Determining the life cycle of bolts using a local approach and the Dang Van criterion

The fatigue behaviour of bolts under axial load has always been considered from the component point of view for which fatigue limit is usually taken equal to 50 MPa, and few results are available to designers for limited lifetimes. Here, we take up this problem from a material point of view using a local approach. For each case of fatigue testing, using finite‐element (FE) model of the bolt, we determine the stabilized local stress at the root of the first thread in contact with the nut. To characterize bolt behaviour with these numerical results, we use Dang Van multiaxial fatigue criterion for which we extend application to the medium fatigue life. These results can be correlated with the experimental numbers of cycles to failure to determine material parameters of the generalized criterion. Using statistical Gauss method, we can make lifetime predictions for any level of risk of failure. In addition, we propose an analytical model to rapidly determine the local stress condition from nominal loading data (mean stress and alternating stress). This model dispenses us from a new modelling if the bolt is stressed in the same manner as the bolts used for behaviour characterization. Using this model and the generalized criterion, it is extremely easy to make lifetime predictions whatever the risk considered.     

MULTIAXIAL CREEP-FATIGUE LIFE EVALUATION UNDER PROPORTIONAL LOADING

A new method was proposed for the multiaxial creep-fatigue life evaluation under proportional loadings. Because this method was derived from the strain range partitioning method with a multiaxiality factor, it was possible to consider the influence of both creep-fatigue interaction and multiaxial stress state on fatigue life. In order to predict the combined axial-torsional fatigue life the damage under combined loading was defined as linear summation of the damages under axial loading and torsional loading. Axial-torsional creep-fatigue tests were carried out using tubular specimens of 316LC austenitic stainless steel and the ferritic rotor steel. This rotor steel was developed for the permanent magnet type eddy current retarder in heavy trucks. Experimentally obtained lives of both steels were well corresponded with the lives predicted by the proposed method. It was found that the proposed method was effective in multiaxial fatigue life evaluation under proportional creep-fatigue Ioadings.     

可靠性强化试验通用夹具研究

针对可靠性强化试验中全轴随机振动试验的通用夹具问题展开研究，首先提出了基于全轴随机振动环境多轴非比例加载，非高斯幅值分布、宽频带等特性的全新夹具设计要求，然后通过理论分析得出了夹具设计的一般原则，最后设计实现了一种可靠性强化试验通用夹具，并对该夹具进行了测试验证，全轴随机振动试验的夹具设计是可靠性强化试验在工程应用中的关键技术，该文的研究可以为可靠性强化试验的推广应用提供广泛借鉴．     

A weight function-critical plane approach for low-cycle fatigue under variable amplitude multiaxial loading

Low‐cycle fatigue data of type 304 stainless steel obtained under axial‐torsional loading of variable amplitudes are analyzed using four multiaxial fatigue parameters: SWT, KBM, FS and LKN. Rainflow cycle counting and Morrow's plastic work interaction rule are used to calculate fatigue damage. The performance of a fatigue model is dependent on the fatigue parameter, the critical plane and the damage accumulation rule employed in the model. The conservatism and non‐conservatism of predicted lives are examined for some combinations of these variables. A new critical plane called the weight function‐critical plane is introduced for variable amplitude loading. This approach is found to improve the KBM‐based life predictions.     

A Review of Critical Plane Orientations in Multiaxial Fatigue Failure Criteria of Metallic Materials

The paper presents a review of multiaxial fatigue failure criteria based on the critical plane concept. The criteria have been divided into three groups, according to the fatigue damage parameter used in the criterion, i.e. (i) stress, (ii) strain and (iii) strain energy density criteria. Each criterion was described mainly by the critical plane orientation. Multiaxial fatigue criteria based on the critical plane concept usually apply different loading parameters in the critical plane whose orientation is determined by (a) only shear loading parameters (crack Mode II or III), (b) only normal loading parameters (crack Mode I) or sometimes (c) mixed loading parameters (mixed crack Mode). There are also criteria based on few critical plane orientations and criteria based on critical plane orientations determined by a weighted averaging process of rotating principal stress axes.     

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.     

Probabilistic approach in high-cycle multiaxial fatigue: volume and surface effects

The stress gradient and the size of a component are known to influence the fatigue strength of metallic components. Indeed, in high‐cycle fatigue, experiments prove that the stress distribution as well as the size of the loaded specimen can be responsible for changes in the fatigue limit (for instance, the fatigue limits in tension and bending are different, and decrease with the size of the specimen). When dealing with multiaxial load conditions, those effects still act but a relevant criterion must be used to account for the complex state of stress. The weakest‐link concept together with a multiaxial endurance criterion based on a microplasticity analysis are then combined to describe the fatigue limit distribution of different metallic materials. Several load conditions are analysed: tension–compression, torsion, rotating bending and plane bending. By means of the proposed model, all the known effects on fatigue strength can be reflected. First, the endurance probability can be adequately predicted for any complex load conditions knowing some reference data from uniaxial fatigue tests. It can be linked to the probability of finding a defect with a critical size. The weakest‐link theory also accounts for the decrease of multiaxial fatigue limit with the stressed volume. For the same load condition (i.e. for the same stress distribution in the volume), the probability of finding a critical defect increases with the component size and then according to the weakest‐link theory the fatigue strength drops. A second model, based only on the damage developed at the surface, is also proposed. While the original Weibull theory makes no distinction between potential initiation sites at the free surface and in the volume and can lead to unsatisfactory predictions when applied to materials containing defects such as nodular cast iron, the new surface approach distinguishes between surface and volume effects.     

A unifying approach to estimate the high-cycle fatigue strength of notched components subjected to both uniaxial and multiaxial cyclic loadings

This paper proposes an engineering method suitable for predicting the fatigue limit of both plain and notched components subjected to uniaxial as well as to multiaxial fatigue loadings. Initially, some well‐known concepts formalized by considering the cracking behaviour of metallic material under uniaxial cyclic loads have been extended to multiaxial fatigue situations. This theoretical extension allowed us to form the hypothesis that fatigue limits can be estimated by considering the linear–elastic stress state calculated at the centre of the structural volume. This volume was assumed to be the zone where all the main physical processes take place in fatigue limit conditions. The size of the structural volume was demonstrated to be constant, that is, independent from the applied loading type, but different for different materials. Predictions have been made by Susmel and Lazzarin's multiaxial fatigue criterion, applied using the linear–elastic stress state determined at the centre of the structural volume. The accuracy of this method has been checked by using a number of data sets taken from the literature and generated by testing notch specimens both under uniaxial and multiaxial fatigue loadings. Our approach is demonstrated to be a powerful engineering tool for predicting the fatigue limit of notch components, independently of material, stress concentration feature and applied load type. In particular, it allowed us to perform predictions within an error interval of about ±25% in stress, even though some material mechanical properties were either estimated or taken from different sources.     

Nonlinear cumulative damage model for multiaxial fatigue

On the basis of the continuum fatigue damage theory, a nonlinear uniaxial fatigue cumulative damage model is first proposed. In order to describe multiaxial fatigue damage characteristics, a nonlinear multiaxial fatigue cumulative damage model is developed based on the critical plane approach. The proposed model can consider the multiaxial fatigue limit, mean hydrostatic pressure and the unseparated characteristic for the damage variables and loading parameters. The recurrence formula of fatigue damage model was derived under multilevel loading, which is used to predict multiaxial fatigue life. The results showed that the proposed nonlinear multiaxial fatigue cumulative damage model is better than Miner’s rule.