Luca Susmel

Fatigue design in the presence of stress concentrations

This paper reports a comparative study of some recent methods developed for the estimation of high-cycle fatigue behaviour of components containing stress concentrations. It begins by reviewing some existing methods for the prediction of fatigue limits: the stress-life method, linear elastic fracture mechanics, the Kitagawa-Takahashi and Atzori-Lazzarin approaches and the method of Smith and Miller. Two new methods are described which have been developed during the last few years: the crack modelling method (CMM) and the critical distance method (CDM). These methods were tested by comparing their predictions with experimental data using a large database of 88 different notch geometries and materials. Notches were divided into three types: blunt, sharp and short. The CDM was found to be very successful for all types of notch, giving predictions within 20 per cent of experimental values in the great majority of cases. The CMM encountered difficulties with short notches; correction factors were developed to overcome this problem. Both methods can be used very easily in conjunction with finite element analysis, making them more useful than previous methods for the prediction of high-cycle fatigue in engineering components.

An Elasto-Plastic Reformulation of the Theory of Critical Distances to Estimate Lifetime of Notched Components Failing in the Low/Medium-Cycle Fatigue Regime

This paper is concerned with a novel elasto-plastic reformulation of the Theory of Critical Distances (TCD) specifically devised to estimate lifetime of notched metallic materials (ferrous and nonferrous) failing in the lowlmedium-cycle fatigue regime. We used the classic Manson-Coffin and Smith-Topper-Watvon approaches, but applied in conjunction with the TCD. We assumed that the materials critical distance is a constant whose value does not depend on either the sharpness of the notch or on the number of cycles to failure. The accuracy and reliability of the proposed approach was checked by using a number of experimental results generated by testing cylindrical specimens made of En3B, which is a commercial low-carbon steel, and A16082, which is a conventional aluminum alloy, containing different geometrical features and tested at applied load ratios of R = -1 and R =0. The resulting predictions of fatigue life were highly accurate, giving estimates falling within an error factor (in lifetime) of about 2. This result is undoubtedly encouraging, especially in light of the fact that the pieces of experimental information needed to calibrate our method can easily be generated by using standard testing equipment, and the necessary stresslstrain fields acting on the fatigue process zone can be determined by directly postprocessing elasto-plastic finite element results.

Fatigue behaviour of AA356-T6 cast aluminium alloy weakened by cracks and notches

Abstract In this paper the static and fatigue behaviour of AA356-T6 cast alloy is analysed in order to provide engineers with some practical rules for a preliminary assessment of this material in an early stage of the design process. The study is divided into two different parts: in the first part a systematic reanalysis of some data taken from literature highlighted the influence of the main metallurgical parameters on the static and fatigue properties of the considered material, whereas in the second part an experimental investigation was performed in order to verify the applicability of the Atzori–Lazzarin diagram to the AA356-T6 cast aluminium alloy.

Multiaxial fatigue life estimations for 6082-T6 cylindrical specimens under in-phase and out-of-phase biaxial loadings

Fully reversed bending/torsion fatigue tests were conducted on 6082-T6 solid cylindrical specimens under force control. Specimens were subjected to pure bending, pure torsion, in-phase and out-of-phase bending/torsion loadings and the investigated fatigue lives ranged between 104 and 2.106 cycles to failure. The actual strains were measured by means of strain gauges positioned in correspondence of critical points. Experimental strain measurements highlighted that all the tests were conduced in pure elastic stress conditions. The material fatigue behaviour was studied by analysing the cracks pattern due to the considered biaxial loadings. All the tests showed that crack initiation was always MODE II dominated (that is, it occurred on the plain of maximum shear stress amplitude), whereas the crack propagation was MODE I governed. Just in the presence of pure torsional loadings cracks grew under MODE II loadings. A good correlation with measured fatigue lives was obtained by applying the Susmel and Lazzarins criterion valid for homogeneous and isotropic materials, despite the slight degree of anisotropy showed by the material.

Estimation of the fatigue strength of light alloy welds by an equivalent notch stress analysis

Abstract In this work the well known local approach to predict the fatigue strength of sharply notched components, based on the analytic expressions of the local stress field as proposed in literature, is applied to welded joints in aluminium alloys in a simplified form oriented to practical applications. A particular value of the general expression of the local stress field parameter is taken into account, which the fatigue strength depends on. Then a simple model is proposed by the authors in order to estimate such a parameter, based on the calculation of a geometric (or structural) contribution to the local stress field, depending on the overall joint geometry, and a local contribution evaluated by considering a specimen with lateral V-notches characterised by the same weld toe profile and a depth proportional to the weld throat thickness. Doing so, the estimation of the fatigue strength of a welded joint can be reduced to the estimation of the fatigue strength of the equivalent V-notch subjected to a remote stress equal to the structural stress (that can be regarded as a ‘hot spot’ stress). Finally a simple fatigue strength diagram, in the form recently proposed by Atzori and Lazzarin and calibrated on experimental fatigue test results, is proposed, so that one can estimate the fatigue strength of a welded joint, in terms of structural stress at a given number of cycles, as a function of the equivalent V-notch depth. By considering this diagram, the scale effect and the effectiveness of the methods to improve the fatigue strength by smoothing the weld toe radius are also taken into account.

Critical plane approach to multiaxial variable amplitude fatigue loading

A new critical plane approach based on the modified Manson-Coffin curve method (MMCCM) is presented in this paper for predicting fatigue lifetime under variable amplitude (VA) multiaxial fatigue loading. The critical plane is assumed to coincide with that material plane experiencing the maximum variance of the resolved shear strain. Fatigue damage is hypothesized to be a function of both the amplitude of the resolved shear strain and the so-called critical plane stress ratio. The latter quantity depends on the mean value and the variance of the stress perpendicular to the critical plane as well as on the variance of the shear stress resolved along the direction experiencing the maximum variance of the resolved shear strain. Load cycles are counted from the resolved shear strain time history by using the classic rain flow counting method. Palmgren-Miner’s linear damage rule is applied to estimate cumulative fatigue damage. The accuracy and reliability of the proposed approach is checked by using several experimental data taken from the literature. The estimated fatigue lives based on the new approach are seen to be in sound agreement with the experimental results.

Estimating Lifetime of Notched Components Subjected to Variable Amplitude Fatigue Loading According to the Elastoplastic Theory of Critical Distances

The present paper is concerned with the use of the elastoplastic theory of critical distances (TCD) to perform the fatigue assessment of notched components subjected to in-service variable amplitude (VA) fatigue loading. The elastoplastic TCD takes as its starting point the assumption that the detrimental effect of stress/strain concentrators of any kind can efficiently be taken into account by directly postprocessing the entire elastoplastic stress/strain field in the vicinity of the notch apex. Thanks to its specific features, the TCD can be formalized in different ways by simply changing size and geometrical features of the domain used to calculate the required effective stress. The so-called point method (PM) is the simplest form in which this theory can be applied. This formalization of the TCD postulates that the elastoplastic stress/strain state to be used to estimate fatigue damage has to be determined at a given distance from the tip of the notch being assessed. According to the TCDs philosophy, such a distance is treated as a fatigue property. Therefore, given the material, this critical length does not change as either the features of the assessed stress/strain concentrator or the profile of the investigated loading path vary. In the present study, the above design strategy is attempted to be used to estimate lifetime of notched component subjected to VA loading, the required critical distance being determined under constant amplitude (CA) loading. The accuracy and reliability of the devised approach were checked by using a number of experimental results generated by testing, under both concave upward and concave downward spectra, notched samples containing geometrical features having a different sharpness. Such a validation exercise allowed us to prove that the elastoplastic TCD, used in the form of the PM, is highly accurate in estimating fatigue damage also in notched components subjected to in-service VA loading.

Nominal stresses and Modified Wöhler Curve Method to perform the fatigue assessment of uniaxially loaded inclined welds

The present paper summarises an attempt of proposing a simple formula suitable for estimating the fatigue strength of welded connections whose weld beads are inclined with respect to the direction along which the fatigue loading is applied. By explicitly considering the degree of multiaxiality of the nominal stress state damaging the weld toe, such a formula is directly derived from the so-called Modified Wöhler Curve Method (MWCM). The MWCM is a bi-parametrical critical plane approach which postulates that, independently from the complexity of the assessed load history, fatigue strength can accurately be estimated by using the stress components relative to that material plane experiencing the maximum shear stress range. The accuracy and reliability of the proposed design technique were checked against a number of experimental results taken from the literature and generated by testing steel plates with inclined fillet-welded attachments. This validation exercise allowed us to prove that the devised formula can successfully be used in situations of practical interest to design against fatigue welded joints whose welds are inclined with respect to the direction along which the cyclic force is applied.

Eurocode 3’s Standard Curves and Theory of Critical Distances to Estimate Fatigue Lifetime of Steel Weldments

This paper reports on the use of the Modified Wöhler Curve Method (MWCM) applied along with the Theory of Critical Distances (TCD) to estimate fatigue lifetime of steel welded joints subjected to both uniaxial and multiaxial cyclic loading. In a recent work [1] we have proved that the above engineering method is highly accurate when calibrated by using standard fatigue curves characterised by a probability of survival equal to 50%. In order to better check its accuracy and reliability, in the present study our approach is systematically applied to a large amount of experimental data by calibrating it using standard fatigue curves having a probability of survival equal to 97.7%. This exercise allowed us to prove that the in-field application of such an engineering procedure results in estimates which fully comply, from a statistical point of view, with Eurocode 3’s recommendations. This result strongly supports the idea that our approach can safely be employed to perform the fatigue assessment of real mechanical assemblies, with the advantage over other existing methods that fatigue lifetime under any kind of fatigue loading can be estimated by simply post-processing linear-elastic Finite Element Models.

Estimation of fretting fatigue life using a multiaxial stress-based critical distance methodology

This work presents a methodology for life estimation of mechanical couplings subjected to fretting fatigue. In this approach, a stress-based multiaxial fatigue parameter is evaluated at a critical distance below the contact surface. The fatigue parameter is based on an improved formulation of the Modified Wohler Curve Method, in which the shear stress amplitude is measured via the Maximum Rectangular Hull method. To apply the Theory of Critical Distances in the medium-cycle fatigue regime, the critical distance is assumed to depend on the number of cycles to failure. Available fretting fatigue data, conducted on a cylinder-plane contact configuration made of Al alloy 4% Cu, were used to assess the methodology. Most of the life estimates were within an error band given by a factor of 2.