Constant Amplitude Loading Research Articles

Piecewise stochastic rainflow counting for probabilistic linear and nonlinear damage accumulation considering loading and material uncertainties

A new framework is proposed for probabilistic fatigue life prediction considering randomness from both loadings and material properties. Piecewise stochastic rainflow counting (PSRC) is proposed to transform random loading spectrums to block loadings in a piecewise way with block randomization. The PSRC can be integrated with both linear and nonlinear damage accumulation rules. Mean stress corrected random fatigue limit model is proposed for uncertainty quantification of material fatigue properties under constant amplitude loadings. Probabilistic fatigue life prediction with both loading and material uncertainties is conducted using Monte Carlo simulation and is validated with experimental data from literature and in-house testing. Impact of different mean stress correction models on the fatigue life prediction under random loadings is investigated in detail. The influence of block piece length and block sequence randomization is discussed with respect to the mean and scatter behavior of the probabilistic life prediction results.

Fatigue life prediction of woven composite laminates with initial delamination

AbstractAn engineering approach for fatigue life prediction of fibre‐reinforced polymer composite materials is highly desirable for industries due to the complexity in damage mechanisms and their interactions. This paper presents a fatigue‐driven residual strength model considering the effect of initial delamination size and stress ratio. Static and constant amplitude fatigue tests of woven composite specimens with delamination diameters of 0, 4 and 6 mm were carried out to determine the model parameters. Good agreement with experimental results has been achieved when the modified residual strength model has been applied for fatigue life prediction of the woven composite laminate with an initial delamination diameter of 8 mm under constant amplitude load and block fatigue load. It has been demonstrated that the residual strength degradation‐based model can effectively reflect the load sequence effect on fatigue damage and hence provide more accurate fatigue life prediction than the traditional linear damage accumulation models.

Fatigue of structural adhesives under stress concentrations: Notch effect on fatigue strength, crack initiation and damage evolution

The effect of stress concentrations on the fatigue behaviour of two structural adhesives, relevant materials in lightweight applications, was investigated regarding fatigue strength, crack initiation lifetime, damage evolution and fracture behaviour. Internally and externally notched adhesive bulk specimens were tested under constant amplitude loading with a stress ratio of 0.1. Majority of fatigue lifetime (60–95%) was spent on crack initiation, which was shortened by an increasing stress concentration factor. Crack initiation causes a sudden damage increase near to failure. A model was proposed correlating the fatigue strength of notched specimens with highly stressed region and stress concentration factor.

Application of the S-N Curve Mean Stress Correction Model in Terms of Fatigue Life Estimation for Random Torsional Loading for Selected Aluminum Alloys.

The paper presents the experimental fatigue test results for cyclic constant amplitude loading conditions for the case of the torsion of the PA4 (AW-6082-T6), PA6 (AW-2017A-T4) and PA7 (AW-2024-T3) aluminum alloy for a drilled diabolo type test specimen. The tests have been performed for the stress asymmetry ratios R = −1, R = −0.7, R = −0.5 and R = −0.3. The experimental results have been used in the process of a fatigue life estimation performed for a random generated narrowband stress signal with a zero and a non-zero global mean stress value. The calculations have been performed within the time domain with the use of the rainflow cycle counting method and the Palmgren−Miner damage hypothesis. The mean stress compensation has been performed with the S-N curve mean stress model proposed by Niesłony and Böhm. The model has been modified in terms of torsional loading conditions. In order to obtain an appropriate R = 0 ratio S-N curve fatigue strength amplitude, the Smith−Watson−Topper model was used and compared with literature fatigue strength amplitudes. The presented solution extends the use of the correction model in terms of the torsional loading condition in order to obtain new S-N curves for other R values on the basis of the R = −1 results. The work includes the computational results for new fatigue curves with and without the mean stress effect correction. The results of the computations show that the mean stress effect plays a major role in the fatigue life assessment of the tested aluminum alloys and that the method can be used to assess the fatigue life under random conditions.

Fatigue Crack Growth Behaviour of Sandwiched Metal Panel of Aluminium and Mild Steel under Constant Amplitude Loading

Fatigue Crack Growth Behaviour of Sandwiched Metal Panel of Aluminium and Mild Steel under Constant Amplitude Loading

Fatigue Flexural Performance of Short-Span Reinforced Concrete T-Beams Considering Overloading Effect

Traffic volume increase and higher proportion of heavier trucks have raised the potential risk of fatigue failure of short-span reinforced concrete beams. To investigate the fatigue behavior of short-span reinforced concrete beams with and without the overload effect, nine 5 m reinforced concrete T-beams were cast and tested. Two beams were tested under static loading to determine the ultimate strength; the remaining seven beams were subjected to cyclic loading with constant-amplitude load ranges. In addition, two of the seven beams were subjected to instant overloading. It was observed that the typical failure mode under cyclic loading was the fatigue fracture of tensile reinforcing bars. The introduction of instant overloading resulted in a remarkable reduction of fatigue life. Among all the parameters, the stress range of the reinforcing bars showed the highest effect on the fatigue life. In the end, the fatigue safety provisions in the current reinforced concrete beam design codes were evaluated based on the fatigue limits and S-N curves.

Validation of the fatigue strength assessment of HFMI-treated steel joints under variable amplitude loading

A recommendation for the application and fatigue assessment of the HFMI post-treatment was published by the IIW in 2016. Recently, the therein recommended HFMI design curves in case of constant amplitude loading (CAL) were validated involving test data with different base material yield strengths, increased plate thicknesses, and elevated load ratios. Continuative to this previous work, this paper focuses on the fatigue assessment of HFMI-treated steel joints under variable amplitude loading (VAL). Four test data sets including randomly distributed VAL and a sufficient amount of tested specimens to ensure a statistically verified assessment are investigated. It is shown that an application of the recommended equivalent stress range approach and a further comparison of the test results to the design curves under CAL lead to a conservative fatigue assessment if the recommended value of the specified damage sum of D = 0.5 is used. Furthermore, an increased value of D = 1.0 still maintains a conservative design as presented in the study. Based on this work involving the analysed data sets, it can be concluded that the recommended procedure is well applicable and a conservative fatigue design is facilitated.

Influence of bolts on seismic performance of earthquake-resilient prefabricated sinusoidal corrugated web steel beam-column joints

Earthquake-resilient structures have been widely recognized and applied in the seismic field of prefabricated steel structures due to their excellent performance. The prefabricated sinusoidal corrugated web steel beam-column joint (PSCWJ) with the earthquake-resilient design concept has been previously proposed. To study the impact caused by the bolt parameters on the seismic behavior of the new PSCWJ, five specimens were designed, with varying the number of flange connecting bolts, type of bolt holes, and interval between the middle bolts. A low cycle reciprocating load test and the finite element (FE) simulations were conducted on the specimens to determine the failure mode, energy dissipation capacity, ductility, hysteretic curves, sliding curves, strain curves, skeleton curves, and other main indexes on seismic performance. And the study indicates that the PSCWJ has excellent bearing capacity and seismic performance, the new prefabricated joint can realize the dual energy dissipation by buckling and sliding of the flange cover plate (FCP), and the number of flange connecting bolts directly determines the sliding load of FCPs. A rational interval between middle bolts can control the buckling load of FCPs and provide the joint with a satisfactory bearing capacity. The setting of slotted hole can increase the rotation and energy dissipation capacity of the joint. Further, the energy dissipation performance of the repaired specimens is stable under the low frequency constant amplitude loading, thereby ensuring that the PSCWJ can be used as a damper.

Low-Cycle Fatigue Life Estimation Curve for Buckling-Restrained Braces Based on Cumulative Plastic Deformation

ABSTRACT Buckling-restrained braces (BRBs) are commonly used as a kind of energy dissipator in structures, which can be quickly replaced after strong earthquakes. However, there is no reasonable and effective damage assessment method to quantitatively analyze the damage degree in a BRB. Since the cumulative plastic deformation (CPD) of a BRB is closely related to its loading history, the CPD can reflect the low-cycle fatigue life of a BRB. In this paper, two CPD curves of BRBs under low-cycle fatigue damage are presented: C-CPD curves under a constant strain amplitude (CSA) loading history and R-CPD curves under a random strain amplitude (RSA) loading history. The solving process and the shape of two curves are given. In the C-CPD curve, the influence of different fatigue parameters on the curve characteristics is thoroughly studied. In the R-CPD curve, the rationality of the maximum plastic strain range (Δεpmax) as the evaluation index of the R-CPD curve is verified through a sensitivity analysis. Finally, a parametric analysis of the R-CPD curve is presented. The analysis results show that the two curves both pass through the zero point and present an obvious characteristic of “increasing then decreasing”. The C-CPD curve describes the relationship between Δε p and CPD c of BRBs under CSA loading, which can be derived directly from Coffin-Manson curves. Therefore, the C-CPD curve is only influenced by the fatigue parameters. The R-CPD curve describes the relationship between Δε pmax and CPD c of BRBs under RSA loading, which is fitted with many IDA results. The R-CPD curve is both greatly influenced by the fatigue parameters, and slightly influenced by the building height, the Kd/Kf value and the structure layout. Therefore, the C-CPD curve and the R-CPD curve are inherent curves of BRB. In addition, the sensitivity analysis of the R-CPD curve shows that CPD c is most sensitive to Δε pmax, so the Δε pmax is a reliable parameter to reflect the RSA loading history. The two curves provide a theoretical basis for the low-cycle fatigue life evaluation of BRB.

Study on Crack Closure Considering Welding Residual Stress Under Constant Amplitude Loading and Overloading

Welding residual stress in the engineering structure has a non-negligible influence on crack propagation, and crack closure is a significant factor affecting the crack propagation. Based on the elastoplastic finite element method and crack closure theory, we studied crack closure and residual compressive stress field of butt-welded plates under constant amplitude loading and overloading regarding the stress ratio, maximum load, overload ratio, and number of overloads. The results show that the welding residual tensile stress can decrease the crack closure because of a decrease in the residual compressive stress in the wake zone, but the effect is gradually reduced with increased stress ratio or maximum load. And the combined effect of welding residual tensile stress and overload can produce a stronger retardation effect on crack propagation.

A new multiaxial fatigue life prediction model considering additional hardening effect

The established linear fatigue life prediction model based on the Miner rule has been widely applied to fatigue life prediction under constant amplitude uniaxial and multiaxial loading. Considering the physical significance of crack formation and propagation, a multiaxial equivalent linear fatigue life prediction model is put forward based on Miner rule and critical plane method under constant amplitude loading. The essence of this approach is that the equivalent strain, which consists of the shear strain and normal strain on the critical plane, replaces the relevant parameter of uniaxial nonlinear fatigue damage model. The principal axes of stress/strain rotate under non-proportional loading. Meanwhile, the microstructure of material and slip systems change, which lead to additional hardening effect. The ratio of cyclic yield stress to static yield stress is used to represent the cyclic hardening capacity of material, and the influence of phase difference and loading condition on the non-proportional hardening effect is considered. The multiaxial fatigue life is predicted using equivalent stain approach, maximum shear stain amplitude model, CXH model, and equivalent multiaxial liner model under proportional and/or non-proportional loading. The smooth and notched fatigue specimens of four kinds of materials (Q235B steel, titanium alloy TC4, Haynes 188, and Mod.9Cr-1Mo steel) are used in the multiaxial fatigue experiments to verify the proposed model. The predicted results of these materials are compared with the test results, and the results show that these four models can achieve good effect under proportional loading, but the proposed model performs better than the other three models under non-proportional loading. Meanwhile, it also verifies that the proposed enhancement factor can reflect the influence of phase difference and material properties on additional hardening.

Fatigue Life Behaviour of Transverse Fillet Weld and Transverse Fillet on Weld of the HSLA S460G2+M Followed by HFMI/PIT

This study deals with the fatigue life assessment of the transverse fillet weld and transverse fillet weld on weld fatigue specimen of the offshore steel S460G2+M with a thickness of 10 mm. These specimens were joined using gas metal arc welding (GMAW) with ER80S-N1 filler metal of 1.0 mm in diameter and mixed gases of 80% Ar + 20% CO2 as the consumables. Upon the welding completion, some of the fatigue specimens are treated using high-frequency mechanical impact device called pneumatic impact treatment (HFMI/PIT). The treatment procedure uses 90Hz of frequency, 6 bars of pneumatic pressure and 2 mm pin radius with aims to enhance the lifespan of the specimen. These fatigue specimens are classified in as-welded and HFMI/PIT. The fatigue test was conducted to all fatigue specimens until failure using a 250KN Instron fatigue machine with a constant amplitude loading, a stress ratio of 0.1 and stress loading from 55% to 75% of the yield strength of the base material. The fatigue data were evaluated based on the International Institute of Welding (IIW) evaluation procedures. Further, the fatigue life comparison between the as-welded and HFMI/PIT of both fatigue specimens also with the FAT class recommendation of the IIW for transverse fillet weld is plotted in the S-N curve diagram. Based on the assessment, it is found that the HFMI/PIT fatigue specimens attained higher fatigue life than the as-welded of both fatigue specimens. The most significant of fatigue life improvement after the HFMI/PIT is the HFMI/PIT transverse fillet weld. These treated welds obtained 256 MPa of FAT class which is 79 % higher than FAT class recommended by the IIW for the transverse fillet weld. Besides, the multi-pass welds on the groove weld of the transverse fillet weld on welds are found to contribute to a lower fatigue life of this specimen due to the existing weld defects on the fractured surface of the groove weld.

A cohesive zone model to predict fatigue-driven delamination in composites

A cohesive zone model is proposed to analyse composite delamination propagation under high-cycle fatigue loading. A new method to compute the strain energy release rate at any point within the element fatigue life cycle range is presented. The proposed scheme is based on the J-integral method evaluated at an estimated position of the crack-tip within the element, instead of the element integration points. Furthermore, a new fatigue damage evolution law is proposed to account for the unwanted quasi-static damage during the element fatigue degradation process. The model prediction capabilities were verified against experimental data available in the literature and theoretical solutions using a double cantilever beam configuration for mode I loading, four-point end-notched flexure configuration for mode II loading, and mixed-mode bending configuration for mixed-mode loading. The simulations were performed at both constant and variable amplitude loading. The numerical predictions obtained using the proposed model correlated very well with literature’s experimental data.

Cumulative damage model based on equivalent fatigue under multiaxial thermomechanical random loading

AbstractA new creep–fatigue damage cumulative model is proposed under multiaxial thermomechanical random loading, in which the damage at high temperature can be divided into the pure fatigue damage and the equivalent fatigue damage from creep. During the damage accumulation process, the elementary percentage of the equivalent fatigue damage increment is proportional to that of the creep damage increment, and the creep damage is converted to the equivalent fatigue damage. Moreover, combined with a multiaxial cyclic counting method, a life prediction method is developed based on the proposed creep–fatigue damage cumulative model. In the developed life prediction method, the effects of nonproportional hardening on the fatigue and creep damages are considered, and the influence of mean stress on damage is also taken into account. The thermomechanical fatigue experimental data for thin‐walled tubular specimen of superalloy GH4169 under multiaxial constant amplitude and variable amplitude loadings were used to verify the proposed model. The results showed that the proposed method can obtain satisfactory life prediction results.

Fatigue properties of as-welded and post-weld-treated high-strength steel joints: The influence of constant and variable amplitude loads

In HSS welded structures, HFMI allows fatigue strength improvement factors by inducing compressive residual stresses, cold-worked surface region and modifying the weld toe shape. According to the literature, the factors are proposed based on failures at CAL and also checked with a limited dataset at VAL, the latter being more realistic of service loadings. Therefore, this paper investigates the behaviour of HFMI welds at CAL and VAL for R = −0.43. Studies are also performed at the microstructural level for locating the crack initiation and hardness. Fatigue damage sums are evaluated and discussed with the recommended values in the literature.

Fatigue crack growth of a corner crack at the edge of a hole

The fatigue crack growth (FCG) behavior of a corner crack at the edge of a hole has not been well understood. To address this issue, we first conducted fatigue tests under constant amplitude loading. The results show that the FCG rate along the thickness direction varies nonlinearly with the stress intensity factor range (ΔK) in a log-log scale. This is because the crack-tip stress relaxation at the depth point gets increasingly pronounced as the crack propagates. Finally, we proposed a crack-tip constraint independent FCG rate and the corresponding FCG equation to correlate the crack-tip constraint independent FCG rate with ΔK.

Influence of dynamic-strain aging due to excess Mg on fatigue crack growth rate scatter in Al6061-T6 alloy

Fatigue failure results in high industrial costs, and its mechanism requires close examination; however, current methods are costly and time-consuming due to the need for a large number of test specimens. The purposes of this study are to investigate the influence of dynamic strain aging on fatigue crack growth rate (FCGR) scatter in Al 6061-T6 alloys and to present a new approach to evaluate the scatter of FCGR using a limited number of the test specimen. Rotating bending fatigue tests of 6061-T6-based Al alloys with added Zr and excess Mg were performed under constant amplitude loading using smooth specimens. The scatter behavior of FCGR is investigated by examining the fatigue crack growth on the specimen surface and fractographic observation on the fracture surface. The accounting for the interaction effects of multiple surface cracks and fractographic examination on striation formation from previous findings revealed that excess Mg promoted small scatter in Mode I fatigue crack growth. This study showed that local plastic deformation affected the FCGR scatter of microstructurally-large fatigue cracks. These findings suggest that dynamic strain aging of Mg induces stable Mode I crack growth due to pinning of dislocation movement on slip planes during the crack growth process.

Fatigue Crack Growth for Ferritic Steel Under Negative Stress Ratio

Abstract The phenomenon of crack closure is important in the prediction of fatigue crack growth behavior. Many experimental data indicate crack closures during fatigue crack growths both under tensile–tensile loads and tensile–compressive loads at constant amplitude loading cycles, depending on the magnitude of applied load amplitudes and stress ratios. Appendix A-4300 of the ASME Code Section XI provides two equations of fatigue crack growth rates for ferritic steels expressed by stress intensity factor ranges at negative stress ratios. The boundary of the two equations is classified with the magnitude of applied stress intensity factor ranges, in consideration of the crack closures. However, the boundary value provided by the ASME Code Section XI is not technically well known. The objective of this paper is to investigate the influence of the magnitudes of the applied stress intensity factor ranges on the crack closures. Fatigue crack growth tests using ferritic steel specimens were performed in air environment at room and high temperatures. From the crack closures obtained by the tests, it was found a new boundary which is smaller than the definition given by the Appendix A-4300.

Failure analysis of cryogenically treated H13 specimen in rotating bending fatigue

The fatigue failures start at the surface mostly in case of forging die steels like AISI H13. The aim of this work is to analyse the effect of cryogenic treatment on delayed failure of H13 steel specimens subjected to rotating bending fatigue. The specimens were hardened at 1020 °C, double tempered at 500 °C for 2 h, followed bycryogenic treatment in a cryo-chamber at minus 185 °C for 16 h and soft tempering at 100 °C. The room temperature fatigue test was carried out on rotating bending fatigue testing machine at 3000 rpm with constant amplitude loading. X-ray diffraction studies were carried out along with microstructural details. It was established that fine grained structure, precipitation of fine carbides in the tempered marten site, increased carbide density and harder structure were responsible for the delayed crack propagation and thereby increasing the fatigue life of the cryogenically treated H13 steel in comparison with the conventionally treated specimens in high cycle fatigue regime.

Time-variant fatigue reliability evaluation of riveted lap joint under stationary random loading

This article focuses on the time-variant reliability assessment of riveted lap joint structure subjected to fatigue. A physics-based fatigue crack growth model that can take the crack closure into account is derived to calculate the crack length at different time under arbitrary loading. In addition, several uncertainties are quantified, including the material, initial crack size, and loading condition. The stationary random loading is a common service environment in practice, in which the stress range and stress ratio vary with constant statistical characteristics (the mean and standard deviation). The time-variant fatigue reliability of riveted lap joint under stationary random loading is assessed by introducing the outcrossing concept. The experimental data of 2024-T3 aluminum alloy riveted lap joint under constant amplitude loading are used to validate the physics-based fatigue crack growth model. It is verified that this proposed model can predict the fatigue life probability distribution with a reasonable accuracy. In addition, the simulation of riveted lap joint under stationary random loading is performed. The time-variant fatigue reliability is evaluated. The results with or without considering crack closures are also compared. It is noted that the results from the time-variant fatigue reliability assessment considering crack closure has higher reliability level.