R. Tovo

Fatigue crack initiation and propagation phases near notches in metals with low notch sensitivity

Abstract The paper summarizes the results of experimental work carried out in order to analyse the initiation and propagation of fatigue cracks on plates in a deep drawing steel and in a cast aluminium alloy. The plates were characterized by lateral V and U-shape symmetric notches, with a notch root radius ranging from 0.1 to 10 mm, the notch depth being 10 mm and the plate thickness 2 mm for the steel and 5 mm for the light alloy. In order to estimate the crack initiation life two new parameters are proposed; they are no longer based on the peak values of strain and stress, but on the averaged values of such quantities in the neighbourhood of the notch tip. The dimension of the process-zone is correlated to the intrinsic crack length of the material. The estimates need an elastoplastic approach and a numerical solution. Experimantal data and expected values are compared.

Cycle distribution and fatigue damage under broad-band random loading

Fatigue damage under broad-band loading is analysed by summarizing and reviewing available analytical solutions. Relationships between fatigue damage assessment and counting methods are investigated by establishing when, in frequency domain analysis, analytical solutions of expected damage are connected with a counting procedure assumption and how this is related to the rainflow counting procedure. A new approach is also proposed for rainflow damage evaluation. This approach gives accurate approximations of fatigue damage under both broad- and narrow-band Gaussian loading; it is based on the theoretical investigation of possible combinations of peaks and valleys in Gaussian loading and on numerical fitting on several simulated broad-band loads.

Stress field parameters to predict the fatigue strength of notched components

Abstract The stress field parameters, namely the notch stress intensity factors (N-SIFs) according to a more recent definition, can be used to predict the fatigue behaviour of mechanical components weakened by V-shaped re-entrant corners, where the singularity in the stress distribution makes any failure criterion based on the elastic peak stress no longer applicable. When the notch root radius is small but different from zero, the N-SIF can still be used, since a comprehensive analytical approach is available for open sharp and blunt notches. The fatigue strength reduction factor can be given as a function both of the elastic peak stress (only if it has a finite value) and of the N-SIF (for every notch tip radius value), by assuming that the fatigue strength of notched elements depends on a mean stress value in the critical zone. The welded joints are an example of practical N-SIF use in fatigue strength prediction. In this case not only the fatigue crack initiation life but also the fatigue crack propagation phase are strictly correlated to the N-SIF value for the reason that the residual life is mainly dependent on crack propagation in the zone just governed by N-SIFs.

On the fatigue reliability evaluation of structural components under service loading

The fatigue strength evaluation of structural components under service loading is affected by several uncertainties. Proper statistical tools should be used to manage the large amount of causalities and the lack of knowledge on the actual strength-affecting parameters. This paper deals mainly with the statistical analysis to be performed on experimental load histories in order to evaluate fatigue loading spectra and the problems in extrapolating from measured load history to the whole component life. Then, a methodology for assessing the reliability of structural details under random fatigue loading is analysed. This methodology combines (under a linear cumulative rule assumption) the loading spectra, obtained by the new approach, and the constant-amplitude fatigue strength modelled by means of a conventional log-normal distribution. By so doing it is possible to distinguish many causes of uncertainty and suggest evaluations with proper confidence limits. The theoretical aspects developed are applied to mountain bike stems and they show the presence of a large uncertainty margin in reliability evaluation under service loading when there are no considerable quantities of experimental data available (both in load histories and component fatigue strength).

Relationships between local and structural stress in the evaluation of the weld toe stress distribution

Abstract This paper deals with the problem of determining, by proper stress analyses, the stress fields near arc-welded joint toes and the use of such distributions in fatigue strength predictions. In particular, the relationships between the local stress field and the structural (geometrical) stress field are investigated under the hypothesis that highly stressed zones remain under linear elastic conditions. The local stress distribution is given for different joints in terms of the relevant notch stress intensity factors (NSIFs), having modelled their weld beads like re-entrant sharp corners. The structural stress distribution is, in contrast, the stress field linearly distributed through the thickness of the welded plates (and sometimes on the plate surfaces), beyond the zone affected by local effects due to the beads. The aim of the proposed methodology is to provide an explicit link between NSIF values and structural stress at a well-defined distance from the weld toe. Such a distance is chosen equal to the main plate thickness. The expressions obtained allow a direct comparison with the well-known “hot-spot stress” approach; it is demonstrated that there are circumstances of practical interest in which the usual hot-spot stress (which is the simple linear extrapolation at the weld root of the structural field) is not able to predict accurately the fatigue behaviour of the joints, whereas the combination of structural field and NSIF-based field is more advantageous. The complete methodology can be simplified for rapid calculations involving weldments of different types. Some examples are also reported and discussed.

A damage-based evaluation of probability density distribution for rain-flow ranges from random processes

A new method is proposed for the evaluation of a single Weibull distribution approximating the cycles turning out from the rain-flow counting of a random process. The founding hypothesis is a multi-modal distribution assumption, i.e. the probability density is a linear combination of several Weibull distributions; thus a simplified evaluation of a single distribution is proposed as an approximation of the most damaging part of the counted cycles instead of the most frequent range occurrences.

Elastic stress distributions in finite size plates with edge notches

In fatigue crack growth analysis it is essential to know the stress distributions in the neighbourhood of stress raisers. If such distributions ahead of the uncracked notch are known, stress intensity factors may be obtained via the weight function or other methods. The procedure described in the present paper reconsiders the principal elastic stress expressions already reported by the authors for infinite plates with semi-infinite symmetric V-shaped notches and adapts them to some practical cases, in which the mutual influence of the notches as well as that of the plate finite size play an important role in stress distributions. The aim is therefore to give an approximate close-form solution for the longitudinal stress, valid for the entire ligament length, namely from notch tip to notch tip. Theoretical and numerical stress values are compared on this line, examining plates with semicircular, V and U-shaped notches subjected to remote uniaxial tension.

Fatigue damage assessment of a car body-in-white using a frequency-domain approach

This work presents an application of a frequency-domain methodology developed for the fatigue damage and service life assessment of mechanical components under multiaxial random loadings. The road-induced random loadings in a virtual laboratory bench test (four post test rig) are determined using an integrated Multi-Body/Finite Element (MB/FE) analysis. A method (i.e. the variance method) based on the statistics of the observed multiaxial loadings is used to determine the critical direction. The shear stress resolved in the critical direction is then assumed as the reference loading for the subsequent fatigue analysis. A frequency-domain approach recently proposed in the literature (i.e. the non-Gaussian TB method), capable to include the load non-normality into the fatigue assessment procedure, is used to estimate the loading spectrum. A comparison between the observed and the estimated loading spectrum, extrapolated from shorter to longer time (e.g. the entire vehicle service life), is shown. The presented results show how the proposed methodology could be a very useful tool for the reliable and quick analysis of components under multiaxial random loadings.

Predicting the fatigue strength of small thickness welded joints using the implicit gradient method

This paper discusses the problem of the fatigue behaviour of small thickness welded joints using the implicit gradient method. Welds have been designed using 3D CAD and then subjected to finite element analysis, using the same computational procedure developed in the past for large thickness welded joints. In order to determine the Woehler curves for the various test series described in the literature, reference shall be made to either a monoaxial strength criterion or a multiaxial strength criterion capable of more efficiently evaluating the effect of a complex stress state while maintaining linear elastic behaviour for the material. The fatigue fault initiation zone is automatically evaluated by the computational procedure which indirectly returns the Woehler curve for the particular test. Application of the computational procedure to several test series taken from the literature has been performed for 2 mm thick sheets, predicting that the implicit gradient method may be applied to assess welded joints independently of the dimensions of the main plate and the shape of the weld bead.

Multiaxial fatigue of aluminium friction stir welded joints: preliminary results

The aim of the present research is to check the accuracy of the Modified Wohler Curve Method (MWCM) in estimating the fatigue strength of friction stir (FS) welded tubular joints of Al 6082-T6 subjected to in-phase and out-of-phase multiaxial fatigue loading. The welded samples being investigated were manufactured by equipping an MTS I-STIR process development system with a retracting tool that was specifically designed and optimised for this purpose. These specimens were tested under proportional and non-proportional tension and torsion, the effect of non-zero mean stresses being also investigated. The validation exercise carried out by using the generated experimental results allowed us to prove that the MWCM (applied in terms of nominal stresses) is highly accurate in predicting the fatigue strength of the tested FS welded joints, its usage resulting in estimates falling with the uniaxial and torsional calibration scatter bands.