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Engineering components/structures with geometric discontinuities normally bear complex and variable loads, which lead to a multiaxial and random/variable amplitude stress/strain state. Hence, this study aims how to effectively evaluate the multiaxial random/variable amplitude fatigue life.

Recent studies on critical plane method under multiaxial random/variable amplitude loading are reviewed, and the computational framework is clearly presented in this paper.

Some basic concepts and latest achievements in multiaxial random/variable amplitude fatigue analysis are introduced. This review summarizes the research status of four main aspects of multiaxial fatigue under random/variable amplitude loadings, namely multiaxial fatigue criterion, method for critical plane determination, cycle counting method and damage accumulation criterion. Particularly, the latest achievements of multiaxial random/variable amplitude fatigue using critical plane methods are classified and highlighted.

This review attempts to provide references for further research on multiaxial random/variable amplitude fatigue and to promote the development of multiaxial fatigue from experimental research to practical engineering application.

Welded components are often subjected to variable amplitude service loads, increasing the uncertainty of fatigue life due to material strength, notch geometries, defect content and residual stresses. In the case of friction stir welding (FSW) of aluminium alloys no data were found available concerning fatigue behaviour under variable amplitude loading. The purpose of this paper is to determine the fatigue strength of friction stir welds in AA6082‐T6 under constant and variable amplitude loading and analyse the validity of Miner's rule for these specific welding conditions.

Fatigue tests were carried out in a servo‐hydraulic testing machine using a stress ratio of R=0. Typified Gassner amplitude spectra were considered, using four shape exponent values. Microhardness tests were performed to characterize the Vickers hardness profile in the vicinity of the weld area. Relatively to the base material (BM), the FSW process leads to a decrease of the static mechanical properties.

Detailed examination revealed a hardness decrease in the thermo‐mechanically affected zone and the nugget zone average hardness was found to be lower than the base alloy hardness. The comparison with data collected from the literature shows that FSW specimens present higher fatigue resistance than specimens welded by metal inert gas and tungsten inert gas processes. However, they still have lower fatigue lives than the BM. Using the equivalent stress calculated by Miner's rule, a good agreement was observed between constant and variable fatigue loading results. The characteristic curve obtained for friction stir welds is higher than the International Institute of Welding (IIW) fatigue class for fusion welds with full‐penetration both‐sided butt joints.

No data are available concerning fatigue behaviour under variable amplitude loading for friction stir welds of aluminium alloys. Furthermore, this paper analyses the fatigue strength of friction stir welds in AA6082‐T6 under constant and variable amplitude loading in order to verify the validity of Miner's rule for this specific welding process. A comparison between characteristic fatigue curves, using IIW fatigue classes (FAT), is also performed.

Engineering components/structures are usually subjected to complex and variable loads, which result in random multiaxial stress/strain states. However, fatigue analysis methods under constant loads cannot be directly applied to fatigue life prediction analysis under random loads. Therefore, the purpose of this study is how to effectively evaluate fatigue life under multiaxial random loading.

First, the average phase difference is characterized as the ratio of the number of shear strain cycles to the number of normal strain cycles, and the new non-proportional additional hardening factor is proposed. Then, the determined random typical load spectrum is processed into a simple variable amplitude load spectrum, and the damage in each plane is calculated according to the multiaxial fatigue life prediction model and Miner theory. Meanwhile, the cumulative damage can be calculated separately by projection method. Finally, the maximum projected cumulative damage plane is defined as the critical plane of multiaxial random fatigue.

The fatigue life prediction capability of the method is verified based on test data of TC4 titanium alloy under random multiaxial loading. Most of the predicting results are within double scatter bands.

The objective of this study is to provide a reference for the determination of critical plane and non-proportional additional hardening factor under multiaxial random loading, and to promote the development of multiaxial fatigue from experimental studies to practical engineering applications.

The purpose of this paper is to deal with the FE analysis of strain constraint around the crack tip under cyclic loading and its utilization using crack growth prediction strip yield model (SYM). During cycling, the constraint develops based on the load history. The monotonic loading is analyzed mostly, but during cyclic loading the conditions are different. The constraint is analyzed after several loading cycles applied in upwards part of the cycle and the formula for its development is proposed.

The study is based on the 3D FE analysis of middle-cracked tension specimen M(T). The strain constraint is described by Newman’s factor α. The variability of constraint factor α was analyzed for several load levels and specimen thicknesses. The crack is considered as non-propagating with straight crack front. The material is modelled as elastic-perfectly plastic. The SYM is modified by implementing variable constraint and the experimental results are compared with the simulation.

In major part of the loading cycle, it was found by FE analysis, that the constraint factor α_g is lower after overloads than when creating monotonic plastic deformation on the same load level. The value of α_g is governed by the ratio of thickness B over the plastic zone size r_p. By implementing the variable constraint factor into the SYM, the improvement of the predicted specimens lives under variable amplitude loading was shown.

The new phenomenon on the variability of strain constraint during cyclic loading is presented. The development of constraint factor α_g during cyclic loading is different from the monotonic loading and should be accordingly implemented into prediction models.

Scholars mainly propose and establish theoretical models of cumulative fatigue damage for their research fields. This review aims to select the applicable model from many fatigue damage models according to the actual situation. However, relatively few models can be generally accepted and widely used.

This review introduces the development of cumulative damage theory. Then, several typical models are selected from linear and nonlinear cumulative damage models to perform data analyses and obtain the fatigue life for the metal.

Considering the energy law and strength degradation, the nonlinear fatigue cumulative damage model can better reflect the fatigue damage under constant and multi-stage variable amplitude loading. In the following research, the complex uncertainty of the model in the fatigue damage process can be considered, as well as the combination of advanced machine learning techniques to reduce the prediction error.

This review compares the advantages and disadvantages of various mainstream cumulative damage research methods. It provides a reference for further research into the theories of cumulative fatigue damage.

This paper deals with crack propagation under programme‐fatigue loading; the programme being derived from a gust spectrum. The validity of the Palmgren‐Miner rule for crack propagation has been studied and its usefulness for design purposes is discussed.

The prediction of fatigue crack growth behaviour is an important part of damage tolerance analyses. Recently, the author’s work has focused on evaluating the FASTRAN retardation model. This model is implemented in the AFGROW code, which allows different retardation models to be compared. The primary advantage of the model is that all input parameters, including those for an initial plane-strain state and its transition to a plane-stress-state, are objectively measured using standard middle-crack-tension M(T) specimens. The purpose of this paper is to evaluate the ability of the FASTRAN model to predict correct retardation effects due to high loading peaks that occur during variable amplitude loading in sequences representative of an aircraft service.

This paper addresses pre-setting of the fracture toughness K _R (based on J-integral J _Q according to ASTM1820) in the FASTRAN retardation model. A set of experiments were performed using specimens made from a 7475-T7351 aluminium alloy plate. Loading sequences with peaks ordered in ascending-descending blocks were used. The effect of truncating and clipping selected load levels on crack propagation behaviour was evaluated using both experimental data and numerical analyses. The findings were supported by the results of a fractographic analysis.

Fatigue crack propagation data defined using M(T) specimens made from Al 7475-T7351 alloy indicate the difficulty of evaluating the following two events simultaneously: fatigue crack increments after application of loads with maximum amplitudes that exceeded J _Q and subcritical crack increments caused by loads at high stress intensity factors. An effect of overloading peaks with a maximum that exceeds J _Q should be assessed using a special analysis beyond the scope of the FASTRAN retardation model.

Measurements of fatigue crack growth on specimens made from 7475 T7351 aluminium alloy were carried out. The results indicated that simultaneously evaluating fatigue crack increments after application of the load amplitude above J _Q and subcritical increments caused by the loads at high stress intensity factors is difficult. Experiments demonstrated that if the fatigue crack reaches a specific length, the maximal amplitude load induces considerable crack growth retardation.

The purpose of this paper is to determine the ultra-high cycle fatigue behavior and ultra-slow crack propagation behavior of selective laser melting (SLM) AlSi7Mg alloy under as-built conditions.

Constant amplitude and two-step variable amplitude fatigue tests were carried out using ultrasonic fatigue equipment. The fracture surface of the failure specimen was quantitatively analyzed by scanning electron microscope (SEM).

The results show that the competition of surface and interior crack initiation modes leads to a duplex S–N curve. Both manufacturing defects (such as the lack of fusion) and inclusions can act as initially fatal fatigue microcracks, and the fatigue sensitivity level decreases with the location, size and type of the maximum defects.

The research results play a certain role in understanding the ultra-high cycle fatigue behavior of additive manufacturing aluminum alloys. It can provide reference for improving the process parameters of SLM technology.

Examination of steel moment resisting frames after the 1994 Northridge earthquake showed fatigue cracks presented in the beam–column connections of the frames. These observations indicate that fatigue failure may occur in the steel components of building structures in an earthquake event. To apply the fatigue design approach using the Palmgren–Miner’s rule for steel components of the moment resisting frames requires the knowledge regarding the damage index value at fatigue failure. The purpose of this paper is to perform fatigue tests to give the first damage values of steel components subjected to real earthquake-induced loadings.

The added-damping-and-stiffness steel plates which are used in building structures for earthquake mitigation were fabricated and tested by constant amplitude, SAC block and earthquake-induced loadings to failure. The earthquake loadings were obtained from the dynamic analysis of a steel frame with the mentioned plates. The load cycles of the SAC block and the calculated earthquake loadings were counted using the rainflow-counting method, and the damage index value of each specimen were calculated using the Palmgren–Miner’s rule.

Reverse stiffness obtained from cyclic load-displacement loops is a robust and consistent parameter that can be used for determining fatigue failure of tested components. The Palmgren–Miner’s damage values at failure, caused by earthquake loadings, are smaller than 1, and in addition, are also smaller than those obtained from the tests of the SAC block loading. The large-amplitude cycles in the earthquake loading produce large damage on the specimens, and intermediate range cycles also produce damage that should not be neglected in the fatigue analysis.

Today’s building design code allows large plastic deformation to occur in steel frames during an earthquake. However, the pre-Northridge earthquake steel frames showed fatigue cracks without the expected substantial plastic deformation at beam flanges. Proposed solutions to this problem were the reduced beam section neglecting the existence of the cracks at beam–column connections. This study considered the fatigue phenomenon in steel frames and provided the first set of tested fatigue damage values for steel components subjected to realistic earthquake loadings, which offered a possible method of dealing with fatigue cracks in the steel components of a building structure.

The purpose of this paper is to develop an approach to optimize the cycles‐to‐failure of a peened component with respect to laser peening (LP) variables: pressure magnitude, mid‐span, and spot size when the component is subject to a variable amplitude loading.

To optimally design an LP process, an experimentally validated 3D finite element simulation of the LP process, a cycles‐to‐failure estimation capability incorporating residual stress, and a particle swarm optimization strategy were developed and employed to maximize the cycles‐to‐failure of a component of a titanium turbine disk.

The most critical finding of this research is that a minor difference in the residual stress profile can lead to a large difference in the cycles‐to‐failure. This finding implies that selecting the optimization objective to be the cycles‐to‐failure is a better option as compared to the residual stress profile.

The LP‐induced residual stresses are assumed static and do not change as number of load cycles increase.

The paper develops a framework that relates the LP variables and the cycles‐to‐failure of a peened component. A modified particle swarm optimization approach is developed to optimize the fatigue life of a turbine disk.