Two methods for predicting the multiaxial fatigue limits of sharp notches

In this paper the problem of the multiaxial fatigue limit estimation of sharply notched components has been addressed using two different methods: a critical distance method and a method involving modified Wöhler curves. These two methods had been previously developed by the authors, but required modification for use in conjunction with finite element stress analysis of sharply notched specimens subjected to multiaxial loadings. Initially, it was demonstrated mathematically that these methods are equivalent in terms of multiaxial stresses near the notch tip. Subsequently, by employing some well‐known uniaxial notch fatigue concepts, some assumptions have been made in order to extend the use of these methods to in‐phase multiaxial notch fatigue situations. Experimental data were obtained from tests conducted on V‐notched specimens subjected to in‐phase mixed Mode I and Mode II loadings. Both methods were successful in giving fatigue limit predictions with an error usually less than 15%. This is interesting because the two methods make quite different assumptions about the nature of fatigue crack growth in the vicinity of the notch.     

A stress-based method to predict lifetime under multiaxial fatigue loadings

This paper extends to low/medium‐cycle fatigue a stress‐based method recently proposed by the same authors for high‐cycle multiaxial fatigue assessments. By considering the plane of maximum shear stress amplitude coincident with the microcrack initiation plane, the method requires the calculation both of the maximum shear stress amplitude and the maximum normal stress relative to the same plane. Multiaxial fatigue life estimates are made by means of bi‐parametric modified Wöhler curves, which take into account the mean stress effect, the influence of the out‐of‐phase angle and the presence of notches by using a generalization to multiaxial fatigue of the fatigue strength reduction factor K_f. Approximately 700 experimental data taken from the literature are used to demonstrate that the method is a useful tool to summarize fatigue strength data of both smooth and notched components, subjected to either in‐phase or out‐of‐phase loads. Finally, a simple practical rule for the calculation of the multiaxial fatigue strength reduction factor is proposed.     

A unifying approach to estimate the high-cycle fatigue strength of notched components subjected to both uniaxial and multiaxial cyclic loadings

This paper proposes an engineering method suitable for predicting the fatigue limit of both plain and notched components subjected to uniaxial as well as to multiaxial fatigue loadings. Initially, some well‐known concepts formalized by considering the cracking behaviour of metallic material under uniaxial cyclic loads have been extended to multiaxial fatigue situations. This theoretical extension allowed us to form the hypothesis that fatigue limits can be estimated by considering the linear–elastic stress state calculated at the centre of the structural volume. This volume was assumed to be the zone where all the main physical processes take place in fatigue limit conditions. The size of the structural volume was demonstrated to be constant, that is, independent from the applied loading type, but different for different materials. Predictions have been made by Susmel and Lazzarin's multiaxial fatigue criterion, applied using the linear–elastic stress state determined at the centre of the structural volume. The accuracy of this method has been checked by using a number of data sets taken from the literature and generated by testing notch specimens both under uniaxial and multiaxial fatigue loadings. Our approach is demonstrated to be a powerful engineering tool for predicting the fatigue limit of notch components, independently of material, stress concentration feature and applied load type. In particular, it allowed us to perform predictions within an error interval of about ±25% in stress, even though some material mechanical properties were either estimated or taken from different sources.     

Fatigue limit evaluation of notches,small cracks and defects: an engineering approach

In this paper, the average stress method for the fatigue limit evaluation of stress raising geometrical features is revised and extended. In particular, an analytical close‐form approach was used and the linear elastic stress equations were modified by taking into account the effect of nominal stress on the local stress distribution. Hence, the average tangential stress was correctly evaluated over a distance of 2a₀, where a₀ was El Haddad's short crack constant, for long and small notches as well as for crack‐like notches. When this model is applied to a wide range of geometrical features subjected to mode I fatigue loading, the classical shape of the curves of the Kitagawa–Takahashi diagram was obtained for changes in crack‐like notch size. Similarly, notch sensitivity was estimated by reducing the notch tip radius. The accuracy of the proposed method in predicting fatigue limits was then checked by using experimental data taken from the literature and generated on testing specimens weakened by rounded and sharp notches as well as by small artificial defects.     

Notch fatigue behaviour of low-temperature gaseous carburised 316L austenitic stainless steel

ABSTRACT

The influence of low-temperature gaseous carburisation on notch fatigue behaviour of 316L steel under cyclic axial loading was investigated. After carburisation, the carburised case was well distributed at the surface region and was not influenced by the notch geometry. Low-temperature carburisation considerably enhanced the notch fatigue performance, which led to 32% and 44% increase in the endurance limits for the specimens with stress concentration factors K _t?=?1.91 and 3.91, respectively. The notch sensitivity of 316L steel reduced after carburisation. Irrespective of the applied stress amplitude, the fatigue crack nucleation sites were always at the notch root surface for the untreated specimens. For the carburised specimens, fatigue cracks nucleation changed from surface at high-level stress to subsurface at low-level stress.     

Similarities of stress concentrations in contact at round punches and fatigue at notches: implications to fretting fatigue crack initiation

A linear elastic model of the stress concentration due to contact between a rounded flat punch and a homogeneous substrate is presented, with the aim of investigating fretting fatigue crack initiation in contacting parts of vibrating structures including turbine engines. The asymptotic forms for the stress fields in the vicinity of a rounded punch-on-flat substrate are derived for both normal and tangential loading, using both analytical and finite element methods. Under the action of the normal load, P , the ensuing contact is of width 2 b which includes an initial flat part of width 2 a . The asymptotic stress fields for the sharply rounded flat punch contact have certain similarities with the asymptotic stress fields around the tip of a blunt crack. The analysis showed that the maximum tensile stress, which occurs at the contact boundary due to tangential load Q , is proportional to a mode II stress intensity factor of a sharp punch divided by the square root of the additional contact length due to the roundness of the punch, Q /(√( b − a )√ π b ). The fretting fatigue crack initiation can then be investigated by relating the maximum tensile stress with the fatigue endurance stress. The result is analogous to that of Barsom and McNicol where the notched fatigue endurance stress was correlated with the stress intensity factor and the square root of the notch-tip radius. The proposed methodology establishes a 'notch analogue' by making a connection between fretting fatigue at a rounded punch/flat contact and crack initiation at a notch tip and uses fracture mechanics concepts. Conditions of validity of the present model are established both to avoid yielding and to account for the finite thickness of the substrate. The predictions of the model are compared with fretting fatigue experiments on Ti–6Al–4V and shown to be in good agreement.     

Notched fatigue testing of Inconel 718 prepared by selective laser melting

Selective laser melting (SLM) was used to prepare notched high‐cycle fatigue test specimens made from nickel‐based superalloy Inconel 718. Samples were designed to have 1 of 3 different notch geometries, including V notches with K_t of 2.2 or 3.1, a U notch with K_t of 2.0, and were printed in either vertical or horizontal orientations. Samples were tested with as‐printed dimensions and surfaces after heat treatment, but a separate set of SLM samples were printed as plates and machined to final dimensions comporting to the V‐notch specimen with K_t = 3.1. High‐cycle fatigue testing showed that machined SLM specimens behaved similar to wrought Inconel 718 plate specimens, but testing with as‐produced surfaces led to a decrease in fatigue life. The explanation for this difference is based on approximations of linear elastic fracture mechanics solutions for short cracks emanating from notch roots, with intrinsic surface features of SLM materials serving as the cracks. Analysis of the actual notch geometries after SLM fabrication indicates that stress intensity in the presence of these features plays a prominent role in determining number of cycles before fatigue crack initiation and propagation occurs.     

Fatigue life assessment of nodular cast iron containing casting defects

The fatigue behaviour of a nodular cast iron containing casting defects has been investigated in the high-cycle fatigue regime. In this paper, we propose a fatigue life assessment model for flawed materials based on a fracture mechanics approach which takes into account the position and size of the defect, short crack behaviour and the notch effect introduced by the defect. The fatigue behaviour of smooth samples, and long and short crack behaviour have been experimentally determined in order to identify the relevant mechanical parameters; these being introduced into the model. An experimental study has been made both in air and in vacuum in order to account for the position of the defect, noting that internal defects are supposed to be under vacuum conditions. Experimental results, which are based on a two-crack front-marking technique specially developed for this study, show that the propagation of natural cracks is controlled by the effective stress intensity factor in air as well as in vacuum. The K calculation for a short crack in the stress field of a notch is analysed using numerical elastic–plastic results. Comparison between experimental results and the computation of fatigue life for fatigue lives less than 10⁶ cycles shows that the fatigue behaviour of nodular cast iron is controlled by a propagation process. The model proposed is thus relevant for fatigue lives less than 10⁶ cycles so that the defect can be considered as a crack and the initiation stage neglected. Closer to the fatigue limit, this study shows that the initiation stage should be considered in the assessment of fatigue life of nodular cast iron, because a single macroscopic propagation assessment is not enough to describe the whole fatigue life. The defect cannot be considered as a pre-existent crack in the high-cycle fatigue range (>10⁶ cycles), and the initiation stage that contains microcrack propagation around the defect should be evaluated when assessing the high-cycle fatigue life of nodular cast iron.     

Influence of notch severity on thermomechanical fatigue life of a directionally solidified Ni‐base superalloy

The aim of this work is to understand the influence of notches under thermomechanical fatigue (TMF) in a directionally solidified Ni‐base superalloy. Experiments were performed utilizing linear out‐of‐phase and in‐phase TMF loadings on longitudinally oriented smooth and cylindrically notched specimens. Several notch severities were considered with elastic stress concentrations ranging from 1.3 to 3.0. The local response of the notched specimens was determined using the finite element method with a transversely isotropic viscoplastic constitutive model. Comparing the analysis to experiments, the locations observed for crack nucleation in the notch, which are offset from the notch root in directionally solidified alloys, are consistent with the maximum von Mises stress. Various local and nonlocal methods are evaluated to understand the life trends under out‐of‐phase TMF. The results show that a nonlocal invariant area‐averaging method is the best approach for collapsing the TMF lives of specimens with different notch severities.     

Mean stress and plasticity effect prediction on notch fatigue and crack growth threshold,combining the theory of critical distances and multiaxial fatigue criteria

In the present work, we propose a robust calibration of some bi‐parametric multiaxial fatigue criteria applied in conjunction with the theory of critical distances (TCD). This is based on least‐square fitting fatigue data generated using plain and sharp‐notched specimens tested at two different load ratios and allows for the estimation of the critical distance according to the point and line method formulation of TCD. It is shown that this combination permits to incorporate the mean stress effect into the fatigue strength calculation, which is not accounted for in the classical formulation of TCD based on the range of the maximum principal stress. It is also shown that for those materials exhibiting a low fatigue‐strength‐to‐yield‐stress ratio σ_fl,R = ?1/σ_YS, such as 7075‐T6 (σ_fl,R = ?1/σ_YS = 0.30), satisfactorily accurate predictions are obtained assuming a linear‐elastic stress distribution, even at the tip of sharp notches and cracks. Conversely, for any materials characterized by higher values of this ratio, as quenched and tempered 42CrMo4 (σ_fl,R = ?1/σ_YS = 0.54), it is recommended to consider the stabilized elastic‐plastic stress/strain distribution, also for plain and blunt‐notched samples and even in the high cycle fatigue regime still with the application of the TCD.     

Fatigue notch sensitivity of steel blunt-notched specimens

The notch sensitivity of three steels with similar plain fatigue limits was analysed and modelled. The analysis was made by using a model previously derived which estimated the fatigue limit of blunt notched components by means of the parameter k_td defined as the stress concentration introduced by the notch at a distance d from the notch root surface equal to the distance between microstructural barriers. The analyses show how the first two or three microstructural barriers define the fatigue limit and the fatigue notch sensitivity of blunt notched specimens.     

Comparative analysis of fatigue life predictions in central notched specimens of Al–Mg–Si alloys

The fatigue behaviour of an Al–Mg–Si alloy was studied using notched specimens. Fatigue tests were conducted at two stress ratios R= 0 and R= 0.4 on thin plates with a central hole. Constant and block variable loading amplitudes were applied to the specimens using a servo‐hydraulic machine. The applicability of the local strain approach method to the prediction of the fatigue life was investigated for this type of discontinuity. Two methods, the equivalent strain energy density approach and a modified stress–strain intensity field approach, were used to predict the fatigue strength. For the second one an elastic–plastic finite element analysis was carried out in order to obtain the local strain and stress distributions near the notch root. Based on Miner's rule an equivalent stress was used to correlate the fatigue lives for the variable amplitude histories. The experimental results were compared with the predicted results obtained by the two methods investigated and better agreement was found with the stress–strain field intensity approach, while the strain energy approach gave more conservative results. Miner's rule gives a good correlation between the variable amplitude and constant amplitude results.     

A new proposal for assessment of the fatigue strength of steel butt‐welded joints improved by peening (HFMI) under constant amplitude tensile loading

Experimental fatigue data for butt‐welded joints in as‐welded condition and under constant amplitude tensile loading were analysed using the effective notch stress system and a new master curve analysis that takes the local stress ratio, R_local, into account. The local stresses needed for computation of R_local are calculated with the notch strain approach in conjunction with the reference radius concept. The main focus was to predict with the derived master curve the fatigue strength of peened butt‐welded joints. The lowest surface residual stresses after peening were first estimated based on reported measurements and an analytical lower bound result. The predictions showed quite similar strength dependences and FAT values as reported for high‐frequency mechanical impact treated welds for applied stress ratio R = 0.1. The benefits of peening reduce faster for higher strength steels when R increases. When R = 0.5, the FATs are practically the same for all steel grades.     

Fatigue crack growth rates under sequential mixed-mode I and II loading cycles

One common mode of failure that occurs in rolling bodies such as gears, bearings and rails is due to the fatigue process. Several research workers suggest that rolling contact fatigue cracks are subjected to mixed mode I and II loading cycles. It is believed that the correct modelling of loading cycles can help us to study the mechanics of crack growth because fatigue comprises a major safety consideration in the design process. Experiments have been performed under nonproportional mixed-mode I and II loading cycles with fixed degrees of overlap, so that coplanar cracks were produced. Three empirical crack propagation laws have been established which are related to both mode I and mode II effective stress intensity factor ranges.     

Fatigue Limit of Steel with an Arbitrary Crack under a Stress Controlled Constant with a Positive Mean Stress

In this paper, push–pull fatigue tests of notched specimens under R=−1, 0 and 0.5 are carried out on annealed 0.1 % carbon steel and quenched-tempered 0.5 % carbon steel with H_{rm B} simeq 600. The fatigue limit of a long crack, sigma_w2, is obtained from that of a notched specimen with a sharp and deep notch whose radius is smaller than the branch point rho₀. Using the present and past sigma_w2 data, the effect of the positive mean stress on the dKw of the long crack is evaluated using 3.2 H_{rm B} (simeq sigma_{rm B}) and sigma_{rm S}(3.2 H_{rm B}), where dKw is the stress intensity factor range for predicting the fatigue limit of a metal with an arbitrary crack, sigma_{rm S} is the lower yield stress or 0.2% proof stress, sigma_{rm B} is the ultimate tensile strength and H_{rm B} is the Brinell hardness. Although the sigma_w2 decreases with the mean stress, sigma_w2 is cut off by the threshold stress sigma_we of the plastic deformation at the crack tip. For the quantitative prediction of the fatigue limit of a cracked steel with an arbitrary crack length under a positive mean stress, the sigma_w2 and sigma_we values are approximated by simple formulae.     

A synthesis of the push‐pull fatigue behaviour of plain and notched stainless steel specimens by using the specific heat loss

The energy dissipated to the surroundings as heat in a unit volume of material per cycle, Q, was recently proposed as fatigue damage index, and it was successfully applied to rationalise fatigue data obtained by carrying out stress‐controlled and strain‐controlled fatigue tests on AISI 304 L stainless steel plain and hole specimens. In this paper, it is shown that the Q parameter is independent on thermal and mechanical boundary conditions occurring during experiments. After that, additional stress‐controlled fatigue tests on plain and notched specimens characterised by smaller notch tip radii than those tested previously have been performed. Present data have been compared with previous ones, and it was found that all available results can be synthesised in terms of the energy parameter Q into a unique scatter band, independently on the testing conditions (stress‐controlled or strain‐controlled) and on the specimens' geometry (plain or notched). About 100 data were included in the statistical analysis to characterise the energy‐based scatter band of the material. Finally, some limitations of applicability of the experimental technique adopted in the present paper are discussed.     

Effect of small notch and absorbed hydrogen on the fatigue fracture in two-step stress test within fatigue limit diagram

It is usually regarded as a common understanding that fatigue failure would not occur if all stresses were kept within fatigue limit diagram. However, it was shown that fatigue failure occurred in some special cases of variable amplitude loading condition even when all stresses were kept within fatigue limit diagram in the case of small-notched specimen. The cause of such a phenomenon was examined using two-step stress pattern for low alloy steel SCM440H. In the case of constant stress amplitude loading, non-propagating crack was formed only at low mean stress and not formed at high mean stress. However, in the case of two-step stress pattern in which the first step stress was chosen as  R  =−1 and the second step stress was with high mean stress, a non-propagating crack was formed by the first step stress. This crack functioned as a pre-crack for the second step stress with high mean stress. Consequently, fatigue failure occurred by the stresses within fatigue limit diagram. In this study, the effect of notch size and shape were examined. The effect of absorbed hydrogen was also investigated. Absorption of 0.3 ppm hydrogen caused more reduction of fatigue limit.     

Fatigue performance and fatigue damage parameter estimation of spot welded joints of aluminium alloys 6111‐T4 and 5754

In the present study, fatigue behaviours of spot welded joints of aluminium alloys 6111‐T4 and 5754 have been experimentally investigated. Fatigue results indicate that fatigue strength of spot weld primarily depends on specimen loading type and gauge thickness. Effects of base material and load ratio on fatigue resistance of welded specimen are insignificant. An equivalent stress based fatigue damage parameter is derived to consolidate empirical data and develop predictive capabilities for automobile designers. The fatigue damage parameter defined in this study is proven effective in consolidating a large amount of fatigue data into a narrow band and is especially suitable for the comparative fatigue strength evaluation of components and specimens.     

Development of fatigue cracks from mechanically machined scratches on 2024‐T351 aluminium alloy—Part II: finite element analysis and prediction method

A prediction method to evaluate the effect of scratch geometry on fatigue life of aluminium structures containing scribe marks was developed on the basis of the experimental results described in Part I of this paper. Finite element calculations were performed on scribed samples to investigate the local stress around scribes. Elastic and elastic‐plastic stress and strain distributions at the scribe root were computed under monotonic and cyclic tensile and bending loads evaluating the driving force behind initiation and propagation from scribes. Scribe shape, size and cladding regulated stress and strain distributions in the neighbourhood of scribe roots. Fatigue life of tested scribed samples was divided into initiation life, defined as the cycles spent to develop a 50 µm deep crack at scribe roots, and the remaining propagation life up to failure. Striation counting measurements were used to calculate propagation lives by integrating linear elastic da/dN versus ΔK curves. Only up to a maximum of 38% of total fatigue life was spent to propagate an initial 50 µm deep crack from scribe roots. The theory of critical distances was successfully applied to predict initiation lives of scribed samples from elastic stress distributions. A plastic correction was also suggested, in the frame of the theory of critical distances, to correlate initiation lives of clad and unclad specimens.     

Effect of notch on fatigue behaviour of a directionally solidified superalloy at high temperature

The effect of notch types and stress concentration factors (K_t) on low cycle fatigue life and cracking of the DZ125 directionally solidified superalloy has been experimentally investigated. Single‐edge notched specimens with V and U type geometries were tested at 850 °C with stress ratio R = 0.1. High temperature in situ optical method was used to observe crack initiation and short crack propagation. Scanning electron microscope observation of fracture was used to analyse the failure mechanism. The results reveal that fatigue resistance decreases with K_t increasing from 1.76 to 4.35. The ratcheting is found to be affected by both K_t and the nominal stress from the displacement–force curve. In situ observations indicate that the cracking does not occur at the notch apex but at the location where the max principal stress or Hill's stress is the highest. According to the scanning electron microscope observations, the failure of the notched specimens strongly depends on the anisotropy microstructures.