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Fatigue damage and life assessment of multiaxial loadings is still an issue yet to resolve. Many methods have been proposed with promising agreements with the experimental results. However, the performance of such methods is, more than often, purely based on fatigue tests with simple loading conditions. In this work the stress scale factor (SSF) criterion and the virtual cycle counting (vcc) method are used to estimate fatigue life and damage accumulation with two damage accumulation rules. Fatigue tests were carried out with three different variable amplitude random loadings, applied to several specimens made from a 42CrMo4 high-strength steel. Fatigue crack plane measurements were compared with predictions from several critical plane models. The applied methods provided very acceptable results making the SSF package (SSF equivalent stress and virtual cycle counting method) a good method to estimate fatigue life and assessment of the damage accumulation in random fatigue loadings. [ABSTRACT FROM AUTHOR]

The very high cycle region of the S-N fatigue curve has been the subject of intensive research on the last years, with special focus on axial, bending, torsional and fretting fatigue tests. Very high cycle fatigue can be achieved using ultrasonic exciters which allow for frequency testing of up to 30 kHz. Still, the multiaxial fatigue analysis is not yet developed for this type of fatigue analyses, mainly due to conceptual limitations of these testing devices. In this paper, a device designed to produce biaxial fatigue testing using a single piezoelectric axial exciter is presented, as well as the preliminary testing of this device. The device is comprised of a horn and a specimen, which are both attached to the piezoelectric exciter. The steps taken towards the final geometry of the device are presented. Preliminary experimental testing of the developed device is made using thermographic imaging, strain measurements and vibration speeds and indicates good behaviour of the tested specimen. [ABSTRACT FROM AUTHOR]

In this work, the performance of the SSF criterion is evaluated under variable amplitude loading conditions. The main objective was to inspect the validity of the hypothesis in which the SSF damage map remains valid for any high strength steel. In order to achieve that, fatigue life correlation of the 1050QT steel and 304L stainless steel was analyzed under multiaxial loading conditions. The loading block considered in the study comprises 360 proportional loading cycles with different stress amplitude ratios and stress levels. Despite being made of proportional branches, this loading block is a non-proportional loading due to its principal directions variation. This feature allows the evaluation of combined loading effects under variable amplitude loading conditions, which makes this loading block suitable to mimic the loading effects usually found in the field. Results show very good agreements, which reinforces the aforementioned hypothesis. [ABSTRACT FROM AUTHOR]

Axles and shafts are of prime importance concerning safety in the transportation industry and railway in particular. Design rules for axles and shafts are mainly based on endurance curves for the material used according to the established standards and procedures. Recently, the knowledge of fatigue crack growth under typical loading conditions of axles and shafts with rotating bending and steady torsion is being object of research and industrial studies in order to apply damage tolerance concepts, mainly for maintenance purposes. The effect of a steady torsion on fatigue crack growth under rotating bending is focused in this paper. While axles and shafts in the transportation industry are traditionally designed on steels, the need for weight reduction due to fuel economy and eco-design constraints, lightweight materials must be considered for these applications. In this study, fatigue crack growth on rotating bending axles and shafts with or without an applied steady torsion is presented. Fracture mechanics approaches are used to analyze the results based on Stress Intensity Factors developed for bending and torsion in shafts and show fatigue crack growth retardation when steady torsion is applied. Fractographic observations using SEM are presented and helped to explain the fatigue crack growth retardation observed when steady torsion is applied to rotating bending. Results are compared for the same loading conditions on steels and relevant differences on fatigue crack growth are commented. [ABSTRACT FROM AUTHOR]

Abstract: Damage accumulation is a well known concept in multiaxial fatigue but the achievement of damage quantification and associate it to fatigue life estimation is still a big challenge. The aim of this work is to study the damage accumulation generated in 42CrMo4 steel due to different sequential biaxial loadings. It was implemented several loading paths with the same final history but with different trajectories. The loading paths were carried out with a biaxial servo-hydraulic fatigue machine, and for each specimen the crack initiation angle was measured. The number of cycles at failure and the crack angles were correlated with two theoretical critical plane models. The obtained results are discussed and allow to improve the understanding of fatigue damage accumulation. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

In this study the uniaxial/biaxial low-cycle fatigue behaviour of three structural steels (Ck45 normalized steel, 42CrMo4 quenched and tempered steel and AISI 303 stainless steel) are studied, evaluated and compared. Two parameters are considered for estimating non-proportional fatigue lives: the coefficient of additional hardening and the factor of non-proportionality. A series of tests of uniaxial/biaxial low-cycle fatigue composed of tension/compression with cyclic torsion were carried out on a biaxial servo-hydraulic testing machine. Several loading paths were carried out, including proportional and non-proportional ones, in order to verify the additional hardening caused by different loading paths. The experiments showed that the three materials studied have very different additional hardening behaviour. Generally, the transient process from the initial loading cycle to stabilized loading cycle occurs in a few cycles. The stabilized cyclic stress/strain parameters are controlling parameters for fatigue damage. A factor of non-proportionality of the loading paths is evaluated based on the Minimum Circumscribed Ellipse approach. It is shown that the microstructure has a great influence on the additional hardening and the hardening effect is dependent on the loading path and also the intensity of the loading. [ABSTRACT FROM AUTHOR]

Fatigue crack path prediction and crack arrest are very important for structural safety. In real engineering structures, there are many factors influencing the fatigue crack paths, such as the material type (microstructure), structural geometry and loading path, etc. In this paper, both experimental and numerical methods are applied to study the effects of loading path on crack orientations. Experiments were conducted on a biaxial testing machine, using specimens made of two steels: 42CrMo4 and CK45 (equivalent to AISI 1045), with six different biaxial loading paths. Fractographical analyses of the plane of the stage I crack propagation were carried out and the crack orientations were measured using optical microscopy. The multiaxial fatigue models, such as the critical plane models and also the energy-based critical plane models, were applied for predicting the orientation of the critical plane. Comparisons of the predicted orientation of the damage plane with the experimental observations show that the shear-based multiaxial fatigue models provide good predictions for stage I crack growth for the ductile materials studied in this paper. [ABSTRACT FROM AUTHOR]

In order to study the use of a local approach to predict crack-initiation life on notches in mechanical components under multiaxial fatigue conditions, the study of the local cyclic elasto-plastic behaviour and the selection of an appropriate multiaxial fatigue model are essential steps in fatigue-life prediction. The evolution of stress–strain fields from the initial state to the stabilized state depends on the material type, loading amplitude and loading paths. A series of biaxial tension–compression tests with static or cyclic torsion were carried out on a biaxial servo-hydraulic testing machine. Specimens were made of an alloy steel 42CrMo4 quenched and tempered. The shear stress relaxations of the cyclic tension–compression with a steady torsion angle were observed for various loading levels. Finite element analyses were used to simulate the cyclic behaviour and good agreement was found. Based on the local stabilized cyclic elastic–plastic stress–strain responses, the strain-based multiaxial fatigue damage parameters were applied and correlated with the experimentally obtained lives. As a comparison, a stress-invariant-based approach with the minimum circumscribed ellipse (MCE) approach for evaluating the effective shear stress amplitude was also applied for fatigue life prediction. The comparison showed that both the equivalent strain range and the stress-invariant parameter with non-proportional factors correlated well with the experimental results obtained in this study. [ABSTRACT FROM AUTHOR]

A computerized procedure is presented and evaluated for application examples of long-life fatigue analyses of metallic materials under complex multiaxial loading. The method is based on the stress invariants and uses the minimum circumscribed ellipse approach for evaluating the effective shear stress amplitude under complex multiaxial loading. The applicability of the procedure for handling non-proportional loading is examined through typical examples such as combined normal/shear stresses and combined bi-axial normal stresses with complex stress time histories. The effects of phase shift angles, frequency ratios and waveforms on fatigue endurance were re-analysed and compared with available experimental results from the literature. The comparison shows that the presented procedure based on stress invariants is a potential conservative engineering approach, very suitable for fast fatigue evaluation in the integrated computer aided fatigue design. [ABSTRACT FROM AUTHOR]

Fatigue damage assessment of multiaxial random loadings is a complex issue and a subject of actual interest in mechanical design. In this work, the performance of the stress scale factor (SSF) criterion is evaluated under variable amplitude loading conditions, and damage accumulation approaches. This evaluation is performed by taking into account two types of loading spectra, namely the loading block spectra (where the loading pattern is well identified and repeated until rupture), and the random loading spectra (where the stochastic behaviour of the axial and shear loading components do not allow a direct identification of the loading pattern). Moreover, the validity of the hypothesis in which the SSF damage map remains valid for any high strength steel under variable amplitude loading conditions is also inspected by analysing fatigue life correlation of the 1050 QT steel and the 304L stainless steel under a multiaxial loading block. [ABSTRACT FROM AUTHOR]

The very high cycle region, up to 10E10 cycles of the S-N fatigue curve has been the subject of intensive research on the last decades, with special focus on axial, bending, torsional and fretting fatigue tests. This can be achieved using ultrasonic exciters which allow for frequency testing of up to 30 kHz. Still, the multiaxial fatigue analysis is not yet developed for this type of fatigue analyses, mainly due to conceptual limitations of these testing devices. In this paper, a special designed cylindrical specimen is tested at 20 kHz on a bi-axial loading condition, with axial and torsional components on the specimen throat, using a new biaxial ultrasonic fatigue testing machine. The characterization of the specimen loading is measured by rotational and axial laser transducers at the bottom of the specimen and additionally by strain gauges applied at its throat. Strain gage data from very high frequency excitation is compared to strain gage data obtained from equivalent specimen geometry at 0.5 Hz in a biaxial servohidraulic machine. Results indicate good correlation between strain measurements for both fatigue tests at low and ultrasonic frequency tests. This data will help to extend very high cycle fatigue curves for biaxial loading conditions and serve as groundwork for future research on this field. [ABSTRACT FROM AUTHOR]

Axles and shafts are of prime importance concerning safety in energy equipment, transportation industry and general machinery. Case studies relating failure of axles and shafts are widely reported in the literature. Design rules for axles and shafts are mainly based on endurance curves for the material used according to long time established standards and procedures. Safe life design, based on endurance curves is being complemented by damage tolerance, where crack growth is taken into account. Recently, the knowledge of fatigue crack growth under typical loading conditions of axles and shafts with rotating bending and steady torsion has been object of research in order to apply damage tolerance concepts, mainly for maintenance and failure analysis purposes. The effect of a steady torsion on fatigue crack growth under rotating bending is focused in this paper. While axles and shafts in the transportation industry are traditionally designed on steels, the need for weight reduction due to fuel economy and eco-design constraints, lightweight materials must be considered for these applications. In this study, fatigue crack growth on rotating bending axles and shafts with or without an applied steady torsion is presented. Fracture mechanics approaches are used to analyze the results based on stress intensity factors developed for bending and torsion in shafts. Results are compared for the same stress ratio and relevant differences on fatigue crack growth are commented based on crack closure concepts. Discussion of the effect of crack growth retardation due to steady torsion is also discussed. Fractographic observations are presented and helped to explain fatigue crack growth under this mixed mode loading when steady torsion is applied to rotating bending. [ABSTRACT FROM AUTHOR]

Railway sector plays an important role in the means of transportation and the safety of wheels and rails is a greater concern for the manufacturers and operators of the railway network. In the wheel–rail contact, damage may occur due to wear or fatigue and in the latter case Rolling Contact Fatigue (RCF) is a growing problem due to the operation increase of high speed railway trains, where increased number of loading cycles due to the passage of the wheels over the rails, will be present in the wheel–rail contact. The present study focuses on the RCF failure analysis, analytical, numerical and experimental approaches are applied to investigate the problem. It is widely known that Hertz contact theory was the first approach to explain the stress state in the contact area through the calculation of the curvature of ellipse of contact and the stresses governing rolling contact between wheel and rail. The contact zone was studied for semi-elliptical shape, governed with multiaxial, out-of-phase state of stress with constant change in directions of principal stresses occurring due to rolling. Following, Finite Element analysis of the wheel–rail contact was implemented with the realistic loads, boundary conditions and material properties. Since a multiaxial stress state is present in the contact zone with normal and shear stresses, multiaxial fatigue tests in tension torsion were carried out on specimens taken from wheels and rails. Results from the multiaxial fatigue tests were analysed through multiaxial fatigue models, either stress invariant or critical plane models, such as modified Sines, Findley, Wang–Brown, Fatemi–Socie and Smith–Watson and Topper. Orientation of fatigue crack paths were also predicted by applying the above models and comparisons with measured crack orientation were carried out. The difficulties of the experimental measurement and analysis of the crack initiation are discussed and analysed within this complex stress state where alternate shear stresses are present in a strong compression stress and in a confined zone environment. [ABSTRACT FROM AUTHOR]

Abstract: Fatigue damage prediction under a general multiaxial service loading consists of three main steps: multiaxial cycle counting, damage evaluation for an identified cycle (or reversal), and damage accumulations. The accuracy of fatigue life predictions depends on all the above steps. This paper reviews the evolutions of various multiaxial fatigue damage models, a comparative study is conducted about the physical basis, the computational efficiency, and the application range of the approaches. Based on the comparative studies, a new procedure is proposed to evaluate fatigue damage under general multiaxial random loading, which uses the Wang and Brown´s multiaxial cycle counting method for identifying cycles (or reversals), the modified procedure of the minimum circumscribed ellipse (MCE) approach for fatigue damage evaluation for an identified cycle (or reversal), and the Miner´s linear damage law for fatigue damage accumulations. By comparisons of the predicted life results with experimental results and with other approaches, it is shown that the proposed procedure is very efficient and suitable for computer aided structural optimization against fatigue. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: This study deals with simulation for cyclic stress/strain evolutions and redistributions, and evaluation of fatigue parameters suitable for estimating fatigue lives under multiaxial loadings. The local cyclic elastic–plastic stress–strain responses were analyzed using the incremental plasticity procedures of ABAQUS finite element code for both smooth and notched specimens made of three materials: a medium carbon steel in the normalized condition, an alloy steel quenched and tempered and a stainless steel, respectively. Emphasis is on the studying of ‘intelligent’ material behaviors to resist fracture, such as stress redistribution and relaxation through plastic deformations, etc. For experimental verifications, a series of tests of biaxial low cycle fatigue composed of tension/compression with static and cyclic torsion were carried out on a biaxial servo-hydraulic testing machine (Instron 8800). Different multiaxial loading paths were used to verify their effects on the additional cyclic hardening. The comparisons between numerical simulations and experimental observations show that the FEM simulations allow better understanding on the evolutions of the local cyclic stress–strain and it is shown that strong interactions exist between the most stressed material element and its neighboring material elements in the plastic deformations and stress redistributions. Based on the local cyclic elastic–plastic stress–strain responses, the energy-based multiaxial fatigue damage parameters are applied to correlating the experimentally obtained lives. Improved correlations between the predicted and the experimental results are shown. It is concluded that the improvement of fatigue life prediction depends not only on the fatigue damage models, but also on the accurate evaluations of the cyclic elasto-plastic stress/strain responses. [Copyright &y& Elsevier]

Many fatigue models proposed in literature are validated by the author’s data and usually they are not corroborated with other author’s lab work. In this paper, two multiaxial fatigue criteria, the Minimum Circumscribed Ellipse (MCE) and the Stress Scale Factor (SSF), are used to assess fatigue life under multiaxial loading conditions. Two different sets of fatigue data obtained from two different steels and from two different research groups were used in order to evaluate the accuracy of the models MCE and SSF regarding multiaxial fatigue life assessment. The fatigue data used here have two major features: stress concentrations, always present in mechanical components, and the loading path effects, with the inherent changing on the principal stress directions and/or the variation of the stress amplitude ratio (tau/sigma). Furthermore, different failure criteria were adopted for each material and different testing setup. For the Ck45 material, the failure criterion was the crack initiation, for the C40 material was the total rupture. Another factor to point out is that the Ck45 fatigue results were obtained under bending/torsion conditions and the C40 fatigue results were achieved in axial/torsion loading conditions. Results show good correlation between experiments and fatigue life estimations. Some remarks and conclusions concerning the performance of the MCE and SSF models are presented. [ABSTRACT FROM AUTHOR]

Highlights: [•] The scale factor which relates normal and shear damage is not constant. [•] A new concept of multiaxial fatigue life criterion is proposed. [•] A stress scale factor (ssf) as a function of SAR and stress level is presented. [•] A experimental methodology to determine the material ssf function is provided. [ABSTRACT FROM AUTHOR]

Abstract: In this paper the multiaxial loading path effect on the fatigue crack initiation, fatigue life and fracture surface topology are evaluated for two different crystallographic microstructures (bcc and hc): high strength low-alloy 42CrMo4 steel and the extruded Mg alloy AZ31B-F, respectively. A series of multiaxial loading paths were carried out in load control, smooth specimens were used. Experimental fatigue life and fractographic results were analyzed to depict the mechanical behavior regarding the different microstructures. A theoretical analysis was performed with various critical plane models such as the Fatemi–Socie, SWT and Liu in order to correlate the theoretical estimations with the experimental data. A new approach based on maximum stress concentration factors is proposed to estimate the crack initiation plane, estimations from this new approach were compared with the measured ones with acceptable results. To implement this new approach a virtual micro-notch was considered using FEM. Moreover, the multiaxial loading path effect on stress concentration factors is also studied. The obtained results clearly show the effect of the applied load conditions on local microstructures response. [Copyright &y& Elsevier]

Abstract: Most of catastrophic mechanical failures in power rotor shafts occur under cyclic bending combined with steady torsion: Mode I (ΔK I) combined with Mode III (K III). An analysis of the influence of steady torsion loading on fatigue crack growth rates in shafts is presented for short as well as long cracks. Long cracks growth tests have been carried out on cylindrical specimens in DIN Ck45k steel for two types of testing: rotary or alternating bending combined with steady torsion in order to simulate real conditions on power rotor shafts. The growth and shape evolution of semi-elliptical surface cracks, starting from the cylindrical specimen surface, has been measured for several loading conditions and both testing types. Short crack growth tests have been carried out on specimens of the same material DIN Ck45k, under alternating bending combined with steady torsion. The short crack growth rates obtained are compared with long crack growth rates. Results have shown a significant reduction of the crack growth rates when a steady torsion Mode III is superimposed to cyclic Mode I. A 3D Finite Element analysis has also shown that Stress Intensity Factor values at the corner crack surface depend on the steady torsion value and the direction of the applied torque. [Copyright &y& Elsevier]