Variable Amplitude Loading Research Articles

A Hybrid ANN Multiaxial Fatigue Model for the Assessment of Fretting Fatigue under Variable Amplitude Shear Loading.

To foresee the life of fretting fatigue with variable shear amplitude loading, a hybrid model incorporating non-local multiaxial fatigue parameters and artificial neural networks (ANN) in conjunction with cumulative damage models has been proposed. The model has been developed based on equivalent stress parameters associated with crack nucleation and Miner's cumulative damage rule-inspired models, enabling the assessment of the impact of variable amplitude loading. To validate the models, fretting fatigue tests conducted under variable shear loading amplitude are employed to compare the predictions of four different models. The results demonstrate that while all models provide satisfactory estimates falling within the two-band limit, the hybrid model combining two ANN models outperforms the others and emerges as the most effective in predicting fretting fatigue life under these conditions. The proposed methodology effectively addresses the inherent complexities of fretting fatigue under variable amplitude stress, while also examining the influence of load block order on material behavior. Additionally, these types of fatigue ANN models have been demonstrating a strong capacity for generalization, making them highly promising for future industrial applications.

Fatigue behaviour of SLM maraging steel under variable-amplitude loading

One of the most challenging issues for additive manufactured materials is fatigue endurance. Engineering components often operate under complex, variable amplitude loadings, in which existing technological imperfections promote fatigue cracks growth and damage of elements eventually. In this study the effects of different variable-amplitude strain levels on fatigue life, 18Ni300 steel was tested. The work presents various behaviours of the material depending on the load level.

Fatigue strength of adhesively bonded deep drawn sheet specimens under multiaxial loading with variable amplitudes

Adhesive bonding is a frequently used joining technology in the manufacturing of vehicle bodies. In comparison to conventional spot-welded designs, adhesive bonding provides a higher stiffness due to a planar load transfer. Furthermore, there are advantages in damping behavior and chemical separation in multi-material designs.Up to now, there exists still quite some uncertainty in the fatigue assessment of adhesively bonded joints due to a lack of reliable assessment approaches. This is especially true for the case of more complex in-service loading conditions as variable amplitude loading, due to the sparse database of experimental fatigue results, which are needed for the development of new methods. For this reason, the results of such tests are presented in this paper on component-like specimens, so called bowl specimens, where even uniaxial loading results in multiaxial stress state due to the complexity of the geometry. These specimens consist of a deep drawn sheet that is bonded with a thermosetting structural adhesive to a planar sheet and are subjected under cyclic loading. They were loaded uniaxially and multiaxially, with (φ = 90°) and without phase shift (φ = 0°).As a complex shaped and stressed sheet metal specimen, the bowl specimen closely resembles components of e.g. vehicle bodies, which is why the conducted tests are presented for a better understanding of such vehicle structures. It is shown that a phase shift leads to an increase of the fatigue life. Furthermore, the cyclic stiffness degradation is discussed, which often serves as a failure relevant parameter in real structures.

Fatigue Analysis of Steering Knuckles Using the Local Strain Approach

The study investigates the mechanical properties and fatigue behavior of steering knuckles used on commercial vehicles. The steering knuckle is made of hot forged bainitic steel (18MnCrMoV6-4-8), which is known to demonstrate high levels of fatigue strength, toughness, and hardness. The local strain concept was adopted to assess the durability of the steering knuckle based on the stabilized cyclic material behavior. For this purpose, experimental investigations have been conducted on both the steering knuckle as well as fatigue specimens under constant and variable amplitude loadings. The fatigue specimens were removed from the area next to the crack initiation location, to represent the microstructure in the critical area of the component. Fatigue life estimations were performed under different load ratios using the FKM guideline nonlinear, employing damage parameters PRAM and PRAJ. The assessment enables a fatigue strength assessment for the steering knuckle by considering the local non-linear material behavior. The estimations of the material's fatigue lifetime using the FKM guideline nonlinear approach were unsatisfactory.

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.

Solution to the problem of low sensitivity of crack closure models to material properties

The paper focuses on differences between crack closure obtained by numerical models and by experimental fatigue crack growth rates, namely for three different steels (bainitic steel, predominantly pearlitic steel and additively manufactured austenitic stainless steel). The experimental data revealed a load ratio effect different from that predicted by the most used plasticity-induced crack closure (PICC) models. The term “irreversibility of plastic deformation” was proposed in this work to be used as a material property to estimate how strong the PICC effect would be in a material. Two basic phenomena, which are usually omitted in other models, were considered in the explanation: (i) cyclic softening/hardening, (ii) brittle microcracking at the maximum load. The strip-yield model has the ability of conducting fast and accurate simulations under the variable-amplitude loading. It was demonstrated that the results of this model are practically independent of the material properties. This is caused by the consideration of only monotonic elastic–plastic material properties. To simulate real load ratio effects, the parameter β in the strip-yield model (constraint factor in compression) is proposed to be used as a variable. It enabled a generation of different ratios of monotonic and cyclic plastic zones, which in turn helped to reproduce the crack closure values observed experimentally. Discussion and explanations were provided regarding the material microstructure. The proposed approach considers unequal tensile and compressive yield stresses caused by the different irreversibility of plastic deformation, which explains the dissimilarities in the load ratio effect observed in the investigated materials. It can also improve the accuracy of residual fatigue life estimations.

The Fatigue Response’s Fingerprint of Composite Materials Subjected to Constant and Variable Amplitude Loadings

This paper discusses the theoretical and experimental correlations between fatigue and static strength statistical distributions. We use a two-parameter residual strength model that obeys the qualitative strength-life equal rank assumption (SLERA) for guidance. The modeling approach consists of recovering the model’s parameters by best fitting the constant amplitude (CA) fatigue data at a given stress ratio, R, and the experimental Weibull parameters of the static strength distribution function. An extensive set of fatigue life and residual strength data for AS4 carbon/epoxy 3k/E7K8 Plain Weave Fabric with [45/−45/90/45/−45/45/−45/0/45/−45]S layups, obtained at different stress ratios, R, have been analyzed. The modeling approach consists of recovering the model’s parameters from pure tension or compression fatigue data at R = 0.1 and R = 5, respectively. Once the parameters are fixed, the model’s capabilities, potential, and limits are discussed by comparing its predictions with residual strength and fatigue life data obtained at stress ratios with mixed tension/compression loadings, namely R = −0,2 and R = −1. Moreover, from a preliminary analysis, the theoretical extension of the model’s capabilities to variable amplitude loadings is conceptualized. The application of Miner’s rule is also discussed and compared with a new damage rule to analyze the fatigue responses under variable amplitude loadings.

Fatigue life prediction considering individual modulus for unidirectional needled C/SiC composites under variable amplitude loading

Needled C/SiC composites are widely used in the aerospace field, making the evaluation of fatigue damage critically important. A fatigue damage model associated with the individual modulus is proposed. Compared to the fatigue damage model by S-N curve, the proposed fatigue damage model can better characterize the fatigue damage behavior of UN-C/SiC composites. By combining the rainflow counting method, the Goodman equation, and the Palmgren-Miner damage accumulation rule, a fatigue life prediction method considering the individual modulus is developed for UN-C/SiC composites under variable amplitude loading. Compared with the experimental life, the predicted fatigue life shows a good result.

Experimental Data-Driven approach for the evaluation of crack tip opening loads under variable amplitude loading

In this paper, we present a new data-driven approach for the evaluation of crack tip opening load (Pop) values under variable amplitude loading. These values are analysed for CT specimens manufactured from common aircraft grade aluminium alloys and subjected to several load sequences, all of which have a relatively high R-ratio content without significant overloads and underloads. Direct experimental measurements and outcomes of numerical simulations indicate that the Pop change abruptly from cycle to cycle. For this type of fatigue loading (including a military transport aircraft load spectrum with more than 400,000 turning points) and materials, it was found that Pop is well described by a linear function of the preceding minimum and maximum values of the applied loading. This finding provides a new simple way to evaluate the effective stress intensity factor range, which is often considered as a fatigue crack driving force. It is also verified via the use of machine learning that the proposed approach is capable of predicting the mean stress (R-ratio) effect on Pop for block loading. Therefore, the developed data-driven approach is a promising alternative to the computational methods, which currently dominate advanced fatigue life assessment procedures.

A generalization ability-enhanced image recognition based multiaxial fatigue life prediction method for complex loading conditions

A generalization ability-enhanced image recognition based multiaxial low-cycle fatigue life prediction is proposed for complex conditions, including multiaxial variable amplitude fatigue, fatigue-creep interaction, and anisotropic materials. Notably, a novel modified dynamic hysteresis image plotting method is introduced for multiaxial variable amplitude loading. Building on a pre-trained convolution neural network (CNN) model, fine-tuning is used across three cases. It makes the error decrease to 25%. Besides, fine-tuning improves training efficiency and generalization. Based on fine-tuning results, each layer of the model is attributed with physics significance. Furthermore, regression activation map (RAM) is used for interpretation, illustrating that the model focuses on the inner and edges of hysteresis images.

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.

Effects of pre-tension and fatigue loadings on the evolution of welding residual stresses in welded plates

Welding-induced residual stresses evolve under external loading and fatigue actions. This paper examines the effects of a variety of influencing factors on the residual stress evolution, such as the pre-tension, load ratio, variable amplitude loading, overloading, plate thickness, and crack depth, for which a comprehensive understanding is yet to be nurtured. The experimental and numerical findings demonstrate that the variable amplitude loading and overloading impose significant effects on the evolution of residual stresses during the cyclic loading test. Based on the experimental observations and numerical analysis, this paper presents four evolution forms of residual stresses and reveals their mechanical principles by the effective stress-strain curves in both the undamaged specimens and the fatigue-cracked specimens. The interaction between the positions with different incremental plastic strains changes the magnitude of residual stress and thus dominates the residual stress evolutions.

Overload and variable amplitude load effects on the fatigue strength of welded joints

Different load spectra and individual load peaks might substantially relax high residual stresses as well as induce compressive residual stresses in welded components and, consequently, affect the fatigue performance of these joints. Consideration of peak loads and resulting relaxation of residual stresses in fatigue analyses can substantially enhance the accuracy of life prediction. The aim of the current study is to experimentally investigate the fatigue strength of welded joints subjected to different levels of overloads and variable amplitude (VA) loads and to develop local fatigue assessment method to account for the relaxation of residual stresses via a mean stress correction using the 4R method. The 4R method applies a local stress ratio for the mean stress correction considering material strength, residual stresses, applied stress ratio of external loading and local weld geometry in elastic–plastic material behaviour. Fatigue tests were carried out on fillet-welded longitudinal gusset joints made of S700 high-strength steels under applied stress ratio R = 0–0.1. A mild strength steel (S355) and ultra-high-strength steel (S1100) were selected as reference steel grades for the fatigue testing to study the material strength effects. Numerical analyses were conducted to evaluate the fatigue notch factors using the effective notch stress concept with the reference radius of rref = 1.0 mm and theory of critical distance (TCD) using the point method. The experimental results indicated that a substantial improvement in the fatigue strength capacity can be claimed in the joints subjected to tensile overloads, particularly in the studied S700 and S1100 steels. The higher-level overload (0.8fy), corresponding to the nominal cross-sectional area, improved the mean fatigue strength of the welded joints manufactured of high-strength S700 steel by approximately 60%, while the lower overload (0.6fy) improved the mean fatigue strength by 20%. In addition, a use of equivalent nominal stresses for the joints subjected to VA loads resulted in conservative assessments when employing S–N curves obtained for the CA loading. The 4R method, via the local mean stress correction for individual cycles, provided higher accuracy for the fatigue assessments.

Cyclic deformation and fracture behaviour of additive manufactured maraging steel under variable-amplitude loading

The cyclic deformation and fracture behaviour of 18Ni300 maraging steel produced by laser beam powder bed fusion is studied under variable-amplitude loading. The tests were conducted under fully-reversed strain-controlled conditions with a loading sequence comprising three ascending cycles and three descending cycles repeated sequentially until failure. After the tests, fracture surfaces were examined using height and volume surface topography parameters to characterise the fractographic features. Fracture surfaces were also analysed through scanning electron microscopy to identify the main failure modes. Fatigue life was predicted by using the Smith-Watson-Topper and the Basquin-Coffin-Manson models with the Palmgren-Miner damage rule. The former approach was more accurate leading to mean errors close to zero. The values of the kurtosis parameter obtained from both sides of the fracture surfaces correlated well with the fatigue life. SEM analysis showed a mixed ductile–brittle mode of fracture with a predominance of brittle fracture. Crack initiation occurred from manufacturing defects located at the surface or near-surface.

Experimental study on effects of cyclic loading paths on cracking behavior and fracture characteristics of granite

To investigate the impact of cyclic loading paths on the Mode I fracture characteristics of granite, a series of fracture tests were conducted on semi-circular bend (SCB) specimens using acoustic emission (AE), digital image correlation (DIC) and 3D scanning. The tests included monotonic loading, variable amplitude (VA) cyclic loading, and tiered constant amplitude (TCA) cyclic loading. The results demonstrated that VA cyclic loading leads to an average enhancement of 5.6% in fracture toughness, whereas TCA cyclic loading results in an average reduction of 3.7% in fracture toughness. During cyclic loading and unloading, the TCA loading path exhibits a higher rate of cumulative plastic deformation growth and greater magnitude cumulative plastic deformation compared to the VA loading path. Additionally, detailed observations from 3D scanning revealed that under cyclic loading, the fracture trajectories and surface morphology exhibit more tortuosity and roughness compared to monotonic loading, particularly in the case of TCA cyclic loading. Furthermore, according to the AE and DIC analysis, the proportion of microcrack initiation and stable propagation stage, cumulative AE counts and fracture process zone (FPZ) size generated under VA cyclic loading are greater than those generated under TCA cyclic loading, displaying a consistent variation pattern with fracture toughness. The changes of fracture properties can be attributed to a competition between the compaction-induced hardening effect and the cracking-induced damage effect. A higher cyclic upper limit and incomplete unloading are more likely to accelerate the growth of the irreversible crack damage and rapid crack extension, resulting in weakened rock fracture properties. These findings provide important references for rock instability control in underground rock engineering.

Prediction of Remaining Fatigue Life of In-Service Bridge Cranes

At present, bridge crane accidents occur frequently, resulting in significant losses and casualties; to ensure the safe use of in-service bridge cranes, it is necessary to predict the residual fatigue life of in-service bridge cranes. Firstly, a static analysis of the most dangerous working conditions of in-service bridge cranes is carried out to find the fatigue failure point. Subsequently, a three-parameter Weibull distribution model is established for the characteristic parameters affecting the acquisition of the stress spectrum. Latin hypercubic sampling is applied to randomly sample the characteristic parameters to produce a random sample set of characteristic parameters for use in obtaining the stress–time history. The amplitude and mean values of the stress spectra are obtained by cycle counting using the rainflow counting method. Finally, Forman’s formula and Miner’s continuous damage accumulation theory were used to derive the remaining life prediction equations for constant and variable amplitude loads. Comparing the remaining life obtained from the simulation and test, the error is about 9.145%, which proves that the remaining life obtained from the simulation is more accurate. The results show that the combined method of simulation and testing is feasible and can predict the remaining life more accurately. In the past, the prediction of residual life was performed with either testing or simulation, which is long and costly. Simulation is low-cost and takes a short time, but the accuracy is not high. In this paper, the combination method of testing and simulation improves the efficiency of production and reduces the cost of use.

Crack growth in high strength mooring line steel under variable amplitude loading

Mooring lines are of key importance for the safe and reliable operation of numerous floating offshore structures. Due to the constantly changing wind and wave conditions acting on such structures, any fatigue crack growth in a mooring line will occur under cyclic loading of distinctly variable amplitude. This paper considers a long-term load history for mooring lines on a North Sea offshore platform. For fatigue testing purposes, a characteristic load sequence representing the actual load history in a condensed and simplified form is developed and presented. Fatigue crack growth rate test results for a grade R4 high strength mooring chain steel subjected to this variable amplitude load sequence is furthermore presented, including tests performed in air as well as under free corrosion conditions in artificial seawater. Based on comparison testing performed under variable- and constant amplitude conditions, the validity of a linear damage rule hypothesis for stable crack growth under the characteristic load sequence is investigated. This damage rule converts the load spectrum to an equivalent constant load range, making it a potentially useful tool for estimating fatigue crack growth in mooring chains when test data for a representative characteristic load sequence are unavailable. Results from the comparison testing are used to show that under stable fatigue crack growth conditions, while subjected to the characteristic load sequence developed for this offshore platform, the linear damage rule can be a reasonable assumption.

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.

An investigation into the influence of variable amplitude creep-fatigue loading on plasticity-induced crack closure

Finite element simulations of fatigue crack growth (FCG) and creep-fatigue crack growth (CFCG) under constant amplitude (CA) and variable amplitude (VA) loading waveforms are performed to investigate the mechanics of crack opening and closing, which has implications on crack growth rate. The material of study is the ferritic-martensitic steel 9Cr-1Mo (modified 9Cr-1Mo) at 625 °C. Two-dimensional finite element analyses of compact tension (CT) specimens are performed to simulate crack growth under several VA loading scenarios, considering elastic–plastic and creep deformations of the material at the crack tip. In this study, the relevant variable influencing crack growth rate is the crack opening load, caused by the phenomenon of plasticity-induced crack closure. A series of loading conditions were simulated using the finite element method, i.e., fatigue overload (OL) in either CA FCG or CFCG waveforms, creep-fatigue OL in CFCG waveforms, and underload (UL) in CFCG waveforms. The crack opening loads obtained from this study for CA loading in both FCG and CFCG, agree with data from published studies. This study also found that a significant reduction in crack opening loads is experienced by the growing crack when an OL or UL cycle was introduced. Immediately after the OL or UL cycle is applied, the crack opening load increases during both fatigue OL and creep-fatigue OL to values larger than those recorded during CA FCG and CFCG loading, whereas UL waveforms result in consistently lower crack opening loads. The increase in crack opening loads is proportional to both the extent of OL and the duration of hold time in the OL cycle. However, following the application of a UL, the crack opening loads in the subsequent cycles were not influenced by the magnitude of the UL or the duration of hold time in the UL cycle.

Multiaxial cycle counting method based on path-dependent line integral

A multiaxial cycle counting method was proposed by path-dependent line integral (PDLI). In the proposed PDLI multiaxial cycle counting method, the length increment of loading path is assigned a positive or negative sign in the strain space, and the interval from zero to the maximum value of PDLI is defined as a half-cycle. A very concise recursive algorithm is provided to implement the proposed multiaxial cycle counting method. The experimental verification showed that the proposed multiaxal cycle counting method was used to count multiaxial cycle, which can obtain satisfactory life prediction results under multiaxial variable amplitude loading. In addition, the PDLI multiaxial cycle counting method can be reduced to a uniaxial rainflow counting form.