Constant Amplitude Fatigue Limit Research Articles

Extension of the peak stress method to estimate the fatigue limit of welded joints by means of the cyclic R-curve method

A new simplified and effective method has been formalised to estimate the Constant Amplitude Fatigue Limit (CAFL) of stress-relieved steel welded joints subjected to uniaxial push–pull loading and failing from the weld toe. Starting from the sharp V-notch assumption of the NSIF approach and the cyclic R-curve of the material in the heat affected zone, the proposed method identifies the CAFL as threshold level of the local stress field at the V-notched weld toe in the uncracked configuration. Such threshold stress field assures the crack arrest at the V-notched weld toe, according to the cyclic R-curve analysis. The method has been validated against experimental results and proved effective for a straightforward assessment of the CAFL of welded joints, as the stable crack propagation analysis of classical fracture mechanics approaches can be avoided.

Fatigue performance evaluation of steel-UHPC composite orthotropic deck in a long-span cable-stayed bridge under in-service traffic

Ultra-high-performance concrete (UHPC) emerges as an advanced material that is promising to improve the fatigue performance of bridge decks. This study evaluates the fatigue performance of steel-UHPC composite deck in the Junshan Yangtze River Bridge, which is a long-span cable-stayed bridge, under in-service traffic loads. The bridge was instrumented with strain gauges that provided in-situ strain data at fatigue-prone details. The strain data of fatigue-prone details were used to evaluate the maximum and effective stress ranges and fatigue life of steel-UHPC deck. A finite element model was established to analyze stress distributions and validated by the in-situ strain monitoring data. The results showed that the UHPC layer significantly reduced the maximum stress ranges and the effective stress ranges of fatigue-prone details and increased fatigue life. Attention should be paid to rib splice joints in bridge inspection and maintenance because its maximum stress range exceeded the constant-amplitude fatigue limit by 40%.

Fatigue Characteristic of Designed T-Type Specimen under Two-Step Repeating Variable Amplitude Load with Low-Amplitude Load below the Fatigue Limit

In order to investigate the non-linear fatigue cumulative damage of joints in ocean structural parts, one type of low carbon steel Q345D was employed to prepare designed T-type specimens, and a series of fatigue experiments were carried out on the specimens under two-step repeating variable amplitude loading condition. The chosen high cyclic loads were larger than the constant amplitude fatigue limit (CAFL) and the chosen low cyclic loads were below the CAFL. Firstly, the S-N curve of designed T-type specimen was obtained via different constant amplitude fatigue tests. Then, a series of two-step repeating variable load were carried out on designed T-type specimens with the aim of calculating the cumulative damage of specimen under the variable fatigue load. The discussions about non-linear fatigue cumulative damage of designed T-type specimens and the interaction effect between the high and low amplitude loadings on the fatigue life were carried out, and some meaningful conclusions were obtained according to the series of fatigue tests. The results show that fatigue cumulative damage of designed T-type specimens calculated based on Miner’s rule ranges from 0.513 to 1.756. Under the same cycle ratio, the cumulative damage increases with the increase of high cyclic stress, and at the same stress ratio, the cumulative damage increases linearly with the increase of cycle ratio. Based on the non-linear damage evaluation method, it is found that the load interaction effect between high and low stress loads exhibits different damage or strengthening effects with the change of stress ratio and cycle ratio.

Mean stress effect in stress-life for hard steels

This paper examines the effect of mean stress on the fatigue behavior of very hard carburized steels. Current theories suggest that the maximum stress at the fatigue limit continuously decreases with decreasing minimum stress whereas the results of this study indicate that the maximum stress remains constant for minimum stresses less than the fully reversed constant amplitude fatigue limit minimum stress. The theory proposed by the authors corrects this error by maintaining the maximum stress at the fatigue limit constant with decreasing minimum stress in the compressive mean stress region.

Impact of Road Traffic Tendency in Europe on Fatigue Assessment of Bridges

Fatigue load models for road bridges given in the Eurocode EN1991-2 have been calibrated considering real traffic measurements that became available around 1990. Since then, traffic composition has evolved considerably, also considering the issuing of the 96/53/EC Directive, which legitimated member states, on an equal and not discriminatory basis, to allow the circulation of Long and Heavy Vehicles (LHVs). Thus, the appropriateness of fatigue load models to cover also the effects of these vehicles, which are longer, heavier and potentially more damaging than common Heavy Goods Vehicles (HGVs), became an issue. The aim of the study is to assess how the evolution of European traffic influences the fatigue assessment of bridges. To capture the essence of the problem, three different real traffic measurements are compared in terms of fatigue damage: the Auxerre (FR) traffic, adopted to define fatigue load models in EN1991-2; the Moerdijk (NL) traffic, characterized by a high percentage of LHVs; and the Igualada (ES) traffic. To assess the current relevance of fatigue load models LM2 and LM4 of EN1991-2, the aptitude of these models to adequately reproduce the effects caused by LHVs is discussed in detail. The results demonstrate that the Auxerre traffic is still the most onerous; that the Moerdijk traffic is generally more severe than the Igualada traffic, and that the fatigue load models of Eurocode do not require major updates. The study is further supplemented by investigating the suitability of the formulae provided in the Eurocodes for the damage equivalence factors λ2 and λ3 to express the influence of the total lorry volume on the fatigue damage. In that latter case, the conclusion is that the formulae proposed in the Eurocodes, based on the assumption of a linear fatigue strength S–N curve with constant conventional slope m, could lead to erroneous, even unsafe, estimates of the fatigue life, especially when details are characterized by constant amplitude fatigue limit ΔσD, thus calling for further improvements of the formulae themselves.

A finite element based approach for fatigue life prediction of headed shear studs

Steel shear studs in bridges are subjected to rapidly fluctuating stresses causing fatigue failure. Research on fatigue of shear studs mainly focused on tests. Both AASHTO and Canadian design curve for fatigue resistance of shear studs are based on the tests conducted in the mid1960s by Slutter and Fisher. This paper presents a finite element based approach using push-out specimen for fatigue life estimation of headed shear stud connectors. Both crack initiation and crack propagation life are estimated and an excellent correlation is found when compared against test results. In addition, since a significant amount of push-out tests data on headed shear studs are now available, this paper evaluates the fatigue design curves of different standards, with special focus given to evaluation of the value of constant amplitude fatigue limit (CAFL) given in the current AASHTO and Canadian code (CSA S6-14). The regression analysis also shows that the current fatigue curves in different codes can be used for shear studs as large as 31.8 mm. Thus, restriction of use of studs larger than 25 mm (1 in.) in different bridge codes (CSA S6, Eurocode 4, and AASHTO) can be waived.

Proposed criterion for fatigue strengthening of riveted bridge girders

Most existing guidelines and recommendations for the fatigue design of riveted members are not considering the effect of stress ratio on the constant amplitude fatigue limit (CAFL). However, fatigue test data show that there is a substantial influence of the stress ratio on the CAFL. In this study, a simple fatigue design criterion for riveted members is proposed taking into account the effect of stress ratio. The applied method is based on the constant life diagram (CLD) methodology. The accuracy of the pro-posed design criterion has been verified using existing test data in the literature. This consideration enables the application of an effective solution for prevention of fatigue failure in riveted members, namely the application of prestressed retrofitting systems, which results in a reduction of the stress ratio. A procedure is therefore presented for the fatigue design of the riveted members strengthened with prestressed and non-prestressed retrofitting systems subjected to constant and variable amplitude loadings. The proposed design procedure is then used in a numerical example to determine the prestressing force and the section modulus re-quired for prevention of fatigue cracking in both the prestressed and non-prestressed retrofitting systems.

New framework for calibration of partial safety factors for fatigue design

In Eurocode standards, three verification schemes are proposed for fatigue design under variable amplitude loadings: 1) Based on constant amplitude fatigue limit; 2) Based on constant amplitude equivalent stress range at 2 ⋅ 106 cycles; 3) Based on accumulated damage. Characteristic values of fatigue resistance and load effects as well as partial safety factors are introduced in design equations in order to achieve a target reliability level. In this paper a new framework for calibration of fatigue partial safety factors is presented. Three different fatigue limit state functions are formulated for direct comparison with the three verification schemes proposed in Eurocodes. The variable amplitude S-N curves used in this framework are defined using an original probabilistic approach. The presented framework is then applied to two typical bridge fatigue sensitive welded joints. The comparison of results with partial safety factors values recommended in Eurocodes shows that the Eurocode-based partial safety factors should be revised by considering different fatigue sensitive details and by further differentiating between the three verification schemes.

High-cycle fatigue performance of high-mast illumination pole bases with pre-existing cracks

This paper presents the results of high-cycle fatigue testing of high-mast illumination poles (HMIPs) with pre-existing cracks at the pole-to-base plate connection detail. Resonant bending fatigue tests were conducted on five pairs of HMIP base specimens at nominal stress ranges of 41.4MPa (±20.7MPa), 27.6MPa (±13.8MPa), 20.7MPa (±10.3MPa) and 6.9MPa (±3.4MPa). The length and depth of pre-existing cracks was measured and the propagation of the individual crack was monitored throughout the testing using an ultrasonic inspection technique. The experimental results suggested that the fatigue lives of the tested specimens can exceed the predicted life for AASHTO fatigue category E details and approach category D details even in the presence of pre-existing cracks. The results provide insight into the fatigue response of HMIP with pre-existing cracks at the base connections at very low stress ranges and high cycle counts. The findings suggest that the pre-defined constant amplitude fatigue limits for AASHTO details may not strictly apply to HMIP details with pre-existing cracks.

Probabilistic S-N curves for constant and variable amplitude

Welded details in steel bridges are subjected to fatigue lives up to 200·106 cycles due to traffic loads. While the majority of these stress ranges are below the Constant Amplitude Fatigue Limit (CAFL), some few high stress cycles can trigger the start of fatigue damage and lead the remaining load spectra to become damaging. The behaviour under spectra loading is thus of major importance for the fatigue design of steel bridges. This paper focuses on the fatigue behaviour of welded joints under variable amplitude loads. Fatigue tests have been conducted under constant and variable amplitudes on a typical bridge detail. Experimental crack growth curves were obtained using the Alternative Current Potential Drop method (ACPD), which showed the detrimental effect of stress ranges below the conventional CAFL. A two-step model with initiation-propagation was established to estimate the experimental fatigue lives, using a local strain approach for the initiation life and fracture mechanics for crack propagation. The model was implemented in a probabilistic Monte Carlo framework to include variability on the main parameters and establish S-N curves for Constant and Variable amplitude. The results of the simulations show that load spectra shape can be correlated with the S-N curves, namely the 2nd slope value below the CAFL.

Structural Designs with Consideration of Both Material and Structural Failures

AbstractThis paper provides a simplified formula for modeling the transition between material and structural failures in static and dynamic loading situations. For static situations, the transition equation allows for the calculation of the ultimate capacity between buckling structural failure and compression material failure modes. For dynamic situations, the transition equation allows for the calculation of a smoothed S-N curve between the constant amplitude fatigue limit, namely, the endurance limit, and the low-cycle, high-stress fatigue limit. The simplified formula is based on a quadratic solution that is curve fit to each failure mode and is verified with existing experimental data.

Fatigue Capacity of Headed Shear Studs in Composite Bridge Girders

AbstractShear connectors are commonly used in steel bridges to join the concrete deck and steel superstructure, providing a mechanism for shear transfer across the steel–concrete interface. The most common type of shear connector is the headed shear stud. In the current American Association of State Highway and Transportation Officials (AASHTO) LRFD Bridge Specifications on composite design, shear stud fatigue often governs over static strength, and a large number of shear connectors often result. The stud fatigue capacities presented in the AASHTO standard are largely based on a limited sample of composite fatigue tests performed in the 1960s, with limited fatigue test data at lower stress ranges leading to a somewhat arbitrary constant amplitude fatigue limit (CAFL). This often governs the composite design for bridges with moderate-to-high traffic demands. This paper presents results from an experimental and analytical study of the fatigue behavior of headed shear studs to address the lack of existing e...

Fatigue Performance of a Lightweight Composite Bridge Deck with Open Ribs

An innovative lightweight composite deck (LWCD) is proposed for steel bridges to avoid premature fatigue cracking. The composite deck is composed of an open-ribbed orthotropic steel deck (OSD) and a thin ultrahigh-performance concrete (UHPC) layer. This study is based on a suspension steel bridge in China, namely, the Second Dongting Lake Bridge. The following investigations were performed: (1) preliminary finite-element analysis (FEA) was carried out to evaluate the vehicle-induced stress ranges (i.e., Δσ = σmax − σmin) of six typical fatigue-prone details; (2) parameter analyses were performed to investigate the effects of the shape of cutouts and the thickness of the floor beams; and (3) two fatigue tests, one that used a full-scale LWCD panel and another that used a LWCD beam specimen, were conducted to reveal fatigue performance of the OSD and the stud shear connectors, respectively. Results of the preliminary FEA show that, with the contribution of the UHPC layer, the vehicle-induced stress ranges at some fatigue details of the LWCD, such as the rib–deck plate welded joints and the splice welds of the longitudinal ribs, were reduced to be less than their constant-amplitude fatigue limits, which indicates theoretically infinite fatigue lives of these details. The parameter analyses reveal that the apple-shaped cutout had relative good fatigue properties among the four cutout schemes and that the thickness of the floor beams is recommended to be 14–18 mm. According to the fatigue tests on the composite panel specimen and on the composite beam specimen, both the open-ribbed OSD and the stud shear connectors exhibited satisfactory fatigue endurances, which were much greater than 2 million cycles. The current theoretical and experimental investigations reveal that the proposed open-ribbed LWCD has favorable fatigue performances.

Reliability based fatigue assessment of existing motorway bridge

This paper provides an original framework for the fatigue reliability analysis of a road bridge; the framework is applied to the Venoge bridge, a composite steel–concrete bridge within the A1 Swiss highway. Two critical details are selected by inspection: a longitudinal weld attachment and a cover plate welded attachment. Weigh in Motion (WIM) data from Denges station (1km far from the bridge) and a refined three-dimensional Finite Element (FE) model of the bridge are used to get realistic time-stress response at two critical locations. The fatigue failure probability of the bridge at two selected locations under the long-term effect of highway traffic is calculated for a 100year-design life. The original contribution consists in computing the failure probability as joint probability of two events: (1) the exceeding of the constant amplitude fatigue limit (CAFL); and (2) the critical fatigue damage accumulation. The results show that fatigue is not a concern both for the longitudinal attachment detail and for the cover plate detail.

Evaluation of Torsional Vibrations in Steel Truss Bridge Members

Long and torsionally slender H-shaped cross sections, often used as tension members in truss bridges, can exhibit wind-induced torsional motions. These motions have produced high-cycle fatigue damage for some bridges. There is limited information available to evaluate the torsional response on the fatigue performance of the members and connections. An in-service bridge with a documented history of wind-induced torsional motions in the verticals was instrumented to capture the wind speed and direction that induced torsional motions in the verticals. Sensors also captured the rotation angle amplitudes and numbers of cycles. Laboratory tests were conducted on a full-size replica of a vertical-and-chord connection to establish the relationship between rotation and normal stresses in the cross section from warping restraint at the connection locations. Analytical methods were shown to accurately predict the rotations and warping stresses along the member length. Applying the experimental and analytical results, the stress ranges were determined for the field-measured torsional responses, and the fatigue potential was evaluated. The results showed the measured stress ranges are near the constant amplitude fatigue limit, but the large cycle counts and frequency of events in the historical wind record that could produce torsional response indicate the need for continued monitoring and a long-term mitigation strategy.

Fatigue Testing of Full Scale Girth Welded Pipes Under Variable Amplitude Loading

In the fatigue design of steel catenary risers, there are concerns regarding the fatigue damage to girth welds from low stresses, below the constant amplitude fatigue limit, in the loading spectrum and the validity of Miner's cumulative damage rule. These fundamental issues were addressed in a recent joint-industrial project (JIP). A key feature was development of the resonance fatigue testing rigs to enable them to test full-scale pipes under variable amplitude loading. Such tests were performed under a loading spectrum representative of that experienced by some risers, with many tests lasting over 100 million cycles to investigate the fatigue damage due to small stresses as well as the validity of Miner's rule. However, the resonance rigs are only capable of producing spectrum loading by gradually increasing or decreasing the applied load whereas more “spiky” random load sequences may be relevant in practice. Therefore, the program also included fatigue tests in conventional testing machines on strip specimens cut from pipes to compare the two types of loading sequence. This paper presents the results of these tests, conclusions drawn, and recommendations for changes to current fatigue design guidance for girth welded pipes regarding the definition of the fatigue limit, allowance for the damaging effect of low stresses, and the validity of Miner's rule.

Fatigue reliability analysis of steel bridge details based on field-monitored data and linear elastic fracture mechanics

This article presents the fatigue reliability analysis of welded details of a 40-year old steel box-girder bridge, based on the linear elastic fracture mechanics (LEFM) and the long-term stress monitoring. The fatigue crack growth is described by using the LEFM, based on which the ultimate limit state is established as a function of the crack size. Effective stress ranges are obtained from daily stress range histograms, and lognormal probability density functions (PDFs) are used to model the uncertainties in stress data. Details at discontinuous backing bar splices, which have not been explicitly listed in the American Association of State Highway and Transportation Officials (AASHTO) specification, and the welded details at the base of bridge bents are evaluated on their fatigue reliabilities. It is found that the backing bar splice detail may have high fatigue reliability, considering that low stress ranges and small number of cycles occurred in the monitoring period. For the weld detail at the base of bent, stress ranges higher than the constant amplitude fatigue limit (CAFL) existed, and currently the reliability indexes are all below the target value, showing that maintenance or retrofit actions may be required. For the details at the upper base of bridge bents, sufficient reliabilities are expected throughout the service life.

Fatigue Performance of Stiffened Pole-to-Base Plate Socket Connections in High-Mast Structures

AbstractFatigue performance of stiffened pole-to-base plate socket connection in high-mast lighting structures was evaluated by experimental and analytical studies. In absence of sufficient experimental data, constant amplitude fatigue limit (CAFL) of longitudinal stiffener terminations on pole walls is classified as Category E′ in the existing American Association of State Highway and Transpiration Officials (AASHTO) specification. Fatigue performance of this connection in the thin-walled tubular structures is controlled by localized secondary bending stress, the magnitude of which depends on the relative stiffness of the connecting elements. Ten full-size high-mast specimens having stiffened socket connection were tested under constant amplitude reversal loading to determine the fatigue resistance of this connection in finite and infinite life regimes. The specimen design was optimized by parametric finite-element analysis (FEA) and local stress approaches. FEA results were verified by conducting static...

Nitinol Fatigue Life for Variable Strain Amplitude Fatigue

Nitinol fatigue testing results are presented for variable strain amplitude cycling. The results indicate that cycles smaller than the constant amplitude fatigue limit may contribute to significant fatigue damage when they occur in a repeating sequence of large and small amplitude cycles. The testing utilized two specimen types: stent-like diamond specimens and Z-shaped wire specimens. The diamond specimens were made from nitinol tubing with stent-like manufacturing processes and the Z-shaped wire specimens were made from heat set nitinol wire. The study explored the hypothesis that duty cycling can have an effect on nitinol fatigue life. Stent-like structures were subjected to different in vivo loadings in order to create more complex strain amplitudes. The main focus in this study was to determine whether a combination of small and large amplitudes causes additional damage that alters the fatigue life of a component.

Bilinear S-N Curves and Equivalent Stress Ranges for Fatigue Life Estimation

With the magnitude of some stress cycles in a live load stress range spectrum being higher than the constant amplitude fatigue limit (CAFL) of a structural detail, the development of a fatigue crack could be expected. The current procedure in the AASHTO specifications for fatigue life estimation utilizes an equivalent constant amplitude stress range with the direct extension of the S-N lines of slope −3 to below the CAFL. This approach is conservative; however, it often results in overprediction of fatigue damage and underestimation of the safe useful life of structural details. A set of bilinear S-N curves with the knee at the CAFL for the AASHTO fatigue strength categories and a slope of −4 below have been produced analytically for estimating fatigue life of existing structures subjected to variable live load stresses. This paper provides information regarding the development of the new equivalent constant amplitude stress ranges for the bilinear S-N curves. The results from a few examples are presented. Adoption of the procedure presented herein for fatigue life estimation is recommended.