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Automotive parts are usually subjected to random loads with large mean tensile/compressive stresses under working conditions. It is important for automotive parts to have a long fatigue life under mean stress in practical engineering applications. An equivalent strain model is established here to predict fatigue life considering the influence of mean strain and stress under asymmetric cycles. To predict the fatigue life more accurately, the coefficient of surface roughness and temperature correction is introduced in this model. The effectiveness of the improved equivalent strain (IES) model is verified by comparing it with multiple sets of experimental data. The IES is also compared with Smith–Watson–Topper (SWT), Manson–Coffin, and equivalent strain models. The results show that the developed model has a higher prediction accuracy than the other models. An improved fatigue strength exponent is introduced to modify the equivalent strain model, and the effectiveness of the model is verified by experimental data. The IES model demonstrates significantly reduced standard deviations under various strain ratios (−0.06, 0.06, 0.5), with measurements of 0.0936, 0.0721, and 0.0636, respectively. The method provides a certain reference for the life prediction of automotive parts. [ABSTRACT FROM AUTHOR]

Fatigue testing is a crucial technique for assessing the fatigue performance of materials and components. However, the testing process often involves numerous uncertainties, such as variations in part roughness and size, and the collected data typically constitutes small samples. This paper proposes an improved bootstrap method with cycle of uncertainty to address the limitations of traditional bootstrap methods in estimating uncertainties in small sample sizes. The proposed method was applied to estimate the effect of surface roughness and common normal size on fatigue tests, resulting in improved estimation accuracy. The research contributes to the development of improved methods for fatigue life estimation, which has practical implications for mechanical component design and optimization. Highlights: Virtual data are expanded by assigning samples to a normal distribution.Bootstrap method is improved by introducing cycle of uncertain.The effect of uncertainties is considered in the fatigue test on the results. [ABSTRACT FROM AUTHOR]

Purpose: Scholars mainly propose and establish theoretical models of cumulative fatigue damage for their research fields. This review aims to select the applicable model from many fatigue damage models according to the actual situation. However, relatively few models can be generally accepted and widely used. Design/methodology/approach: This review introduces the development of cumulative damage theory. Then, several typical models are selected from linear and nonlinear cumulative damage models to perform data analyses and obtain the fatigue life for the metal. Findings: Considering the energy law and strength degradation, the nonlinear fatigue cumulative damage model can better reflect the fatigue damage under constant and multi-stage variable amplitude loading. In the following research, the complex uncertainty of the model in the fatigue damage process can be considered, as well as the combination of advanced machine learning techniques to reduce the prediction error. Originality/value: This review compares the advantages and disadvantages of various mainstream cumulative damage research methods. It provides a reference for further research into the theories of cumulative fatigue damage. [ABSTRACT FROM AUTHOR]

Automotive drive shaft is an indispensable key component of the transmission system, and the use of composite drive shafts has shown great promise. The epoxy matrix of the shaft is susceptible to the effects of temperature in comparison to carbon fiber. To investigate the influence of the environmental temperature on the fatigue life of a carbon fiber‐reinforced plastic drive shaft, a temperature‐based property curve and performance fraction model for the shaft are established. The temperature coefficient is calculated and introduced by combining the collected temperature data with the property fraction function. A generalized S‐N surface of the composite drive shaft is proposed based on experimental data. The fatigue life under collected and processed random loads of the carbon fiber‐reinforced plastic drive shaft is predicted by modified Miner's law. The effect of mean, amplitude of load and ambient temperature on fatigue life are taken into account. Highlights: Drive shaft load spectrum was acquired and preprocessed.Model of the carbon fiber‐reinforced plastic (CFRP) drive shaft was built for torsion strength with temperature.The temperature coefficient was calculated via temperature distribution and the model.Fatigue life of CFRP drive shaft was predicted by combining improved S‐N surfaces. [ABSTRACT FROM AUTHOR]

Springs are widely used in the automobile industry. They can produce large elastic deformation under the action of load. The fracture failure of springs will cause significant loss or maintenance costs. The fatigue life of springs is greatly affected by load eccentricity and residual stress. Some existing methods are not accurate enough to predict the life of springs. The cracked spring stresses are computed considering load eccentricity. Based on the Walker model, a method for predicting the spring fatigue life is proposed. The model combines the superposition principle and the closure effect, and it can consider residual stress, crack closure effect, and load eccentricity at the same time. The results demonstrate that the improved model has a better performance than the Walker model. Highlights: Load eccentricity is used to correct the critical crack size.Superposition principle is applied to spring life prediction.A spring life model considering crack closure effect and residual stress is proposed.This model is suitable for the fatigue life of coil springs. [ABSTRACT FROM AUTHOR]

To meet the different functional requirements of the components, irregularities and geometric discontinuities occur in the structural design of the components. These geometrical discontinuities lead to local stress concentrations, which inevitably introduce notch effects. The unyielding internal material still supports the high‐stress area on the plane due to the supporting effect of the notch. This effect can lead to inaccurate prediction of fatigue life. So, the notch support factor and strain were used as damage parameters to modify the life prediction model of the notched specimens in this research. And an improved critical plane method is applied in selecting damaged planes. It considers the damage at the notch before loading and uses dynamic weights to measure the effect of the maximum stress plane on the damaged plane. The model was validated using TC4 and GH4169 notch data and compared with other models, and the revised model has higher accuracy. The damaged plane and damage parameters to modify the fatigue life of the notched specimen make more physical sense and are more consistent with the fatigue failure mechanism. Highlights: Correction of multiaxial fatigue life models using damage parameters.Improving critical plane model by considering damage before loading of notched members.A fatigue life model was developed using modified critical plane and damage parameters. [ABSTRACT FROM AUTHOR]

To predict fatigue life more accurately, we consider the relationship between static toughness and fatigue toughness in fatigue failure process, the numerical model of total dissipated plastic strain energy (TDPSE) and fatigue life is established. And considering the effect of surface roughness and surface processing coefficient on fatigue life, the life prediction method of TDPSE is modified. In addition, the fatigue life of Non-Masing and Masing materials are predicted by TDPSE and modified TDPSE method, respectively. Compared with TDPSE method, the life estimated by the modified TDPSE method are closer to the test results, and the modified TDPSE method lays a technical foundation for the development of mechanical components. [ABSTRACT FROM AUTHOR]

In this paper, a modified degradation model is proposed to simulate the residual strength of 45 steel under cyclic loading, which is then applied to analyse the rule of strength degradation of the metal. The degradation data of 45 steel tests shows the relationship between the ratio of cycle number and residual strength. The model is built by considering a series of cycle ratio errors between loading times and fatigue life on the basis of the Schaff theory and power degradation model criterion. The model is applied to numerical simulation of 35CrMo, with the outcome being presented to illustrate the applicability and efficiency of the model. Moreover, the results provide some theoretical references for the fatigue life analysis of metals. [ABSTRACT FROM AUTHOR]

The small load has fuzziness on the strengthening and damage of the component under the action of random fatigue load. This paper introduces the two‐dimensional membership function in fuzzy mathematics to characterize the relationship between stress amplitude, mean value, and damage below the fatigue limit. An exponential function is used to describe the strengthening effect. Under the two‐dimensional load spectrum, the influence of various levels on the component's life is comprehensively considered, and the fatigue life prediction model under random load is proposed. Through the small sample experiment of the car swing support rod, the relevant parameters of the model are obtained. The difference between the modified two‐dimensional and the two‐dimensional load spectrum is compared in fatigue life prediction results. The rules of membership function selection and parameter setting are summarized, and it makes the estimation of component load spectrum life more reasonable. [ABSTRACT FROM AUTHOR]

In the engineering application of high strength steel and surface strengthening steel, fisheye failure is often happened in high cycle fatigue. To explore the effect of fisheye failure on high cycle fatigue properties of materials, a high cycle fatigue life model was established based on the Murakami and Tanaka's fatigue strength models. The model introduces the error circle to evaluate fisheye size, and discusses the influencing factors of fatigue strength. The results show that the size and depth of fisheye failure will affect performance of materials. The proposed model considering the size and depth of defect quantitatively shows the influence of fisheye details on material performance, and effectively predicts the high/ultra-high cycle fatigue life. [ABSTRACT FROM AUTHOR]

In order to determine the effect of different loads on fatigue damage, a strength degradation model is proposed according to the law of residual strength degradation of metal materials. The model is verified with the strength degradation test data, and the results show that the model can describe the strength degradation process of general metal materials well. Combined with the strength degradation model, an improved equivalent damage model for different loading sequences is proposed. On this basis, a nonlinear fatigue cumulative damage model based on strength degradation is derived. The cumulative damage model is applied to the estimation of fatigue residual life under two-, three-, and four-stage loads to investigate the effects of different loading sequence on fatigue damage under various loading conditions. Combining with experimental data, it is verified that the cumulative damage model can accurately estimate the fatigue life under two-, three-, and four-stage loads. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to introduce error ellipse into the bootstrap method to improve the reliability of small samples and the credibility of the S-N curve. Design/methodology/approach: Based on the bootstrap method and the reliability of the original samples, two error ellipse models are proposed. The error ellipse model reasonably predicts that the discrete law of expanded virtual samples obeys two-dimensional normal distribution. Findings: By comparing parameters obtained by the bootstrap method, improved bootstrap method (normal distribution) and error ellipse methods, it is found that the error ellipse method achieves the expansion of sampling range and shortens the confidence interval, which improves the accuracy of the estimation of parameters with small samples. Through case analysis, it is proved that the tangent error ellipse method is feasible, and the series of S-N curves is reasonable by the tangent error ellipse method. Originality/value: The error ellipse methods can lay a technical foundation for life prediction of products and have a progressive significance for the quality evaluation of products. [ABSTRACT FROM AUTHOR]

To accurately predict the degraded fatigue life of components under random loads, anelasticity effect of metal on life estimation needs to be explored. Weighting coefficient and dynamic elastic modulus are introduced to modify the calculation process of the model. By establishing an equal‐amplitude fatigue median surface and applying Miner linear fatigue cumulative damage theory, a fatigue life prediction model of the component under random loads is proposed. The model can be used to calculate the degraded fatigue life of components, which provides a theoretical basis for life estimation under random load spectrum. The two‐dimensional load spectrum is compared with the unprocessed two‐dimensional load spectrum and the one‐dimensional program spectrum in life prediction results. With the comparison of the target life and simulation life and the data calculated by the model of the automobile front stabilizer bar, it is concluded that the data obtained by the modified model are more reasonable and accurate. [ABSTRACT FROM AUTHOR]

In fatigue test, the fatigue life of metal components is affected by many factors, such as test temperature, stress ratio and loading frequency. In order to study the influence of temperature on fatigue life of bolted joints, thermal stress and fast coefficient are introduced. A numerical method of fatigue crack initiation life is proposed based on Manson-Coffin strain fatigue formula. The crack initiation life of 2024 aluminum alloy at different temperatures can be obtained by this method, which provides a theoretical basis for the fatigue life prediction of metals. Then, the stress severity factor SSF is introduced to calculate fatigue life of plane bolted joints. The data obtained from the model show that the crack initiation life of aluminum alloy specimen decreases significantly with test temperature rises, the same as the fatigue life of bolted joints. [ABSTRACT FROM AUTHOR]

In the field of fatigue crack, crack size is a worthy topic to discuss. The relationship between crack length and depth is studied based on the Paris law, and a numerical model is established. The validity of the model is proved by comparing theoretical data with experimental data. In addition, the analysis of stress distribution of liquid-storage tank is carried out and the influence of hoop stress on the liquid-storage tank is considered. Remaining life of the tank is predicted through the numerical model. The feasibility of the numerical method is verified by predicting the remaining life of the tank, which provides a simple way for fatigue life prediction of the liquid-storage tank. [ABSTRACT FROM AUTHOR]

Fatigue life prediction is an important part of the reliability and durability analysis of automobile components. Based on Wang and Brown's framework, multiaxial random fatigue damage was adopted to predict the fatigue life of half-shaft. The stress analysis of half-shaft was resolved analytically to determine the local stress tensor in the potential area of fracture. The maximum shear strain fatigue damage parameter and the normal stress fatigue damage parameter were evaluated to predict the fatigue life of half-shaft. The results show that the prediction method is reliable and meets the service life and safety requirements. [ABSTRACT FROM AUTHOR]

To eliminate the limitations of the peak‐over‐threshold (POT) extrapolation method, the paper proposes an improved POT extrapolation method to reconstruct the load sequence and frequency of the part. A threshold model is established based on a generalized Pareto distribution (GPD). Assuming a road surface's irregularity obeys a normal distribution, the load between the upper and lower thresholds is reconstructed to obtain more dynamic road load data. Rain‐flow counting method is used to calculate the peak‐to‐valley value and frequency of the load signal, and the characteristics of the load mean and amplitude before and after the improvement of the POT extrapolation method were discussed. The effectiveness and conservativeness of the enhanced method are verified by predicting the fatigue life of a swing support rod. [ABSTRACT FROM AUTHOR]

To predict the service life of clutch sleeve, major reasons for the change of clearance between the clutch sleeve and shell in service period are analysed. A mathematical model of the clearance is established considering abrasion of the step outside sleeve caused by friction. To determine the size of abrasion, a micro‐convex body model for the friction surface is built. Based on surface fatigue abrasion theory, an abrasion model is established. A life model is established based on the entire abrasion of the sleeve. Fatigue life of sleeve is predicted using the model based on actual surface morphology parameters of the enterprise products. Major factors affecting the abrasion speed are discussed and determined after the prediction result is analysed. [ABSTRACT FROM AUTHOR]

In actual engineering, the actual road test or indoor bench test is usually used to collect the data of the road load of the parts to acquire the fatigue life estimation of the auto parts. This paper proposes a method for load spectrum construction based on the mixed distribution probability model using the data of the road load spectrum collected in the test site. Pau Ta criteria outlier elimination and wavelet signal denoising are applied to analyze the original road load spectrum data. Then the maximum likelihood estimation method is used to estimate the generalized Pareto distribution parameters of all excesses. The Pareto distribution is also employed to extrapolate the load spectrum. Through the characteristic analysis of the load spectrum, the one-dimensional and two-dimensional program load spectrum of the hub is established based on the mixed probability distribution model, which provides a theoretical basis for the life prediction of the hub. In addition, the research results of this paper provide inspirations for the fatigue life prediction and fatigue durability bench test of automotive parts subjected to the complexity and variability of random loads. [ABSTRACT FROM AUTHOR]

• Calculation method of crack initiation size is improved by basic model of fatigue crack initiation size. • The elastic–plastic fracture mechanics (EPFM) method is used to study the short crack fatigue life. • The calculation model of fatigue crack initiation size is established by symmetric cyclic torsional alternating stress. • The feasibility of EPFM method is verified by comparing with the crack initiation size. To solve the fatigue crack initiation problem, it is necessary to calculate the fatigue crack initiation size. According to the aspect of macroscopic crack development, the calculation method of crack initiation size is determined by the critical dimension of fatigue crack initiation. Simultaneously, the elastic–plastic fracture mechanics (EPFM) method is used to study short crack fatigue life by considering the cumulative damage rule of crack initiation life, and the calculation model of fatigue crack initiation size caused by symmetric cyclic torsional alternating stress is established under low strain. The crack initiation dimension of component is estimated, which lays a foundation for the study of fatigue life. Then the feasibility of this method is verified by comparing with the crack initiation size, which is determined by predicting the non-propagating crack size (NPCS). [ABSTRACT FROM AUTHOR]

The bootstrap method is mostly used to estimate statistical characteristics of small sample data. However, the limitations of the bootstrap method itself lead to a reduction in the reliability of small-sample estimates. In this article, an improved bootstrap method is developed to address this problem. In the statistically significant error range (the sample average error and the limit error of sampling) of the original single sample data, expanding the virtual test data that obey two distributions to overcome the limitations of the bootstrap method itself. This article compares and analyses these two methods through the case; the result indicates that the improved bootstrap method can enhance the reliability of the estimation results without changing its probability distribution. We also discussed how to reduce the fluctuation of the improved bootstrap method. And the effectiveness and feasibility of this improved method are discussed in the analysis of fatigue life test data. [ABSTRACT FROM AUTHOR]

The study discusses how some challenges from a small sample fatigue test can be analysed statistically and resolved. In terms of data dispersion, fatigue data are initially processed by confidence, and then, the fatigue life curve is replaced by the parabolic reliability approximation. Fatigue data under various reliability levels are obtained. Instead of the traditional single S-N curve, the mean value curve and mean square deviation curve of the S-N curve are computed based on the processed fatigue data. The S-N curve with reliability is deduced by applying quantile theory. The S-N curve is improved by considering the effects of low-amplitude load strengthening. The benefits of the modification are visible in the comparison of the fatigue life before and after low-amplitude load strengthening. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

• The functional relationship between fatigue fracture entropy and loading amplitude is clarified. • Analyzing the normalized fatigue cumulative entropy and cycle correlation properties. • The entropy generation rate is proportional to the loading amplitude. • The cumulative entropy is inversely proportional to the loading amplitude. To determine the relationship between thermodynamic entropy generation rate and cumulative entropy and fatigue performance of metal components during fatigue. The surface temperatures of the specimens under different loading amplitudes and frequencies were recorded by infrared thermography. The effect of internal friction is not considered. Then the entropy generation rate and cumulative entropy are calculated, and the relationship between fatigue life and entropy is constructed. The calculation results show that under the same loading frequency, the entropy generation rate is proportional to the loading amplitude, the fatigue cycle is relatively low, and the cumulative entropy is inversely proportional to the loading amplitude. The cumulative entropy is only related to the loading amplitude, but not the loading frequency. A fatigue life prediction model based on the thermodynamic entropy of metals is established, which can be used for the real-time assessment of fatigue damage of metal components. [ABSTRACT FROM AUTHOR]

• EIFS is improved for corrosion fatigue life prediction. • Corrosion fatigue life prediction model is developed via I-EIFS. • Corrosion fatigue life of COST is predicted with proposed model. • The validity of life prediction method for COST is verified by comparing service life. Corrosion fatigue is identified as the main failure mechanism for structures working in severe corrosive medium subjected to cyclic rotating bending fatigue, for example crude oil storage tank (COST). Emphasis is placed on the study of corrosion pit formation and the development of cracks from pits. An improved equivalent initial flaw size (I-EIFS) is proposed for corrosion fatigue life prediction. Based on the concept of equivalent initial flaw size (EIFS), pitting corrosion and small crack growth are equivalent to a part of long crack growth process in corrosion fatigue process. Pitting and crack propagation are quantified throughout the fatigue loading thereby allowing a model to be developed that included the stages of pit development, pit-to-crack transition and crack growth in order to predict the fatigue life. A corrosion fatigue life prediction case is adopted to demonstrate the effectiveness of the proposed model. Based on the proposed model, failure analysis and stress calculation are performed to predict the corrosion fatigue life of COST, which provides a method for the life prediction of COST. The validity of proposed method is verified by comparing the service life of COST. [ABSTRACT FROM AUTHOR]

• Developed a life estimation model for metal fatigue that considers multiple influencing factors. • Based on the mean and amplitude distribution characteristics of the extrapolated load signal, a two-dimensional joint probability distribution is established using a mixed distribution model. • An eight-level, two-dimensional stress spectrum and life spectrum have been developed for the engine support. The impact of random loading on the fatigue life of mechanical components contains numerous uncertainties. This study aims to enhance the precision of life prediction by developing mean and amplitude distribution models based on the road load spectrum and extrapolating the operational load beyond the threshold value in the time domain. Additionally, it considers the influence of high cycle fatigue (HCF) and low cycle fatigue (LCF) loads on the initiation life of metal cracks. To address this, a load correction factor is introduced, and critical stresses for high and low cycle loads are proposed. Furthermore, a two-dimensional programmed load spectrum is prepared, taking into account the mean and amplitude. The accuracy and rationality of the fatigue life model are validated through examples using 45# steel and 316L, while experiments on engine support are conducted to confirm the effectiveness and accuracy of the over-threshold extrapolation life prediction method under random loading. [ABSTRACT FROM AUTHOR]

• A novel probabilistic notch fatigue analysis model is constructed. • Weibull distribution is integrated into TCD to construct the probabilistic model. • HSV method with SCF is introduced to characterize the size effect. • The fatigue test of ATG is performed and the P S N curves are estimated. Notch fatigue is regarded as a major issue of damaging the structural integrity for notched components in engineering. Based on the theory of critical distance (TCD), this study proposes a novel probabilistic fatigue analysis model to quantify the influence of notch size effect on fatigue life. Specifically, Weibull distribution is integrated into TCD for probabilistic modelling, and the impact of size effect on critical distance is characterized with highly stressed volume (HSV) method and stress concentration factor (SCF). The effectiveness and superiority of the proposed model with point method (PM) and line method (LM) are verified and compared by the experimental data of En3B, TC4 and Al-7075-T6 materials respectively. Moreover, the fatigue test of notched automobile transmission gear (ATG) is conducted, and the corresponding P S N curves are estimated with the proposed model. The test data are basically scattered in the predicted P S N curves, and the results under 50% survive probability are better than the traditional TCD, which indicates the availability of predicted P S N curves and the accuracy of the proposed model. [ABSTRACT FROM AUTHOR]

• The peak over threshold extrapolation method is improved by reconstructing load sequence. • The mean samples are fitted by mixed distribution model of normal distribution. • The low load strengthening is introduced into the compilation of load spectrum. • The effect of low load strengthening on fatigue life is discussed. To improve the shortcomings of peak over threshold (POT) extrapolation method and reflect the diversity and dynamics of road conditions, an improved POT extrapolation method to reconstruct the load sequence in the middle of threshold is proposed. Based on the improved extrapolated load, the distribution characteristics of mean and amplitude are analyzed and the two-dimensional joint probability distribution is established. To discuss the influence of low load strengthening characteristics on fatigue life under random load, based on the two-dimensional joint probability distribution, the theory of low load strengthening is introduced in compiling load spectrum. The fatigue life predicted by 8-level load spectrum and 10-level strengthened load spectrum are compared with the test results, respectively. Which verifies the effectiveness and accuracy of life prediction based on improved POT extrapolation and low load strengthening under random load. [ABSTRACT FROM AUTHOR]

• A method to evaluate the reliability of air spring is proposed. • The assess of reliability take the road spectrum into consideration. • Failure analyses were performed based on reliability analyses. • The failure result of air spring unit is compared with actual failure condition. The air spring bears complex multi-dimensional random load in the running of the vehicle, and its excellent performance plays a very important role in ensuring the safety and stability of the running of the rail vehicle and improving the comfort of the ride. Taking a certain type of air spring system capsule of Shanghai Metro as the research object, a composite rubber material failure and reliability analysis method based on the virtual joint simulation experimental platform of dynamics software, finite element simulation software and fatigue calculation software is proposed, considering the influence of the train load on track irregularity. The fatigue life assessment and internal damage mechanism analysis of the air spring system are realized by this virtual simulation technology, and reduce the dependence on the actual material test. The effectiveness of the proposed method is verified by comparing it with the actual failure of air springs. This method has an important reference value for the fatigue characteristics study of complex rubber parts with multi-physical field coupling characteristics. It can help urban rail vehicle maintenance units to more accurately understand the remaining service life of air springs, thus reducing safety hazards economic waste and other issues. [ABSTRACT FROM AUTHOR]