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.

The effect of notches and biaxial fatigue loading on the crack paths was studied in detail for thin-walled tube specimens with a passing-through hole, paying special attention to the short-crack period. The study was focused on the high cycle fatigue regime. The material was a carbon steel and the tests were under load control, at Rσ=−1. The crack initiation point on the notch surface and the crack direction were studied with an optical microscope on the specimen outer surface and with a scanning electron microscope and a non-contact 3D optical profilometer on the fracture surface. The crack direction was analyzed for several crack lengths, ranging from the length of one average grain to the length of twenty average grains, all lengths within the short-crack regime, in order to carefully observe the evolution of the crack direction in the Stage I and during the transition from Stage I to Stage II. A statistical analysis of the crack initiation point and the experimental crack directions was carried out. In general, the crack initiation point was close to the maximum principal stress point. The crack direction during the first grains was approximately the Mode I direction. There was no initiation in Mode II. The crack continued in the Mode I direction as it got longer, within the short-crack period. The experimental fatigue limits were compared with the predictions calculated with two models from the literature. The direction of the straight lines used by the models to make the predictions were compared with the average crack directions measured experimentally. The goodness of the models, not only from the point of view of the fatigue limit value prediction but also from the closeness of the direction of the line used for the prediction to the experimental crack direction, was discussed.

Current models for predicting the fatigue endurance of notched solids use the stresses along a straight line, beginning at the notch root, as a simplification of the real crack propagation path. In this work, the experimental crack paths for hollow notched samples were analysed through different microscopy techniques, with the objective of establishing high cycle fatigue crack growth directions in a mild steel. Fully reversed tension–compression fatigue tests (R=−1) of thin-walled tube specimens with a passing-through hole were carried out. The crack paths observed in the outer cylindrical surface were studied in each case, with special attention to the crack initiation point and the crack direction along the first grains. Moreover, the analysis of the fracture surfaces allowed the same analysis to be performed to determine the internal crack paths. It was observed that the crack initiation point was close to the maximum principal stress point at the hole contour as obtained from linear elastic finite element analysis, and the crack direction in its initiation was generally close to Mode I direction, contrary to the conventionally accepted 45∘ crack growth direction.

The most common current models for predicting the fatigue limit in notched solids use the stresses along a straight line, beginning at the notch root, to make the prediction. This line represents a simplification of the path of a real crack, which usually has a first part, known as stage I, in the direction of the maximum tangential stress, and a second part, known as stage II, in the direction perpendicular to the maximum normal stress. In this work, experimental crack paths for notched solids are analysed, with the objective of establishing the directions and lengths of stages I and II of fatigue crack growth from notches. The material was a mild steel, the geometry of the specimen was a thin-walled tube with a passing-through hole and the tests were axial, with R = -1. From the tests, the S-N curves were constructed and the fatigue limits were calculated. For the high cycle fatigue tests, the cracks paths were studied, with special attention to the crack initiation point and the crack direction along the first grains. The cracks paths on the specimen outer surface were studied with an optical microscope. In this surface, the crack initiation point was close to the maximum principal stress point at the hole contour. The direction of the crack in the first and second grain showed great variability. This variability noticeably decreased as the crack reached a length of 10-20 grains, approaching the direction of Mode I. However, the crack might actually start at an interior point on the surface of the hole, which has a depth of 1500 μm. In fact, the point of maximum principal stress of the entire specimen is not at the specimen outer surface but on the internal surface of the hole at 750 μm from the outer surface, that is, half the thickness of the specimen. The crack path in the plane transverse to the hole containing this point of maximum principal stress was analysed. For this, the fracture surfaces, at both sides of the hole, were analysed with a non-contact 3D optical profiler. The crack path in this internal transverse plane followed the trend described for the crack path on the specimen outer surface: the initiation point close to the maximum principal stress point at the hole contour, great variability in the direction of the crack along the first grains and tendency to Mode I direction when the crack gets longer.

This work shows an analysis of several models of multiaxial fatigue for notches: Navarro-Rios’ model, which analyses the interaction between the crack and its associated plastic zone with the material microstructural barriers, and three models that combine a critical volume method for notches with a critical plane model for multiaxial fatigue in unnotched solids. Specifically, the application of these models for the prediction of the fatigue limit for a plate with a circular hole subjected to axial, shear and in-phase biaxial cyclic loading is studied. The effects of two parameters are analysed: the radius of the hole and the relationship between the torsional and axial fatigue limits. For all the analysed models, cases are observed in which an increase in the hole radius produces an increase in the predicted fatigue limit, that is, the evolution of the fatigue limit with an increasing hole radius is not always monotonically decreasing, as would be expected. These effects, which we have called “humps” because of their appearance on the prediction graphs, mainly occur in shear loading. No humps were observed in the studied experimental results, but the number of available experimental results is too small to assure this tendency. The results shown in the work indicate that a greater knowledge of the physics of multiaxial fatigue in notches is necessary to achieve models that are capable of providing increasingly accurate predictions.

A microstructural model is presented to assess pit-to-crack transition and corrosion fatigue strength in pitted components in different environments. The model is first validated using available experimental data in the literature for pitting corrosion fatigue strength and S-N curves for both carbon and stainless steels. The value of the method proposed and its applicability is then shown by the development of fatigue knock down factor maps to the in-air S-N curve. Finally, the influence of pit local topology on pit-to-crack transition damage tolerance and the links to the NDE methods quantitative resolution necessary to account for defect shape or acuity in structural integrity assessments are discussed.

We investigate how the fatigue limit of notched specimens calculated with the Theory of Critical Distance (TCD) changes when variations in the value of the critical distance itself are considered. We motivate our study by showing how attempts at introducing a plastic zone correction in the derivation of the formula for the critical distance lead to a new length which can be significantly larger than the original one. The predictions effected with both lengths were not found to be so different, though. And this led us to study circular holes and V-notches, for which solutions for the ratio Kf∕Kt can be derived analytically.

Many methods have been proposed to predict fatigue failure in the presence of notches, among which is the Navarro-Rios model. This model is based on short-crack fracture mechanics. Specifically, the model analyses the capacity of the crack, which is formed at the notch root by cyclic loading, to overcome successive microstructural barriers such as grain boundaries. This model provides a fairly reasonable explanation of crack growth from a notch under cyclic loading and has been successfully used for many years to predict the fatigue limit in some notched geometries, as shown in several published works. However, the application of this model is not easy, mainly for two reasons: the first is that to build the equations of the model, it is necessary to know the stress field generated by a dislocation in the vicinity of the specific notch, which is a complicated elasticity problem except for very simple notch geometries. The second is related to the resolution of the equations of the model, which are singular integral equations that are difficult to solve except for very simple cases. This work shows a simplified version of the Navarro-Rios model, which allows us to overcome these two difficulties. First, the elastic problem of a dislocation near a notch is simplified to that of a dislocation in an infinite medium, which has a known analytical solution. Second, the study of the equilibrium at the crack line is simplified by using the elastic stress at the midpoint of the crack line instead of using the full stress gradient. After this simplification, the singular integral equation has a known and simple solution. This simplified Navarro-Rios model is applied to some notched geometries and provides similar fatigue limit predictions to those of the classic Navarro-Rios model. It is also compared with results in the literature, where it provides similar predictions to the experimental fatigue limits. The simplified Navarro-Rios model can be a relatively simple alternative to critical distance models for predicting the fatigue limit in notched solids.

The present work provides an efficient formulation to assess the growth of short fatigue cracks in metallic components. The proposed technique consists on the iterative combination of a micromechanical short-crack growth model and the Finite Elements Method. The interaction of the crack with the microstructure of the material is evaluated through the dislocations distribution technique. The finite elements analysis of the problem is needed to obtain the stress gradient ahead of the notch. The division of the main problem into simpler scenarios makes the resolution of the method easier since cases with known solutions are required exclusively. The iterative method formulation is properly described and application examples are given in order to show its usefulness.

Cyclic plasticity constitutive equations are required in fatigue and fracture analysis for the quantification of the plastic zone at notches or during fatigue crack growth. This work describes a constitutive model that reproduces the behaviour of stabilized metals subjected to multiaxial cyclic loads. The model is based on the idea of distance in the stress space which is calculated with a metric tensor. This metric tensor is a material property and can be empirically determined. In addition, the flow rule employs another material property known as hardening modulus. Procedures to calculate these material properties from experimental data are developed for the non-proportional loading case. The model gives good results for complex loading histories both from the qualitative and quantitative point of view. It also predicts the stabilized stress values in 90 degrees out-of-phase tensile-torsion tests.

In this work, the assessment of a short crack emanating from arbitrarily shaped notches under Mode I loading is done. A parametric algorithmic tool is used to create a wide range of different two dimensional notch shapes for the evaluation of notch fatigue strength by means of the Distributed Dislocation Technique. Comparisons between V-notches, U-notches and semi-elliptical notches establishing similar geometrical parametric relations are shown, so that the simplicity and versatility of the designed tool is demonstrated. This useful properties and advantages make this tool applicable to industrial problems such as the modelling and assessment of the effect of corrosion pits on fatigue strength.

Results of a large set of fatigue tests on AISI 304L stainless steel cylindrical round specimens with a circumferential notch of semicircular profile and subjected to uniaxial loading ( R = –1) are reported. The outer diameter of the specimens has been kept fixed, whereas the radius of the notch has been increased progressively. A whole range of configurations is studied, from combinations of notch radius and specimen diameter where the remaining ligament is much larger than the notch (semi-infinite problem) to configurations where the ligament is much smaller than the notch (finite problem) and where interaction effects have a noticeable influence on the shape of the stress gradient. An S–N curve has been obtained for each configuration. The experimentally obtained fatigue limits for the different notch radii have been compared with predictions made with several methods. However, a strong divergence between the experimental values and the theoretical predictions, which were extremely conservative, has been found and this has been attributed to work-hardening and residual stress effects connected with the machining process. It has also been suggested that a geometrical notch strengthening effect, possibly connected with stress triaxiality due to the notch, and the accompanying hydrostatic tensile stress, may also be a contributing factor. A simple practical engineering method to account for these effects has been proposed.

This work shows the results of a set of tests in 7075-T6 aluminium alloy specimens. The tests were under load control at R = -1. From the tests, the corresponding S-N curves were built, and the endurance limits were calculated for 1 million cycles. The ratio between the pure torsion and tension endurance limits was 0.58, i.e., the behaviour of this material in fatigue is of the von Mises type. Specimens with circular holes of various diameters under tension, torsion and in-phase biaxial loading were tested. The directions of the cracks that grew from the holes were studied with an optical microscope, a scanning electron microscope (SEM) and a non-contact 3D optical profiler. In particular, the points where the cracks began and the direction in which the cracks propagated along the first 150 mu m were analysed. In general, the initiation point was close to the maximum principal stress point, and the crack direction was close to the maximum principal stress direction. The endurance limit predictions were close to the experimental results.

The presence of non-propagating cracks at notches subjected to cyclic loads around the fatigue limit is well known. The basic reason for their formation is the existence of a stress gradient created by the notch, which can initiate a crack but not its propagation through the solid. In this paper, the application of the Navarro and de los Rios microstructural model (NR model) for the length prediction of non-propagating cracks is presented. A simplified version of the NR model has been used, that basically requires the elastic gradient in front of the notch, which can be easily achieved using finite element analysis. The model correctly predicts the difference in length of non-propagating cracks between sharp and blunt notches and between small, medium and large notches. Finally, the non-propagating crack lengths taken from the literature have been analysed, and the predictions provided by the model are relatively close.

An extensive experimental program was conducted on AISI 4140 steel under cyclic proportional and nonproportional biaxial strain histories. The application of a plasticity model for cyclically stable material behaviour based on the idea of distance in stress space is described. A detailed explanation is provided of the methodology to derive from the experimental data the metric coefficients needed for calculating distances and the hardening modulus function required in the flow equations. The model gives accurate results for the cyclic stress-strain curves obtained in proportional strain tests. It also calculates correctly the stabilized stress values in 90 out-of-phase experiments. For more complicated non-proportional cyclic strain paths, the stresses calculated with the model reproduce strikingly well the qualitative evolution of the experimental response. The quantitative agreement is also good, but obviously not as good as for the simpler strain histories. (C) 2015 Elsevier Ltd. All rights reserved.

Fatigue failures generally initiate at notches or discontinuities. Many methods have been proposed to predict fatigue limits at notches. Navarro and De los Rios developed a method based on a continuous distribution of dislocations to study the growth of short fatigue cracks under zero mean stress conditions. The crack growth rate decreases as the crack approaches a grain boundary and accelerates once it has spread into the neighboring grain. The fatigue limit is defined as the minimum stress that allows the crack to overcome the successive grain boundaries. This Model has been applied to predict the fatigue limit for some notch geometries. In this paper, an approximation of the model to facilitate its application to potential users from the industry is proposed. This approximate model requires the stress gradient, based on a linear elastic analysis, ahead of the notch, due to the remote loading. The stress gradient can be calculated with the finite element analysis (FEA), Which means that the notch geometry is not a limitation. This approximation has been applied to circular holes and V-notches subjected to Mode I loading and its error which respect to the exact model is below 12%. These results are promising and encourage the use of this simplification of the model to predict fatigue limits for any notched geometry. (C) 2016 Elsevier Ltd. All rights reserved.

High cycle fatigue tests were conducted for stainless steel AISI 304L. The geometry was a thin walled tube with a passing through hole. The tests were axial, torsional and in-phase axial-torsional, all of them under load control with R = ?1. The S-N curves were constructed following the ASTM E739 standard and the fatigues limits were calculated following the method of maximum likelihood proposed by Bettinelli. The crack direction along the surface was analysed, with especial attention to the crack initiation zones. The notch fatigue limits for different hole diameters were compared with the predictions done with a microstructural fracture mechanics model.

High cycle fatigue tests have been conducted for stainless steel AISI 304L. The geometry is a thin-walled tube with a passing-through hole. The tests are axial, torsional and in-phase axial-torsional, all of them under load control with R=-1. From the tests, the S-N curves are constructed and the fatigue limits are calculated. The crack surface is analyzed, with especial attention to the first 500μm. The crack has begun close to the point of maximum principal stress at the hole surface and has followed, approximately, the maximum principal stress direction.

This paper shows an implementation of the Microstructural Finite Element Alternating Method (MFEAM) to calculate fatigue strength of engineering components subjected to complex loading conditions. These conditions include combination of primary cyclic loading and residual stress fields or localised stress distributions due to the contact of two solids. The alternating method uses the finite element method (FEM) to solve the boundary value problem of the un-cracked body, allowing treatment of arbitrary shaped components, in conjunction with a short crack model to account for the interaction of the crack with the microstructural barriers, implemented within the distributed dislocation technique (DDT) to assess the crack problem in an infinite medium. An iterative scheme between the FEM and the DDT solutions is proposed in order to predict the required applied load to propagate the crack in the finite size body. Comparisons of results with reported data in the literature show that the MFEAM can be used effectively to analyse finite size components and that it is capable of capturing the effect of localised stress concentration features on cyclic behaviour.

This paper describes the implementation of an alternating technique that uses a short crack growth model in combination with the Finite Element Method (FEM) to calculate fatigue limits. Components of any size and shape can, in principle, be analyzed, but the technique is specially suitable for "small" notched components, i.e., components that are obviously larger than the crack itself but not so large as to allow the adoption or use of infinite-medium solutions and where the "back" surfaces or boundaries of the component (other than the notch itself) may influence the propagation of the fatigue crack. This work represents a first application of the technique and is limited to plane problems where fatigue cracks, for reasons of symmetry, for example, grow in mode I alone. The tool is validated by applying it to several problems of specimens with notches of different forms and sizes. Comparisons with experimental results and with prediction obtained by other methods ale presented. (C) 2015 Elsevier Ltd. All rights reserved.