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.     

随机声载荷作用下的复杂薄壁结构Von Mises应力概率分布研究

随机声载荷作用下的某些复杂薄壁结构的振动疲劳属于多轴疲劳,Von Mises 应力准则是多轴疲劳损伤分析的一条有效途径。本文通过对有限带宽高斯白噪声载荷作用下结构Von Mises应力概率分布研究,分析提出Von Mises应力服从双参数Weibull分布或Lognormal分布,并且给出了估算这两种概率分布参数的方法,进而得到了Von Mises应力峰值概率密度函数,从而为结构的疲劳损伤寿命估算提供依据。在工程应用中采用耦合的有限元和边界元方法计算了某型航空发动机燃烧室火焰筒薄壁结构在随机声载荷作用下的振动应力响应功率谱密度,着重分析了Von Mises应力响应的概率分布特征,并对分析结果采用Kolmogorov-Smirnov (K-S)检验进行了比较验证。     

Multiaxial fatigue damage parameter and life prediction for medium-carbon steel based on the critical plane approach

The tension–torsion fatigue characteristics were investigated under proportional and non-proportional loading in this paper. The fatigue cracks on the surface of multiaxial fatigue specimens were observed and analyzed by a scan electron microscope. On the basis of the investigation on the Kindil–Brown–Miller and Fatemi–Socie’s critical plane approaches, a shear strain based multiaxial fatigue damage parameter was proposed by von Mises criterion based on combining the maximum shear strain and the normal strain excursion between adjacent turning points of the maximum shear strain on the critical plane. The proposed multiaxial fatigue damage parameter does not include the weight constants. According to the proposed multiaxial fatigue damage parameter, the multiaxial fatigue life prediction model was established with the Coffin–Manson equation, which is used to predict the multiaxial fatigue life of medium-carbon steel. The results showed that the proposed multiaxial fatigue damage parameter could be used under either multiaxial proportional or non-proportional loading.     

EVALUATION OF LOW CYCLE FATIGUE UNDER NON-PROPORTIONAL LOADING

Abstract— A series of low cycle fatigue experiments have been conducted on a 42CrMo steel under tension-torsion loading. Thin-walled tube specimens were used. Low cycle fatigue under various loading paths, including circular and square paths, have been investigated.
The plastic work criterion for low cycle fatigue failure has previously been generally accepted, but it is difficult to calculate stress and strain for complex loading paths, especially for non-proportional loading. This present study suggests a simple method for the calculation of the stable cyclic stress and strain values based on a Modified Endochronic Constitutive Theory (MECT) that redefines an intrinsic time scale. The loading path effect under non-proportional loading is also considered when evaluating fatigue life.
The results show that the plastic work approach using the MECT method in multiaxial fatigue calculations correlates reasonably well the data and is a reflection of loading path dependence.     

A critical plane-strain energy density criterion for multiaxial low-cycle fatigue life under non-proportional loading

A series of multiaxial low-cycle fatigue experiments was performed on 45 steel under non-proportional loading. The present evaluations of multiaxial low-cycle fatigue life were systematically analysed. A combined energy density and critical plane concept is proposed that considers different failure mechanisms for a shear-type failure and a tensile-type failure, and from which different damage parameters for the critical plane-strain energy density are proposed. For tensile-type failures in material 45 steel and shear-type failures in material 42CrMo steel, the new damage parameters permit a good prediction for multiaxial low-cycle fatigue failure under non-proportional loading. The currently used critical plane models are a special and simple form of the new model.     

Online multiaxial fatigue damage evaluation method by real‐time cycle counting and energy‐based critical plane criterion

To realize online multiaxial fatigue damage assessment for the mechanical components in service, an online multiaxial cycle counting method is proposed coupled with the segment processing technique and Wang‐Brow's relative equivalent strain concept. Meanwhile, considering all the stress and strain components, which contribute to the fatigue damage on the critical plane, a multiaxial fatigue damage model without any weight coefficients is also proposed in an equivalent form of shear strain energy. Then, an online fatigue damage evaluation method for multiaxial random loading is developed by combining with the proposed damage model and online cycle counting method. The experimental results showed that the proposed online cycle counting method can be successfully applied to the calculation of multiaxial fatigue damage under random loading. Moreover, the proposed online multiaxial fatigue damage evaluation method can provide satisfactory predictions.     

Life prediction based on weight‐averaged maximum shear strain range plane under multiaxial variable amplitude loading

Based on Wang and Brown's reversal counting method, a new approach to the determination of the critical plane is proposed by the defined plane with a weight‐averaged maximum shear strain range under multiaxial variable amplitude loading. According to the determined critical plane, a detailed procedure of multiaxial fatigue life prediction is introduced to predict lives in the low‐cycle multiaxial fatigue regime. The proposed approach is verified by two multiaxial fatigue damage models and Miner's linear cumulative damage law. The results showed that the proposed approach can effectively predict the orientation of the failure plane under multiaxial variable amplitude loading and give a satisfactory life prediction.     

Multiaxial fatigue life estimation in welded joints using the critical plane approach

Many engineering structures experience multiaxial fatigue states of stress–strain in the vicinity of welded joints. Fatigue assessment of welded joints under proportional (in-phase) cyclic loading can be performed by using conventional hypotheses (e.g., see the von Mises criterion or the Tresca criterion) on the basis of local approaches. On the contrary, the fatigue life predictions of welded joints under non-proportional (out-of-phase) cyclic loading are generally poor if these conventional hypotheses are used. In the present paper, the critical plane-based multiaxial fatigue criterion proposed by Carpinteri and Spagnoli for smooth and notched structural components is extended to the fatigue assessment of welded joints under in- and out-of-phase loadings. The applicability of this criterion, expressed in terms of nominal stresses, to the fatigue life prediction of welded specimens is investigated by using experimental data available in the literature.     

Multiaxial fatigue criterion for a high‐density polyethylene thermoplastic

The multiaxial fatigue behaviour of a high‐density polyethylene was investigated at room temperature and constant frequency. As a consequence of the mode of failure, an end‐of‐life criterion for fatigue tests is discussed in the first part of the work, in order to define the number of cycles to failure. Based on force controlled fatigue tests under tension, compression and torsion at two stress ratio, a multiaxial fatigue criterion including the stress‐ratio effect is proposed for the fatigue design of this polymer. This criterion is based on the maximum and mean values of the second invariant of the stress tensor.     

A simple energy‐based model for nonproportional low‐cycle multiaxial fatigue life prediction under constant‐amplitude loading

From the literature concerning the traditional nonproportional (NP) multiaxial cyclic fatigue prediction, special attentions are usually paid to multiaxial constitutive relations to quantify fatigue damage accumulation. As a result, estimation of NP hardening effect decided by the entire history path is always proposed, which is a challenging and complex task. To simplify the procedure of multiaxial fatigue life prediction of engineering components, in this paper, a novel effective energy parameter based on simple material properties is proposed. The parameter combines uniaxial cyclic plastic work and NP hardening effects. The fatigue life has been assessed based on traditional multiaxial fatigue criterion and the proposed parameter, which has been validated by experimental results of 316 L stainless steel under different low‐cycle loading paths.     

Strain-based multiaxial fatigue damage modelling

A new multiaxial fatigue damage model named characteristic plane approach is proposed in this paper, in which the strain components are used to correlate with the fatigue damage. The characteristic plane is defined as a material plane on which the complex three‐dimensional (3D) fatigue problem can be approximated using the plane strain components. Compared with most available critical plane‐based models for multiaxial fatigue problem, the physical basis of the characteristic plane does not rely on the observations of the fatigue crack in the proposed model. The cracking information is not required for multiaxial fatigue analysis, and the proposed model can automatically adapt for different failure modes, such as shear or tensile‐dominated failure. Mean stress effect is also included in the proposed model by a correction factor. The life predictions of the proposed fatigue damage model under constant amplitude loading are compared with a wide range of metal fatigue results in the literature.     

An application of the implicit gradient method to welded structures under multiaxial fatigue loadings

This paper deals with the problem of fatigue strength assessment of welded joints subjected to multiaxial loading. Three-dimensional solid modelling and linear elastic stress analysis, by means of numerical methods, are used to investigate the local stress field at weld toes and roots, geometrically regarded as sharp notches. Starting from the stress field obtained from a linear elastic analysis and taking advantage of the so-called implicit gradient approximation, an effective stress index connected with the material strength is calculated. In particular, there will be an investigation into the possibility of applying the implicit gradient approach to welded structures, under both uniaxial and multiaxial loading conditions, by introducing a multiaxial criterion into the implicit gradient framework. The multiaxial criterion consists of an improvement of the well-established Crossland-like criteria. It will deal with multiaxiality caused by external loadings as well as multiaxial stress fields caused by severe stress raisers. In order to validate the devised approach, theoretical fatigue damage estimations are compared with experimental data. In particular, the proposed approach is applied to a series of applicative examples taken from scientific literature and related to welded joints subjected to uniaxial or in-phase multiaxial fatigue loading.     

Multiaxial low‐cycle fatigue life evaluation under different non‐proportional loading paths

This paper presents analytical and experimental investigations for fatigue lives of structures under uniaxial, torsional, multiaxial proportional, and non‐proportional loading conditions. It is known that the rotation of principal stress/strain axes and material additional hardening due to non‐proportionality of cycle loading are the 2 main causes resulting in shorter fatigue lives compared with those under proportional loading. This paper treats these 2 causes as independent factors influencing multiaxial fatigue damage and proposes a new non‐proportional influencing parameter to consider their combined effects on the fatigue lives of structures. A critical plane model for multiaxial fatigue lives prediction is also proposed by using the proposed non‐proportional influencing factor to modify the Fatemi‐Socie model. The comparison between experiment results and theoretical evaluation shows that the proposed model can effectively predict the fatigue life due to multiaxial non‐proportional loading.     

Multiaxial notch fatigue life prediction based on the dominated loading control mode under variable amplitude loading

A new calculation approach is suggested to the fatigue life evaluation of notched specimens under multiaxial variable amplitude loading. Within this suggested approach, if the computed uniaxial fatigue damage by the pure torsional loading path is larger than that by the axial tension–compression loading path, a shear strain‐based multiaxial fatigue damage parameter is assigned to calculate multiaxial fatigue damage; otherwise, an axial strain‐based multiaxial fatigue damage parameter is assigned to calculate multiaxial fatigue damage. Furthermore, the presented method employs shear strain‐based and axial strain‐based multiaxial fatigue damage parameters in substitution of equivalent strain amplitude to consider the influence of nonproportional additional hardening. The experimental data of GH4169 superalloy and 7050‐T7451 aluminium alloy notched components are used to illustrate the presented multiaxial fatigue lifetime estimation approach for notched components, and the results reveal that estimations are accurate.     

Fatigue failure modes of rib-to-deck joints under the multiaxial stress states caused by various wheel loading characteristics

Orthotropic steel bridge decks (OSBDs) are characterized by overall structural asymmetries and severe local stress concentrations; meanwhile, complicated service loadings always cause relevant rib-to-3deck (RD) welded joints in multiaxial stress states. Under such circumstances, a full-scale OSBD model was established. Six loading cases were applied, and the multiaxial fatigue deviation was calculated to represent the multiaxial stress state of the bridge deck. Based on the effective traction structural stress method, the most unfavorable loading case for the failure mode of the RD joint under a multiaxial stress state was analyzed, and the failure mode transition in the process of wheel load movement was discussed. The results indicated that the fatigue failure mode of the RD joint was determined by the transverse loading locations. In-between-rib loading can cause the initiation of toe-rib cracks. Cracks are prone to occur under over-rib loading and riding-rib loading, and the arrangement of diaphragms can increase the risk that the fatigue crack originates from the weld root.     

Multiaxial fatigue of rubber: Part I: equivalence criteria and theoretical aspects

This paper investigates commonly used approaches for fatigue crack nucleation analysis in rubber, including maximum principal strain (or stretch), strain energy density and octahedral shear strain criteria. The ability of these traditional equivalence criteria, as well as a recent equivalence criterion (the cracking energy density) to predict multiaxial fatigue behaviour is explored. Theoretical considerations are also introduced relating to the applicability of various fatigue life analysis approaches. These include the scalar nature of traditional equivalence criteria, robustness of the criteria investigated for a wide range of multiaxial loadings, effects of crack closure and applications to non‐proportional multiaxial loadings. It is shown that the notion of a stress or strain amplitude tensor used for the analysis of multiaxial loading in metals is not appropriate in the analysis of rubber due to nonlinearity associated with finite strains and near incompressibility. Taken together, these considerations illustrate that traditional criteria are not sufficiently consistent or complete to permit confident analysis of arbitrary multiaxial loading histories, and that an analysis approach specific to the failure plane is needed. Of the three traditional criteria, maximum principal strain is shown to match most closely to the cracking energy density criterion, in terms of a failure locus in principal stretch space.     

Multiaxial high-cycle fatigue criterion considering crack initiation and non-propagation

A new criterion for multiaxial high-cycle fatigue limit is proposed using two parameters: one governing crack initiation and the other governing initial crack growth. The axial fatigue limit and the true fracture strength are used as the material properties required in estimations. The prediction accuracies using conventional criteria and the proposed criterion were compared using known data about fatigue limits under different loading conditions. The comparison was made for the effects of phase difference, mean stress, and the combination of phase difference and mean stress. The estimation error of the proposed criterion was approximately 10%, which is better than that of the other criteria used for comparison.     

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.     

Multiaxial fatigue life prediction method in the ground vehicle industry

The extensive progress which has been made in the multiaxial fatigue area over the past 5 to 10 years has allowed wider application of the multiaxial fatigue method in component durability design in the ground vehicle industry. The method adopts the long established local strain–life approach and includes several new features. (1) A three-dimensional cyclic stress–strain model, used to simulate the elastic–plastic material behavior under complicated loadings. (2) The critical plane approach, which requires the fatigue analysis to be performed on various potential failure planes before determining the lowest fatigue life. (3) A biaxial damage criterion, to better quantify fatigue damage under various loading conditions. (4) A multiaxial Neuber equivalencing technique, used to estimate, from the elastic finite element stress results, the multiaxial stress and strain history of plastically deformed notch areas. This paper examines the application of the above features to the fatigue analyses of three generic service/test histories: a constant amplitude (baseline) test history, a history directly recorded by strain gages mounted on the critical location of a structural component, and a loading history recorded in multichannels for a complex structure.