Variable Amplitude Loading Research Articles

Fatigue life prediction based on a novel improved version of the Corten-Dolan model considering load interaction effect

Corten-Dolan nonlinear damage accumulation model can well describe the fatigue behavior of engineering materials and structures under variable amplitude loads, while the determination of parameter d is difficult and still open. In this paper, a new improved version of Corten-Dolan model is proposed in which the parameter d is modified by introducing the power form of the stress ratio between two consecutive load levels to reflect the nonlinear effect of load interaction. Furthermore, a generalized expression of the new model is developed, which gives a unified theoretical formulation for the presented and some typical existing versions. The proposed model is validated by comparison with existing versions based on the experimental data of typical engineering materials under two-level and multilevel loads. An effective validation scheme is introduced to comprehensively investigate the validity and applicability of the developed model. In this scheme, parts of data those are not used in modeling are regarded as the check data to examine the prediction accuracy. The results show that the developed model can well reflect load interaction effect and give more satisfactory prediction of fatigue life.

An Ordinary State-Based Peridynamic Model for Fatigue Cracking of Ferrite and Pearlite Wheel Material

To deal with a new-developed ferrite and pearlite wheel material named D1, an alternative ordinary state-based peridynamic model for fatigue cracking is introduced due to cyclic loading. The proposed damage model communicates across the microcrack initiation to the macrocrack growth and does not require additional criteria. Model parameters are verified from experimental data. Each bond in the deformed material configuration is built as a fatigue specimen subjected to variable amplitude loading. Fatigue crack initiation and crack growth developed naturally over many loading cycles, which is controlled by the parameter “node damage” within a region of finite radius. Critical damage factors are also imposed to improve efficiency and stability for the fatigue model. Based on the improved adaptive dynamic relaxation method, the static solution is obtained in every loading cycle. Convergence analysis is presented in smooth fatigue specimens at different loading levels. Experimental results show that the proposed peridynamic fatigue model captures the crack sensitive location well without extra criteria and the fatigue life obtained from the simulation has a good correlation with the experimental results.

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.

Quantitative analysis of overload effect at crack tip on crack growth rate of 7005 aluminum alloy

A new fatigue crack growth rate model is proposed considering overload effect, which could quantitatively describe the crack growth rate considering overload from variable-amplitude load. Residual stress intensity factor Kq caused by overload was put forward by defining stress ratio Rc and obtained by XFEM. Three typical overload situations are studied and reappearance of the threshold stage was elaborated by compact tension tests. The effective scope of the overload is the width of the plastic zone, within the region the stress ratio rises quickly and then become stable. Threshold stage reappeared only when overloads by the higher preload effect were conserved.

Interior microscopic cracking behavior and microstructure-fatigue based damage evaluation of case-hardened steels under variable amplitude loading

Variable amplitude loading tests were performed to clarify the interior cracking behavior for three case-hardened steels under stress ratios in high-cycle and very-high-cycle regimes, and to develop a microstructure-fatigue based damage evaluation approach. The round beach marks are observable within fisheye, and the fine granular area is more obvious under compressive stress. The microcrack effect is responsible for fatigue cracking in very-high-cycle regime. The approach mainly involves: (i) definition of remaining life factor, (ii) conversion of correlation function and (iii) reconstruction of stress-life curve with failure behavior. The agreement between predicted and experimental results is good within factor-of-two boundaries.

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.

Residual stress relaxation in HFMI-treated fillet welds after single overload peaks

The induction of near-surface compressive residual stress is an important factor for fatigue life improvement of HFMI-treated welded joints. However, the relaxation of these beneficial residual stresses under single overload peaks under variable amplitude and service loads may significantly reduce fatigue life improvement. For this reason, several recommendations exist to limit the maximum applied load stress for this kind of post-treated welded joints. In this work, the effect of single tension and compression overloads on the relaxation behavior of HFMI-induced residual stresses was studied experimentally by means of X-ray and neutron diffraction techniques complemented by numerical simulation at transverse stiffeners made of mild S355J2 steel and high strength S960QL steel. Loads were applied close to the real yield strength of the base material. Significantly different relaxation behavior was observed for S355J2 and S960QL steel. Furthermore, high compression loads lead to full residual stress relaxation at the weld toe of S960QL and moderate relaxation for S355J2. High tension loads lead only to slight relaxation.

Cyclic Behavior of Steel Frame Joints in the Offshore Atmospheric Environment

The natural deterioration of mild steel elements exposed to offshore atmospheric environments compromises the long-term safety of existing steel buildings. An experimental study was conducted to investigate the effect of the offshore atmospheric environment on the seismic performance of steel frame joints. An indoor accelerated corrosion test was conducted to simulate the degradation of the mechanical properties of the materials and steel frame joints in the offshore atmospheric environment. After determining the corrosion rate by weighing after rust removal, the yield strength, ultimate strength, modulus of elasticity, and elongation of three test specimen with different thicknesses were obtained by regression of the tensile failure test, which demonstrated a linear decay relationship with the corrosion rate. Under four different corrosion degrees and three different low-cycle reciprocating loads, the failure modes of 12 steel frame joints were all plate-tearing at welded through holes. However, the difference is that the joints had ductile failure under equal-amplitude 90 mm loading and brittle failure under variable-amplitude loading. The effects of corrosion on the hysteresis behavior, deformation degradation, strength degradation, and energy dissipation capacity of steel frame joints were analyzed. The test results indicate that corrosion has significant effects on the seismic performance of steel frame joints. With the increase in corrosion degree, the energy dissipation capacity of steel frame joints declines more significantly than other performance indicators, and the yield platform of the steel frame joints is not evident.

Fatigue Crack Growth Kinetics in a 2024-T3 Aluminum Alloy during Alternating Cyclic Loading

The fatigue crack growth kinetics in a 2024-T3 aluminum alloy during constant- and variable-amplitude loading a various stress ratios in the medium-amplitude segment of a fatigue crack growth rate curve is studied. Variable-amplitude loading is represented by quasi-random samples of standard random loading spectra, which were preliminarily schematized using a rainflow algorithm. Parameters are proposed to estimate the character of random loading. The influence of the character of random loading using various standard spectra on the fatigue crack growth rate is analyzed. The fatigue crack growth time is estimated with allowance for fatigue crack closure and the character of random loading using a proposed formula and a cycle-by-cycle calculation method.

Application of life-dependent material parameters to lifetime calculation under multiaxial constant- and variable-amplitude loading

This study investigated the application of the life-dependent material parameter concept to stress-based fatigue criteria for fatigue life prediction under multiaxial variable-amplitude loading. Different multiaxial fatigue criteria were applied to the fatigue life calculation with fixed and life-dependent material parameters under constant- and variable amplitude loading. Uniaxial variable-amplitude loading was applied to select the appropriate damage accumulation rule. The verification was based on experimental tests with 133 specimens made of S355 steel. Significant improvements in the fatigue life prediction under both constant- and variable-amplitude loading were observed with the applied concept.

Fatigue crack growth modelling of Fão Bridge puddle iron under variable amplitude loading

This study addresses the fatigue crack growth behaviour of a material from an old riveted steel bridge, the Portuguese Fão Bridge, based on an experimental program of constant and variable amplitude loading tests. The material under consideration is a centenary puddle iron, for which information on fatigue crack growth under variable amplitude loads is not available in the literature. Additionally, the experimental program aimed at analysing the fracture surfaces of the specimens through observations under Scanning Electron Microscopy (SEM), and correlate their characteristics with macroscopic fatigue crack growth behaviour. Furthermore, a crack closure analysis was performed using electrical strain gauges applied on the back face of the CT specimens. The fatigue crack propagation along the parallel to the rolling direction (L) revealed to be higher when compared with the transverse direction (T). The experimental data obtained in this study were compared with existing fatigue crack propagation models, such as the Paris model with linear damage accumulation, according to Miner’s rule, as well as with more complex crack propagation models, with capacity for modelling retardation effects of single overloads. The Paris model with linear damage accumulation, despite its simplicity, led to the best predictions for the generality of variable amplitude random block loading. The original Wheeler model is enough to correlate the crack propagation data under overloads, since the application of more sophisticated models would not be justified by the extremely high scatter observed in these old materials.

Experimental Research on Anchoring Behavior of Chemical Anchor Bolt under Repeated Loading

To study the anchoring behavior of chemical anchors under repeated loading, 33 test pieces were designed and fabricated based on the specifications. Each 3 test pieces were 1 set, that is, 1 set of comparative test pieces and 10 sets of test pieces, respectively, for static force. Bonding and anchoring performance tests for loading and reloading. Through the analysis of the test phenomena and results, the following conclusions are drawn: when the loading load exceeded 0.9 times the ultimate bearing capacity of the anchor; when the loading load was equal to 0.6 or 0.75 times, the test piece would undergo splitting damage after the set number of loading times, and its bearing capacity would increase. As the number of loading increased, the energy consumption would gradually decrease, and the decreasing amplitude would gradually increase. Compared with constant amplitude loading and variable amplitude loading, it is found that the slip value of variable amplitude loading increased by 42.1% and the bearing capacity decreased by 12%, which indicated that variable amplitude loading has a great influence on the bonding and anchoring performance of specimens.

Online fatigue damage evaluation method based on real-time cycle counting under multiaxial variable amplitude loading

To realize on-line multiaxial fatigue damage evaluation for the servicing mechanical components, a real-time multiaxial cycle counting method is proposed, meanwhile, an online multiaxial fatigue damage evaluation method based strain-critical plane model is given and validated by the fatigue experimental data of En15r steel. Investigation showed that the proposed on-line multiaxial fatigue damage evaluation method could provide satisfactory evaluation results, and the real-time performance of the proposed cycle counting method is path-dependent.

Real-time damage evaluation method for multiaxial thermo-mechanical fatigue under variable amplitude loading

A real-time multiaxial thermo-mechanical damage evaluation method was proposed under variable amplitude loading. In order to achieve real-time damage evaluation, a real-time multiaxial cycle counting method that can take into account temperature loading history was proposed. The proposed multiaxial cycle counting method can obtain the reversals one by one in order with the reading of the load-time history data, which can realize the damage calculation immediately as a single reversal is counted out. At the same time, to consider the effect of temperature loading on the damage accumulation, an equivalent temperature was determined for the time period of the counted reversal. A fatigue-oxidation-creep damage model that can consider the influence of the non-proportional additional hardening on the fatigue, oxidation and creep damages was used to predict the lives in cases of isothermal axial-torsional fatigue, uniaxial thermo-mechanical fatigue and axial-torsional thermo-mechanical fatigue under constant and variable amplitude loadings. The results showed that the prediction errors were within a factor of 2.

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.

Fretting fatigue under variable amplitude loading considering partial and gross slip regimes: Numerical analysis

The main aim of this work was to numerically investigate the effect of sequences of variable amplitude shear loading on contact tractions/stresses and on the development of life estimation methodologies for these more challenging loading histories. In this setting, a finite element (FE) model has been implemented in order to simulate a cylinder on plane contact problem for an aeronautical Al 7075-T651 alloy. High-Low (H-L) and Low-High (L-H) shear amplitude loading sequences under partial and gross slip conditions were considered in three different case studies. For the case studies where gross slip was involved, the proposed life estimation procedure was enhanced to include the effect of material loss due to wear. More explicitly, such procedure was based on the use of (i) the SWT (Smith-Watson-Topper) multiaxial fatigue model, (ii) the Theory of Critical Distances, (iii) Miner's cumulative damage rule and (iv) the numerical update of the contact surfaces profiles (for loading blocks under gross slip). The numerical analyses for the case studies under partial slip revealed that, when the presence of wear is neglected in the modelling, the Miner's rule provided a divergence between the expected life for the H-L and L-H loading blocks. This difference was considerably larger when gross slip took place. For the case study involving the presence of gross slip in one of the shear loading blocks, the calculated life tended to infinite when the damage generated by the high amplitude block is greater than a certain critical value. These studies are the basis for an experimental programme which will be carried out in the 4 actuators fretting fatigue rig of the University of Brasilia.

Applying fractographic analysis for the evaluation of the effects of variable-amplitude loads on fatigue crack growth rates for the 2024-T3 aluminium alloy

Applying fractographic analysis for the evaluation of the effects of variable-amplitude loads on fatigue crack growth rates for the 2024-T3 aluminium alloy

Fatigue life prediction under variable amplitude loading using a microplasticity-based constitutive model

We predict the fatigue life of a P355NL1 steel alloy under variable amplitude loading conditions using a newly-developed small-strain-based implicit plasticity model. The core idea behind the fatigue model is its capability to capture the inelastic work dissipation due to microplasticity whose critical value determines the fatigue life. Fatigue tests under different variable amplitude load spectra are simulated numerically and the results are compared with experimental data as well as other models for fatigue. It is shown that the model is able to describe the experimental data better than current empirical approaches, using only a few measured, physically motivated parameters.