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.     

A fatigue model for sensitive materials to non-proportional loadings

The present study proposes a novel fatigue model based on virtual strain energy. This model separates loading paths based on their non-proportionality where directly takes into account the loading in fatigue life prediction. The proposed fatigue model is expressed in two tension-based and shear-based equations for two tensile and shear cracking failure modes. The model was validated against several experimental datasets available in the literature. In addition, obtained results were compared to predicted lives through some well-known fatigue models comprising maximum shear strain, Smith–Watson–Topper, and Fatemi–Socie. The results were strongly correlated with the experimental data indicating accuracy of the model.     

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.     

Damage-based modification for fatigue life prediction under non-proportional loadings

This paper proposes a new fatigue model based on virtual strain energy to predict fatigue life under both proportional and non-proportional loadings for different materials including, 1045 Steel, 30CrNiMo8HH, Titanium TC4, and AZ31B magnesium. The results were strongly correlated with experimental results available in the literature. In addition, two damage-based modifications for fatigue life prediction under non-proportional loadings are studied. These modifications are then applied to the fatigue parameters including Smith–Watson–Topper, Fatemi–Socie, maximum shear strain, and the proposed parameter for fatigue life predictions of the studied materials. The results show considering these modifications significantly improves the accuracy of the models.     

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.     

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.     

Multiaxial fatigue and life prediction of elastomeric components

Elastomeric components have wide usage in many industries. The typical service loading for most of these components is variable amplitude and multiaxial. In this study a general methodology for life prediction of elastomeric components under these typical loading conditions was developed and illustrated for a passenger vehicle cradle mount. Crack initiation life prediction was performed using different damage criteria. The methodology was validated with component testing under different loading conditions including constant and variable amplitude in-phase and out-of-phase axial–torsion experiments. The optimum method for crack initiation life prediction for complex multiaxial variable amplitude loading was found to be a critical plane approach based on maximum normal strain plane and damage quantification by cracking energy density on that plane. Rainflow cycle counting method and Miner’s linear damage rule were used for predicting fatigue life under variable amplitude loadings. The fracture mechanics approach was used for total fatigue life prediction of the component based on specimen crack growth data and FE simulation results. Total fatigue life prediction results showed good agreement with experiments for all of the loading conditions considered.     

Random multiaxial fatigue: A comparative analysis among selected frequency and time domain fatigue evaluation methods

Fatigue analysis of mechanical components subjected to random loads has been recently upgraded through several developments of calculation procedures, with the scope to support the designer within the loading condition numerical simulation. Under such scenario, the frequency domain approach is characterized by interesting features, which support its adoption in alternative or in conjunction with the classic time-domain approach, especially when the frequency domain is applied for the individuation of the component critical locations. The major goal of this paper consists of an overview about the strength and weaknesses of frequency approach with respect to the time domain one by comparing the reference time domain methods with their frequency domain translation. A significant test case development will be shown, representing a classic automotive one (chassis validation). Promising results of the frequency method application will be presented, encouraging its adoption on large scale.     

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.     

High temperature fatigue tests of un-notched and notched specimens made of 40CrMoV13.9 steel

The present paper summarizes data from uniaxial-tension stress-controlled fatigue tests on specimens made of 40CrMoV13.9 steel. Tests are performed varying temperature, from room temperature up to 650 °C. This steel is commonly employed for hot-rolling of metals and it is subjected, in service, to a combination of mechanical and thermal loadings. Two geometries are considered: plain specimens and plates weakened by symmetric V-notches, with opening angle and tip radius being equal to 90 degrees and 1 mm, respectively. The present work is motivated by the fact that, at the best of authors’ knowledge, only a limited number of works dealing with high-temperature fatigue are reported in the literature for the medium/high cycle fatigue regime; in particular, no results seem to be available for 40CrMoV13.9 steel when tested at elevated temperature in the presence of notch effects.After a brief review of the recent literature, the experimental procedure is described in detail and the new data from un-notched and notched specimens are summarized in terms of stress range, at the considered temperatures, for a total of 60 new experimental data. Finally, fatigue data from un-notched and notched specimens are re-analyzed by means of the mean value of the strain energy density (SED), employed here as the critical fatigue parameter, able to summarize in the same scatter band data from different temperatures.     

The role of oxidation damage in fatigue crack initiation of an advanced Ni-based superalloy

The effects of prior oxidation on the room temperature fatigue life of coarse-grained Ni-based superalloy, RR1000, have been investigated. High cycle fatigue tests were conducted, on both machined and pre-oxidised testpieces, at room temperature at an R ratio of 0.1. The oxidation damage was produced by pre-exposures at 700 °C for either 100 or 2000 h. Pre-oxidised testpieces tended to fail with shorter fatigue lives than those obtained from the as-machined testpieces although they were also observed to outperform the as-machined test pieces at peak stress levels around 900 MPa. The chromia scale and intergranular alumina intrusions formed during pre-oxidation are prone to crack under fatigue loading leading to early crack nucleation and an associated reduction in fatigue life. This has been confirmed to be the case both below and above a peak stress level of ∼900 MPa. The better fatigue performance of the pre-oxidised specimens around this stress level is attributed to plastic yielding of the weaker γ′ denuded zone, which effectively eases the stress concentration introduced by the cracking of the chromia scale and intergranular internal oxides. This γ′ denuded zone is also a product of pre-oxidation and develops as a result of the selective oxidation of Al and Ti. Over a limited stress range, its presence confers a beneficial effect of oxidation on fatigue life.     

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.     

Non-proportional multiaxial whole-life transformation ratchetting and fatigue failure of super-elastic NiTi shape memory alloy micro-tubes

Experimental observations are performed to investigate the non-proportional multiaxial whole-life transformation ratchetting and fatigue failure of superelastic NiTi SMA micro-tubes in stress-controlled loadings at human-body temperature (310 K). The effects of axial mean stress and stress hold on the whole-life transformation ratchetting and fatigue life are investigated with uniaxial, torsional and five different multiaxial loading paths. The results show that the stress holds on the upper or lower transformation plateaus will both promote forward and reverse transformation, and lead to shorter fatigue life. The multiaxial fatigue lives of NiTi shape memory alloy depend significantly on loading paths and applied stress levels.     

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.     

Determination of the critical plane by a weight-function method based on the maximum shear stress plane under multiaxial high-cycle loading

A weight function method for the determination of the critical plane is here proposed for the case of specimens under combined bending and torsion in the high cycle fatigue regime. The critical plane is assumed to be coincident with the mean maximum absolute shear stress plane, which is calculated by averaging the instantaneous angle between the specimen axis and the normal to the maximum absolute shear stress plane. Two kinds of weight functions are proposed to determine such a plane. The proposed method to determine the critical plane is verified by employing fatigue data available in the literature in terms of experimental fracture planes, and the multiaxial fatigue life is also predicted by a reformulation of the criterion proposed by Carpinteri et al. to verify the determined critical plane. The results show that the proposed method can be applied to determine the critical plane under both constant and variable amplitude loading.