Fatigue behaviour and life predictions of case-hardened steels

This paper presents experimental and analytical results on fatigue behaviour of case-hardened steel. Fully reversed strain-controlled constant amplitude axial fatigue tests were performed on through-hardened case, through-hardened core and case-hardened steel specimens. Surface versus sub-surface cracking and the role of residual stresses and their relaxation are discussed. Multi-layer models of the case-hardened specimens were used to predict crack nucleation sites as well as fatigue lives, and the predictions corresponded well with the experimental results. Linear elastic fracture mechanics (LEFM) was also used to conduct fatigue crack growth analysis to further explain the experimental observations from the fracture surfaces of the case-hardened specimens. A fatigue strength estimation method based on hardness and inclusion size was used to estimate the fatigue limit of the materials investigated. Fractography of fracture surfaces and crack nucleation location are also presented.     

Application of the weakest-link concept to the endurance limit of notched and multiaxially loaded specimens of carburized steel 16MnCrS5

Based on the weakest‐link concept a method is developed, from which the endurance probability of every surface and volume element of a case‐hardened part, which is loaded near the endurance limit, can be calculated. A prerequisite for the calculation is knowledge of the hardness and residual stress distribution, the surface roughness and the surface oxidation depth. By multiplication of the endurance probabilities of neighboured elements the endurance probability of a limited region or of the whole part can be calculated, which includes an endurance limit determination. It is shown, that this model can be applied successfully to specimens of a carburized steel. The necessary model parameters can be gained from a set of reference specimens. Because of the possibility to formulate an endurance probability for every volume and surface element, there are no geometrical restrictions on the parts to be assessed.     

Durability analysis of carburized components using a local approach based on elastic stresses

The carburizing of non‐homogeneously stressed components is often used to improve the fatigue properties. In order to predict fatigue life curves the local behavior has to be analyzed. Therefore, cyclic material properties of the carburized surface layer and the core were investigated. In general it is challenging to obtain the input data necessary for a durability analysis of carburized components with the local strain approach. Therefore, a simple method is proposed to estimate the life curve of carburized components under proportional constant‐ and variable‐amplitude loading. With a S‐N curve for a similar component as input local elastic stresses can be back‐calculated. Experimental results show a strong influence of the highly stressed volume on the fatigue properties of the carburized surface layer. This effect can be taken into account with a size correction factor calculated on the basis of a weakest link model. Based on an appropriate local elastic stress‐life curve and regarding the size effect, durability analysis can be improved in an early stage of design. Fatigue tests on notched specimens and components of vehicle transmission cases were used to compare experimental and numerical results.     

Predicting the effects of material properties gradient and residual stresses on the bending fatigue strength of induction hardened aeronautical gears

This paper proposes an experimental methodology to characterize complex parts presenting various gradients using aeronautical induction surface hardened spur gears. A 3D fatigue model taking into account residual stresses, microstructure variations, and surface roughness is then proposed for the prediction of the bending endurance limit. The model is based on the well-known Crossland criterion; calibrated with representative axial and torsion laboratory specimens. The results are compared with testing performed on a custom-made single tooth bending fatigue (STBF) rig. Fracture surface analysis using electronic microscopy is used to investigate the crack initiation sites. It is shown that residual stresses can have a significant impact on bending fatigue and that two induction treatments can present very different fatigue resistance even if the shape and depth of the hardened layer is identical in the root. The proposed methodology could be adapted to other geometries and surface treatments.     

Probabilistic approach in high-cycle multiaxial fatigue: volume and surface effects

The stress gradient and the size of a component are known to influence the fatigue strength of metallic components. Indeed, in high‐cycle fatigue, experiments prove that the stress distribution as well as the size of the loaded specimen can be responsible for changes in the fatigue limit (for instance, the fatigue limits in tension and bending are different, and decrease with the size of the specimen). When dealing with multiaxial load conditions, those effects still act but a relevant criterion must be used to account for the complex state of stress. The weakest‐link concept together with a multiaxial endurance criterion based on a microplasticity analysis are then combined to describe the fatigue limit distribution of different metallic materials. Several load conditions are analysed: tension–compression, torsion, rotating bending and plane bending. By means of the proposed model, all the known effects on fatigue strength can be reflected. First, the endurance probability can be adequately predicted for any complex load conditions knowing some reference data from uniaxial fatigue tests. It can be linked to the probability of finding a defect with a critical size. The weakest‐link theory also accounts for the decrease of multiaxial fatigue limit with the stressed volume. For the same load condition (i.e. for the same stress distribution in the volume), the probability of finding a critical defect increases with the component size and then according to the weakest‐link theory the fatigue strength drops. A second model, based only on the damage developed at the surface, is also proposed. While the original Weibull theory makes no distinction between potential initiation sites at the free surface and in the volume and can lead to unsatisfactory predictions when applied to materials containing defects such as nodular cast iron, the new surface approach distinguishes between surface and volume effects.     

Anwendung des Fehlstellenmodells auf die Dauerfestigkeit des Stahls 100Cr6 im bainitischen Zustand

Application of the Weakest-Link Model to the Fatigue Limit of the Steel SAE 52100 in a Bainitic Condition The influence of notches and loading condition on the fatigue limit of the high strength steel SAE 52100 is investigated on specimens with ground surfaces. The behaviour can be described quantitatively by a three-parametric high-cycle fatigue criterion and the weakest link model. This includes the possibility of calculating local and total survival probabilities depending on the nominal stress amplitude. Crack initiation sites and the fatigue limit can be predicted, too. The basic relation between the size distribution of crack initiating inclusions and the fracture probability was proved on push-pull specimens.     

Modelling the effects of surface finish on fatigue limit in austenitic stainless steels

Existing short fatigue crack models have been reviewed to determine the most suitable fatigue model to analyse the effect of the surface finish on the fatigue limit of Type 304 austenitic stainless steels. A mechanistic model firstly proposed by Navarro and Rios (N‐R model) was selected as the most suitable generic model, because the model can include the effects of surface finishing parameters such as surface roughness and residual stress depth profile on the fatigue limit. The N‐R model has been implemented for fatigue specimens with various surface finishing conditions, and the effect of the surface finish on the fatigue limit was simulated. The material/surface properties required for the implementation were fully characterized by experiments. The applicability of the model to this study was also discussed. It is concluded that a development of the model would be required for proper prediction of the surface effects on fatigue in austenitic stainless steels.     

Prediction of fatigue limit of induction surface hardened 1.05Cr–0.23Mo steel alloy using extreme value statistics

Fatigue characteristics of the surface hardened steel are different from that of normal steel, so the prediction of the fatigue limit of surface hardened steel is very complicated. In this paper, specimens are tested using rotary bending, and the surface of 1.05Cr–0.23Mo steel alloy is hardened by induction surface hardening. Variation of the distribution of microvickers hardness and residual stress is discussed, and the difference of S-N diagram between surface hardened steel and unhardened steel is examined. The maximum defect size of surface hardened specimen is calculated by the extreme value statistics to predict conservative fatigue limit. Actual shape of defect in the specimen is three dimensional, so a conversion method from 2D to 3D defect size based on examination volume and inclusion size is used to predict statistical maximum defect size. The predicted results can be defined as a lower fatigue limit which may be useful to predict conservative fatigue limit of surface hardened specimen.     

Experimental characterization of the bending fatigue strength of threaded fasteners

The fatigue strength in bending of pre-stressed steel bolts is investigated and compared to the fatigue strength in axial tension. The strength is measured in terms of maximum engineering stress amplitude, neglecting any stress concentration in the threads. The experimental results reveal that the fatigue limit is 76% higher in bending than in axial tension. A finite element model is used to compute the stress state in the threaded region for both axial tension and bending. It allows fitting a volume based weakest link model to the experimentally observed failure probabilities. Based on the good fit of the weakest link model it is argued that randomly distributed defects in the highly stressed thread root determine the fatigue strength.     

Fatigue strength of steel fibre reinforced concrete in flexure

The paper presents a study on the fatigue strength of steel fibre reinforced concrete (SFRC). An experimental programme was conducted to obtain the fatigue-lives of SFRC at various stress levels and stress ratios. Sixty seven SFRC beam specimens of size 500×100×100 mm were tested under four-point flexural fatigue loading. Fifty four static flexural tests were also conducted to determine the static flexural strength of SFRC prior to fatigue testing. The specimens incorporated 1.5% volume fraction of corrugated steel fibres of size 0.6×2.0×30 mm. Concept of equivalent fatigue-life, reported for plain concrete in literature, is applied to SFRC to incorporate the effects of stress level S, stress ratio R and survival probability L_R into the fatigue equation. The results indicate that the statistical distribution of equivalent fatigue-life of SFRC is in agreement with the two-parameter Weibull distribution. The coefficients of the fatigue equation have been determined corresponding to different survival probabilities so as to predict the flexural fatigue strength of SFRC for the desired level of survival probability.     

Microstructurally-dependent model for predicting the kinetics of physically small and long fatigue crack growth

Based on the proposed concept of the fatigue threshold stress intensity factor ranges, a model has been developed that describes the kinetics of physically small fatigue crack and long fatigue crack growth. The model allows the calculation of the crack growth rate under the regular fully-reversed uniaxial loading from the data on the static characteristics of mechanical properties and the microstructure of the initial material. The crack depth at which the cyclic plastic zone size ahead of the crack tip will exceed the grain size should be considered as a criterion of the small-to-long crack transition. Under high-cycle fatigue conditions physically small fatigue crack growth will be divided into two phases of growth: the first phase is when the crack propagates along the slip planes of individual grains, and the second one is when the crack changes the mechanism of growth and propagates in the plane perpendicular to the loading direction. The model validity has been tested using the experimental data on the growth of the long cracks in specimens of titanium alloy VT3-1 in seven microstructural states and the small cracks in specimens of titanium alloy Ti–6Al–4V and aluminum alloy 2024-T3. Good agreement between the calculated and experimental results is obtained.     

Synchrotron diffraction investigation of the distribution and influence of residual stresses in fatigue

This paper presents some results obtained from synchrotron diffraction investigations into two somewhat related areas of interest to the fatigue community. Firstly, the influence of fatigue cycling on the distribution and magnitude of residual strains and stresses and, secondly, the residual strains and stresses engendered around a growing fatigue crack. Its main premise is that modern tools such as automated synchrotron strain scanning offer the potential for more complete insight into the distribution of residual strains and stresses and their influence on fatigue performance. The first part of the work was accomplished using friction‐stir welded (FSW) and metal‐inert gas (MIG) welded specimens. The particular interest in these specimens was obtaining detailed knowledge regarding as‐welded variation in residual stresses between specimens, the location of peak values relative to local microstructure and stress concentrations, and of their modification during fatigue cycling. Such information may indicate a route forward to the selection of welding process parameters for optimised fatigue performance. The second part of the work considered an established fatigue crack in a compact tension (CT) specimen and examined the ability of synchrotron diffraction to characterize the stresses associated with the plastic enclave around a fatigue crack. This work is of interest in the context of better knowledge of crack‐tip shielding by plasticity‐induced closure and its incorporation into life prediction methodologies.     

Influence of residual stresses from shot peening on fretting fatigue crack growth

One method to improve fretting fatigue life is to shot peen the contact surfaces. Experimental fretting life results from specimens in a Titanium alloy with and without shot peened surfaces were evaluated numerically. The residual stresses were measured at different depths below the fretting scar and compared to the corresponding residual stress profile of an unfretted surface. Thus, the amount of stress relaxation during fretting tests was estimated. Elastic–plastic finite element computations showed that stress relaxation was locally more significant than that captured in the measurements. Three different numerical fatigue crack growth models were compared. The best agreement between experimental and numerical fatigue lives for both peened and unpeened specimens was achieved with a parametric fatigue growth procedure that took into consideration the growth behaviour along the whole front of a semi‐elliptical surface crack. Furthermore, the improved fretting fatigue life from shot peening was explained by slower crack growth rates in the shallow surface layer with compressive residual stresses from shot peening. The successful life analyses hinged on three important issues: an accurate residual stress profile, a sufficiently small start crack and a valid crack growth model.     

Fatigue strength evaluation of linear flow split profile sections based on hardness distribution

A concept to evaluate the fatigue strength of linear flow split profile’s sections using a local strain approach based on the hardness distribution is presented. For this purpose established correlations between hardness and cyclic material properties are adapted to fit experimental results derived by fatigue tests on smooth, non-homogeneous specimens extracted from such profiles. For validation a numerical fatigue strength evaluation of a four-point-bending fatigue test of linear flow split profiles is presented using an elastic–plastic FE model with the material property distribution derived. The developed approach allows an improved estimation of the fatigue strength of the component analysed.     

Determination of normal and shear residual stresses from fracture surface mismatch

The contour method of residual stress measurement has recently been adapted to measure fractured, rather than cut specimens. The fracture contour method was capable of determining normal residual stresses acting prior to the plane-strain failure of a large aluminium alloy forging, but shear residual stresses could not be measured (Prime et al., 2014).We demonstrate that the application of digital image correlation to topographic measurements of a fracture surface pair allows the determination of shear residual stresses in addition to the normal stress component. Miniature compact tension samples were extracted at an angle from a bent beam to give a known variation in normal and shear residual stress on the fracture plane. The material used was a metal matrix composite, which could be deformed plastically to introduce a known distribution of stresses and also present limited plasticity upon fracture, allowing plane-strain condition in a small specimen. The samples were fractured at cryogenic temperatures to further restrict plasticity. Although the fracture surface was non-planar and evidence suggested the occurrence of plasticity near the edges, experimental results correlated fairly well with the calculated normal and shear residual stress profiles.     

Standing contact fatigue

A novel experimental method for testing the resistance of a material to contact fatigue, called standing contact fatigue (SCF), is presented. It comprises a spherical indenter, repeatedly pressed onto a plane specimen in pure normal contact without lubrication, friction or wear. The SCF method is here applied to three case-hardened steels, and results in ring/cone cracks initiated at the surface. The connection between SCF and spalling is discussed. The experimental results are presented in the form of P–N curves, where P is the normal contact load and N the number of cycles required for fatigue crack initiation. The experimental results are supported by numerical simulations of the tests. The elasto-plastic properties of case-hardened materials are graded, i.e. functions of the depth from the carburized surface. The gradation is estimated from independent experiments and is included in the analysis.     

Experimental observation and numerical modeling of formation of local plastic zones in hardened surface layers due to contact overloading

The problem of formation of plastic zones in case-hardened metallic bodies due to contact overloading is studied both experimentally and numerically. Metallic materials exposed to surface hardening demonstrate spatial variation of the material hardness and yield strength with a decreasing profile with depth and belong to the class of so-called plastically graded materials. The presented experimental program employs micro-Vickers hardness tests to map the variation in material hardness and corresponding yield strength for both virgin and loaded case-hardened specimens made of a chromium tool steel. It is shown that, depending on the profile of the yield strength in the near-surface zones and contact parameters, a plastic deformation can originate underneath the hardened layer. The distribution of the effective plastic strain extracted from the micro-hardness increment measurements are found in good agreement with the results of finite element simulations of a plastically graded material subjected to similar loading conditions. Numerical analysis reveals significant perturbations in the stress field distribution within the hardened layer due to formation of a closed-shaped plastic zone in the gradient layers, including development of a tensile stress on the boundary between the elastic and plastic zones as well as an overall increase in the effective stress intensity. It is shown that the hardened layer behaves similar to an elastic beam on a compliant foundation. These stress field perturbations in the hardened layers with low deformation capacity can greatly affect the durability and serviceability of surface treated mechanical parts.     

Evaluating the fatigue limit of metals having surface compressive residual stress and exhibiting shakedown

The objective of the study described in this article is to evaluate the effect of shakedown of surface compressive residual stresses introduced by shot peening on fatigue limit of stainless steel. First, the tension‐compression fatigue tests were conducted on ASTM CA6NM specimens under controlled load and displacement conditions to acquire a fatigue limit diagram under various compressive mean stress. The results showed that shakedown of negative mean stress occurs under controlled displacement. We then carried out in‐plane–bending fatigue tests under controlled load conditions on welded ASTM 309 stainless steel specimens with surface compressive residual stress introduced by ultrasonic shot peening. The results provide a fatigue limit of 415 MPa, which agrees with the value of 404 MPa calculated based on a modified Goodman line considering shakedown. Therefore, it is suggested that the surface layer is restricted by the internal bulk that creates controlled displacement conditions and the shakedown of surface compressive residual stress occurs.     

Cold rolling influence on residual stresses evolution in heat-treated AA7xxx T-section panels

This article describes a novel cold working method for relaxing residual stresses in extra-long quenched T-section panels. Distortion led by quench-induced residual stresses in components is usually a great concern for the aviation industry. In this study, the influence of cold rolling on the residual stresses in a scale-down quenched AA7050 T-section specimen is experimentally and numerically investigated. An integrated numerical model was built to predict the quenching and the subsequent cold rolling processes. High levels of compressive stress around the surfaces of quenched T-profile specimens and the tensile surface residual stresses (RS) in the quenched and cold rolled specimens were predicted via numerical analysis, the surface stresses magnitude and distribution have, therefore, been quantified via X-ray diffraction (XRD) technique. The deflection of quenched specimens experienced 1.5% and 3% cold rolling was measured as well. In addition, to examine the cold rolling effect on the mechanical properties of T-profile specimens, hardness tests were carried out on quenched and cold rolled T-section specimens. It concludes that with 1.5% cold rolling the residual stresses in the core part of quenched material can be effectively relieved to an extent of lower than 83 MPa, with limited change for the material properties.     

Beitrag zur Abschätzung der Dauerfestigkeit nitrierter bauteilähnlicher Proben

Estimation of the fatigue limit of nitrided component-type specimens The “weakest link” model of Kogaev and Serensen comprehend the statistical and the stress mechanical size effect on the fatigue limit. In combination with the concept of the local fatigue limit on the basis of the damage parameter according to Smith, Watson and Topper, it allows the consideration of component specific effects on the fatigue limit of surface strengthened materials. The applicability of the concept has been proved by experiments at nitrided specimens with different geometries and type of loads.