Remarks on multiaxial fatigue limit criteria based on prismatic hulls and ellipsoids

This paper focuses on a class of multiaxial fatigue limit criteria where the equivalent shear stress amplitude is calculated by means of a scalar measure associated with a hypersurface enclosing the deviatoric stress history at a material point. We consider two hypersurfaces proposed by the authors, namely the maximum prismatic hull and the minimum Frobenius norm ellipsoid. Previous results obtained with elliptic and non-elliptic stress paths strongly suggested that such measures might always be the same. In this work we consider two counter-examples which show that these approaches are distinct. Fatigue limit criteria based on the linear combination of these measures with the maximum hydrostatic stress were applied to experimental data including: axial–torsional, biaxial tension and plane stress tests performed under harmonic and non-harmonic, synchronous and asynchronous waveforms. The predictions for both criteria fell within a 15% scatter band.     

A FATIGUE LIFE PREDICTION METHOD BASED ON A MESOSCOPIC APPROACH IN CONSTANT AMPLITUDE MULTIAXIAL LOADING

The aim of this paper is to present a high cycle multiaxial fatigue life prediction method for metallic materials based on Papadopoulos' previous works and limited to constant amplitude loading. The initiation process of a crack is treated as a mesoscopic phenomenon taking place on a scale of the order of a grain or a few grains. The damage variable chosen is the accumulated plastic strain at this mesoscopic scale. Its estimation requires a macro-meso passage and the location of the plane subjected to maximum damage. Initiation is achieved as soon as a critical value of the accumulated plastic mesostrain is reached in these grains, so-orientated that their easy glide directions coincide with a particular direction of the critical plane. The detrimental effect of out-of-phase loading on damage accumulation is taken into account through a newly defined coefficient estimated from mechanical loading parameters; no adjustable parameter is required. A good agreement has been found between the predicted and experimental results for in-phase and out-of-phase sinusoidal constant amplitude loadings by examining a large amount of experimental data.     

Prediction of fatigue life in aircraft double lap bolted joints using several multiaxial fatigue criteria

In this research, the effects of torque tightening on the fatigue strength of 2024-T3 aluminium alloy double lap bolted joints have been studied via experimental and multiaxial fatigue analysis. To do so, three sets of the specimens were prepared and each subjected to different levels of torque i.e. 1, 2.5 and 5 N m and then fatigue tests were carried out at various cyclic longitudinal load levels. A non-linear finite element ANSYS code was used to obtain stress and strain distribution in the joint plates due to torque tightening of bolt and longitudinal applied loads. Fatigue lives of the specimens were estimated with six different multiaxial fatigue criteria by means of local stress and strain distribution obtained from finite element analysis. Multiaxial fatigue analysis and experimental results revealed that the fatigue life of double lap bolted joints were improved by increasing the clamping force due to compressive stresses which appeared around the hole.     

High temperature fatigue of nickel-base superalloys – A review with special emphasis on deformation modes and oxidation

Low cycle fatigue, high cycle fatigue, fatigue crack propagation and thermo-mechanical fatigue in Ni-base superalloys are reviewed in terms of fundamental deformation mechanisms, environmental effects, and interactions between environment and deformation mode. These factors are related to the chemical composition and underlying microstructure for all currently-used product forms (i.e. powder metallurgy, wrought, conventionally cast and single crystal). The basic principles that are developed are used to show how both intrinsic and extrinsic variables can be manipulated to control fatigue behaviour and as a guide for formulation of engineering life prediction models.     

Effect of steady torsion on fatigue crack initiation and propagation under rotating bending: Multiaxial fatigue and mixed-mode cracking

Axles and shafts are of prime importance concerning safety in transportation industry and railway in particular. Knowledge of fatigue crack growth under typical loading conditions of axles and shafts with rotating bending and steady torsion is therefore essential for design and maintenance purposes. The effect of a steady torsion on both small and long crack growth under rotating bending is focused in this paper. For small crack growth, a modified effective strain-based intensity factor range is proposed as the parameter that correlates small fatigue crack growth data under proportional or non-proportional multiaxial loading conditions. Results show that this parameter is appropriate for determining fatigue crack growth of small cracks on rotating bending with an imposed steady torsion.     

Micromechanical study of the loading path effect in high cycle fatigue

In this work, an analysis of both the mechanical response at the grain scale and high cycle multiaxial fatigue criteria is undertaken using finite element (FE) simulations of polycrystalline aggregates. The metallic material chosen for investigation, a pure copper, has a Face Centred Cubic (FCC) crystalline structure. Two-dimensional polycrystalline aggregates, which are composed of 300 randomly orientated equiaxed grains, are loaded at the median fatigue strength defined at 10⁷ cycles. In order to analyse the effect of the loading path on the local mechanical response, combined tension–torsion and biaxial tension loading cases, in-phase and out-of-phase, with different biaxiality ratios, are applied to each polycrystalline aggregate. Three different material constitutive models assigned to the grains are investigated: isotropic elasticity, cubic elasticity and crystal plasticity in addition to the cubic elasticity. First, some aspects of the mechanical response of the grains are highlighted, namely the scatter and the multiaxiality of the mesoscopic responses with respect to an uniaxial macroscopic response. Then, the distributions of relevant mechanical quantities classically used in fatigue criteria are analysed for some loading cases and the role of each source of anisotropy on the mechanical response is evaluated and compared to the isotropic elastic case. In particular, the significant influence of the elastic anisotropy on the mesoscopic mechanical response is highlighted. Finally, an analysis of three different fatigue criteria is conducted, using mechanical quantities computed at the grain scale. More precisely, the predictions provided by these criteria, for each constitutive model studied, are compared with the experimental trends observed in metallic materials for such loading conditions.     

Long life fatigue under multiaxial loading

A life prediction model in the field of high-cycle (i.e. long-life) fatigue is presented in this paper. The proposed model applies in the case of constant amplitude multiaxial proportional and non-proportional loading. The problems of the fatigue limit criterion and of the fatigue life prediction are both addressed and comparisons with experimental data are shown. Some limited discussion of the stress gradient effect is also offered. Although the particular model developed here is better suited for ferritic steels, it is explained in the paper that the methodology used to obtain this model can be adequately adapted to derive mathematically consistent models for other classes of metallic materials.     

The theory of critical distances: a review of its applications in fatigue

This paper attempts to review the most interesting findings in the use of the theory of critical distances (TCD) to predict fatigue strength of notched mechanical components. Initially, the most modern formalisations of the TCD are considered, showing their peculiarities and differences. An ad-hoc section is then focused on the multiaxial high-cycle fatigue problem, considering all the open questions arising in the presence of complex stress fields damaging the fatigue process zone in the vicinity of the stress concentrator apex. Subsequently, the physical idea on the structural volume concept is briefly investigated showing some peculiar results generated in the high-cycle fatigue regime under both uniaxial and biaxial fatigue loading. Finally, our idea to extend the use of the TCD down to the low-medium cycle fatigue regime is briefly explained.Working in collaboration with Prof. David Taylor, we have spent the last five years investigating this theory both to better understand its physical meaning and to systematically check its accuracy in predicting notch fatigue strength under different loading conditions. After so much work done in this area we feel so confident to proudly and loudly say that the TCD is a powerful engineering tool suitable for assessing real mechanical components in situations of practical interest. Finally, it can be highlighted also that the best TCD formalisations were seen to be those based on the use of linear-elastic stresses. This suggests that such a theory can successfully be used to post-process simple linear-elastic finite element (FE) models reducing time and costs of the design process.     

Improvements of multiaxial fatigue criteria computation for a strong reduction of calculation duration

Fatigue life criteria are tools used for engineering and designing against fatigue. Even if computers capacities increase more and more, the complex geometry of mechanical components treated nowadays require to improve the swiftness of the calculations realized in any point of the structure. This paper contains two proposals concerning the computation of the most commonly used fatigue criteria, whatever their formulation is based upon the critical plane concept or upon a global approach. The application of many fatigue criteria requires to examine all the material planes passing through the considered point either to find out the critical plane or to make some average of stress quantities over all of them. In both cases, all the possible oriented planes have to be explored. The first proposal deals with the way to obtain an homogeneous distribution of the orientation of the practically considered planes. The second proposal of this paper concerns the determination of the smallest circle surrounding to the loading path that describes the tip of the shear stress vector acting on a material plane during one stress cycle. The mean shear stress is determined by the centre of this circle; the shear stress amplitude and the alternate component of the shear stress are established from this circle also. The principles of these two proposals are explained in detail and the algorithms for the fastest calculations are given. The efficiency of the new proposals relatively to what is commonly realized is assessed in terms of time saving.     

An experimental technique for determining biaxial fatigue lifetimes in biomedical elastomers

A novel test apparatus was developed to determine fatigue lifetimes of elastomeric materials. Thin elastomeric sheets (membranes) are biaxially fatigued while contained within a temperature controlled liquid environment. Membranes are displaced in a smooth sinusoidal motion by pumping the surrounding fluid through the equipment's inner cells. An electrical signal (AC) passes through the membrane during fatigue and is used to monitor changes in the elastomer's physical characteristics. In addition, the test cell is designed to allow optical observation of the membrane throughout the fatiguing process. Thus the design results in a test rig apparatus that permits failure determination by both material property changes and obvious fracture. Cyclic fatigue frequencies range from 0.2 to 1.2 Hz.     

A GENERALIZED FATIGUE LIMIT CRITERION AND A UNIFIED THEORY OF LOW-CYCLE FATIGUE DAMAGE

Abstract— A generalized fatigue limit criterion for multiaxial stress state conditions of isotropic materials is presented. This criterion includes four material parameters and uses two invariants of stress amplitudes and furthermore two invariants of mean stresses. It is shown that the fatigue criteria of Sines and Crossland are particular cases of the formulated criterion. Practical recommendations for the use of different fatigue limit criteria are established. Theoretical predictions are compared with experimental data. Finally a continuum damage mechanics theory for low cycle fatigue of isotropic materials is proposed. This theory describes simultaneously the influence of the stress amplitude and the mean stress on the fatigue damage suffered by materials. The proposed theory is based on four material parameters. Special damage theories with a smaller number of material parameters are obtained. Practical recommendations for the use of these fatigue damage theories are presented.     

High cycle fatigue analysis in presence of residual stresses by using a continuum damage mechanics model

This study attempts to predict the high cycle fatigue life of steel butt welds by numerical method. At first, FE simulation of plate butt welding is carried out to obtain the weld-induced residual stresses employing sequentially coupled three-dimensional (3-D) thermo-mechanical FE formulation. Then, a nonlinear damage cumulative model for multiaxial high cycle fatigue based on continuum damage mechanics (CDM), which can incorporate the effect of welding residual stresses, is derived using FE technique. The high cycle fatigue damage model is applied to the butt welds subjected to cyclic fatigue loading to calculate the fatigue life considering the residual stresses, and the computed total fatigue life which takes into account the fatigue crack initiation and the propagation is compared with the test result. In addition, the fatigue life prediction of the welds without considering the residual stresses is implemented to investigate the influence of welding residual stresses on the fatigue performance. The FE results show that the high cycle fatigue damage model proposed in this work can predict the fatigue life of steel butt welds with high accuracy, and welding residual stresses should be taken into account in assessing the fatigue life of the welds.     

A comparison of maximum likelihood models for fatigue strength characterization in materials exhibiting a fatigue limit

In this study, various probabilistic models were considered to support fatigue strength design guidance in the ultra high-cycle regime (beyond 10⁸ cycles), with particular application to Ti-6Al-4V, a titanium alloy common to aerospace applications. The random fatigue limit model of Pascual and Meeker and two proposed simplified models (bilinear and hyperbolic) used maximum likelihood estimation techniques to fit probabilistic stress-life curves to experimental data. The bilinear and hyperbolic models provided a good fit to large-sample experimental data for dual-phase Ti-6Al-4V and were then applied to a small-sample data set for a beta annealed variant of this alloy, providing an initial probabilistic estimate of beta annealed Ti-6Al-4V fatigue strength in the gigacycle regime. The bilinear and hyperbolic models are recommended for use in estimating probabilistic fatigue strength parameters in support of very high-cycle design criteria for metals with clearly defined fatigue limits and fairly constant scatter in fatigue strength.     

Crack initiation and growth path under multiaxial fatigue loading in structural steels

In real engineering components and structures many accidental failures occur due to unexpected or additional loadings, such as additional bending or torsion. There are many factors influencing the fatigue crack paths, such as the material type (microstructure), structural geometry and loading path. It is widely believed that fatigue crack nucleation and early crack growth are caused by cyclic plasticity. This paper studies the effects of multiaxial loading paths on the cyclic deformation behaviour, crack initiation and crack path. Three types of structural steels are studied: Ck45, medium carbon steel, 42CrMo4, low alloy steel and the AISI 303 stainless steel. Four biaxial loading paths were applied in the tests to observe the effects of multiaxial loading paths on the additional hardening, fatigue crack initiation and crack propagation orientation. Fractographic analyses of the plane orientations of crack initiation and propagation were carried out by optical microscope and SEM approaches. It is shown that these materials have different crack orientations under the same loading path, due to their different cyclic plasticity behaviour and different sensitivity to non-proportional loading. Theoretical predictions of the damage plane were conducted using the critical plane approaches, either based on stress analysis or strain analysis (Findley, Smith–Watson–Topper, Fatemi–Socie, Wang–Brown–Miller, etc). Comparisons of the predicted crack orientation based on the critical plane approaches with the experimental observations for the wide range of loading paths and the three structural materials are shown and discussed. Results show the applicability of the critical plane approaches to predict the fatigue life and crack initial orientation in structural steels.     

Optimization of a cold-working process for increasing fatigue life

This paper introduces a method which allows the calculation of the optimal radial interference and the optimal mandrel shape on a cold-expanded bushing–hole connection commonly used in aerospace structures, in order to obtain the desired values of the residual stresses on the hole surface. This method has been developed by an extended campaign of FE analysis, planned and evaluated with statistical techniques on the basis of a previous presented closed-form method to determine the residual stress field. The method will give the possibility to reduce the zone of the hole surface subject to negligible residual radial stresses, obtaining also compressive residual circumferential stresses on the entire hole surface.An experimental axial fatigue test plan on aeronautical components with optimized cold-expanded bushing–hole connections and subjected to cyclic loads showed a substantial improvement in fatigue life.     

Experimental and numerical study on crack initiation under fretting fatigue loading

Press-fitted railway axles and wheels are subjected to fretting fatigue loading with a potential hazard of crack initiation in press fits. Typically, the resistance against crack initiation and propagation in press fits is investigated in full-scale tests, which procedure is both costly and time consuming. In this context, combined experimental and numerical approaches are of increasing practical importance, as these may reduce the experimental effort and, moreover, provide a basis for the transferability of experimental results to different axle geometries and materials. This study aims at evaluating stress–strain conditions under which fretting fatigue crack initiation is likely to occur. Experiments on small-scale specimens under varying fretting fatigue load parameters and their finite-element modelling to characterize the resulting stress–strain fields are performed. Subsequently, different multiaxial fatigue parameters are applied to predict crack initiation under fretting fatigue conditions.     

A MICROCRACK GROWTH LAW FOR MULTIAXIAL FATIGUE

Within the past decade, critical plane approaches have gained increasing support based on correlation of experimentally observed fatigue lives and microcrack orientations under predominately low cycle fatigue (LCF) conditions for various stress states. In this paper, we further develop an engineering model for microcrack propagation consistent with critical plane concepts for correlation of both LCF and high cycle fatigue (HCF) behavior, including multiple regimes of small crack growth. The critical plane microcrack propagation approach of McDowell and Berard serves as a starting point to incorporate multiple regimes of crack nucleation, shear growth under the influence of microstructural barriers, and transition to linear crack length-dependent growth related to elastic-plastic fracture mechanics (EPFM) concepts. Microcrack iso-length data from uniaxial and torsional fatigue tests of 1045 steel and IN 718 are examined and correlated by introducing a transition crack length which governs the shift from nonlinear to linear crack length dependence of da/dN. This transition is related to the shift from strong microstructural influence to weak influence on the propagation of microcracks. Simple forms are introduced for both the transition crack length and the crack length-dependence of crack growth rate within the microcrack propagation framework (introduced previously by McDowell and Berard) and are employed to fit the 1045 steel and IN 718 microcrack iso-length data, assuming preexisting sub-grain size cracks. The nonlinear evolution of crack length with normalized cycles is then predicted over a range of stress amplitudes in uniaxial and torsional fatigue. The microcrack growth law is shown to have potential to correlate microcrack propagation behavior as well as damage accumulation for HCF-LCF loading sequences and sequences of applied stress states.     

Multiaxial fatigue and failure analysis of helical compression springs

Multiaxial fatigue criteria are applied to the analysis of helical compression springs. The critical plane approaches, Fatemi–Socie and Wang–Brown, and the Coffin–Manson method based on shear deformation, were used to predict fatigue lives of the springs under constant amplitude loading. Experimental fatigue lives are compared with the multiaxial fatigue criteria predictions. The stress analysis was carried out in the finite element code ANSYS, and the multiaxial fatigue study was performed using the fatigue software nCode. A failure analysis was conducted in order to determine the fatigue crack initiation point and a comparison of that location with the most damaged zone predicted by the numerical analysis is made. The Fatemi–Socie critical plane approach gives a good prediction of fatigue life. While the Wang–Brown criterion overestimates spring fatigue life, the Coffin–Mason model gives conservative results.     

Multiaxial fatigue of a short glass fibre reinforced polyamide 6.6 – Fatigue and fracture behaviour

The multiaxial fatigue behaviour of a short glass fibre reinforced polyamide 6.6 (PA66-GF35) is investigated on hollow tubular specimens in the range of fatigue lives between 10² and 10⁷ cycles. Fatigue experiments included pure tension, pure torsion, combined tension–torsion at different biaxiality ratios and phase shifting angles between the stress components. Tests were carried out with load ratio R = 0 and R = −1 at room temperature as well as at 130 °C. The influence of biaxiality ratio, phase angle between load components and load ratio is discussed.An extensive analysis of the fracture behaviour is performed on the specimens to recognise the crack nucleation and propagation mechanisms; failure modes were evaluated via optical and scanning electron microscopy.