Variable Amplitude Load Histories Research Articles

Fatigue behavior of a nodular cast iron subjected to a variable amplitude strain-based load spectrum applied in bench tests of an Off-highway axle

Nodular cast irons are commonly adopted in off-highway applications, owing to the possibility to shape complex components and to guarantee good mechanical properties. In the fatigue strength assessment of axles made of nodular cast irons, engineers have to deal with external loads that turn into local strain spectra at the fatigue crack initiation zones, which are usually located in areas weakened by notched geometrical details. Moreover, off-highway axles are subjected to variable amplitude load histories during their service life; during the design phase, the field load histories are usually applied to the axles in the form of simplified bench load spectra. In this paper, the mechanical properties of EN-GJS-500-7 have been investigated through static tensile tests and strain-controlled fatigue tests performed on specimens with machined surface extracted from an axle. Furthermore, a local strain-based spectrum has been derived by means of strain gauges which have been applied at the failure location of the axle during the bench tests. Finally, the damage index to failure relevant to the simplified bench load spectrum has been calculated by adopting Miner's linear damage rule and the Smith, Watson and Topper mean stress corrected life equation.

Fatigue behavior of transverse attachments under constant and variable amplitude loading from a Swiss motorway bridge

This paper investigates the fatigue behavior of non-load-carrying transverse welded steel attachments by reporting on an experimental characterization under constant and variable amplitude loading. Fatigue cracks have been monitored using DIC and ACPD techniques and fracture surfaces are analyzed to obtain information about nucleation sites and crack depth. The applied variable amplitude load history has been obtained from traffic measurements from a Swiss road bridge. A procedure has been proposed resulting in a Markov transition matrix representative for the measured strain signal and the random resampling of the stress history to be applied for the variable amplitude fatigue tests.

Research on Damage Mechanism and Performance-Based Design Process of Reinforced Concrete Column Members

In order to understand the seismic damage assessment of reinforced concrete column members, the coupling relationship between the capacity degradation and the accumulated hysteretic energy and the displacement history was considered. The energy-based damage index under the random variable amplitude loading history was proposed. On the basis of preliminary research, the corresponding relationship between the damage index and the construction member parameters and seismic parameters was established, the damage mechanism was analyzed according to the damage index, and then the performance-based design process was proposed. It was found that increase in the stirrup ratio can slow down the damage, and the slowing effect was initially fast and then slows. When the reinforcement ratio is doubled, the damage index decreased by 0.063. The longer the earthquake duration was, the more serious the damage was, and this phenomenon was more obvious when the ductility coefficient was larger. With the increase in the ductility coefficient, the damage continuously increased. Therefore, it is an effective way to decrease the damage by controlling the ductility coefficient. Among all the influencing factors, the fundamental period and seismic intensity contributed more significantly to the damage indicators. When the damage index (performance objective) was determined, the target stirrup ratio can be obtained according to the proposed performance design process, that is, this design process can be used in the performance-based design. The design method based on damage index can make up for the deficiency that the design method based on the ductility coefficient does not consider the earthquake duration.

Optimizing the Voce–Chaboche Model Parameters for Fatigue Life Estimation of Welded Joints in High-Strength Marine Structures

This work studies the Voce–Chaboche (V–C) material model parameter optimization for high-strength steel welded joints subjected to cyclic loading. The model parameters of each material zone in a S690 steel butt-welded joint were determined using an optimization algorithm based on the Newton trust region (NTR) method and an accumulated true strain parameter. The model parameters were fitted to stress–strain histories from uniaxial strain-controlled cyclic tests. To validate the model, fully-reversed variable amplitude fatigue experiments were performed under load control. The experimental results were then compared to numerical results from a finite element analysis. When the elastic modulus is optimized as a V–C parameter, the results indicate that the V–C model slightly underestimates the strain range, leading to conservative fatigue life estimates. However, the results can be improved by using an elastic modulus obtained experimentally. In this case, the resulting material model slightly overestimates the strain range, leading to a non-conservative, but more accurate, fatigue life estimation. It can be concluded that the NTR-based accumulated true strain approach successfully determined the V–C model parameters for different material zones in the welded joint, and closely estimated the strain range and the fatigue life for a variable amplitude load history.

Fatigue Life Scatter Modeling and Failure Probability Prediction of Multisite Damage Structural Part under Variable Amplitude Load History

An “index stress” (a constant amplitude cyclic stress) is introduced to characterize the scatter of the fatigue life under a variable amplitude load history. It is defined as a fatigue damage weighted average of the amplitudes of the individual stress cycles in a variable amplitude load history. The fatigue test results show that the scatter of fatigue life under variable amplitude load histories can be well characterized by such defined index stress. For probabilistic fatigue life prediction and failure probability estimation, a multiple-site damage structural part is taken as a series system, and the total probability theorem is applied to reflect the effect of load history uncertainty on failure probability.

Analysis Of Real-Life Multi-Input Loading Histories For The Reliable Design Of Vehicle Chassis

In order to reliably design automotive structures, engineers need to determine and justify validation conditions and levels. These must stem from a thorough knowledge of structural damage induced by service loading conditions. From multi-input variable amplitude loading histories applied on a car’s wheel axles, we propose a multidimensional pseudo-damage description for the design of car chassis weak points. We present a multivariate description of client loading histories. We use it in a statistical analysis of a labelled measurement campaign to explain the heterogeneity of car driver profiles. Finally, we explore the question of complex load damage reconstruction using proving ground reference loads.

Low-cycle fatigue life evaluation of buckling-restrained braces based on cumulative plastic deformation curves

To quantitatively evaluate the low-cycle fatigue life of buckling-restrained braces (BRBs), an evaluation method for BRBs based on the combination of the CPD curves and CPD measurement meter (CMM) is established herein. The difference between two CPD curves (i.e., the CPD curves under constant strain amplitude loading history (C-CPD) and under random strain amplitude loading history (R-CPD)), and their selection criteria to evaluate the low-cycle fatigue life of BRBs are discussed. An example under the variable strain amplitude (VSA) loading history and an example under the multiple earthquakes are carried out. Finally, the CPD limit values of BRBs in the ANSI/AISC 341-10 and FEMA-450 are discussed by statistical analysis of the test results of BRBs. The analysis results show that the C-CPD curve can be used to evaluate the low-cycle fatigue life of BRBs under the VSA loading, and the R-CPD curve can be used to evaluate the low-cycle fatigue life of BRBs under the multiple earthquakes. The degree of reliability of the current CPD limit value is not enough. A CPD limit curve is recommended in this study to quantify the low-cycle fatigue performance of BRBs.

On fatigue life scatter under variable-amplitude load history

Fatigue life scatter under a variable amplitude load history is determined by many factors such as the amplitudes of the individual load cycles, the number of the load cycles with different load levels, and the differences between the load levels as well. Besides an brief overview on the studies and experiments on the scatter of fatigue life under variable amplitude load histories, the present paper conducted a series of fatigue tests, demonstrates the life scatters under different load histories, and discusses the dominant factors of fatigue life scatter. It shows that all the load cycles play their roles for the life scatter.

Cyclic behaviour and hysteretic model of austenitic stainless steel bolted T-stubs

The aim of this paper is to investigate the hysteretic behaviour of stainless steel bolted T-stub connections. A total of 22 bolted T-stubs in austenitic grade EN 1.4301 were tested under monotonic loading and cyclic loading under both variable and constant amplitudes. The tested T-stubs were carefully designed with two different bolt configurations and were fabricated with two types of stainless steel bolts – A4–70 and A4–80 thus allowing different failure modes to be obtained. Three additional bolted T-stubs in carbon steel grade Q345B were used as benchmark specimens to facilitate a direct comparison of the performance of carbon and stainless steel T-stubs under cyclic loads. Monotonic loading tests were conducted to acquire basic parameters of the cyclic loading protocols employed in the cyclic loading tests. The hysteretic responses of the tested T-stubs under two variable amplitude loading histories and three proportional constant amplitude loading histories were recorded and were further analysed in terms of failure characteristic, hysteresis response, skeleton curve, energy dissipation and strength degradation. Based on the evolution of the hysteresis curves, standard hysteresis loops were acquired and were used to develop a novel hysteretic model able to simulate the initial loading branch, the unloading branch and reloading branch of the hysteretic response. It has been demonstrated that the developed hysteretic models provide a close agreement with the obtained experimental results and can thus be used to estimate the expected energy dissipation of bolted stainless steel connections subjected to cyclic loads.

A review of effective-strain based and multi R-ratio crack propagation models and a comparison of simulated results using the two approaches

Several theories and methodologies for running effective-strain and effective-stress based crack propagation models are reviewed. Crack closure behaviour and effective crack growth rate data for various steels were collected and showed that the effective crack growth rate is independent of steel hardness and R-ratio.Crack propagation simulations on a centre elliptical notched specimen were run under constant amplitude and variable amplitude load histories. Two crack propagation models were employed: 1. An effective-strain based model; and 2. A multi R-ratio crack propagation model. A comparison of simulated results from the two models with experimental data shows a good match.

Effects of Axial and Multiaxial Variable Amplitude Loading Conditions on the Fatigue Life Assessment of Automotive Steering Knuckle

In this paper, the author has attempted to investigate the effects of different loading conditions including axial and multiaxial variable amplitude loading (VAL) on the fatigue life assessment of automotive components under various maneuvers. To this end, a case study was conducted on the cast iron steering knuckle of a passenger car. In fact, the various VAL histories are entered on the three joints of knuckle, namely steering linkage, lower control arm, and MacPherson strut. However, previous studies have shown that this high super-critical component fails through the steering linkage. Moreover, the rotation of the steering linkage is the most destructive load. Hence, in this research, different loading cases such as axial (destructive load as means 1 channel), multiaxial (only relates to loading on the joint of knuckle and steering linkage means 3 channels), and full multiaxial (including all loading time histories means 9 channels) were considered. Afterward, finite element analysis was performed for each case, and fatigue life of the component was predicted under different conditions. Next, fatigue life of the component was evaluated using the time histories of stress tensor in the root of steering linkage which is extracted by transient dynamic analysis and applying probabilistic approach based on the Liu–Zenner equivalent stress criterion. Eventually, the responses from both techniques were compared in different cases. The results reveal that life predicted using two methods are slightly different. But, the results of probabilistic approach are more accurate than the results of FEM in comparison with experimental data for the axial state. Also, one of the major achievements of this study is that for the components with complex geometry and under multi-input loading like the steering knuckle, it is essential to perform fatigue analysis by considering all real conditions and cannot be only focused to the destructive loading.

Remaining Useful Life Predictions in Lithium-ion Battery under Composite Condition

In these days, there is a tendency that research of Prognostics and Health Management (PHM) of lithium-ion battery that prevent accidents in advance by predicting the Remaining Useful Life (RUL). However, there is a difficulty in battery evaluation for composite condition of an operating conditions and a storage conditions, due to the time consuming. Research on the RUL of lithium-ion battery in composite condition are progressing by combining an operating condition and a storage condition. Conventional method such as Miner’s Rule may not fully meet the needs of battery evaluation for RUL. Because it does not take into account overloads caused by a variable amplitude loading history. In order to solve the problem of accurately predicting the RUL of lithium-ion battery, two approaches applied to predicting the RUL of lithium-ion battery. We demonstrate the usefulness of two proposed methods by comparing with real-data of composite condition.

Incorporation of Mean/Maximum Stress Effects in the Multiaxial Racetrack Filter

This work extends the Multiaxial Racetrack Filter (MRF) to incorporate mean or maximum stress effects, adopting a filter amplitude that depends on the current stress level along the stress or strain path. In this way, a small stress or strain amplitude event can be filtered out if associated with a non-damaging low mean or peak stress level, while another event with the very same amplitude can be preserved if happening under a more damaging high mean or peak stress level. The variable value of the filter amplitude must be calculated in real time, thus it cannot depend on the peak or mean stresses along a load event, because it would require cycle identification and as so information about future events. Instead, mean/maximum stress effects are modeled in the filter as a function of the current (instantaneous) hydrostatic or normal stress along the multiaxial load path, respectively for invariantbased and critical-plane models. The MRF efficiency is evaluated from tension-torsion experiments in 316L stainless steel tubular specimens under non-proportional (NP) load paths, showing it can robustly filter out nondamaging events even under multiaxial NP variable amplitude loading histories. KEYWORDS. Multiaxial racetrack filter; Mean/peak stress effects; Nondamaging events; Multiaxial loads.

An elasto-plastic approach to estimate lifetime of notched components under variable amplitude fatigue loading: a preliminary investigation

The present paper is concerned with the formulation of an elasto-plastic strain based approach suitable for assessing fatigue strength of notched components subjected to in-service variable amplitude cyclic loading. The hypothesis is formed that the crack initiation plane is closely aligned with the plane of maximum shear strain amplitude, its orientation and the associated stress/strain quantities being determined using the Maximum Variance Method. Fatigue damage is estimated by applying the Modified Manson-Coffin Curve Method (MMCCM) along with the Point Method (PM). In the proposed approach, the required critical distance is treated as a material property whose value is not affected either by the sharpness of the notch being assessed or by the profile of the load spectrum being applied. The detrimental effect of non-zero mean stresses and degree of multiaxiality of the local stress/strain histories is also considered. The accuracy and reliability of the proposed design methodology was checked against several experimental data taken from the literature and generated under different uniaxial variable amplitude load histories. In order to determine the required local stress/strain states, refined elasto-plastic finite element models were solved using commercial software ANSYS®. This preliminary validation exercise allowed us to prove that the proposed approach is capable of estimates laying within an error factor of about 2. These preliminary results are certainly promising, strongly supporting the idea that the proposed design strategy can successfully be used to assess the fatigue lifetime of notched metallic components subjected to in-service multiaxial variable amplitude loading sequences.

A methodology for variable amplitude fatigue analysis of HFMI treated welds based on fracture mechanics and small-scale experiments

A methodology is developed using strain-based fracture mechanics (SBFM) and an effective strain-life (ESL) model for the fatigue analysis of as-received and high frequency mechanical impact (HFMI) treated structural steel welds. The methodology includes a crack closure model and accounts for the residual stress state at the weld toe. Several required input parameters for mild structural (CSA 350W) steel were obtained using relatively simple and inexpensive small-scale fatigue tests of smooth specimens, conventional monotonic and cyclic materials tests, laboratory measurements, and residual stress measurements. The ESL modelling component of the methodology is validated using direct crack growth measurements. The SBFM model is evaluated using the results of fatigue tests on weld specimens and is found to be capable of accurately or conservatively predicting the fatigue performance of the as-received and impact treated welds under one constant and two variable amplitude loading histories.

Fatigue bearing failure of CFRP composite in bolted joints exposed to biaxial variable amplitude loading at elevated temperature

Hybrid structures that contain composite–aluminium interfaces tend to develop internal loads at elevated temperatures. In long bolted joints, the thermally induced bolt loads are superimposed onto the mechanically applied load and can induce a biaxial bearing load state. This paper presents an experimental and numerical study of the bearing fatigue failure of carbon–epoxy laminate specimens, exposed to uniaxial and biaxial variable amplitude loading at 90°C. A specifically designed experimental rig was used, where both the mechanical and the thermally induced bolt loads were applied by means of mechanical load actuators. A fatigue model based on the kinetic theory of fracture for polymers, which was previously implemented for constant amplitude loading, is expanded to account for the variable amplitude load history. The results suggest that the biaxial loading gives a longer fatigue life than the uniaxial loading for the same maximum peak resultant force. This result can be utilized as a conservative dimensioning strategy by designing biaxially loaded joints in terms of maximum peak resultant bearing load using uniaxial fatigue data.

Generalization of the moment of inertia method to estimate equivalent amplitudes for simplifying the analysis of arbitrary non-proportional multiaxial stress or strain histories

Several models have been proposed in the literature to account for fatigue damage under multiaxial load histories. Most of them require some measure of an equivalent stress or strain amplitude, in the sense of causing the same damage as the original history, which may be difficult to obtain for generic non-proportional multiaxial variable amplitude load histories. To identify individual load cycles, a multiaxial rainflow-like algorithm must be employed. For each rainflow-counted cycle, the equivalent stress or strain amplitude along its path is often computed using the so-called convex enclosure methods, which find minimum spheres, ellipsoids, or rectangular prisms that contain the load path in a deviatoric stress or strain space. However, such procedure involves information loss, in special if the path shape is very different from the shape of the enclosing convex surface, resulting in poor estimates of equivalent stress or strain amplitudes. To overcome this problem, the moment of inertia (MOI) method has been proposed in Meggiolaro and Castro (Int J Fatigue 42:217–226, 2012) to calculate equivalent amplitudes and mean components of two-dimensional stress or strain paths, generated, e.g., by tension–torsion or biaxial histories. In this work, the MOI method is extended to deal with generic 6D stress or strain paths, which include all normal and shear components. To accomplish that, the load history path is first represented in a 5D deviatoric stress or strain space and then assumed to be a homogeneous wire with unit mass, whose perimeter centroid is used to estimate the location of the path mean component. Then, the polar moment of inertia (PMOI) of such a hypothetical wire with respect to its mean component is calculated. The PMOI represents the distribution of the path about a single point, the perimeter centroid, giving a measure of how much the path stretches away from its mean component, which is used in the calculation of the equivalent amplitudes. Experimental results for 13 different multiaxial load histories prove the effectiveness of the proposed method to predict equivalent amplitudes and multiaxial fatigue lives.

Fatigue behavior of AHSS lap shear and butt arc welds including the effect of periodic overloads and underloads

The effect of periodic overloads and underloads, which is a common occurrence in service load histories, on the fatigue behavior of AHSS (Advanced High Strength Steel) single lap shear and butt arc welds is investigated. A series of constant amplitude tests under tensile loading condition (R=Pmin/Pmax=0.1) were performed to obtain load amplitude-life curves for each type of arc welded joint. Variable amplitude load history tests, one with periodic overloads and another with periodic underloads were then conducted for each type of welded joint. Additional constant amplitude fatigue tests at a high load ratio (R≈0.6) representing the small cycles in the periodic underload loading were also performed. The validity of linear cumulative damage rule in the prediction of the fatigue life of these structures under variable amplitude loading is investigated. The results of the tests show that while periodic overloads did not affect the fatigue life of the welded joints, periodic underloads decreased the fatigue life. Finite element analyses were conducted to simulate the stress and strain states at the weld locations under overloads and underloads, the results of which were used to explain the observed experimental observations.

Influence of Semi-Circular Cracks on Threaded Connection Fatigue by Means of Kitagawa-Takahashi Diagram and El Haddad Equation

Evaluation of semi-circular surface crack influence on threaded connection fatigue behavior, made of 42CrMo4 heat treatable steel, was carried out. Crack diameters were defined as 0.02, 0.05, 0.1, and 0.15 mm. Influence of semi-circular surface cracks was investigated by means of Kitagawa–Takahashi diagram and El Haddad equation. Assessments were done for survival probability of 99% on detailed FE model with normal metric thread profile and preload force at 70% of force at bolt yield point. The most critical location on threaded connections usually are thread roots which contain a very high notch effect. In order to accurately consider multiaxial stress field in thread root, multiaxial fatigue stress criterion based on a critical plane theory for fatigue assessment, was used. Mean stress influence was taken into account by means of Haigh diagram. Variable amplitude loading history of low-high (Lo-Hi) sequence spectrum was analyzed with the numerical algorithm of Rainflow cycle counting in the time domain. Fatigue damage was calculated according to the modified Palmgren-Miner linear damage accumulation hypothesis.

A round robin study of high-frequency mechanical impact (HFMI)-treated welded joints subjected to variable amplitude loading

High-frequency mechanical impact (HFMI) treatment has been significantly developed as a reliable, effective and user-friendly method for post-weld fatigue strength improvement technique for welded structures. The development of an International Institute of Welding best practice guideline for implementing HFMI has been hindered by the lack of directly comparable experimental data for numerous HFMI methods. In this study, nominally identical longitudinal attachments in high-strength steel were manufactured in one welding workshop and distributed to four HFMI equipment manufacturers for treatment. Specimens were fatigue tested on a machine using identical variable amplitude loading histories. HFMI groove measurements were done for each specimen and X-ray diffraction-based residual stress measurements were performed on 10 specimens. The HFMI groove dimensions and the residual stress states showed similarity in general, however small changes were observed. Experimental results indicate that all of the HFMI-improved welds from the HFMI equipment manufacturers satisfied the previously proposed characteristic S-N line based on both the yield strength and the specimen geometry. Results of the study are valuable and promising with respect to the development of a future guideline. The goal of the study has not been to compare treatments, so specific data points are not associated specific HFMI equipment manufacturers.