Fatigue life assessment under a complex multiaxial load history: an approach based on damage mechanics

In order to assess the fatigue behaviour of structural components under a complex (cyclic or random) multiaxial stress history, methods based on damage mechanics concepts can be employed. In this paper, a model for fatigue damage evaluation in the case of an arbitrary multiaxial loading history is proposed by using an endurance function which allows us to determine the damage accumulation up to the final failure of the material. By introducing an evolution equation for the endurance function, the final collapse can be assumed to occur when the damage D is complete, that is when D reaches the unity. The parameters of this model, which adopts the stress invariants and the deviatoric stress invariants to quantify the damage phenomenon, are determined through a Genetic Algorithm once experimental data on the fatigue behaviour of the material being examined are known for some complex stress histories. With respect to traditional approaches to multiaxial fatigue assessment, the proposed model presents the following advantages: (1) the evaluation of a critical plane is not necessary; (2) no cycle counting algorithm to determine the fatigue life is required, because it considers the progressive damage process during the fatigue load history; (3) the model can be applied to any kind of stress history (uniaxial cyclic loading, multiaxial in‐phase or out‐of‐phase cyclic loading, uniaxial or multiaxial random loading).     

A new approach of fatigue life prediction for metallic materials under multiaxial loading

Based on experimental data found in literatures, four traditionally multiaxial fatigue life criteria are analyzed and verified. It is discovered that these conventional criteria cannot reflect well the combined effect both under tension and torsion loadings for some materials, such as 6082-T6 and AlCu4Mg1, due to lack of enough consideration about the influence of stress amplitude ratio and stress level on fatigue life even under proportional loading. In order to solve this problem, a new approach of fatigue life prediction, based on the equal-life curve, is proposed and it is composed of three parts: the multiaxial fatigue life surface, a new path-dependent factor for multiaxial high-cycle fatigue and a material parameter describing material sensitivity to non-proportional loading. Finally, the precision of the presented approach is systematically checked against the experimental data found in literatures for four different materials under proportional and non-proportional loadings.     

Fatigue life prediction under variable loading based on a new damage model

To examine the performance of nonlinear models proposed in the estimation of fatigue damage and fatigue life of components under random loading, a batch of specimens made of 6082 T 6 aluminium alloy has been studied and some of the results are reported in the present paper. The paper describes an algorithm and suggests a fatigue cumulative damage model, especially when random loading is considered. This paper contains the results of mono-axial random load fatigue tests with different mean and amplitude values performed on 6082 T 6 aluminium alloy specimens. Cycles were counted with rainflow algorithm and damage was cumulated with a new model proposed in this paper and with the Palmgren–Miner model. The proposed model has been formulated to take into account the damage evolution at different load levels and it allows the effect of the loading sequence to be included by means of a recurrence formula derived for multilevel loading, considering complex load sequences. It is concluded that a ‘damaged stress interaction damage rule’ proposed here allows a better fatigue damage prediction than the widely used Palmgren–Miner rule, and a formula derived in random fatigue could be used to predict the fatigue damage and fatigue lifetime very easily. The results obtained by the model are compared with the experimental results and those calculated by the most fatigue damage model used in fatigue (Miner’s model). The comparison shows that the proposed model, presents a good estimation of the experimental results. Moreover, the error is minimized in comparison to the Miner’s model.     

Low‐cycle fatigue life prediction of various metallic materials under multiaxial loading

This paper proposed a simple life prediction model for assessing fatigue lives of metallic materials subjected to multiaxial low‐cycle fatigue (LCF) loading. This proposed model consists of the maximum shear strain range, the normal strain range and the maximum normal stress on the maximum shear strain range plane. Additional cyclic hardening developed during non‐proportional loading is included in the normal stress and strain terms. A computer‐based procedure for multiaxial fatigue life prediction incorporating critical plane damage parameters is presented as well. The accuracy and reliability of the proposed model are systematically checked by using about 300 test data through testing nine kinds of material under both zero and non‐zero mean stress multiaxial loading paths.     

Application of continuum damage mechanics to vibration fatigue life prediction

It is pivotal to predict the multiaxial vibration fatigue life during mechanical structural dynamics design. An algorithm of the finite element method implementation for multiaxial high cycle fatigue life evaluation is proposed, on the basis of elastic evolution model of continuum damage mechanics. By considering structural dynamic characteristics, namely, resonant frequencies and mode shapes, this algorithm includes a modal analysis and harmonic analysis, which makes this different from existing fatigue life prediction methods. A 10% decrease in the resonant frequency is regarded as the failure criterion. A critical damage value was obtained, which indicates mesocrack initiation fulfilment. To validate the effectiveness of the algorithm, auto‐phase sine resonance track‐and‐dwell experiments were conducted on notched cantilever beams made of Ti‐6Al‐4V alloy. The life predictions are conservative and in good agreements with the experimental results, which are mainly distributed within a scatter band of 2. This investigation could provide technical support for structural dynamics design and the analysis of reusable spacecraft.     

Fatigue life prediction of composites under two-stage loading

In order to predict the fatigue life under two-stage loading by formulating a cumulative fatigue damage rule for composite materials, the fatigue process in SiC–Al and glass-fibre reinforced plastics were investigated. A microcrack occurred within the composites which resulted in cumulative fatigue damage that increased linearly with the number of cycles. The mechanical conditions of damage growth and failure were determined by characterizing the microdamage governing the fatigue. The ultimate failure is shown to occur when the product of the stress amplitude ratio and microdamage density is beyond a critical value and an expression for the remaining fatigue life is derived. This revised version was published online in November 2006 with corrections to the Cover Date.     

Fatigue life prediction of a structural steel under service loading

Fatigue life prediction techniques for variable amplitude load histories are reviewed. The fatigue crack growth rate and crack closure responses of BS4360 50B steel are determined for a service load history experienced by a gas storage vessel. Crack propagation rates are found to be independent of specimen thickness. Crack growth is successfully predicted by linear summation using the Paris law; no significant improvement is achieved by incorporating crack closure into the analysis. The particular choice of cycle counting technique is also found to have an insignificant effect on the predicted fatigue life. The load-interaction model proposed by Willenborg et al correctly indicates the absence of retarded growth, whilst the Wheeler and Führing models erroneously predict retarded crack growth.     

Notch fatigue life prediction considering nonproportionality of local loading path under multiaxial cyclic loading

An innovative numerical methodology is presented for fatigue lifetime estimation of notched bodies experiencing multiaxial cyclic loadings. In the presented methodology, an evaluation approach of the local nonproportionality factor F for notched specimens, which defines F as the ratio of the pseudoshear strain range at 45° to the maximum shear plane and the maximum shear strain range, is proposed and discussed deeply. The proposed evaluation method is incorporated into the material cyclic stress‐strain equation for purpose of describing the nonproportional hardening behavior for some material. The comparison between multiaxial elastic‐plastic finite element analysis (FEA) and experimentally measured strains for S460N steel notched specimens shows that the proposed nonproportionality factor estimation method is effective. Subsequently, the notch stresses and strains calculated utilizing multiaxial elastic‐plastic FEA are used as input data to the critical plane‐based fatigue life prediction methodology. The prediction results are satisfactory for the 7050‐T7451 aluminum alloy and GH4169 superalloy notched specimens under multiaxial cyclic loading.     

Fatigue life prediction method of face-centered cubic single-crystal metals under multiaxial nonproportional loading based on structural mechanical model

Based on the characteristics of the sliding surface, sliding direction, and fatigue damage mechanism of metal materials, the mechanical model of a body–bar–plate structure is proposed with consideration to the plastic damage mechanism. The elastoplastic constitutive equations and damage constitutive equations of the face-centered cubic (FCC) structure subjected to multiaxial cyclic loading were derived, and the damage evolution law of the body–bar–plate mechanical model was investigated. Then, the meso-damage evolution equation was established under multiaxial nonproportional loading. Subsequently, the relationship between the fatigue performance and microstructure under multiaxial nonproportional loading was investigated, and a damage mechanics–finite element method (FEM) with consideration to the damage evolution is proposed. The proposed model and method provide a new approach for predicting the fatigue life of metal materials.     

Fatigue life prediction of offshore tubular joints using fracture mechanics

ABSTRACT Fatigue crack growth calculations were performed on offshore tubular joints using the Paris crack growth law. The stress intensity factors required for such calculations were obtained from T‐butt solutions previously proposed by the authors. The applicability of the solutions to tubular joints was first demonstrated by comparing the fatigue life of a base case with that obtained from a mean S–N curve, and the influence on fatigue life of various factors including load shedding, the size of initial defects, weld geometry, etc. was investigated. The solutions were then used to predict the lives of tubular T‐joints from an experimental database. The results show that the solutions underestimate the fatigue life; this underestimation was shown to be primarily due to ignoring the combined effects of load shedding and the intersection stress distribution. In general, however, the trends in the predicted fatigue lives with joint geometry and other details were seen to be superior to predictions from the S–N approach, with the solutions significantly reducing the dependency on loading mode exhibited by the test data.     

Effects of mean stresses on multiaxial fatigue life prediction based on fracture mechanics

A linear elastic fracture mechanics analysis is presented to explore the effects of mean stress on fatigue life prediction under multiaxial loading conditions based on uniaxial fatigue data. Material damage in the form of small cracks is assumed to exist in a material element of interest. The mixed-mode energy release rate or the J integral is used as the primary fatigue damage governing parameter. The uniaxial Goodman relation is generalized to demonstrate the effects of mean stresses on fatigue life under multiaxial loading conditions. The generalization is also applicable for nonlinear constant fatigue life relations in the Haigh diagram.     

A method for low-cycle fatigue life assessment of metallic materials under multiaxial loading

A new method of fatigue life assessment under multiaxial low-cycle regular and irregular loading is proposed, which is based on the modified Pisarenko-Lebedev criterion, the linear damage accumulation hypothesis, and the nonlinear Manson approach. The results of low-cycle fatigue tests of titanium alloy VT9 under irregular proportional and non-proportional biaxial loading are given. The tests were carried out at three Mises strain levels (0.6, 0.8, and 1.0%) with various combinations of proportional and non-proportional strain paths. All the tests were carried out at room temperature. The proposed method turned out to be effective and to allow for such factors as strain state type, strain path type and loading irregularity. __________ Translated from Problemy Prochnosti, No. 1, pp. 56–59, January–February, 2008.     

Fatigue strength of welded joints under multiaxial loading: experiments and calculations

In reality most welded components are loaded with a combination of different variable forces and moments that often cause a state of multiaxial stress in the fatigue-critical areas. If the multiaxial loading is non-proportional, traditional deformation-based hypotheses are not able to give a reliable lifetime prediction. This investigation is a cooperation between three German research institutes to build an experimental database for the verification of different concepts of lifetime prediction. In accordance with former investigations, a flange-tube connection made of steel P460 was used. The test program was divided into constant amplitude and variable amplitude tests. The ratio between the nominal bending and shear stress is 1. For the variable amplitude tests, a Gaussian-standard is used. A lifetime prediction software for multiaxial state of cyclic stress was developed. The software has a modular structure and allows calculations with different hypotheses and methods. The calculations are based on the local elastic stresses. This is an acceptable method for high-cycle fatigue. In this work, two general types of calculation, the Integral Approach and Critical Plane Approach and a local stress-based modification of the von Mises Criterion, the hypothesis of effective equivalent stress (EESH) are shown. The damage accumulation is performed with the elementary Miner's rule ( S – N curve without fatigue limit). The statistical distributions of the damage sums are also shown.     

Fatigue life analysis and predictions for NR and SBR under variable amplitude and multiaxial loading conditions

This paper investigates the effects of variable amplitude loading conditions on the fatigue lives of multiaxial rubber specimens. Two filled rubber materials were used and compared to investigate the effects of strain-crystallization on crack development NR, which strain crystallizes, and SBR, which does not. The applicability of Miner’s linear damage rule for predicting fatigue lives of variable amplitude tests in rubber and the use of both scalar and plane-specific equivalence parameters to characterize fatigue life results were also investigated. A fatigue life prediction approach that utilizes normal strain to find the critical plane and the cracking energy density on that plane to determine fatigue life is introduced and compared to other approaches. The effects of load sequence and temperature on fatigue life, as well as differences in fatigue lives using both stiffness and critical crack length failure criteria are discussed.     

Fatigue life calculation by means of the cycle counting and spectral methods under multiaxial random loading

The paper contains a new algorithm for estimation of fatigue life in HCF regime under multiaxial random loading using spectral methods. Loading of Gaussian distribution and narrow‐ and broad‐band frequency spectra were assumed. Various characteristic states of multiaxial loading were considered. The equivalent stress history was determined with use of the failure criteria of multiaxial fatigue based on the critical plane. For determination of the critical plane position, the method of variance was applied. During simulation, the authors compared the results obtained by a spectral method in the frequency domain with those from the rain‐flow algorithm in the time domain. The paper also contains the results of fatigue tests for 18G2A structural steel subjected to bending and combined bending with torsion. The tests were performed in order to verify the proposed algorithms for determination of fatigue life. It has been shown that under multiaxial random loading results of fatigue life calculated according to the considered algorithms in frequency and time domains are well correlated with the results of experiments.     

Fatigue life prediction of vulcanized natural rubber under proportional and non-proportional loading

To investigate the multiaxial fatigue properties of vulcanized natural rubber (NR), a series of tests including both proportional and non-proportional loading paths on small specimens were performed. The existing fatigue life prediction approaches are evaluated with life data obtained in the tests. It is shown that the equivalent strain approach presents a good prediction of the fatigue life although it has a certain shortcoming. Compared with the strain energy density (SED) model, the cracking energy density (CED) model represents the portion of SED that is available to be released by virtue of crack growth on a given material plane, so it gives better results in the life prediction. Some of the approaches based on critical plane which are widely used for metal fatigue are also tested in this paper, and the results show that the Chen-Xu-Huang (CXH) model gives a better prediction, compared with the Smith-Watson-Topper (SWT) and Wang–Brown (WB) model. A modified Fatemi–Socie's model has also been introduced, and the results show that the modified model can be used to predict the fatigue life of rubber material well.     

Fatigue life prediction of copper single crystals using a critical plane approach

A critical plane multiaxial fatigue criterion was employed to predict the fatigue life of copper single crystals. The detailed stress-strain response was obtained through the constitutive modeling using a newly developed crystal plasticity theory. The constitutive model was capable of capturing the major deformation features of copper single crystals under cyclic loading including the cyclic stress-strain curves, cyclic hardening behavior, and the evolution of the hysteresis loops with increasing number of loading cycles. Fatigue life prediction of the single crystal copper was conducted based upon the stress-strain response obtained from the cyclic plasticity model. The fatigue criterion takes into account the plastic strain localization within a single crystal. The critical plane (cracking plane) was identified as the material plane where the fatigue damage accumulation first reached a critical value. For copper single crystals with the crystal orientations being within the standard crystallographic triangle, the fatigue criterion can predict both fatigue life and cracking direction consistent with the experimental observations. More importantly, the constants used in the fatigue criterion were found to be identical to those used for the pure polycrystalline copper with different grain sizes and texture.     

Slip-band behavior and crack initiation in polycrystalline copper under multiaxial low-cycle fatigue—a damage mechanics approach

A damage mechanics approach to formation of slip bands and initiation of fatigue cracks was investigated in the present paper. The nucleation and growth behaviors of slip bands and cracks in the low-cycle fatigue region were experimentally observed for pure copper under multiaxial cyclic stresses of combined tension-compression and torsion (the ratios of torsional to axial strain ranges were 0,2 and ∞). The statistical distributions of orientation for slip bands and grain-boundary cracks with respect to the stress biaxiality were examined through observation. Analyses based on geometrical modelings of slip-band formation and grain-boundary cracking were carried out to simulate the experimental results. The approach proposed in the study was found to succeed in evaluating the trends of slip-band and grain-boundary cracks depending on the biaxial stress states.     

Fatigue behavior of laminated composites with a circular hole under in-plane multiaxial loading

A modified fiber failure fatigue model is presented for characterizing the behavior of laminated composites with a central circular hole under in-plane multiaxial fatigue loading. The analytical model presented is based on minimum strength model and fiber failure criterion under static loading available in the literature. The analysis starts with the determination of location of a characteristic curve around the hole and the stress state along the characteristic curve under in-plane multiaxial fatigue loading. Number of cycles to failure and location of failure are determined under given fatigue loading condition. Based on ply-by-ply analysis, ultimate fatigue failure and the corresponding number of cycles are determined. Analytical predictions are compared with the experimental results for uniaxial and multiaxial fatigue loading cases. A good match is observed. Further, studies are carried out for different in-plane biaxial tension–tension and biaxial compression–compression loading cases.     

Fatigue assessment of metallic components under uniaxial and multiaxial variable amplitude loading

In the present paper, the fatigue lifetime of metallic structural components subjected to variable amplitude loading is evaluated by applying 2 different multiaxial high‐cycle fatigue criteria. Such criteria, proposed by some of the present authors, are based on the critical plane approach and aim at reducing a given multiaxial stress state to an equivalent uniaxial stress condition. In particular, the procedure employed by both criteria consists of the following 3 steps: (1) definition of the critical plane; (2) counting of loading cycles; and (3) estimation of fatigue damage. Finally, the previous criteria are validated by comparing the theoretical results with experimental data related to smooth metallic specimens subjected to uniaxial and multiaxial variable amplitude loading.