fatigue damage estimation from the deterministic framework. In order to evaluate the fatigue under random loading conditions, the rainflow counting matrix and sequence transition matrix are mapped to one-dimensional exponential and Laplace distributions based on the stationary random process. Numerical simulation is conducted to validate the proposed mapping distributions. Meanwhile, the impact of the correlation length on the proposed distributions under stationary random loading sequence is investigated as well. Finally, with the given distributions of the rainflow counting matrix and sequence transition matrix, a reconstruction procedure is simulated and discussed for probabilistic fatigue estimation. The proposed model provides a sophisticated approximation to the original loading sequence with a sequence transition effect. The proposed modified fatigue damage model corrects the deficiencies of the linear damage rule with sufficient sequence information from the originally applied loading. Furthermore, the probabilistic fatigue estimation can evaluate the accumulated fatigue damages under a random loading process with the sequence transition effect. [ABSTRACT FROM AUTHOR]

This work explores the effects of underloads on physically short fatigue cracks propagating under near-threshold zero–tension loading in various constraint conditions. A finite element model is employed to model the transient behavior of plasticity-induced crack closure and residual stress, from which propagation behavior can be inferred. The expected behavior of acceleration after an underload is mostly descriptive of the plane stress results, but in axisymmetric and plane strain conditions a post-underload deceleration is predicted with single or scarce underloads. Frequently repeated underloads, however, are found to reduce fatigue strength in all cases considered. Short cracks prove especially vulnerable to underload acceleration when initiated at notch-like defects. Three independent physical mechanisms are recognized, namely, the removal of load history, compressive notch plasticity, and Bauschinger effect, a combination of which explains the underload results. Additionally, tentative guidance for fatigue design in finite and infinite life underload applications is provided. [Display omitted] • Physical mechanisms behind the short crack underload response are revealed. • Single or infrequent underloads may improve fatigue life in plane strain conditions. • Underloads exceeding yield strength may significantly raise following closure levels. • Fatigue life may be decreased to a third when subjected to repeated underloads. • Fatigue limit may be decreased to a third if the loading contains multiple underloads. [ABSTRACT FROM AUTHOR]

Fatigue crack growth and fatigue life prediction always play important roles during the structural service period or safe design. Based on the Forman equation, an improved model that can predict fatigue crack growth under variable amplitude loads is proposed in this study. The model combines both the crack closure and residual stress effect. The initial cracking phase is well described by introducing a damping threshold factor. Overload acceleration and delayed retardation phenomena are achieved by considering the change of crack opening stress. All the parameters can be obtained through one overload test. The predicted fatigue crack growth rates are validated by experimental data of several steels and alloys. Fatigue life prediction of the model is verified by Monte Carlo simulation. The simulation errors under various loading sequences are less than 10%. The achievement of this study may be used for metallic structural fatigue design since it can yield mass of data through a few experiments. [ABSTRACT FROM AUTHOR]

A nonlinear model is proposed in light of the theory of isodamage curves, to assess the cumulative fatigue damage under multistage loading. The isodamage curves were developed through the theory of the S‐N fatigue damage envelope, proposed by Pavlou. The adopted functional form of the fatigue damage is a commonly accepted general form. In the present work, a stress function for the fatigue life exponent is derived with the aid of the S‐N curve only. In the proposed nonlinear model, no adjusting parameters are necessary for fatigue damage estimation. The fatigue life prediction of the derived model is compared with experimental results of various alloys and existing models. The comparison is made for C35, C45, Al‐2024‐T42, 15HM, A336 GR 5, and A387 GR22 for two‐stage loading high‐low and low‐high, and Al 6082‐T6 for multistage loading. Highlights: Nonlinear damage function in light of the theory of the S‐N fatigue damage envelopeValidity of the model in both HCF and LCFVerification of the new fatigue model with various metallic materialsDiscussion of the model effectivenes in relation to the known fatigue damaging process [ABSTRACT FROM AUTHOR]

Quantitative thermographic methodology (QTM), which takes energy dissipation as a fatigue indicator, has been successfully applied to predict the fatigue life of materials and welded joints under constant amplitude loading. This study advances the QTM approach for predicting the fatigue life under variable amplitude loading in both low and high cycle fatigue regimes. Experimental data, obtained by fatigue tests under variable amplitude loading, were used in order to apply the developed QTM approach and to demonstrate that it is able to take into account the loading sequence effect. Good predictions of the fatigue life were achieved. Highlights: A new quantitative thermographic method for variable amplitude loading is established.The proposed method enables life prediction for both low and high cycle fatigue regimes.Both nonlinear damage accumulation and loading sequence effect can be considered.Satisfactory life predictions are achieved on three different types of variable loads. [ABSTRACT FROM AUTHOR]

A fatigue life prediction methodology is proposed based on weight-averaged maximum shear stress range plane.Firstly,based on modified Wang and Brown’s reversal counting method,a new approach to the determination of the critical plane is proposed under multiaxial variable amplitude loading. For the entire loading history,the orientation angle of the critical plane is determined through averaging the orientation angles of maximum shear stress range planes with largest normal tensile stress in all counted reversals. The weight function is defined as the ratio of maximum shear stress range for every counted reversal to the largest shear stress range for all counted reversals. The accuracy of the proposed critical plane approach is verified using experimental data of 7050-T651 aluminium alloy notched tubular specimens. Then,the proposed determination approach of critical plane is combined with multiaxial high-cycle fatigue criterion and Miner damage rule to establish the fatigue life prediction methodology under multiaxial variable amplitude loading. Finally,the proposed fatigue life prediction methodology is verified by the experimental data of 7050-T651 and 2024-T4 aluminum alloy notched tubular specimens,and the results show that the proposed methodology has good prediction results.

In the present paper, the author has attempted to examine fatigue life of automotive safety components under axial variable amplitude loading conditions. To this end, the time components of stress tensor in the critical area of the knuckle and Liu-Zenner criterion were used to calculate the time history of equivalent stress. Then, the probability distribution function (PDF) of stress was extracted by applying the stress level counting technique. The Fourier curve fitting method was employed in order to formulate the PDF. Subsequently, the fatigue life of the component was estimated using the probabilistic approach. Finally, the results of the higher order of Fourier curve fitting and different counting ranges were compared with the experimental results. Thus, the best algorithm for precisely determining fatigue life of automotive components was obtained.

Metallic materials are widely employed in engineering constructions, and one of the most common failure mechanisms in metals is fatigue failure. Even though metal fatigue has been studied for almost 160 years, many problems remain unsolved. Fatigue in metal occurs when the metallic material is subjected to varying loads, resulting in failure due to damage accumulation. The fatigue process consists of a buildup of damage that leads to crack initiation, followed by a period of crack growth until the critical flaw size is reached. The sum of a start phase and a propagation phase represents the total life. To better understand the fatigue phenomenon at its different stages and predict the fatigue life, various types of prediction models have been developed and reported in the literature. This paper reviewed the different models that include microstructure scale parameters that can be used to predict how fatigue cracks start under variable amplitude loading, including the Modified Tanaka-Mura Model, Acoustic Second Harmonic Generation, and the Probability of Crack Initiation on Defects. For perfect life prediction under variable amplitude loading, a stress-based approach, a strain-based approach, and a continuum damage mechanics approach are reviewed. The purpose of this paper is to get overview of the current state of approaches to the life prediction of fatigue crack initiation with variable amplitude. Finally, gaps in knowledge about the prediction of fatigue crack initiation under variable loading at high temperatures are pointed out.

This study aims to investigate the characteristic of the random strain load signal in the time domain to predict durability of the lower arm. Cyclic loading on the suspension arm of vehicles leads to fatigue damage. The suspension arm is subjected to random variable amplitude loading due to different road conditions. Strain load signal data from a previous experiment are used for the analysis, and statistical parameters from the signal, such as mean, standard deviation, root-mean-square, kurtosis, skewness are extracted in time domains, while the power spectrum density in frequency domains. The fatigue life of three different roads was predicted using Coffin–Manson (CM), Morrow and Smith–Watson–Topper (SWT) strain-life models. Results showed the strain life of the lower arm ranges from 4.47 × 106 cycles/block to 8.8 × 109 cycles/block, 2.58 × 106 cycles/block to 3.18 × 1010 cycles/block, and 2.21 × 106 cycles/block to 5.06 × 1010 cycles/block for Coffin–Manson, Morrow and Smith–Watson–Topper model, respectively. Hence, the fatigue life of lower arm can be modeled using the mean stress effects due to compression and tension for various road condition based on the statistical properties of the strain signal i.e., kurtosis and root-mean-square value. [ABSTRACT FROM AUTHOR]

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The paper discusses various partial solutions used for estimating fatigue life under variable amplitude multiaxial loading in the high‐cycle fatigue domain. The concurring effects are treated, and their proposed solutions are commented upon. The major focus is on the categories of the phase shift effect and of cycle counting and on the scope and quality of data, which support discussed theories. Results of own new experimental data set on specimens from S355 steel are provided. Fatigue life estimates for McDiarmid and Findley multiaxial methods and for two different methods of load path decomposition to cycles are shown to highlight some of the points open for discussion. It is concluded that the available experimental data are not sufficient to substantiate a clear decision to follow a definite algorithm. Highlights: Parts of the prediction analyses for multiaxial loading of variable amplitude are analyzedExtremely limited existing experimental evidence for any theories is highlightedOwn experimental data described to document the obtained prediction quality [ABSTRACT FROM AUTHOR]

The consideration of realistic load assumptions is important for the fatigue design of highly stressed nodular cast iron components for wind energy application. Especially in case of overloads causing elastic–plastic deformation, residual stresses may have a strong impact on fatigue life. In strain‐controlled fatigue tests with constant and variable amplitudes, the influence of overloads on lifetime was investigated. During fatigue testing, the transient material behavior, cyclic hardening, cyclic relaxation of the residual stresses, and quasi‐static creep effects of the EN‐GJS‐400‐18‐LT was recorded and evaluated. To quantify the influence of the transient material behavior on the calculated lifetime, fatigue analyses are carried out with the strain‐life approach, both with and without consideration of the transient material behavior. The results show that conservative damage sums are derived if the transient material behavior, especially the relaxation of tensile residual stresses, is neglected. [ABSTRACT FROM AUTHOR]

Fatigue cracks initiated from holes in several zones and structural components of the RRJ‐95 aircraft frames were investigated. Using the method of quantitative fractography, the crack growth duration in the wing panels during full‐scale bench tests and in the brackets of the in‐service airframe was estimated by measuring the spacing of meso‐beach‐marks (MBM) and fatigue striations. The applied program of bench test consisted of blocks of variable loads that were equivalent to the wing loading in flight and reproducing schematized flight‐cycle. It was shown that the duration of fatigue crack propagation in several structural components of the RRJ‐95 aircraft frames was approximately the same as for the crack nucleation duration. The total lifetime is sufficiently long for cracks in the structural components to be detected and reliably monitored with a large operating time interval between adjacent inspections. [ABSTRACT FROM AUTHOR]

This research estimates the high-cycle fatigue (HCF) life of integrated concrete bridge installed on water due to temperature changes. To this end, CATIA software was used to geometrically model of a real-scale bridge. Next, thermal–structural coupling analysis was performed by finite element (FE) simulation in ANSYS WORKBENCH software. The comparison technique with experimental data was used to validate the simulation. Afterward, thermal analysis was performed due to air temperature changes in different modes, including the average monthly temperature changes (large variations) as well as the maximum and minimum monthly temperature changes (small variations). The results showed that the most changes in deck length and subsequent maximum deviation in the upper part of steel piles were related to the three warm seasons in the presence of the water. Eventually, a probabilistic approach was employed to find variable amplitude fatigue lifetime of the component based on the number of annual loading blocks. To achieve the high-accuracy response, the effective parameters of the proposed probabilistic approach, including order of Fourier series and the stress range, were optimized automatically. In addition, to obtain HCF behavior of raw material, axial tension–compression fatigue tests were performed on the standard specimens fabricated from steel piles. The results revealed that considering small variations in the calculation of structural fatigue life led to a 550% reduction in life compared to structural analysis due to large variations. In addition, the obtained results were compared with the finite element results.

• Prediction of fatigue crack propagation lives for through-thickness cracks under variable amplitude spectrum loads. • Simple cycle counting of every load-increasing part of the spectrum profile. • Development of Spectrum Overload Index (SOL-Index) to characterize the overload intensity and density of spectrum profile. • Integrations of crack growth retardation, stress ratio and SOL-Index in a single model. • Results from model predictions show good agreement with those from experiments and literature data. This paper proposes a new method for predicting propagation lives for through-thickness cracks under variable amplitude mode-I spectrum fatigue loads. Only the crack opening, i.e., the increasing parts of the load cycles within spectrum profiles are considered for cycle counting and computing their stress ratios. Moreover, a cycle-by-cycle analysis is also performed throughout the spectrum to compute the so-called Spectrum Overload Index (SOL-Index), which is a multiplier applied on stress intensity factor range used within different crack growth retardation models, in which effects of stress ratio are also included. The SOL-Index is calculated using the average of peak loads for all cycles within the spectrum and their percent deviations from the peaks' average value. Simulation results using the proposed cycle counting method, the integrated crack growth model and the SOL-Index are compared with those from multiple experiments under two different loading spectrums and another study in the literature. The results show that usage of Wheeler's model embodying the Forman or Walker equation and the SOL-Index together yields the closest results to the experiments. [ABSTRACT FROM AUTHOR]

Fatigue lifetime predictions for variable amplitude loading are primarily based on the linear damage accumulation rule of Palmgren–Miner, which does not account for load sequence effects. Various nonlinear models have been developed, but their generalization capability is limited. Although neural network models have been used for prediction of the lifetime of metals subjected to constant amplitude loading, random loading and two-level block loading sequences before, they have never been used for multi-level block loading to the authors knowledge. The primary goal of this study is the development of neural network models for fatigue life estimation of metals subjected to block loading. To achieve this, a sufficient amount of qualitative data is required. Therefore a large number of rotating bending fatigue experiments with constant amplitude and block loading sequences are carried out. This new data is combined with data gathered from literature, leading to the most extensive open-access collection of variable amplitude fatigue data published to date. Neural network models are trained with the developed dataset and compared to four cumulative damage models including the linear Palmgren–Miner rule and three non-linear models. It is concluded that the neural network model for multi-level block loading outperforms all of the considered analytical models. [Display omitted] • Largest open-access block loading experiment dataset gathered to date. • Repeated two- and five-level block loading experiments to analyze scatter. • Artificial neural network models developed for fatigue lifetime prediction. • Neural networks outperform studied linear and nonlinear damage accumulation models. [ABSTRACT FROM AUTHOR]

[Display omitted] • Digital twin enables accurate Δ J computations under elasto-plastic conditions. • Digital twin transforms solely strain data to load–displacement information. • Successful Δ J computations extend traditional fatigue crack growth relationship. • Extended fatigue crack growth relationship predicts fatigue life accurately. This paper introduces a novel digital twin solution for unlocking the elasto-plastic fatigue crack growth within an S550 steel under negative load ratios. The digital twin transforms solely strain data from a strain-interfaced welded plate joint specimen to the load–displacement curve to compute cyclic J -integral values using the η approach, eliminating the need for load and displacement measurements. The accurate computation of the elasto-plastic Δ J effectively extends the fatigue crack growth relationship derived from standard fracture specimens. The extended fatigue crack growth relationship accurately predicts the fatigue life of specimens under separate step-up and step-down variable amplitude loading regimes. [ABSTRACT FROM AUTHOR]

In the present paper, the approach based on the strain energy density (SED) averaged over a structural volume is reformulated to estimate the lifetime of notched components subjected to variable amplitude (VA) uniaxial fatigue loading. The accuracy and reliability of the proposed reformulation of the SED approach was checked against a large number of data taken from the literature and generated, under two different load spectra, by testing specimens of carbon steel C40 containing notches of different sharpness. Such a validation exercise allowed us to demonstrate that the extension of the SED approach as proposed in the present paper is capable of accurately estimating fatigue damage in notched components subjected to inservice VA fatigue loading

Tests under variable amplitude loading on self‐piercing riveted components with semi‐tubular rivets result in longer service lives than those calculated by linear damage accumulation. An overview of the literature shows that damage sums greater than one are found for other types of riveted joints either, while an explanation for this unusual behavior is still missing. Therefore, this behavior is examined in more detail. A correlation is shown between the damage sum and the hardness of the load spectrum. Considering this correlation, the accuracy of the service life estimation can be improved significantly. [ABSTRACT FROM AUTHOR]

Most of the research reported in the literature on cast aluminum alloys is related to constant amplitude loading, while in most applications such components are subjected to variable amplitude loading conditions. In this work, fatigue performance of high pressure die cast (HPDC) A356‐T6 aluminum alloy is evaluated using a real industrial load spectrum. Mean stress effect was also studied by conducting variable amplitude fatigue tests under two different mean stress conditions. Fatigue life estimations were performed following S‐N approach as well as fracture mechanics approach using direct summation method as well as FASTRAN program assuming the defects as initial cracks. The size of fatal defects measured from fracture surfaces as well as the maximum defect size estimated by extreme value statistics were used in fatigue life estimations. The results of life estimations are compared and discussed with reference to the experimental results. [ABSTRACT FROM AUTHOR]

Crack propagation in near neutral pH (NNpH) environment causes significant threat to pipeline integrity. Internal pressure fluctuations during pipeline operation create variable amplitude loading condition that can propagate corrosion fatigue cracks in NNpH environments. This study is aimed at understanding the effect of load interaction due to mean load pressure fluctuations on crack propagation in pipeline steel under NNpH conditions. The loading condition involved underload followed by an overload at set intervals among minor cycles. The effect of minor cycles, magnitude of overload, and NNpH environment were considered and compared to control test in air. Results showed optimum reduction in crack growth rate at low magnitude of overload in mean load pressure fluctuation. Mini striations observed on fracture surface suggest the contributions of minor cycles to crack propagation due to load interaction. Significant increase in crack growth at high magnitude of overload in NNpH environment indicates the influence of hydrogen. [ABSTRACT FROM AUTHOR]