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The present study evaluates and investigates the fatigue design and fatigue life as the crack propagation occurs around the fastener of the mainframe of the central fuselage (CTR) of a rotary-wing aircraft designed based on the conventional safe-life method. For this work, the static and dynamic strain data were acquired according to flight conditions and fastening conditions between the mainframe and rail fitting (bracket). Furthermore, the fatigue life of the mainframe of rotary-wing aircraft was overestimated because of the conventional stress equation, for generating the stress spectrum according to the maneuvering conditions. To improve the existing stress equation, the modified stress equation was proposed by taking into account all force components transferred from the operating rotor system. Based on this equation, by employing the modified Goodman equation and Miner’s rule, the fatigue life of the mainframe of the CTR fuselage is calculated by the S–N diagram. Thereafter, the predicted fatigue life by considering simultaneously the damage of low-cycle fatigue and high-cycle fatigue according to the various flight conditions were compared with the actual life of crack occurrence. As a result, it showed that the predicted fatigue life (655 FHrs) was in a good agreement with the actual life (656.7 FHrs) of crack occurrence using the modified stress equation, respectively.

Temperature probes of different designs were widely used in aero gas turbine engines for measurement of air and gas temperatures at various locations starting from inlet of fan to exhaust gas from the nozzle. Exhaust Gas Temperature (EGT) downstream of low pressure turbine is one of the key parameters in performance evaluation and digital engine control. The paper presents a holistic approach towards life assessment of a high temperature probe housing thermocouple sensors designed to measure EGT in an aero gas turbine engine. Stress and vibration analysis were carried out from mechanical integrity point of view and the same was evaluated in rig and on the engine. Application of 500 g load concept to clear the probe design was evolved. The design showed strength margin of more than 20% in terms of stress and vibratory loads. Coffin Manson criteria, Larsen Miller Parameter (LMP) were used to assess the Low Cycle Fatigue (LCF) and creep life while Goodman criteria was used to assess High Cycle Fatigue (HCF) margin. LCF and HCF are fatigue related damage from high frequency vibrations of engine components and from ground-air-ground engine cycles (zero-max-zero) respectively and both are of critical importance for ensuring structural integrity of engine components. The life estimation showed LCF life of more than 4000 mission reference cycles, infinite HCF life and well above 2000 h of creep life. This work had become an integral part of the health monitoring, performance evaluation as well as control system of the aero gas turbine engine.

The use of externally bonded fibre-reinforced polymer (FRP) increases the fatigue life of reinforced-concrete beams due to a reduction in the steel stress level when compared with unstrengthened beams. For steel stresses up to 80% of the yield stress, fatigue failure is normally marked by the gradual deterioration of the steel reinforcement, which leads to a stress transfer to the FRP, until failure. Higher steel stresses are associated with FRP debonding, while steel stresses below the fatigue limit will never lead to fatigue failure. In this work, the maximum likelihood estimation method was used to determine stress–cycle curves and confidence intervals. Experimental data with runouts of fatigue tests found in the literature and generated through an experimental programme were used to adjust the fatigue model. The aim was to characterise the large scatter between the results of fatigue tests from different sources. The proposed fatigue model was found to represent accurately the slope of the fatigue curve for FRP-strengthened beams.

As a critical component of railway fastening system, the elastic rail clip (e-clip) maintains the rail position using its specified toe load. To understand its fatigue failure during service, the fatigue experiment, finite element analysis (FEA) and failure analysis were performed on e-clip. Under normal wheel load, e-clips with high, normal, and low toe loads were run-out at 5 × 106 cycles. Under the contribution of impact on wheel load, the fatigue lives were reduced to 5468 cycles and 16,839 cycles for e-clips with high and normal toe loads, respectively. For low toe load, the e-clip under the contribution of impact could withstand >5 × 106 cycles. The stress distribution on e-clip was numerically evaluated using FEA, which was in good agreement with that of experiment. Goodman diagram could be used for the fatigue evaluation of e-clip. The mean stresses and stress amplitudes of run-out e-clips were under the line of Goodman equation, while those of failed e-clips were on and above the line of Goodman equation. The fatigue crack was found to nucleate at the location of highest stress. The severity at fatigue crack front increased with the crack length until the overload fracture.

Welding residual stresses have an impact on the performance of welded structures, on their fracture resistance, their resistance against fatigue crack propagation and, most important, their fatigue strength and fatigue lifetime. The present paper provides an overview on the issue mainly from the point of view of the application of fracture mechanics to the determination of the fatigue strength as the topic of this Special issue. Besides own experimental and theoretical data a comprehensive discussion is provided in that context which includes the definition and interaction of short- and long-range (or reaction) residual stresses, the effect of cyclic mechanical loading and its treatment in fracture and fatigue analyses.

A fatigue damage micro-model is developed for two-phase composite materials. Constitutive law is derived at the level of fibre and matrix and extended for a damaged lamina using the reformulation of Mori-Tanaka model. A new non-dimensional effective local stress based on a failure criterion which is rewritten in term of average stress of fibre and matrix is coupled with a fatigue damage model for prediction of fatigue damage and fatigue life. The proposed model is able to distinguish between damage in fibre and matrix and also stiffness reduction of the matrix and transverse direction during fatigue loading using three different damage variables. The fatigue behaviour of unidirectional carbon/epoxy and glass/epoxy laminates are studied under off-axis loading conditions. Fatigue life of unidirectional composites is predicted at different stress levels, stress ratios and fibre orientations under tension-tension and tension-compression fatigue. The obtained numerical results from the proposed model are in good agreement with the experimental data.

Mean stress effects in pressurized steel blocks were examined under constant amplitude fatigue loading. The tests were performed to provide experimental data needed to study the effect of mean stress on fatigue lives of subject specimen, and to substantiate the use of analytical expressions to account for the mean stress. The mean stress was the result of subjecting the specimens to an autofrettage pressure which induced compressive residual stresses at the crossbore intersection of the specimens. Fatigue tests were carried out under both tensile and compressive mean stress levels. Test results were compared to several mean stress accounting relationships such as the Smith-Watson Topper, Bergmann and Seeger, modified Goodman, Gerber and Soderberg. Test results indicated that the modified Goodman equation is favorable in accounting for the effect of both tensile and compressive mean stresses on fatigue life (up to a compressive mean stress to ultimate stress ratio of −0.2). The behavior under compressive mean stress to ultimate stress ratio of less than −0.2 indicated that a linear correction relationship was required.

The analytical solution of the fatigue crack forming life based on the nonlinear cumulative damage model was deduced by using the simply supported beam with mid-span loads as the study model. Then the fatigue whole life model by the Paris formula with the crack length factor was established. Flexural-tensile strength test and fatigue test were made by using the trabecular specimen at different temperatures. By the contrast of the asphalt mixture fatigue life at different temperatures and stress ratios, it was found that as increasing of temperature, the fatigue life of the trabecular specimen will reduce. When it is at the same temperature, the fatigue life will reduce as the stress ratio increasing. The fatigue developing life of the asphalt pavement will occupy a higher ratio of the whole fatigue life when the temperature is higher. The fatigue developing life is shorter when the temperature is lower. The values of the fatigue damage parameter a∗ and p were obtained by the regression of the test data. The expressions of the functional relation between a∗ and p with temperature T were deduced. The change law between the crack developing speed and the stress intensity factor amplitude was studied to determine the parameters A and n in the formula Paris under different stress ratio. The established model in this paper was verified effectively by contrast of the calculation values of the fatigue whole life model and the test values.

Fatigue damage has special relevance on the life span of mechanical components and structures, as it takes responsibility for a large majority of the registered structural failures in service. The continuous need for the weight reduction and improved design optimization of components and a growing need for greater lifespans of equipment, forced the understanding of the fatigue behavior of materials either under multiaxial loading cycles or under increased number of loading cycles. Fatigue tests were always performed under uniaxial fatigue loads. However, it is generally recognized that multiaxial stresses occur in many full-scale structures, being rare the occurrence of pure uniaxial stress states. In the following, a wide range of multiaxial fatigue failure criteria have been developed that may be applied to different metallic materials. These failure criteria may be classified as strain based for high strain loading conditions or stress based for higher lifespans in the elastic loading regime. These criteria are nowadays used in design optimization also contributing to the weight reduction and improved lifespans of modern equipment. Present manuscript is a review of the main specimens and equipment where research can be carried out for performing multiaxial fatigue tests under bi-axial stress states. Being a personal view, it will be based on the author experience on the performance of multiaxial fatigue tests under axial/torsion loading using mechanical actuated or servo-hydraulic fatigue testing machines or biaxial fatigue tests using electromagnetic actuators in cruciform specimens. Further research is needed and is being carried out concerning multiaxial very high cycle fatigue in order to achieve better improvements in weight reduction of components and structures and also in complex variable amplitude loading with adequate damage accumulation models.

Low density foam core sandwich composites are recerving increasing attention and application in marine engineering. In order to solve the damage failure problem of sandwich L-joints for ship structures, the ultimate strength and fatigue properties of full scale L-joints were researched by experimental method. On the basis of the research on the static strength, the fatigue life and failure mode of this kind of connection were analyzed in different load amplitudes by a series of fatigue tests. The generation and development of cracks in the whole process were revealed and S-N curves were also drawn. The results show that fatigue life and stiffness of sandwich L-joints are decreased with the increase of load levels, and the major failure modes are in the form of sandwich debonding, sandwich face/core delamination, and gelcoat damage. Finally, a fatigue life model has been developed with stress level r and crack length a i and validated with test results.

A new proposal of generalization of the fatigue Kohout-Věchet (KV) model for different fatigue damage parameters is proposed. The purpose of this generalized model is to describe all fatigue regimes from very low-cycle fatigue (VLCF) to very high-cycle fatigue (VHCF), and accounting for several fatigue damage parameters, such as, strain parameter, Smith-Watson-Topper (SWT) parameter, Walker-like strain parameter, energy-based parameter in uniaxial loading conditions, among others. The full range of fatigue life responses for all loading regimes of materials and structural components are extremely important in the fatigue design. Engineering structures are subjected to different types of loading that cause fatigue failure. These loadings can range from quasi-static monotonic loading to long term dynamic/cyclic loading. In this paper, a proposal of generalization of the KV model for several fatigue damage parameters was verified and compared with experimental fatigue results under uniaxial loading conditions available in literature. This study validates the importance and applicability of full range fatigue life models for different damage parameters in fatigue life prediction of materials and structural components.

In this paper, the fatigue lives of U-notched polymethyl methacrylate (PMMA) plate at different temperatures are numerically investigated on the basis of local stress approach. First, a local stress approach for fatigue damage at the U-notch is presented based on the principle of equivalent damage life. Second, the strength and stiffness degeneration criterions during the fatigue process are established to take account of the nonlinear cumulative fatigue damage. Finally, the commercial software ABAQUS is employed to predict the fatigue S-N curves of the U-notched PMMA plate at various constant temperatures of −55 °C, 23 °C and 60 °C using a user-defined material (UMAT) subroutine. The numerical results of the fatigue life are in good agreements with the experimental data, which verify the effectiveness of the local stress approach.

Fibre-reinforced composites experience a degradation of stiffness and strength during fatigue life. Understanding the reduction of these properties is fundamental to establish a reliable fatigue life prediction methodology. This work investigates the loss of stiffness and strength in advanced unidirectional carbon/epoxy laminates under on-axis tension-tension loads. A phenomenological stiffness-based fatigue model is formulated within the framework of continuum damage mechanics, where damage is described by the reduction of the in-plane longitudinal stiffness. The particularity of the model is to assume that the ultimate strain remains constant after fatigue damage. Thus, the residual strength model and the S-N curves are deduced from the residual stiffness model. This assumption reduces the experimental characterization of phenomenological-based approaches. The experimental challenges found in the fatigue experiments are also discussed. The accuracy of the model is verified by comparing the experimental data with the derived S-N curves.

Cyclic deformation and fatigue behavior of two short fiber thermoplastic composites (SFTCs) under a number of loading and environmental conditions are investigated. The considered environmental effects include those of low and elevated temperatures as well as moisture (or water absorption). Fatigue behavior is also explored under the action of non-zero mean stress (or R ratio) in addition to fully-reversed ( R = −1), as well as various cyclic loading frequencies. Material anisotropy and geometrical discontinuity effects (i.e. stress concentration) are other aspects considered in this study. Mechanisms of fatigue failure are also assessed under environmental effects. Based on experimental observations and analysis, a number of analytical and empirical models are developed for estimating fatigue behavior under different conditions. Empirical equations are presented to characterize self-heating under cyclic loading. Tsai-Hill criterion is applied to account for the effect of fiber orientation on fatigue life. Mean stress effect is corrected with several mean stress parameters and a shift factor of Arrhenius type is defined to characterize the effect of temperature on fatigue life. Two methodologies are presented to estimate fatigue properties based on tensile properties, in addition to approximation of strain-life curves based on load-controlled fatigue data. Estimation of notched fatigue behavior based on smooth (un-notched) fatigue behavior is also presented.

This article presents selected aspects connected to the methods of identification of strain energy density that are used to calculate the fatigue strength of materials. The authors focus on selected methods for determination of energy-based (stress-strain) characteristics of the fatigue life of materials (Wa − Nf), including a new approach for the determination of strain energy density parameter Wa. The paper also contains description and evaluation of models for determining the stress amplitudes σa in the elastic-plastic range, for bending. The developed procedure should give new capabilities in fatigue life calculations.

The application of multiaxial high-cycle fatigue criteria to the analysis of the subsurface rolling contact fatigue of structures working in contact conditions is discussed. In such objects, an increase in compressive and shear stresses is strongly non-proportional. Therefore, the first part of the paper is devoted to the comparison of the results of six recently used high-cycle fatigue criteria estimating the effort for both different multiaxial proportional and non-proportional loads. In the second part of the paper, the issue of frictionless and tractive rolling contact fatigue is discussed. The fatigue load capacity of a crane wheel has been estimated using recently popular criteria. The orientation of critical planes and location of dangerous points are determined and discussed in detail. It has been found that the Dang Van criterion, which is often proposed in rolling contact fatigue analysis, underestimates the equivalent fatigue stress for such type of loads. Comparison of the results obtained using different multiaxial criteria with the results of the experimental tests enables a selection of criteria suitable for fatigue assessment of machine parts working in cycling rolling contact conditions.

In order to analyze the stress and strain fields in the fibers and the matrix in composite materials, a fiber-scale unit cell model is established and the corresponding periodical boundary conditions are introduced. Assuming matrix cracking as the failure mode of composite materials, an energy-based fatigue damage parameter and a multiaxial fatigue life prediction method are established. This method only needs the material properties of the fibers and the matrix to be known. After the relationship between the fatigue damage parameter and the fatigue life under any arbitrary test condition is established, the multiaxial fatigue life under any other load condition can be predicted. The proposed method has been verified using two different kinds of load forms. One is unidirectional laminates subjected to cyclic off-axis loading, and the other is filament wound composites subjected to cyclic tension-torsion loading. The fatigue lives predicted using the proposed model are in good agreements with the experimental results for both kinds of load forms.

This paper studies the deformation evolution of concrete under high-cycle fatigue loads. First, uniaxial and eccentric compressive fatigue loads were exerted on prism concrete specimens to observe the mechanical properties of concrete under fatigue loading. Fatigue tests showed that elastic modulus does not always decrease, but strains always increase as loading cycles accumulate. Moreover, strains on the cross-section of each eccentrically fatigued specimen always maintain linear distributions. Based on these experimental findings, a simplified constitutive model for concrete under high-cycle fatigue loads was adopted; hence, a fatigue deformation prediction model was developed to analyze the strain and stress distributions on a cross-section under both cyclic axial forces and bending moments. The proposed model demonstrated its validity by predicting fatigue deformations in good agreement with experimental results. Finally, based on the new prediction model, a case study was conducted, which found that fatigue could pose a big influence on the long-term deformation of concrete bridges.

This paper investigates cyclic deformation, fatigue behavior, and failure mechanisms for Ti-6Al-4V ELI (extra low interstitial) with and without mean strain/stress. This type of titanium alloy is broadly used in the biomedical and aerospace fields, specifically for implants and structural components, respectively. Fatigue properties were obtained using the strain-life approach with the use of smooth uniform gage section specimens under axial fully-reversed loading. The influence of mean stress on fatigue behavior was studied using four different strain ratios, Re. The generated fatigue data was used to assess some strain-based mean stress fatigue life prediction models, including Morrow, Smith-Watson-Topper, Walker, Kwofie, Ince-Glinka and a modified version of the Smith-Watson-Topper. These models offered acceptable results, specifically the Morrow approach which provided more accurate fatigue life predictions. Fractography analysis was conducted to determine the influence of material defects on fatigue life and no major differences were found for the different strain ratios considered. Overall observations indicate that inclusions found near the surface were of great influence on the fatigue behavior.

Many researches have shown that fatigue behaviour of a number of materials is significantly different in non-proportional loading conditions when compared to proportional ones. These differences concern stress–strain characteristics, fracture, the phenomena taking place in the material, and finally fatigue life. The aim of this study is to provide a survey on basic experimental results and methods of taking into account a material's sensitivity to non-proportionality of loading in multiaxial fatigue life estimation models for metals.

The development of models relating the fatigue strength of materials to their static strength and plasticity is considered. Statistical strength theories were developed to describe the results of fatigue tests and to predict the strength of machine components with variable loads. Experiments show that the strength of materials depends significantly on structural defects, and the limiting stress is a statistical quantity.

Conventionally, the effects of mean stress on fatigue strength of welded structure are regarded to be small. However, based on fatigue damage experience occurring in ship structures, it is obvious that the effect of mean stress on fatigue strength should be large. This relates to the large change of mean stress condition associated with the change in loading conditions during ship operations. In this study, fatigue damage experienced in the end connections of side longitudinal stiffeners of single-hull very large crude oil carriers (SHVLCC) were investigated to understand the effects of mean stress on fatigue strength. The fatigue evaluation method which considers the effect of mean stress was also examined. This method was verified by the evaluation of existing data on fatigue tests and residual stress measurements. This method was confirmed to be effective in understanding the occurrence tendency of fatigue damage in ship structures by its evaluation. This method was applied to the example of actual fatigue damage in the end connections of side longitudinal stiffeners of midsize double-hull tanker to demonstrate the effectiveness of the method.

This work presents a methodology for fretting fatigue life estimation based on the evaluation of a multiaxial fatigue parameter at a critical distance below the contact surface. The fatigue parameter is defined using the Modified Wohler Curve Method together with a measure of shear stress amplitude based on the Maximum Rectangular Hull concept. To apply the approach in the medium-cycle fatigue regime, the critical distance is assumed to depend on the fatigue life. Available fretting fatigue experiments conducted on a cylinder-on-flat contact configuration made of Al–4%Cu alloy were used to evaluate the methodology. Most of the fatigue life estimates were within factor-of-two boundaries.

The fatigue performance of a roof-U rib weld on orthotropic steel bridge decks was studied by fatigue experiments on 40 specimens, considering the influences of amplitude, penetration rate, loading position, and steel strength. Influences of different factors on the fatigue life of crack initiation and specimen failure were studied by analysis of crack propagation in the weld and changes in stress amplitude. In addition, nominal stress amplitudes and hot spot stress amplitudes of the welds were compared and the suggested values of fatigue strength were proposed according to the test results. The study shows that increase of penetration rate can decrease the crack propagation rate and extend failure fatigue life. A larger steel strength can increase the fatigue strength of crack initiation. Under the same loading conditions, the fatigue life of crack initiation is about half of the failure fatigue strength. A nominal stress of 70 MPa and a hot spot stress of 75 MPa are recommended for fatigue strength of roof-U rib welds under the manufacturing process investigated here.

Due to the difficulties of direct tensile testing on concrete, only limited and often conflicting data are available. In this paper, to investigate the effect of loading frequency on the low cycle fatigue behavior of plain concrete in direct tension, several series of cyclic tension tests at different frequencies and stress levels were carried out. Especially the behavior before the initiation of macroscopic fatigue cracks in concrete, such as irreversible strain accumulation and damage evolution with the number of fatigue cycles through experiments. Test results show that the fatigue life increases with the increasing of the applied loading frequency, while decreases with the increasing of stress level. The stiffness degradation shows a typical three-stage process with the number of fatigue cycles. A new damage model considering the effect of the applied loading frequency and stress level is proposed based on the stiffness degradation and the secondary strain rate during low-cycle fatigue tests. Also, a fatigue model is proposed herein to characterize the deformation and damage behavior of concrete under cyclic tension. The calculated fatigue lives of concrete are compared with experimental data and show good fitting results.

The recent development in the eco-friendly energy industry has motivated many researchers to focus on wind turbines. The advancement of wind turbine technology is in accordance with the trends in the last century. Pitch systems, which comprise wind turbines, have a high failure rate. However, the fatigue life of pitch systems has not been sufficiently studied. A pitch system, which greatly affects the power generation efficiency of a wind turbine, consists of a motor, a gearbox, and a pinion. In this work, a fatigue life analysis of a pinion is performed to improve the durability of pitch systems. Frequent changes in rotation are unique to a pitch system in operation. When an impact load exists at an inverse turn, the stress generated from the impact load is the dominant factor to consider in evaluating the fatigue life of a pinion. The stress history at the gear tooth is determined through a finite element simulation. The cumulative damage fraction is calculated via rainflow cycle counting on the basis of the Goodman relation and Miner’s rule. Therefore, we propose a method for evaluating the fatigue life of a pinion, which considers the effect of an impact load. A conservative design of pitch systems is needed to ensure the reliability of wind turbines under an impact load.

The paper presents a synthesis of experimental fatigue tests and theoretical studies of laser stake-welded T-joints in steel sandwich panels. The experiments indicate that the slope of the fatigue strength curves varies significantly depending on the type of loading the joint experiences, but also on the geometry. Therefore, the focus is on the influence of crack tip plasticity when the joints are loaded under tension and bending. This is investigated by two different approaches based on square root of J-integral. With this parameter, the experimental fatigue curves meet at the fatigue limit for all of the loading modes and geometries. To investigate the change in slope in the medium-high cycle fatigue range, the suitability of stress gradient and plastic zone size as defined by Irwin are studied. It is shown that the gradient of principal stress correlates well with the variation of slope, but it does not give a practical tool for fatigue assessment of the joints. Instead, based on the plastic zone approach, a new method is proposed that permits the estimation of number of cycles to failure under bending directly from the tension fatigue curve. The method is verified with experiments.

Fatigue tests were performed on plain concrete under triaxial tension-compression-compression (T-C-C) cyclic loading with constant and variable amplitude using a large multiaxial machine. Experimental results show that, under constant amplitude fatigue loads, the development of residual strain in the fatigue loading direction depends mostly on the lateral compressive stress ratio and is nearly independent of stress level. Under variable amplitude fatigue loads, the fatigue residual strain is related to the relative fatigue cycle and lateral compressive stress ratio but has little relationship with the loading process. To model this system, the relative residual strain was defined as the damage variant. Damage evolutions for plain concrete were established. In addition, fatigue damage analysis and predictions of fatigue remaining life were conducted. This work provides a reference for multistage fatigue testing and fatigue damage evaluation of plain concrete under multiaxial loads.

The paper represents the behavior of wheel hub subjected to different loads for different materials. It gives an insight to various options that can be used for wheel hubs and compare the different materials with each other. The wheel hub presently of cast iron is compared with three different materials viz. Al alloy, SS, Mg alloy. The effect of bump force, braking torque and cornering force are considered in the analysis. The output stress for all the four materials are then utilized to calculate the fatigue life of wheel hub using the Goodman equation. After obtaining the endurance stress for each material hub, the life of wheel are calculated from SN curves for respective materials. The aim is to find a better material than cast iron which will have better life, better strength, less weight which will increase the entire vehicle efficiency and remove the failure of wheel hub occurring at the bolting locations due to crack initiation. A cyclic testing for wheel hub is conducted for 5000 cycles which ensures no failure of wheel hub of new fabricated material.

High-energy shot peening (HESP) was employed to obtain a nanocrystalline surface layer in Ti–6Al–4V alloy with bimodal and lamellar structure. The microstructure and residual stress after HESP treatment were characterized by transmission electron microscope (TEM) and X-ray diffractometer (XRD), respectively. The fracture morphology of fatigue was analyzed by scanning electron microscope (SEM). The results showed that the average grain sizes of Ti–6Al–4V alloy with bimodal and lamellar structure were 18.9 nm and 17.1 nm at the topmost surface layer, respectively. The maximum compressive residual stress of the bimodal structure was −906MPa, which was higher than that of the lamellar structure (−859 MPa). The fatigue limits of the HESP-treated Ti–6Al–4V alloy with the bimodal and lamellar structure were increased by 13.5% and 32.8%, respectively. Finally, a Goodman equation was employed to calculate the local fatigue strength and analyze the residual stress-fatigue strength correlation. Highly defected substructure, reduced effective slip length and improved yield strength were important factors for the improvement of fatigue strength. The synergy effect of surface gradient nanostructure and compressive residual stress improved the fatigue limit of the HESP-treated Ti–6Al–4V alloy with bimodal and lamellar structure.

A physical model and constitutive equations for metal fatigue, to characterize completely the S-N fatigue behavior of structural materials, have been developed on the basis of the macroscopic behavior of fatigue crack growth. The macroscopic behavior that forms the basis is that at any time during fatigue the fractional remaining fatigue life is proportional to the fractional remaining uncracked section size. A crack growth functional has been shown to describe this behavior accurately, and universally, for a wide range of materials, test conditions, and specimen geometries. By integrating this functional and with the introduction of physical boundary conditions, a surprisingly compact constitutive equation for the stress-life (S-N) fatigue behavior is derived. The constitutive equation represents accurately the sigmoidal shape of S-N high cycle fatigue behavior of single crystals and polycrystals, including the asymptotic approach of the fatigue data toward a physical endurance limit stress. Metallurgical fatigue strengthening effects due to pre-strain, alloying and grain refinement have also been shown to be accurately predictable. The equation is then expanded to include the mean-stress effects in various forms, which facilitated the complete prediction of stress-life behavior and fatigue limit, for any mean stress, solely from the S-N behavior of fully reversed fatigue data. A very interesting consequence of this is a new, master constitutive equation capturing the mean stress effect on fatigue behavior. Extensive experimental data, generated at various mean stresses, have been used to validate the present approach.

The critical plane-based multiaxial criterion originally proposed by the authors for plain fatigue is here applied to estimate the crack initiation life of fretting high-cycle fatigued structural components. Although fretting fatigue can be regarded as a case of multiaxial fatigue, the common multiaxial fatigue criteria have to be modified to account for the severe stress gradients in the contact zone. Therefore, the above criterion is used in conjunction with the Taylor’s point method to numerically estimate the fatigue life of Ti-6Al-4V and Al-4Cu specimens under cylindrical contacts.

Based on the fatigue damage mechanism, fatigue life, stiffness degradation, crack width change, bending, shear fatigue properties and other aspects, this paper introduces the research progress of the fatigue properties of ordinary reinforced concrete beams. And the existing reinforced concrete beam flexural, shear fatigue properties of research ideas, methods and results are summarized, providing the basis for further study on the fatigue performance of reinforced concrete beams. At present, the research results show that the fatigue damage of reinforced concrete beam is basically in accordance with the law of the three stages. In the early stage of fatigue, the tensile concrete cracks and exits, and the damage develops rapidly. In the middle of fatigue crack growth, fatigue damage is developed into a more moderate linear growth. In the late stage of fatigue, fatigue fracture occurs in the steel bar, and the bearing capacity of the beam is quickly lost.

The paper presents the results of an experimental and analytical study involving the bond properties of nine specimens externally strengthened with carbon-fiber-reinforced polymer (CFRP) sheets under fatigue loading. The purpose of this study is to investigate the influence of concrete strength and fatigue amplitude on the bond performance of CFRP-concrete interface under fatigue loading. Firstly, modified beam specimens with different concrete strengths were designed and constructed. Secondly, the specimens were tested under fatigue loads with different fatigue amplitudes. The test results show that the fatigue life increased with an increase in concrete strength, but decreased as the fatigue load amplitude increased, and a formula was proposed to predict the fatigue life. Moreover, the concrete strength and fatigue loading amplitude have little effect on the effective bond length under fatigue loading. The test results of bond-slip relationship show that the bond-slip curves continuously degraded with an increase in the number of load cycles, that is, the maximum shear stress decreased with an increase in the number of load cycles. Finally, a bond-slip model was developed considering the effects of concrete strength and fatigue loading amplitude. The comparison between experimental results and this model demonstrated that this developed bond-slip model can be used to describe the bond-slip relationship of the CFRP-concrete interface under fatigue loading.

A nonlinear continuum damage mechanics (CDM) model for multiaxial high cycle fatigue which incorporates the cyclic plasticity constitutive equation is developed in the finite element (FE) framework. FE simulation of T-joint fillet welding is first performed to identify welding residual stresses employing sequentially coupled three-dimensional (3-D) thermo-mechanical FE formulation. The high cycle fatigue damage model is then applied to the T-joint fillet welds subjected to cyclic fatigue loading to compute the fatigue life considering the residual stresses. The calculated total fatigue life which includes the fatigue crack initiation and the propagation is compared with the test result. The FE results demonstrate that the high cycle fatigue damage model proposed in this work gives a correct prediction of the fatigue life of the welds, and welding residual stresses cannot be disregarded in an estimation of the fatigue life of the welds.

Fatigue crack initiation usually starts from defects or inclusion (s) in the material in the zone of stress concentration. The stress concentration zone can be at the surface of the specimen or inside the material. The fatigue crack starts to propagate, depending on stress amplitude, if the range of the stress intensity factor is higher than the fatigue threshold. The aim of this paper is to present the procedure for determining the fatigue crack initial stage by using the Wöhler S-N curve and the fatigue crack propagation parameters obtained by experiment for the loading range R=-1. Determination of the fatigue initial stage has been determined by the analysis of tensile smooth specimens and notched bending specimens. Results show that linear elastic fracture mechanics is applicable in order to establish a model for fatigue crack propagation.

With the material testing machine of electro-hydraulic servo, fatigue test have been carried out on coarse aggregate concrete with pre-crack .The fatigue life and fatigue strength of the concrete have been measured under tension and compression loading. The effect of pre-crack on concrete fatigue behavior has been analyzed based on the test results. Having regression treatment, obtained the concrete S-N curve and S-lgN curve of fatigue life. Mean-while, applying ANSYS finite element software, analysis and comparison of the fatigue behavior have been performed. The results show that pre-crack has a great influence on the fatigue behavior of concrete, and the fatigue life is reduced for 75%~80%.

A series of characterization tests were performed to elucidate the high-cycle fatigue (HCF) behavior in SAE 1050 steel subjected to tensile elastic pre-deformation at different strain rates. In the pre-strained stage, the deformation was maintained constant at 0.16%, which was close to the low yield point at strain rates ranging from 10−5 s−1 to 10−2 s−1. Although pre-deformation occurred entirely in the elastic regime, using different pre-straining rates resulted in the occurrence of heterogeneous microscopic strain at different sites and locations during subsequent fatigue tests. It was found that the effect of pre-straining rate on crack initiation and crack propagation was not monotonous and was influenced by the homogeneity of deformation within grain boundaries, the integrity of the boundary structure, and the fracture toughness. In addition, the rough set theory model was introduced for the attribute reduction of characteristic parameters and provided a scientific basis to establish the fatigue model. The model was able to effectively predict the lifetime of the process of HCF in pre-strained steel. Hence, the pre-straining rate should be an important boundary condition in further studies.

The fatigue property of an asphalt mix is an important issue in pavement design. This property is often determined with the aid of a four-point bending (4PB) test in controlled deflection mode. The fatigue property is related to the decrease in the calculated complex stiffness modulus, however, due to the non- homogenous stress and strain field in the beam, the measured response does not represent the stiffness modulus of the material but a weighted stiffness value. For a correct interpretation, a fatigue damage material model like the Asphalt Concrete Pavement-Fatigue model is needed. After integration, the calculated and measured responses are compared. By varying the model parameters, an excellent comparison between the two responses is obtained up to a certain number of cycles. This number of cycles is denoted as the fatigue life NPH. The accumulated dissipated energy at the surface of the beam in the midsection can be expressed as a constant times the fatigue life NPH to the power z and also ...

This study aims to investigate the fatigue behaviour and determine the fatigue life prediction under biaxial loading. Fatigue tests were performed according to ASTM 2207-02 and the values of tensile stresses are selected from the ultimate tensile strength which is 0.5 Su, 0.6 Su, 0.7 Su, 0.8 Su and 0.9 Su, while the torsion angle representing the shear stresses acting was set at 15 degrees. The biaxial fatigue test was conducted using a combination of two types of stresses acting on the same frequency, namely 1 Hz, on smooth specimens made from medium carbon steel. The biaxial fatigue lives of the specimens are recorded when the specimen has completely fractured. The results indicate that the observed fatigue lives are in good agreement with the predicted lives by using the Coffin–Manson, Morrow, and Smith–Watson–Topper strain-based models. Mohr’s circle approach was used to determine the maximum shear stress and principal normal stress. The maximum shear stress increased from 457 MPa to 486 MPa with the increment of principal normal stress from 612 MPa to 767 MPa. The principal stresses, maximum shear stresses, and energy dissipated were used to explain and describe the behaviour of biaxial fatigue. Both stresses are inversely proportional to the fatigue life. Meanwhile, the energy is linearly proportional to the stress applied, where the values increase in the range 500 kJ/m 3 to 605 kJ/m 3 . Thus, the basic understanding of the material behaviour may be used in the processes of declaring component service lives and the fatigue life prediction of a particular automotive component. Therefore, the cost incurred can be reduced for the development process in material engineering.

The article presents the results of research on low cycle fatigue strength of high-strength structural steel S960QL. During the tests, controlled force was applied using the different total strain amplitude εac and strain ratio Rε = 0.1. The obtained results allowed to determine the value of the cyclic strain hardening exponent n' and the cyclic strength coefficient K' and to draw the cyclic stress-strain curve. Analysis was also carried out of fatigue life based on the Manson-Coffin-Basquin equation. Fatigue values were also determined. Fractographic tests of fatigue fractures allowed to identify the causes of crack initiation and the course of their propagation.

Fatigue of case hardened gears is investigated experimentally and numerically with focus on the finite fatigue life regime. Pulsating tooth bending fatigue experiments are performed at different load levels on two types of gears of different sizes to determine load–fatigue life relations. The experiments are compared with a probabilistic model for the finite life regime based on weakest-link theory. The stress fields, needed in the evaluations, are obtained by finite element simulations taking residual stresses, both due to case hardening and plastic deformation, into account. The stress history at each element is summarized into two different effective fatigue stress measures; one based on the largest principal stress and the Findley multiaxial fatigue stress. The material parameter needed in the Findley stress is determined by a linear correlation of the parameter with the Vickers hardness of the material using multiaxial fatigue data found in the literature. Both equivalent stress measures show equal behaviour and the probabilistic model shows good agreement with the experimental data in the finite fatigue life regime.

High–cycle multiaxial fatigue tests under proportional and non-proportional loading conditions with various combinations of superimposed static mean stresses was carried out on Cu-ETP copper. The results show differences in fatigue life between various ratios of mean stresses. These results are similar to others described in the literature.

The paper presents comparison of the mathematical models for fatigue life calculations including influence of the mean load value. Several model based on stress analysis on the critical plane and energy density parameter were investigated. In this paper three types of materials were tested and subjected to bending, torsion and combination of bending with torsion loading with the participation of mean value of the load. It was found, that the best fatigue life estimations obtained by models taking into account changes of the material behavior under fatigue loading related to the specified numbers of cycles of the load.

It has been shown in our previous effort in the development of an energy-based fatigue life prediction framework that, in order to obtain the fatigue toughness of a nonviscoplastic material at room temperature from the areas of hysteresis loops, a fatigue test need to be conducted at the ideal frequency to minimize the effect of nondamaging energy. For aluminum 6061-T6, the ideal frequency is 0.05 Hz. A fatigue test with such a low frequency requires extensive time to complete. Therefore, the present investigation focuses on modifying the energy-based framework in order to obtain the fatigue toughness from fatigue tests conducted at an arbitrary frequency higher than the ideal frequency. The fatigue toughness is calculated from the average strain range developed in a material during a fatigue test and the Ramberg–Osgood cyclic parameters. The measurement of average strain range by an extensometer associated with a nonviscoplastic test specimen at room temperature is independent of the test frequency. The cyclic parameters are obtained from the fatigue lives at two different stress ranges which are also independent of the test frequency at room temperature. Similar to the case of the previous framework, the modified framework is found to predict the room temperature fatigue life of aluminum 6061-T6 with a promising accuracy.

The effects of residual stresses on fatigue behaviour of welded T-joint are investigated based on a coupled stress and energy criterion which requires two fundamental material parameters: the fatigue threshold value and fatigue limit. Finite element analysis of the welding process determines the residual stresses. It is found that the residual stress effects on fatigue strength are significant for R

Tension–tension fatigue performances of T700/MTM46 composite laminates were investigated in this paper and the fatigue limit was determined. Failure modes of the fatigue specimens are mainly characterized by severe delamination throughout the whole gauge length while the static tension specimens exhibit brittle fractures within a small region. The stiffness degradation shows a quasi-linear slow decline during approximately 0–80% fatigue life and has a sharp decline since 80% fatigue life. Damage evolution was studied by fatigue specimens’ edge view, which showed the damage in 90° plies initiate firstly and propagate most seriously during fatigue. The distribution of fatigue life was determined. Single side allowance factor was proposed to calculate the reliability fatigue life with both reliability and confidence level. The results show that reliability fatigue life reduces more when the reliability increases than when confidence level does to the same degree. A new fatigue model (p–γ–S–N curve) was also established to predict the reliability fatigue life.