Variable Amplitude Fatigue Loading Research Articles

Fatigue performance of stud connectors in joints between top slabs and steel girders with corrugated webs subjected to transverse bending moments

Steel-concrete composite box girders with corrugated steel webs (CSWs) are broadly used in bridge engineering, in which the joints between top RC slabs and steel girders with CSWs are usually subjected to transverse bending moments caused by off-center vehicle loads. Stud connectors arranged in the joints usually bear repeated pull-out forces in this case and are prone to fatigue failure. Therefore, two reduced scale joints between top slabs and weathering steel girders with CSWs were designed and tested, on which variable amplitude fatigue loads were applied to investigate the fatigue performance of studs incorporated in the joints. The two joints presented similar fatigue behavior, i.e., cracks of not more than 0.26 mm in width appeared on the surface of the top slab during the fatigue loading, and the separation of the top RC slabs and the top girder flanges was observed; meanwhile, minute cracks developed along the welds connecting the CSW with the bottom girder flange, and the stiffness of the joints gradually decreased due to the accumulation of fatigue damage. The two joints underwent 2,650,000 and 2,103,600 load cycles respectively before fatigue failure occurred. After partially demolishing the RC slabs, several welded head studs in the joints were observed fractured at the roots and detached from the top girder flange. Whereafter, finite element (FE) models referring to the test joints were developed and analyzed, and the effect of the wave height (WH) of the CSW and the transverse row spacing (TRS) of studs on the distribution of pull-out forces among studs was investigated. It showed that the pull-out force bore by each stud in the joint was distributed unevenly even in the same row. Then, a modification factor α was introduced to revise the pull-out forces of studs calculated in the theoretical method. An equation to determine the factor was fitted, considering the effect of the WH of the CSW and the TRS of studs. Finally, the detail category for studs bearing pull-out forces in the joints was discussed based on the experimental results and the collected test data, and it was preliminarily recommended studs subjected to pull-out forces can be classified into detail category 45 specified by Eurocode 3 in fatigue design.

Mechanical response and energy evolution of interbedded shales subjected to multilevel constant/increasing-amplitude cyclic loading

This study aims to investigate the effects of fatigue loading paths and interbed structure on the mechanical properties and energy evolution characteristics of shales. In the experiments, shale specimens with five types bedded angles (0°, 30°, 45°, 60°, 90°) were prepared, and multilevel constant-amplitude fatigue loading test (MCFT) and multilevel variable-amplitude fatigue loading test (MVFT) were performed. Results indicated that shale's fatigue behaviors were highly affected by the bedding plane angles and the cyclic loading paths. Specifically, with the increasing of bedding angle, the peak strength, total dissipated energy, and total input energy of the shales showed a "U" trend, the ultimate macro-damage mode changed from mixed tension-shear failure to failure along the bedding planes, and the damping ratio firstly increased and then decreased. Test schemes of stepwise increase of the lower stress limit or keeping it constant were the differences between MCFT and MVFT, which significantly influenced the evolution of irreversible deformation of shales. Compared to MVFT, the shale in MCFT displayed reduction in peak strength in the range of 4.3% to 23.9%, greater and more drastic variations in elastic modulus and damping ratios, dissipative energy and elastic strain energy were relatively low by an order of magnitude.

Fatigue failure prediction method and constant amplitude equivalence strategy of adhesive interface under variable amplitude loading

The existing commercial software can only predict the fatigue life of homogeneous materials/structures under constant amplitude loading. This work developed a software tool that could predict the fatigue life of the adhesive interface under variable amplitude loading by embedding a modified fatigue cohesive zone model and amplitude variation function. Central to this innovation is the load sequence effect factor (γ), designed to consider nuanced influences like the shock effect of stepped amplitude changes on the fatigue properties. The effects of the block loading sequence on the fatigue life and crack growth rate of the adhesive interface were investigated numerically, and the influence of stepped amplitude on the evolution of a damage zone ahead of the main crack front was observed. It was found that the loading sequence from Low to High (L-H) accelerated the crack growth rate and reduced the fatigue life, and vice versa. Under the same fatigue life, a constant amplitude fatigue equivalence (CAFE) strategy is proposed, which could convert a variable amplitude road spectrum into a constant amplitude load more suitable for the testing bench. The proposed tool and method are also suitable for bi-material interface failure prediction under variable amplitude fatigue loading.

Similarity learning hidden semi-Markov model for adaptive prognostics of composite structures

Data-driven methodologies have found increasing usage in the last decade for remaining useful life (RUL) prognostics of composite materials utilizing structural health monitoring (SHM) data. Of particular interest is the reliable RUL prediction in cases where the end-of-life is not in between the extreme values within the testing dataset. For example, when unexpected phenomena that severely compromise the structural integrity occur during the service life. Such cases are often referred as outliers and the RUL prognosis based on a data-driven model that learns from past data is often erroneous. This study addresses this challenge by proposing a new stochastic model; the Similarity Learning Hidden Semi Markov Model (SLHSMM), an extension of the Non-Homogenous Hidden Semi Markov Model (NHHSMM). Through the utilization of a nonparametric discrete distribution, which characterizes the similarity between the testing structure and the training structures, a dynamic re-estimation process is employed. This process assigns higher importance to the training structures that display greater similarity to the testing one. As a result, the estimated parameters effectively capture the specific characteristics of the testing structure. The training and testing SHM data sets consist of strain measurements collected from a case study where carbon–epoxy single-stringered panels, are subjected to constant, variable, and random amplitude fatigue loading until failure. RUL estimations from the SLHSMM, the NHHSMM, and the Gaussian Process Regression (GPR) are compared. The SLHSMM clearly outperforms its classical counterpart and GPR providing more accurate outlier and inlier prognostics, demonstrating its capability to adapt to unexpected phenomena and integrate unforeseen data into a prognostic platform.

Examination of the Effects of Different Frequencies on Rock Fracturing via Laboratory-Scale Variable Amplitude Fatigue Loading Experiments

In this study, the characteristics of the fracture evolution of argillaceous shale under increasing-amplitude loading were investigated. The GCTS RTR-2000 test system and in-situ acoustic emission (AE) monitoring were employed to execute the tests. The following results were observed. (1) The strength, deformation, and fatigue life increased with the frequency, and the morphology of the hysteresis curve changed regularly with time. (2) The cumulative damage of the rock at the location in which the stress amplitude suddenly increased exceeded that at the fatigue loading stage. The AE count and AE energy were affected by the loading frequency. (3) The secant modulus exhibited different values for different loading frequencies; the smaller the loading frequency, the fewer loading stages the samples experienced, and the faster the secant modulus decreased. The change in Poisson’s ratio over the entire process was composed of a steady growth stage and a rapid growth stage. (4) The rock exhibited two stages of damage evolution, with rapid damage accumulation occurring at the beginning of the loading and relatively smooth damage occurring thereafter. This study developed a cumulative fatigue damage model that can adequately fit the accumulated damage during the fracturing process. The experiments revealed that variable amplitude fatigue loading at different frequencies significantly influences the damage deterioration and the failure law of the rock. The results are expected to improve the understanding of the frequency effect on the fracture behavior and help predict the lifespan of rock structures. This is of great significance to the promotion of slope management, landslide disaster prevention, and mine reuse at the West Open-pit Mine.

Mechanical responses of freeze–thaw treated natural stone masonry subject to compressive variable amplitude fatigue loading: Insights from stiffness loss and constitutive characterization

• The evolution of natural stone masonry stiffness exposed to multi-level cyclic load is revealed. • A novel secant modulus-based failure prediction method is proposed. • A constitutive model is proposed to characterize stone deformation under multi-level fatigue load. Stiffness loss and catastrophic failure frequently occur in natural stone masonry subject to freeze–thaw action and cyclic stress, which may incur serious engineering disasters and casualties. This work strives to experimentally unveil the mechanical responses of a medium-grained building sandstone exposed to dual effects of freeze–thaw and cyclic stress. Testing results are presented from the insights of volumetric deformation, secant modulus evolution. A drop in secant modulus of the first cycle is observed in the failure cyclic loading stage, whereas all former stages exhibit a modulus increase. This precursor well applies to all samples which is freeze–thaw and stress level independent. The development of Poisson’s ratio as well as stress level at onset of volume reversal are also presented. A theoretical modelling is put forward to characterize the axial and circumferential strains exposed to variable cyclic stress. The model shows decent effectiveness calibrated by testing results, the way to determine constants in models is introduced in detail, which can be used by readers in a broader range of construction materials.

Single and periodic overloading effects on the mode I fatigue crack growth of a ductile adhesive

Variable amplitude fatigue loading, where overloading is included, is commonly experienced by bonded structures. Thus, this work aims the assessment of the influence of overloads on the total fatigue life and fatigue crack growth (FCG) of a ductile adhesive. Double cantilever beam (DCB) specimens were subjected to different fatigue loading spectra including constant amplitude, single and periodic overloads. Stiffness degradation and its rate variation were also evaluated. Results showed that overloads can have a fatigue retarding effect leading to an increase in fatigue life up to 4 times. However, for periodic overloads, this increase in fatigue life was less pronounced.

Research on Interface Slip of Composite Reinforced Steel Truss-Concrete Test Beam and Its Calculation and Analysis Method

In this study, a model of test beam in negative moment area is designed, and the slip characteristics of test beam under overlimit static load and variable amplitude cyclic load are studied, respectively. By constructing the relationship between shear stiffness and slip parameters of the test beam, the deformation calculation method of the test beam under different fatigue cycles is derived, and the accuracy of the calculation model is verified by experiments. The results show that the maximum slip value (0.038 mm) of static load after 10,000 times of limited fatigue load is increased by 58.3% compared with that before overlimit fatigue load is applied (0.024 mm). When the fatigue cycle is 0-2 million times, the total slip is between 0.019 and 0.026 mm and the residual slip percentage is between 4.17 and 8.33%. The maximum residual values are 0.022 mm, 0.027 mm, and 0.028 mm after 1.5 times, 2 times, and 3 times of overload and variable amplitude fatigue loads, respectively, and the slip values have no obvious fluctuation, all of which show good working performance. The average value of the ratio between the deformation value and the measured value of composite beams is 0.89, and the standard deviation is 4.86%. When the fatigue loading times are more than 2.8 million, the ratio between the calculated value and the measured value is less than 0.85, so the adaptability of the calculation model has certain limitations. On the whole, the calculation model proposed in this study fully considers the factors such as the stiffness and fatigue loading times of composite beams, and the error between the calculated results and the measured results is within 5%, with high accuracy, which can be used as a reference for the actual design.

A methodology for detection of crack initiation in adhesively bonded joints under constant and variable amplitude fatigue loading

ABSTRACT The use of adhesively bonded joints is increasing in the lightweight design; however, their fatigue performance in safe-life design is challenging. Therefore, a combination of damage-tolerant design and Structural Health Monitoring (SHM) is often considered. The present work deals with a new approach for detection of crack initiation in adhesively bonded single lap joints (SLJ) subjected to constant and variable amplitude fatigue loading. For this purpose, the so-called backface strain method is used, in which a strain gauge for damage monitoring is placed at a highly sensitive point in the overlap area of SLJs. A striking converging-diverging trend in strain amplitude curves was attained in the tests subjected to constant amplitude loading, which was in a good agreement with the onset of crack initiation observed with video-microscopy. Additionally, this methodology was demonstrated on the SLJs subjected to variable amplitude loading using an additional farfield (outside of the overlap area) strain gauge, which showed a high potential for detection of crack initiation.

Experimental research on variable-amplitude fatigue behavior of cracked mortar after epoxy grouting

This paper presents the experimental results of the fatigue behavior of cracked mortar specimens after epoxy grouting reinforcement under high-frequency variable-amplitude fatigue loading. Grouting can effectively suppress the stress concentration at the crack tip and enhance the fatigue resistance of the sample. The final failure mode of the specimen depends on the loading sequence order. We consider the equivalent coefficient and loading sequence, and the multi-step stress level can be equal to a constant value. A log-linear relationship can be obtained between the equivalent stress level and the total fatigue life for both grouted and cracked specimens. In the process of multi-stage fatigue loading, using strain as the damage parameter, it is found that the damage in each loading stage accumulates non-linearly, and the prediction using Palmgren-Miner's rule may be conservative. We propose a nonlinear damage accumulation prediction model that fully considers the loading sequence, equivalent stress level, stress ratio, and other parameters. The test results show that the model can better meet damage accumulation rules and make better prediction effects for multi-stage variable-amplitude fatigue loading.

A probabilistic fatigue life prediction for adhesively bonded joints via ANNs-based hybrid model

The paper is aimed at developing an efficient and robust probabilistic fatigue life prediction framework for adhesively bonded joints. This framework calibrates the fatigue life model by quantifying uncertainty in the fatigue damage evolution relation using a set of experimental fatigue life data. Probabilistic assessment of fatigue life is simulated through damage evolution along the bondline and Bayesian inference via the Markov chain Monte Carlo (MCMC) sampling method for inverse uncertainty quantification (UQ). To expedite the fatigue life simulation, a hybrid model composed of physics-based fatigue damage evolution relation and a data-driven artificial neural networks (ANNs) model is employed. The degradation of the adhesive is evaluated by the fatigue damage evolution relation which is then mapped to the strain redistribution along the bondline using the ANNs model. Once the mapping is learned by the ANNs, through data from FEA simulations, the probabilistic fatigue life prediction framework involves three successive modules: (I) fatigue damage growth (FDG) simulator, (II) uncertainty quantification (UQ), and (III) confidence bounds for fatigue life prediction. The FDG simulator can be used for simulating fatigue degradation rapidly for a given geometric configuration under any arbitrary fatigue loading spectra. The quantified uncertainties from the framework correspond to the intrinsic statistical material properties that can be used for probabilistic fatigue life prediction in any joint configuration with the same adhesive material. The probabilistic framework is verified using a single lap joint (SLJ) by quantifying uncertainties which are then used for probabilistic fatigue life prediction in laminated doublers in the bending (LDB) joint, that uses the same adhesive material as SLJ, and successfully compared with experimental data. The framework is also tested and validated by estimating probabilistic fatigue life in other joint configurations under constant and variable amplitude fatigue loading spectra.

Interfacial properties of CFRP sheets and concrete subjected to variable amplitude fatigue loading

AbstractIn order to better understand the interfacial fatigue behavior of concrete and fiber‐reinforced polymer (FRP), bending fatigue tests were conducted on plain concrete beams strengthened with carbon FRP (CFRP) sheets under variable amplitude cyclic loading which deteriorates structural performance in actual projects more dramatically than constant amplitude loading. The test parameters were four types of loading modes including static loading, constant amplitude cyclic loading, alternating amplitude cyclic loading and incremental amplitude cyclic loading. Miner damage rule, modified Miner damage rule and Corten‐Dolan cumulative damage rule were used to predict the fatigue life of specimens. The relationship between loads and deflections, the relationship between strains and cycle times and the crack propagation were analyzed. The results have shown that the fatigue life of specimens under variable amplitude cyclic loading, especially alternating one, is shorter than that of specimens under constant one, and the modified Miner damage rule is more suitable to predict fatigue life. The crack lengths on the lateral faces of beams recorded by digital image correlation (DIC) method developed more slowly than those at the bottom sides recorded by strain gauges. A proposed damage model describing the relationship between the crack lengths and fatigue life for specimens under alternating amplitude fatigue loading is consistent with the experimental results well.

Experimental research on fatigue behavior of prestressed concrete beams under constant-amplitude and variable-amplitude fatigue loading

This paper presents the experimental and analytical results of the fatigue behavior of prestressed concrete (PC) beam used in a heavy-haul railway under constant-amplitude and variable-amplitude fatigue loading. The fatigue behaviors including mid-span displacement, bending stiffness and strains of classical materials were investigated comprehensively. Moreover, the residual strain of concrete in compression zone was mainly analyzed and fitted, and the S-N relationships of bottom tensile steel bar and the test beam related to prestressing force were given. The experimental result shows that the fatigue failure mode of PC beam is the fatigue fracture of bottom tensile steel bar in the pure bending section. The main crack width, stiffness degradation and the maximum displacement all show development law of three stages under the constant-amplitude fatigue loading. The fatigue characteristic parameters (stiffness, displacement and strain of concrete in compression zone) of variable-amplitude fatigue test beams exhibit the multi-stage development law due to the addition of multi-level fatigue load. Further, on the basis of the fatigue characterization model of classical materials and the stress analysis of fatigue cracking cross-section, a nonlinear numerical analysis method for the whole fatigue process is proposed. The numerical simulation results are in good agreement with the test data, which shows that the proposed numerical analysis method can simulate the fatigue behavior of PC beams under constant-amplitude and multi-level variable-amplitude fatigue loading. The results of this research provide a reference for fatigue design and fatigue life evaluation of PC beams in heavy-haul railway.

Research on Fatigue Bending Stiffness Degradation of Prestressed Concrete Beams Considering Size Effect

Based on the fatigue damage development law and damage model of concrete, considering the crack propagation of ordinary steel bars and prestressed reinforcement under fatigue load, the residual useful section area of reinforcement was used to reflect the fatigue damage of steel bars. Further, we considered the correction coefficient of the size effect of concrete and steel bars and derived the formula for calculating the section stiffness of prestressed concrete beams of different sizes after fatigue damage. A multi-stage variable amplitude fatigue load test was carried out on prestressed concrete beams. The test results were analyzed, and the accuracy of the equation was verified based on experimental data. The results show that the stiffness degradation of prestressed concrete beams and the development of concrete damage under the multi-stage variable amplitude fatigue loading test have similar laws. According to the theoretical derivation formula, the deviation between the calculated results and the experimental results is small, which has reference value for the study of the fatigue bending stiffness degradation of prestressed beams considering the effect of size effect.

Role of longitudinal reinforcement on the behavior of under reinforced concrete beams subjected to fatigue loading

In this work, the role of steel reinforcement in under reinforced concrete beams when subjected to flexural fatigue loading is studied using the acoustic emission (AE) technique. Three-point bend notched beams of three different sizes and with varying reinforcement ratios are subjected to step-wise increasing variable amplitude fatigue loading. The crack mouth opening displacement (CMOD) and AE parameters are analyzed to study the evolution of damage, load carrying and failure mechanisms in under reinforced concrete beams. It is concluded that the presence of reinforcement substantially increases the fatigue life. Further, the CMOD could be used as a criterion for failure in reinforced concrete beams under fatigue loading.

Constraint corrected cycle-by-cycle analysis of crack growth retardation under variable amplitude fatigue loading

Various models exist to predict load interaction effects on fatigue crack growth in variable amplitude loading conditions. Stress overloads have the potential to strongly retard or even arrest a propagating fatigue crack. Whereas global analysis methods (making use of equivalent quantities) allow to describe stochastic loading scenarios, describing the effects of deterministic overloads requires cycle-by-cycle analysis techniques. Within this category, plastic zone models have proven to be effective and pragmatic in terms of calibration. Current models, however, do not account for the effect of crack tip constraint on the plastic zone size, whose estimation is a requirement. This paper develops a novel (“extended”) crack growth formulation based on the traditional plastic zone based Wheeler’s model, taking into account the effect of out-of-plane constraint (plane stress versus plane strain). Calibration of the model requires characterization of shut-off overload ratios for different stress intensity factor levels. The “extended Wheeler” model gives better agreement with experimental tests results than the original and modified Wheeler model.

Research on Random Load Characteristic Based on Mixture Distribution Model

Abstract Random load is one of the inherent attributes of actual working load. It is regarded as the essential prerequisite in fatigue life prediction and reliability evaluation for enhancing the performance of mechanical systems and the safety of operators. This article proposes a statistics-based method of random load characteristic analysis to handle the variable amplitude fatigue loads collected from vehicle experiments. The mixture distribution model of random load was constructed according to the native behavior of gathered data, and the parameters of mixture distribution are estimated to fit the histogram of load counting. A case study of vehicle load is provided, and the goodness of fit is subsequently tested and verifies the credible result.

Normalized strength reserve principle for variable amplitude fatigue life prediction of adhesively bonded aluminium joints/Normalisiertes Festigkeitsreserve-Prinzip für die Vorhersage der Lebensdauer von geklebten Aluminiumverbindungen bei variablen Lastamplituden

Abstract Over the last several decades, adhesive bonding has been validated as a good alternative to traditional joining methods in metallic construction. On the other hand, the main factor that limits the wider use of structural adhesives in civil engineering industry is scepticism about their long-term performance, especially when subjected to variable amplitude fatigue loading. Most of the research on predicting the fatigue life of adhesive joints subjected to this type of loading dealt with composite adherends. In this paper, straightforward method for prediction of strength degradation and fatigue failure under random spectrum loading is presented and validated for the case of adhesively bonded single lap joints made of aluminium adherends. It is based on the normalized strength reserve principle, proposed by the same authors in their previous research. The normalized strength reserve model is expanded to the case of variable amplitude fatigue, incorporating the cycle mix parameter in order to account for load interaction effects. Very good agreement was obtained between the fatigue life predictions of the presented method and experimental results from the literature.

The Strain energy density to estimate lifetime of notched components subjected to variable amplitude fatigue loading

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

Fatigue damage simulation of tension-tension loaded glass/polyester fiber composites with thickness tapering effects

This study evaluates the capability of a progressive damage method in predicting the fatigue failure in glass/polyester fiber composite materials. Residual material properties in different failure modes have been obtained from testing fatigue-loaded specimens to their ultimate limits. A numerical tool utilizes the experimentally obtained values to simulate the process of damage in more complex models with high interlaminar shear stresses. The tool accounts for fatigue damage through stiffness and strength degradation rules without relying on prior calibration/modifications. Benchmark ply-drop problems under constant and variable amplitude fatigue loadings are simulated and compared against experimental results. Verification case studies show that the numerical tool can predict damage initiation and final fatigue life, successfully.