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• Tubular specimens of AM 18NI300 maraging steel were subjected to multiaxial loading. • Fatigue life of AM 18Ni300 maraging steel is insensitive to axial-torsion phase shift. • Lifetime prediction model was built based on physics-constrained Gaussian process. • Inherent surface defects play a key role in fatigue of AM 18Ni300 maraging steel. The study aims to estimate the role of surface defects in the fatigue life of age-hardened and unmachined additively manufactured 18Ni300 maraging steel and to verify the effectiveness of stress-based life prediction models. Axial-torsional cyclic loading paths involving in-phase and out-of-phase cases are applied. Scanning electron microscopy and micro-computed tomography are performed to detect the fatigue crack initiation sites and paths. The effectiveness of the classic models and a physics-constrained Gaussian process for regression in fatigue life prediction is estimated. Results show that the intrinsic orientation of the surface defects affects the fatigue mechanism by increasing the material sensitivity to axial stress. Additionally, the steel is insensitive to the phase shift between the axial and torsional loading components. The hydrostatic stress and the integrated shear stress amplitudes over the critical plane are pointed as the most effective load-related quantities for life prediction. [ABSTRACT FROM AUTHOR]

Rolling contact loading induces severe plastic deformations and initiates cracks near the rail surface. Prevention of such rolling contact fatigue cracks requires a better understanding about the mechanical behavior of the deformed material in this region. Even so, current rail standards do not consider the plasticity-induced changes to mechanical behavior. They only evaluate the mechanical performance of virgin rail steels under uniaxial loading conditions, which is not representative for the material's performance after years of service. This study proposes a new method for fatigue life evaluation of deformed material under loading conditions similar to rolling contact loading. Both virgin and predeformed test bars with a circumferential notch were subjected to strain-controlled torsional fatigue loading to evaluate the influence of axial loading, predeformation, and torsional loading direction. Superimposed compressive axial loads increase the fatigue life without affecting the torque response. The predeformed test bars exhibited longer lives, an effect we attribute to the combination of different torque responses, hardening, and anisotropy. • A new strain-controlled method for combined axial and shear fatigue-loading is proposed. • Predeformation increases the fatigue resistance of the pearlitic rail steel. • Axial compression prolongs the fatigue life. • The pulsating load direction changes the mean torque for predeformed material, which strongly affects the fatigue life. [ABSTRACT FROM AUTHOR]

• Effect of loading rate on transformation ratcheting was indicated. • Effect of loading path on transformation ratcheting was indicated. • Rate- and path-dependent fatigue lives were investigated. • Transformation ratcheting-fatigue interaction was revealed. To investigate the interaction between the rate-dependent transformation ratcheting and fatigue failure of super-elastic NiTi shape memory alloy (SMA) thin-walled tubes, uniaxial and torsional stress-controlled fatigue tests were conducted at various loading rates. The experimental results show that the uniaxial transformation ratcheting is more obvious than the torsional one and the torsional fatigue lives are significantly longer than the uniaxial ones, which imply that a more obvious transformation ratcheting leads to a shorter fatigue life. The rate-dependent transformation ratcheting and fatigue failure of super-elastic NiTi SMA can be attributed to the significant thermo-mechanical coupling effect. [ABSTRACT FROM AUTHOR]

• Low-cycle multiaxial fatigue experiments are conducted for Q235B steel welded material. • Equivalent cyclic stress-strain curves and hysteresis loops are obtained. • Specimens under non-proportional paths show certain extent of additional hardening effect. • Proposed fatigue parameter incorporates energy on weighted critical plane and orthogonal plane. • The proposed fatigue parameter provides a superior ability to make life prediction. Low-cycle torsional and multiaxial fatigue experiments are carried out for thin-walled Q235B steel welded specimens under both in-phase and 90° out-of-phase loading paths. A remarkable non-proportional additional hardening effect exists in the Q235B steel welded material under the 90° out-of-phase loading paths. A new energy-based fatigue parameter is proposed that incorporates the shear strain energy on the weighted critical plane and the normal strain energy on both the weighted critical plane and orthogonal plane. The proposed energy-based fatigue parameter provides a superior ability to make life prediction for the Q235B steel welded material under the torsional and multiaxial loading paths. [ABSTRACT FROM AUTHOR]

• Martensitic phase transformation was not observed for all loading paths. • Neither accumulated plastic strain nor amplitude could predict phase transformation. • Cyclic Young's and shear moduli did not vary due to martensitic transformation. • Fatigue life estimates were not significantly influenced by secondary hardening. • Crack orientation depended on the strain amplitude for all paths but the axial one. This work investigates the axial-torsional fatigue and cyclic deformation behaviour of 304L stainless steel at room temperature. The testing programme included four fully reversed strain-controlled loading paths (axial, torsional, proportional axial-torsional, and 90° out-of-phase axial-torsional) and a fully reversed shear strain-controlled with static axial stress. The experiments were carried out at equivalent strain amplitudes ranging from 0.20% to 1.00%, resulting in fatigue lives from 102 to 106 cycles. For axial, torsional, and torsional with axial static stress loading, secondary hardening related to martensitic transformation was observed, while it did not occur for nonproportional loading. For proportional loading, secondary hardening occurred only for an equivalent strain amplitude equal to or greater than 0.80%. Neither the accumulated plastic strain nor the equivalent plastic strain amplitude could predict whether secondary hardening would occur for the investigated loading conditions. Almost no variation in the cyclic Young's and shear moduli with the number of loading cycles was observed even for the tests that exhibited considerable secondary hardening. Fatigue life estimates calculated using the stress-strain hysteresis loops at maximum softening and at half-life were similar for the Smith–Watson–Topper, Fatemi–Socie, and Jiang models. It was observed that macroscopic surface crack orientation depends on the equivalent strain amplitude for torsional, proportional, nonproportional and torsional with static stress loading. The capability of the models to estimate the observed crack orientations is discussed. [ABSTRACT FROM AUTHOR]

• Torsional fatigue tests were carried out near the fatigue limit for annealed carbon steels with ferrite-pearlite microstructures. • Shear-mode fatigue cracks tended to propagate in the soft ferrite phase, avoiding the hard pearlite phase. • The interior geometry of fatigue cracks were observed by precise polishing of the specimens. • The torsional fatigue limit is determined by the threshold condition for continuous propagation of a macroscopic Mode I branched crack. Torsional fatigue tests at an R of −1 were carried out near the fatigue limit, using smooth, round-bar specimens of annealed carbon steels with banded ferrite/pearlite and isotropic ferrite/pearlite structures. Precise polishing of the specimens made it possible to observe the interior geometry of fatigue cracks. While the crack-plane was macroscopically of shear-mode, it was irregular microscopically, bearing many kinked and branched cracks. Based on calculation of the stress intensity factor for propagating and non-propagating cracks, it was concluded that the torsional fatigue limit was determined by the threshold condition for continuous Mode I propagation into the ferrite/pearlite structure. [ABSTRACT FROM AUTHOR]

• We performed a series of experiments to explore fatigue performance of smooth and notched specimens made of 34CrNi3Mo alloy steel under torsional loading. • Effect of notch on the fatigue performance of 34CrNi3Mo alloy steel under torsional loading is studied by comparing experimental results. • Micrograph and macrograph fractures of the 34CrNi3Mo specimens have studied to explore their failure mechanism and effect of notch on the fatigue performance. • Fatigue performance of 34CrNi3Mo specimens with v-notch at angles of angles of 45°, 90° and 135° was compared to exploit effect of notch by using validated numerical method. Joint of flange on a marine shaft subjected to torsional loading was more prone to occur fatigue fracture than the other section on the shaft due to stress concentration effect, so torsional fatigue performance in the vicinity of the joint should be payed more attention in terms of safe navigation of ships. The fatigue analysis of 34CrNi3Mo steel as a novel alloy material with a stress concentration factor of 1.45 under cyclic torsional loads was carried out based on the median S - N experimental method by simplifying the flange and shaft joint into 34CrNi3Mo specimens with u-notch subjected to torsional fatigue loading. The S - N curve and fatigue life of 34CrNi3Mo alloy steel were numerically calculated and compared with experimental fatigue life and the plotted S - N curve. It was found that fitting equation of the S - N curve was close to experimental results. Then, the fatigue performance of 34CrNi3Mo specimens with v-notch at angles of 45°, 90° and 135° was compared by means of the validated numerical method. The fracture macrographs and micrographs of the 14 specimens also were provided to explore the effect of notch on fatigue performance of the 34CrNi3Mo materials and to exploit the failure mechanism of fracture. [ABSTRACT FROM AUTHOR]

• Innovative aspects of this work are the proposed effective SIF models that can be adapted for different modes of propagation. • The proposed SIF models can be used to evaluate the effective SIF depending on the instantaneous mode of propagation. • The μ-CT technique was used to understand crack propagation in an AM Ti6Al4V alloy stressed with in-phase multiaxial loading. • A large bulk of new experimental data have been deeply discussed, which can be useful for research in the same area. Selective laser melting (SLM) is one of the most promising additive manufacturing technologies for obtaining end-use components with excellent mechanical properties. However, the presence of manufacturing defects harms mechanical properties and fatigue performance. This work investigated the crack behaviour within an SLM Ti-6Al-4V alloy sample stressed with in-phase axial and torsional loading by X-ray computed μ-tomography (μ-CT). A sub-volume of material that contains the most significant defects was detected and analysed. The critical defect was identified by evaluating the effective strain intensity factor (SIF) using two different proposed models, that consider the effective area of a detected defect according to Murakami's method. The first model is based on the modified Smith Watson and Topper (MSWT) criterion. The second is based on Liu's virtual strain energy (VSE) method. The trend of the crack growth rate was obtained by measuring the effective area for a different number of cycles. The μ-CT data was also exploited to build a finite element model (FEM) of part of the gauge section containing surface defects. Finite element analysis (FEA) results have provided information on the stress state leading to high-stress concentrations at the crack tip influencing the propagation. [ABSTRACT FROM AUTHOR]

• Specimens with a circular hole subject to biaxial fatigue loading. • Experimental crack directions in the initial part for three materials were measured. • Multiaxial fatigue models for notches were analysed. • The models provide good fatigue limit predictions. • Models predictions using the experimental crack direction are generally good. Several models from the literature were used to predict the fatigue limit in notched components subjected to biaxial cyclic loading. The predictions of these models are based on the elastic stresses along a line which is considered to be representative of the crack direction in its initial part. The line used in the models changes considerably. For one of the studied models, the line direction corresponds to Mode I, while for another it is Mode II, and for the other two models considered the direction is between Mode I and Mode II. However, quite naturally, the experimental crack direction is unique. In recent years, a study of experimental fatigue limits and crack directions in its initial part for three materials was carried out in hollow cylindrical specimens with a circular hole subjected to cyclic axial, torsional and in-phase biaxial loading. The directions of the cracks that were measured experimentally are on average similar for the three materials and close to Mode I. The analysed models give, in general, good predictions of the experimental fatigue limits, although they use directions that are completely different and that they too differ markedly from the experimentally found ones. The predictions of the models using, in a forced way, the measured experimental directions are good in most cases, which reveals a surprising insensitivity of these models to the main hypotheses on which their own formulations are based. [ABSTRACT FROM AUTHOR]

Abstract In the past, unexpected failures in wheelset axles lead to catastrophic consequences. To avoid those failures inspection intervals must be defined. The definition of the inspection intervals is based on fracture mechanical approaches. In the present work, the railway axle steel 34CrNiMo6 is investigated. For this material fatigue crack growth data have been experimentally determined for a range of different negative and positive stress ratios. Furthermore, the FORMAN/METTU parameters for different probabilities of survival are identified. In wheelset axles different geometry factors influence the crack growth behaviour. Therefore, different shouldered solid shafts with transition radii and a press fit seat are designed and tested under rotating bending. Moreover, the load situation also has an influence on the crack growth. The main bending load is overlapped with torsional loading at special wheel-rail-situations. With the developed mixed mode test rig, the influence of different load situations on wheelset axles are examined. [ABSTRACT FROM AUTHOR]

Highlights • The means for determining the critical distance of notch fatigue limit is extended to the finite life interval. • The relationship between axial and torsional notch fatigue lives is established. • The detrimental contribution of both tension and torsion to multiaxial fatigue damage can be considered. • Applications of linear elastic stress analysis and PM simplify the computation. Abstract Based on the theory of critical distances (TCD), a new multiaxial notch fatigue life prediction method is proposed in this paper. Firstly, inspired by the means for determining the critical distance of fatigue limit shown in Kitagawa and Takahashi’s diagram, a new measure is proposed to extend the means to the finite life interval. Then, by combining this new measure and the Sih et al. mixed mode fracture criterion, the relationship between axial and torsional notch fatigue lives can be established. Thus, torsional fatigue life can be calculated based on the axial data. Furthermore, on the basis of these obtained data and the modified wöhler curve method (MWCM), the multiaxial notch fatigue life can be estimated. As with the original TCD method, the present method preserves the advantage of effective computation through the so-called point method (PM) and linear elastic stress analysis. However, the new method can more fully takes into account the multiaxiality effect by considering both axial and torsional fatigue damage contribution, which is consistent with the thought of MWCM for plain fatigue assessment. [ABSTRACT FROM AUTHOR]

A multiaxial fatigue criterion is proposed, which can be seen as a modification of a previous criterion presented by the authors. The influence of the unique material state can be taken into consideration, as well as the range and mean value of the variables involved in the fatigue parameter for depicting the influence of the loading condition. Definitions of the out-of-phase failure and out-of-phase failure angle are proposed, as well as an out-of-phase failure parameter that can be used to express the interdependent relationship with the out-of-phase failure, in both normal-type and shear-type failure. An explicit physical interpretation of different failure types is proposed. After validation and comparison with experimental results for different loading conditions and materials, it is concluded that the prediction ability of this modified multiaxial fatigue criterion is better than that of the original Lu’s criterion, as well as than those of the other commonly used multiaxial fatigue criteria. [ABSTRACT FROM AUTHOR]

• Experimental torsion and bending fatigue strengths of 90°, 45°, and 0° LPBF building direction were determined. • Kitagawa diagrams were provided in bending and torsion loading at different building directions. • Bending fatigue behavior is very sensitive to building direction compared to torsion. • Torsion fatigue behavior of LPBF 316L is not sensitive to lack-of-fusion defects. The present study aims to investigate the high cycle fatigue (HCF) performance of steel 316L fabricated by the laser powder bed fusion (LPBF) process. Bending and torsional fatigue test specimens built horizontally (0°), inclined (45°), and vertically (90°) have been prepared and tested. Stress-relieving heat treatment was carried out to reduce the residual stresses. The 90°, 45°, and 0° built near-net-shape and polished specimens have fatigue strengths between 140 and 250 MPa under bending loading and 150 and 170 MPa under torsion loading. This difference illustrates a more pronounced defect sensitivity in bending compared to torsion. Fractographical analyses revealed the fatigue failure mechanisms. As the building direction inclines from vertical to horizontal, the effective areas of inherent defects diminish contributing to improving fatigue strength under bending loading whilst the differences from building directions in torsional fatigue strengths are minor. Microstructural features are seen to compete with inherent defects to affect fatigue performance in the condition that the effective defect sizes are close to the critical fatigue crack size. [ABSTRACT FROM AUTHOR]

• The variable torque of wire rope bending over sheave was obtained by conducting fatigue tests. • The broken wires were counted, and the life of wire rope was predicted accordingly. • The relation between torsional Angle and wire rope elongation was obtained. • The effect of torsion Angle on shape and depth of wear scar was discussed. Regularly replacing steel wire rope (SWR) is a mandatory measure to ensure the safe operation of the hoisting system. However, in the manual rope replacement process, the torsion accumulated in the used rope will be transmitted to the new one, thereby aggravating the damage of the new rope and shortening its fatigue life. For the sake of exploring the effect of additional torsional load on the fatigue characteristics and damage behavior of SWR, a custom fatigue test apparatus was utilized to perform relevant tests. First, the impact of torsional angle on the torque and elongation of SWR was explored; subsequently, the number and distribution of broken wires were counted, based on which the fatigue life of SWR was predicted; finally, the scanning electron microscope and confocal three-dimensional contour measuring instrument were employed to observe the wear and fracture surface morphology of the steel wire. It is found that both twisting and untwisting boost the elongation of SWR, reduce the endurance of SWR almost linearly. Of the two, twisting has a greater impact on the endurance of SWR. The surfaces of wear scars take on a regular elliptical shape in the case of twisting, and the deflection angle, together with the maximum wear depth grows with the increase of the torsional angle. In contrast, the wear scars are irregular in the case of untwisting, and the deflection angle and the maximum wear depth fall as the torsional angle increases. [ABSTRACT FROM AUTHOR]

Due to the abundance of engineering components subjected to complex multiaxial loading histories, being able to accurately estimate fatigue damage under multiaxial stress states is a fundamental step in many fatigue life analyses. In this respect, the Fatemi-Socie (FS) critical plane damage parameter has been shown to provide satisfactory fatigue life correlations for a variety of materials and loading conditions. In this parameter, shear strain amplitude has a primary influence on fatigue damage and the maximum normal stress on the maximum shear plane has a secondary, but important, influence. Additionally, in order to preserve the unitless feature of strain, the maximum normal stress is normalized by the material yield strength. However, in examining some data from literature it was found that, in certain situations, the FS parameter can result in better fatigue life predictions if the maximum normal stress is normalized by the shear stress range on the maximum shear plane instead. These data include uniaxial loadings with large tensile mean stress, and some combined axial-torsion load paths with different normal-shear stress interactions. This modification to the FS parameter was investigated by using fatigue data from literature for 7075-T651 aluminum alloy and a ductile cast iron, as well as additional data from 2024-T3 aluminum alloy fatigue tests performed in this study. [ABSTRACT FROM AUTHOR]

This paper is focused on the VHCF behavior of aeronautical titanium alloy under tensile and torsion fatigue loadings. Tensile tests were carried out with two different stress ratios: R = −1 and R = 0.1. Both surface and subsurface crack initiations were observed. In the case of subsurface crack initiation several fatigue life controlling mechanisms of crack initiation were found under fully-reversed loading conditions: initiation from (1) strong defects; (2) ‘macro-zone’ borders; (3) quasi-smooth facets and (4) smooth facets. Tests with stress ratio R = 0.1, have shown that initiation from the borders of ‘macro-zones’ becomes the dominant crack initiation mechanism in presence of positive mean stress. Like for the tensile results, surface and subsurface crack initiations were observed under ultrasonic torsion in spite of the maximum shear stress location on the specimen surface. But the real reason for the subsurface crack initiation under torsion was not found. [ABSTRACT FROM AUTHOR]

The very high cycle fatigue (VHCF) properties of shot-peened VDSiCr spring steel have been investigated with the ultrasonic fatigue testing method. Fatigue behaviour under cyclic torsion and cyclic tension loading at load ratios between R = −1 and R = 0.5 is compared. For 90% of the VHCF failures under axial loading, fractured grain boundaries or inclusions in the interior of the material act as crack starters. In contrast, the initial crack is produced by cyclic shear in the interior or, less frequently, at the surface for more than 90% of the VHCF failures under torsional loading. The crack path deflects from mode II/mode III to mode I at the border of the initiating shear area. The change of crack path correlates to a stress intensity factor range for a crack loaded in shear mode of Δ K τ,ISA = 5.6 ± 0.5 MPam 1/2 for load ratio R = 0.1 and Δ K τ,ISA = 3.8 ± 0.4 MPam 1/2 for R = 0.35, respectively. Residual stresses due to shot-peening are stable during VHCF axial loading while they are reduced during VHCF torsional loading. [ABSTRACT FROM AUTHOR]

This paper evaluates the methodology for, and effectiveness of, common equivalent stress- and strain-based fatigue life analysis approaches when applied to variable amplitude multiaxial service loading conditions. Experimental results for both un-notched and notched specimens of 2024-T3 aluminum alloy, tested under axial, torsion, and combined axial–torsion loadings, are compared to predictions based on von Mises equivalent stress and strain. Mean stresses were considered using Smith–Watson–Topper, modified Goodman, and modified Morrow models. Variable amplitude life predictions are compared to constant amplitude predictions to highlight similarities and differences in life prediction trends. Overall, mixed results were obtained. Both constant and variable amplitude fatigue lives are predicted well for notched specimens, where a local uniaxial stress state always exists for the geometry considered. However, for un-notched specimens, where multiaxial loading effects come into play, no approach considered is able to predict more than 60% of fatigue data within a factor of ±3 of experimental life. A consistent trend of non-conservative life predictions for variable amplitude loading conditions is observed. The importance of considering stress gradient effects in notched specimen life prediction is also demonstrated. An extensive discussion on areas where improvements can be made with respect to fatigue damage quantification completes the paper. [ABSTRACT FROM AUTHOR]

This work investigates the fatigue and cyclic plasticity of Inconel 718 produced by Selective Laser Melting (SLM) at room and elevated temperature. Strain-controlled axial, torsional and proportional tests with R ɛ = 0 were carried out at 20 °C and 450 °C using thin-walled specimens, resulting in fatigue lives ranging from 10 3 to 10 5 cycles. SLM Inconel 718 exhibits a columnar microstructure along the build direction, and the dominant defect related to the manufacturing process was gas pores. Fatigue crack initiation occurred a carbides and/or metallic inclusions for all tests and, therefore, intrinsic defects related to the manufacturing process did not induce premature initiation of fatigue cracks. The orientation of macroscopic fatigue cracks was consistent with the plane of maximum shear stress for all loading conditions. The fatigue crack propagation mechanism of SLM Inconel 718, on the other hand, depends on the loading path and temperature. Both the equivalent strain amplitude and the Fatemi–Socie criterion could correlate fatigue life of all loading conditions at 20 °C and 450 °C within factor-of-two boundaries. As a general trend, the fatigue endurance of SLM Inconel 718 is inferior to its forged counterpart, especially at 450 °C. The cyclic plasticity behaviour of SLM and forged Inconel 718 is similar at both 20 °C and 450 °C and can be simulated by the Chaboche model. • New multiaxial test data for SLM Inconel 718 at room and elevated temperature. • Comparison with forged specimens under identical loading conditions. • Discussion on the relation between microstructure and fatigue behaviour. • Investigation of the macroscopic cracking behaviour. • Evaluation of life predictions obtained from three fatigue criteria. [ABSTRACT FROM AUTHOR]

• A multiaxial fatigue life prediction method based on single defect is proposed for L-PBF 316L. • Investigated L-PBF 316L shows Mode I crack growth macroscopically under axial and torsional loading. • It is detected that more than 95% of the specimens have defects in the crack initiation zone. A multiaxial fatigue life prediction method based on single defect for 316L stainless steel processed by laser powder bed fusion is studied. Defects are detected in the crack initiation zone of more than 95% of the specimens. A method based on the small crack propagation theory is applied to predict fatigue life under uniaxial and pure torsional loading. The fatigue parameters obtained from the above method are substituted into the Modified Wöhler Curve Method to predict multiaxial fatigue life. The result shows that the predicted fatigue lives are in good agreement with the experimental results. [ABSTRACT FROM AUTHOR]

The local strain approach has been successfully applied in evaluating the fatigue life of notched components under multiaxial loading. In the present work, this approach is combined with the critical plane method. First, it is shown that by considering non-proportional strain hardening in the estimation of local stresses and strains, the accuracy of the results under non-proportional loading can be improved regardless of the applied multiaxiality hypothesis. Three different critical plane hypotheses, SWT (Smith Watson Topper, based on normal strain), FS (Fatemi Socie, based on shear strain) and a short-crack model are used to calculate the fatigue life of notched specimens and compare it to results from an extensive database of test results. The accuracy of the SWT approach is highly dependent on the loading situation. For tests under non-proportional and pure torsional loading, excessively long fatigue lives are predicted. A simple proposal is made for the FS approach to be applied in critical planes with multiple shear strain components. The FS and short-crack approaches predict fatigue lives with high accuracy regardless of the applied load. • Comparison of several types of critical plane models using large database • Strengths and weaknesses of the individual damage parameters were worked out • Marquis and Socies non-proportional hardening method is evaluated on many experiments • The Fatemi-Socie model is used in planes with several shear components in a easy way [ABSTRACT FROM AUTHOR]

Additive manufacturing (AM) is a special technology that offers several advantages compared to the conventional methodologies. For instance, it allows to build components with complex geometry, difficult to make in a different way, build integrated parts deleting joining issues, etc. However, its application in engineering fields is still limited because the dependency between the mechanical properties of the obtained components and the manufacturing parameters is not in depth understood. Improve the performances of AM components, under static and dynamic loadings, is crucial to ensure their durability and reliability and in recent years it became a challenging research field. In this work, the effect of the surface roughness on the multiaxial fatigue resistance of Ti6Al4V thin-walled tubular samples, made by the Selective Laser Melting (SLM) process, was investigated. In particular, experiments under combined axial–torsional loadings were carried out on two batches of samples, made by different surface roughness (machined and as built samples). Maximum valley depth R v was used as a representative parameter of the surface roughness as it geometrically represents a stress concentration zone where crack initiates and propagates. An effective strain intensity factor range, based on the modified Smith Watson and Topper (MSWT) model, that includes the roughness parameter R v , is proposed and used for a better correlation of the fatigue data. To prove the reliability of the proposed model, the Socie and the Reddy & Fatemi effective strain-based intensity factor range were also used but a bigger scattering of results was observed. The MSWT model was also applied to predict the failure plane and the obtained results were compared with the predictions of the Fatemi-Socie model. Results revealed that, for SLM Ti6Al4V alloy components, the MSWT model is more accurate. [ABSTRACT FROM AUTHOR]

[Display omitted] • Investigations of the fatigue surface on steel 42CrMo4 + QT and 7075-T6 aluminum alloy. • Evidence of shear initiation under torsional fatigue of plain and notched specimens. • Mode I and mode III critical distances used as reference scale for crack initiation. • Elastic-plastic FS and SWT combined with the Chaboche kinematic hardening model. • Improved prediction accuracy with elastic–plastic modelling and critical distances. Torsional and axial fatigue tests were performed on steel 42CrMo4+QT and aluminium alloy 7075-T6, and a 3D optical profilometer was used for the investigations of the fracture surfaces. The mode I and mode III critical distances of the two materials were regarded as reference scales for evaluating the initial orientation of the cracks and then identifying the tests valid for the calibration of the normal and those for the shear-fatigue models. The torsional strength of blunt notched specimens was then predicted with the Smith-Watson-Topper and the Fatemi-Socie criteria, combined with the critical distances and the Chaboche model for the steel. [ABSTRACT FROM AUTHOR]

• A multiaxial total life prediction method based on short crack growth is proposed. • The additional damage from non-proportional loading path is characterized. • Effect of shear stress on crack growth under tensile/compressive stress is considered. • The proposed method is verified by two materials under multiaxial loading. A total life prediction method based on short crack propagation considering additional damage from non-proportional loading is proposed under multiaxial fatigue loading. Firstly, a new calculation method of equivalent stress range is proposed to consider the effect of shear stress on crack propagation under tensile or compressive stress, then it is further modified to consider the additional damage. Combined with Paris formula and crack closure correction, a total life prediction method is proposed. The life results were used to verify the proposed method for two materials, which showed that most errors are within a factor of 3. [ABSTRACT FROM AUTHOR]

The effect of mean stress on the multiaxial High Cycle Fatigue (HCF) behaviour of cast A356-T6 alloy containing natural and artificial defects with varying Secondary Dendrite Arming Spacing (SDAS) has been investigated experimentally. Tension, torsion and combined tension–torsion fatigue tests have been performed for two loading ratios: R σ = 0 and R σ = −1. A Scanning Electron Microscopy (SEM) was used to perform fractographic analysis of the fracture surfaces to characterise the defect causing failure. In order to gauge the effect of mean stress and defects, the results are reported with standard Kitagawa and Haigh diagrams. A surface response method has been employed to characterise the influence of defect size and SDAS on the fatigue limit. Relationships and correlations describing the observed behaviour have been incorporated in the Defect Stress Gradient (DSG) criterion with the goal of determining the influence of defects on the fatigue limit through a stress gradient approach. Results clearly show that: (i) the mean stress has a detrimental effect on the fatigue limit. This effect is a function of the loading, which is most pronounced under tension, less under combined tension–torsion, and least pronounced under torsion conditions; (ii) in the absence of defects, the SDAS controls the fatigue limit of cast A356, this effect is much more important under torsion loading; (iii) the DSG criterion is improved by the mean of a parameter describing the microstructure effect through the SDAS. [ABSTRACT FROM AUTHOR]

Smooth AISI 304L stainless steel specimens were tested in fatigue. The tests were axial, torsional and in-phase axial–torsional, all of them under load control with R = −1. S – N curves were constructed following the ASTM E739 standard and the fatigue limits were obtained following the method of maximum likelihood proposed by Betinelli. The ratio between the pure torsion and tension fatigue limits, τ FL / σ FL , was 0.91, close to 1, which is a typical value for fragile materials. The fatigue limits determined by the biaxial tests were represented on σ - τ axes. These experimental values were well fitted with an elliptical quadrant, although this fitting is considered appropriate for ductile materials. The crack direction along the surface was analysed using a microscope, with special attention dedicated to the crack initiation zones. The crack direction along the first grains, or Stage I, was much closer to the Mode I direction than to the Mode II direction. [ABSTRACT FROM AUTHOR]

• Mode III SED control radius determination with an optimized V-notched specimen. • Statistical analysis of the mode III SED control radius, skew-normal distribution. • Larger mode III fatigue SED control radius than mode I for 42CrMo4 + QT and 7075-T6. • Parametric analysis of the variation in terms of notch radius and specimen diameter. The Strain Energy Density (SED) is a fatigue criterion based on a control volume. This parameter is required for a precise assessment of the fatigue strength of any, especially severely, notched component. A newly developed inverse determination procedure is presented here to precisely determine the mode III (or torsional) control radius. The procedure is then extended to the evaluation of the probability scatter of this length which is properly represented by a skew normal distribution. Experimental results of aluminum alloy 7075-T6 and steel 42CrMo4 + QT are presented, and comparisons are provided between mode I and mode III control radii. [ABSTRACT FROM AUTHOR]

• Increases in strain amplitude and strain ratio accelerate cyclic stress softening. • Dynamic strain ageing appears in the torsional direction at a high strain ratio. • The increase in strain ratio promotes the occurrence of planar slip of dislocation. High temperature multiaxial fatigue tests at different strain amplitudes and strain ratios were performed at 600 °C. Dynamic strain ageing (DSA) analysis and microstructure characterization were used to analyze the cyclic deformation and damage mechanisms. Results reveal that the increases in strain amplitude and strain ratio accelerate the cyclic softening. Moreover, the DSA behaviour shows a distinct dependence on the strain amplitude, strain ratio and loading direction. Furthermore, the increase in strain amplitude promotes subgrains growth and dislocation structure transformation. Particularly, the increase in strain ratio promotes the occurrence of planar slip of dislocation. [ABSTRACT FROM AUTHOR]

The present paper focuses on stress-based criterion of Liu & Mahadevan. A computation of this criterion from an implementation of a numerical procedure based on stress solutions leading to unit criterion is proposed. This approach is supported by an analytic analysis for brittle steel materials for validating the numerical study. A singular behavior of the criterion is observed for in-quadrature phase of stresses, when fully reversed bending–torsion experiments are considered. A comparison of results with some experimental data provided by literature is performed. [ABSTRACT FROM AUTHOR]

In this study the rolling contact fatigue (RCF) of case carburized AISI 8620 steel was numerically and experimentally investigated. For the numerical study, a two dimensional finite element (FE) RCF model based on the continuum damage mechanics (CDM) was developed to investigate the fatigue damage accumulation, crack propagation and final fatigue life of carburized AISI 8620 steel under various operating conditions. A randomly generated Voronoi tessellation was used to model the effects of material microstructure topology. The boundaries of the Voronoi elements were assumed to be the weak planes where damage accumulates, cracks initiate and propagate to simulate inter-granular cracks. A series of torsional fatigue tests were conducted on carburized AISI 8620 steel specimens containing 0% and 35% retained austenite (RA) to determine fatigue load (S) vs. life (N) of the material. The S–N results were then used to determine the material parameters necessary for the rolling contact fatigue model. The torsional fatigue test results indicate that the carburized AISI 8620 specimens with higher RA demonstrate higher life than the specimens with lower RA. The RCF model also indicates that the material with higher level of compressive residual stresses (RS) and retained austenite demonstrates higher RCF life. In order to corroborate the results of RCF model, a three-ball-on-rod rolling contact fatigue test rig was used to determine the RCF lives of carburized AISI 8620 steels with different amounts of RA. The fatigue life and cracks evolution pattern from the numerical and experimental results were corroborated. The results indicate that they are in good agreement. [ABSTRACT FROM AUTHOR]

A series of multiaxial ratcheting–fatigue interaction tests have been carried out on Sn–3Ag–0.5Cu lead-free solder specimens. All tests were conducted under cyclic shear strain with the constant axial stress at the room temperature with the shear strain rate of 5 × 10-3 s-1. It was found that the ratcheting strain increased with increasing axial stress and shear strain amplitude while the fatigue life decreased at the same time. The ratcheting strain rate was linear with axial stress in double logarithmic coordinate. The Ohno–Wang II constitutive model was employed to simulate the stress–strain responses. Several fatigue life prediction models were applied to predict the multiaxial ratcheting–fatigue life of the Sn–3Ag–0.5Cu lead-free solder. The Gao–Chen model which adopted the maximum shear strain and the ratcheting strain rate as the damage parameter predicted the multiaxial ratcheting fatigue life well. [ABSTRACT FROM AUTHOR]

• New fatigue test data of 304 stainless steel containing a small cylindrical defect. • Proportional and nonproportional axial/torsional loading conditions. • Early cracking behavior primarily governed by the normal stress. • Evaluation of a tensile-based critical plane criterion for small defects. • Estimated fatigue limits and crack directions correlated well with test data. The influence of a small defect on the multiaxial fatigue strength of 304L stainless steel was experimentally investigated. The fatigue tests were carried out on specimens containing a cylindrical defect with a r e a = 400 µm. Five fully reversed loading paths were employed: tension-compression, torsion, in-phase, 90° out-of-phase, and square shape. Crack orientation in the vicinity of the defect was examined at and just above 2 × 106 cycles (run-out condition). The fatigue limits and crack angles measured were used to evaluate a tensile-based critical plane criterion for small defects. Predicted and measured results were in good agreement, indicating a tensile-dominated failure mechanism in the range of experimental conditions studied. [ABSTRACT FROM AUTHOR]

The high-cycle fatigue life with respect to the multiaxial variable-stress amplitude was evaluated by applying the newly proposed total path length method for calculating the stress amplitude. Variable-stress-amplitude fatigue tests were conducted for verification based on the combined axial and torsional loads on AISI 4340 steel. The fatigue test load waveform denoted that the stress amplitude, mean stress, and load direction varied within one loop. The obtained lives were shorter than those predicted using the Wang–Brown method, longer than those predicted using the PDMR method, and comparable to those predicted using the total path length method. [ABSTRACT FROM AUTHOR]

• Effect of internal friction on torsional fatigue is investigated. • Dissipation energy associate with cyclic torsional loading is greater than Tension-compression. • Fracture fatigue entropy (FFE) of SS304 and SS316 is experimentally evaluated. • FFE is applicable to both tension–compression or torsional fatigue loading. Failure of materials subjected to torsional and axial cyclic loading is studied by applying the principles of thermodynamics of dissipative processes. Extensive experimental tests are conducted using stainless steel (SS) 304 and SS316 materials to gain insight into both torsional and tension–compression fatigue life. It is shown that the higher magnitude of dissipated energy in torsional loading, as reported in many studies, is due to the anelastic deformation in the material and its associated internal friction. It is further shown that proper assessment of the damaging dissipation energy requires one to exclude the non-damaging internal friction from the total amount of energy dissipation. Accumulation of thermodynamic entropy generation as an index parameter using the modified dissipated energy is estimated to predict the fatigue life. The experimental results are found to be in good agreement with the proposed fatigue life prediction. [ABSTRACT FROM AUTHOR]

• A multiaxial fatigue criterion is proposed for arbitrary complicated loadings. • The effect of hydrostatic energy is included in the proposed criterion. • A loading transformation is proposed based on distortional and dilatational energy. • The proposed model is validated under tension-tension and tension-torsion loadings. • The influence of hydrostatic component in damage is discussed. A new energy-based fatigue life prediction model is proposed for arbitrary multiaxial constant loadings in this paper. First, a brief review for existing multiaxial fatigue models is given, especially focusing on energy-based models. It is observed that most multiaxial model formulation and validation are suitable for axial-torsional loadings, but may not be appropriate for biaxial tension-tension loading. One possible reason is the ignorance of hydrostatic stress-state difference under these two types of loadings. In view of this, a new model is proposed by including fatigue damage contributions of equivalent tensile energy, torsional energy, and hydrostatic energy. Next, a loading transformation is proposed to transfer a complicated three-dimensional loading to an effective loading for life prediction. Detailed discussion of different types of multiaxial loading and its relationship with the ratio of distortional energy and dilatational energy is given. The hysteresis energy can be calculated integrating the proposed model with the Garud cyclic plastic model, which is directly linked to the damage accumulation and fatigue life prediction. The proposed model is validated with extensive experimental data under both tension-torsion loadings and biaxial tension-tension loadings from open literature. Comparison with several widely used multiaxial model is also given to show the model performance with respect to different biaxial tension-tension loadings. Finally, concluding remarks and future work based on the investigated materials are discussed. [ABSTRACT FROM AUTHOR]

• Ultrasonic torsional fatigue tester with the capacity to modify the mean stress is developed. • VVery high cycle tensile and torsional fatigue behavior of turbine blade titanium alloy is comparatively studied. • The short crack nucleation and propagation character of interior initiated fatal crack induced by tensile and torsional loadings are analyzed using FIB milling method. Very high cycle tensile and torsional fatigue of TC17 titanium alloy with bimodal microstructure have been firstly and comparatively studied at the stress ratio of 0.1. Like the tensile cracks, torsional cracks were substantiated to nucleate from specimen surface or interior sites and presented in a fatigue life-dependent mode. Internal tensile and torsional fatigue cracks with faceted morphology were analyzed using focus ion beam and unraveled to initiate in modes II + III that driven by maximum shear stress. Particularly, short crack branching and deflection beneath the crack initiation rough area can be observed for torsional loading condition. [ABSTRACT FROM AUTHOR]

• Residual stress from RA transformation. • Utility of RA in fatigue. • Effect of loading. In this work, for development and sustainability of compressive residual stresses (RS) in bearing steel materials is examined. Of particular interest is the role of retained austenite (RA) transformation in fatigue performance. Cyclic torsional loading was performed for a prescribed number of cycles at specific stress levels. Specimens were then examined using X-ray diffraction techniques to observe RS values and RA volume fraction. Based on the experimental results, an empirical model incorporating RA transformation and material relaxation was developed to predict RS formation. The results obtained from the model corroborate well with experimental measurements. Experimental results indicate that much of the RA present is not useful for generating compressive RS. However, by controlling applied loading, compressive RS can be generated and maintained throughout fatigue life. These findings were then translated into rolling contact fatigue (RCF) scenarios to identify loading conditions to maximize the benefits associated with RA transformation. The experimental and modeling results highlight the utility of RA transformation in increasing compressive residual stresses within the material, but emphasize the limitations of RA in the system. [ABSTRACT FROM AUTHOR]

• Experimental results of tension/torsional cyclic tests of two steels. • Unusual fatigue properties of steel C55 (σ c-1 /τ c-1 ratio close to or less than 1). • The definition of the critical plane as the maximum shear stress plane may not be sufficient. • Taking into account failure mode in existing multiaxial criterion may extend their applicability. Dependencies σ a = f(N f) and τ a = f(N f) were experimentally obtained for two steels with different material properties. Specimens of these materials were exposed to multiple tensile and torsional proportional stress combinations. In the present paper, the experimentally obtained fatigue lifetime values are compared with fatigue lifetime estimations calculated by means of selected criteria, namely those of Findley, McDiarmid, Dang Van, Carpinteri-Spagnoli, and Margetin-Ďurka-Chmelko. The results for steel with a high ratio of Rm/Re are different from the results of the second material. The analysis of the results shows the need to take into account the failure mode in the multiaxial fatigue criteria. [ABSTRACT FROM AUTHOR]

This work aimed to study the fatigue behaviour of S355 low carbon steel under uniaxial and biaxial loading conditions and to measure the overload effects under both types of loads. The analysis is performed with a local strain approach and with damage tolerance approach. Local strain based investigation was based on Fatemi-Socie critical plane model. This allows the life reduction caused by growing the crack from a stress raiser to be quantified. The fatigue life reduction caused by applying simultaneously torsional and tension loads was also evaluated with Fatemi-Socie model. In addition, the crack opening displacement (COD) and the effective stress intensity factor (SIF) were evaluated experimentally via full-field technique of digital image correlation (DIC). Both COD and SIF have been useful to understand the transient effects caused by a 40% overload under the two types of load. In addition, COD measurements allowed the offset compliance method for evaluating the opening load to be applied on a cylindrical specimen subjected to tension load. SIF estimation was also useful to quantify the mode mixity (I + II) developed during the experiment under the two types of load. [ABSTRACT FROM AUTHOR]

• Pneumatic device was designed to provide normal load in torsional fretting fatigue test. • The role of torsional stress amplitude on the fatigue behavior was studied. • The effect of fatigue cycle and torsional stress amplitude to evolution of microstructure in contact zone was discussed. • A physical model of micro-crack nucleation was summarized. In this paper, torsional fretting fatigue in LZ50 steel was investigated experimentally using a multiaxial fatigue testing machine. After subjecting the samples to fatigue, they were examined using scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The details of the fretting damage and the evolution of the samples' microstructures in the contact zone were studied under different torsional loads. The results showed how the combined action of fretting and fatigue led to the failure of the specimen. Fretting wear in the contact zone produced a fretting scar and cracks in the specimens initiated in the fretting contact zone. These were caused by the local stress concentrations, and the cracks then propagated due to cyclical torsional fatigue stresses. The modes of microstructural evolution occurring during torsional fretting fatigue were dislocation angling and climbing, and these formed dislocation cells in the structure of the material. Within the LZ50 steel, this pattern of behavior began in the ferrite areas of the structure. For the harder phases, the evolution started later, and in the pearlite structures. The microstructural evolution in the pearlite was accompanied by bending, torsion, and even cracking of the cementite lamellae. The evolution of the microstructures showed that the micro-cracking nucleation mechanism was the deformation of dislocation cells. [ABSTRACT FROM AUTHOR]