A numerical approach to fatigue assessment of spot weld joints

This paper deals with the fatigue strength of spot welds investigated by means of an implicit gradient approach. The material is assumed linear elastic and an effective stress for the fatigue life estimation is considered as a transformation of the maximum principal stress field, which is defined by an inhomogeneous Helmholtz equation. The effective stress is calculated by following the same procedure and by using the same characteristic length of the material, previously considered for the fatigue assessments of thick‐walled arc welded joints. About 450 experimental data under constant fatigue loading, mainly lap‐shear joints, peeling joints, coach‐peel joints and shear‐bending joints, were analyzed. The experimental data relative to these spot‐welded joints, in terms of effective stress, fall into the previous scatter band obtained for transverse fillet welded joints by supplying a possible comprehensive approach to fatigue strength assessment of welded joints.     

Local and structural multiaxial stress states in weldedjoints under fatigue loading

A cylindrical stiffener on a plate and a tube through a hollowed plate, both circularly welded, were tested under uniaxial fatigue loading. Their fatigue cracking behaviour was seen to be really complex due to the fact that crack initiation sites changed their position as the number of cycles to failure increased. To investigate this anomalous behaviour, an accurate numerical investigation was carried out to study the distribution of both local and structural linear elastic stresses along the weld toe circumferences. The numerical results proved that the weld beads were subjected to complex stress states, even though the applied nominal load was uniaxial. By the light of this evidence, the fatigue behaviour of the investigated welded joints was then re-interpreted from a multiaxial fatigue point of view by applying the Modified Wöhler Curve Method in terms of hot-spot stresses. The proposed approach was seen to be successful allowing us to estimate both crack initiation sites and fatigue lifetime with a high precision level. This fact is very interesting because it strongly supports the idea that our method can be used to assess real welded components subjected to multiaxial fatigue loading by simply post-processing linear-elastic finite-element results.     

An implicit gradient application to fatigue of sharp notches and weldments

This paper addresses the problem of stress singularities at the tip of sharp V-notches by means of a non-local implicit gradient approach. A non-local equivalent stress is defined as a weighted average of a local stress scalar quantity computed on the assumption of linear elastic material behaviour. In the case of a crack, we propose an analytical solution for the non-local equivalent stress at the crack tip when the local equivalent stress assumes the analytical form proposed by Irwin. For open notches, several numerical procedures are possible.For welded joints, we assume that the material obeys a linear elastic constitutive law. In this case, the non-local equivalent stress obtained from the implicit gradient approach is assumed as the effective stress for assessments of joint fatigue. Using the principal stress as local equivalent stress and a notch tip or weld toe radius equal to zero, we analyse many series of arc welded joints made of steel and subjected to either tensile or bending loading, and we propose a unifying fatigue scatter band. If the welded joints are subjected only to mode I loading, an analytical relationship between the relevant Notch Stress Intensity Factors (NSIF) of mode I and the effective stress is established; otherwise, the effective stress is evaluated by means of a simplified numerical analysis. For complex welded structures, however, a completely numerical solution is proposed; when different crack initiation sites are present (i.e. either weld toes or roots), the proposed approach correctly estimates the actual critical point.     

The Modified Wöhler Curve Method calibrated by using standard fatigue curves and applied in conjunction with the Theory of Critical Distances to estimate fatigue lifetime of aluminium weldments

This paper is concerned with the application of a novel engineering method we have recently devised to estimate fatigue lifetime of aluminium welded joints subjected to constant-amplitude uniaxial and multiaxial fatigue loading. The assessment technique employed in the present study is based on the use of the so-called Modified Wöhler Curve Method (MWCM), a conventional critical plane approach, applied in conjunction with the theory of critical distances (TCD). In more detail, the MWCM was initially calibrated by using two standard curves: the first one, stated by Eurocode 9, suitable for assessing ground butt welds subjected to uniaxial loading, whereas the second one, suggested by the International Institute of Welding (IIW), suitable for estimating fatigue strength of aluminium welded details loaded in torsion. Subsequently, a unifying critical distance value to be performed to assess aluminium welded joints was calculated by taking full advantage of the master curve supplied by the notch-stress intensity factor (N-SIF) approach and obtained by summarising the uniaxial fatigue strength of cruciform aluminium welded details characterised by different absolute dimensions. Finally, the accuracy and reliability of the devised method was systematically checked by means of several experimental results taken from the literature and generated by testing a variety of welded geometries subjected to uniaxial as well as to multiaxial fatigue loading. Such an extensive validation exercise allowed us to prove that our approach is successful in estimating fatigue damage in aluminium welded details, resulting in predictions mainly falling within the two reference scatter bands adopted to calibrate the method itself. Such a high accuracy level is very promising, especially in light of the fact that our engineering approach can be applied to assess real aluminium welded components by directly post-processing simple linear-elastic finite element (FE) models.     

Modified Wöhler Curve Method and multiaxial fatigue assessment of thin welded joints

The present paper is concerned with the use of the Modified Wöhler Curve Method to estimate fatigue lifetime of thin welded joints of both steel and aluminium subjected to in-phase and out-of-phase multiaxial fatigue loading. The Modified Wöhler Curve Method postulates that, in welded connections subjected to in-service complex time-variable loading, fatigue damage reaches its maximum value on that material plane experiencing the maximum range of the shear stress amplitude, such a stress quantity being calculated according to the Maximum Variance concept. The most important peculiarity of the above multiaxial fatigue criterion is that it can be applied by performing the stress analysis in terms of both nominal and local quantities, where in the latter case the relevant stress state at the assumed critical locations can be estimated according to either the reference radius concept or the Theory of Critical Distances. The accuracy and reliability of our multiaxial fatigue criterion was systematically checked through several experimental results taken from the literature and generated by testing, under in-phase and out-of-phase biaxial loading, welded joints of both steel and aluminium having thickness of the main tube lower than 5 mm. Such a systematic validation exercise allowed us to prove that the Modified Wöhler Curve Method is a powerful tool suitable for performing the fatigue assessment of thin welded joints, this holding true independently of the strategy adopted to perform the stress analysis. Finally, a microstructural motivation of the length scales included in the Theory of Critical Distances can be established by linking this technique to gradient mechanics, as we will argue.     

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.     

A structural stress‐based critical plane method for multiaxial fatigue life estimation in welded joints

This paper aims at proposing a new fatigue life estimation model that is preferably adapted to welded joints subjected to multiaxial loading. First, a mesh‐size insensitive structural stress is defined that enables to characterize the stress concentration effect appropriately. Second, the multiaxial stress state and loading path influence are taken into account in the lifetime prediction model by adopting a suitable critical plane method, originally proposed by Carpinteri and co‐authors. Experimental verification is conducted for a given welded joint geometry under different loading conditions, including uniaxial, torsional and multiaxial loads. The reliability and effectiveness of the new method are validated through substantive fatigue testing data.     

An implicit gradient application to fatigue of complex structures

This paper presents a procedure to evaluate the stress gradient effect on the fatigue strength of steel welded joints and notched components. An effective stress is calculated by solving a second-order differential equation over all the component (the implicit gradient approach) independently of its geometric shape. The solution is obtained by assuming the isotropic linear elastic constitutive law for the material and the maximum principal stress as equivalent stress. The fatigue behaviour of geometrically complex steel welded joints is analysed and compared with previous fatigue scatter bands obtained for two-dimensional joints. In complex details, the actual critical point is derived from the analysis and is not assumed a priori. Implicit gradient analysis is also used to investigate high-cycle fatigue behaviour in the case of notches.In addition, it is shown that critical distance approaches can be obtained from the non-local theory by proper choice of the weight function.     

Multiaxial fatigue life estimation in welded joints using the critical plane approach

Many engineering structures experience multiaxial fatigue states of stress–strain in the vicinity of welded joints. Fatigue assessment of welded joints under proportional (in-phase) cyclic loading can be performed by using conventional hypotheses (e.g., see the von Mises criterion or the Tresca criterion) on the basis of local approaches. On the contrary, the fatigue life predictions of welded joints under non-proportional (out-of-phase) cyclic loading are generally poor if these conventional hypotheses are used. In the present paper, the critical plane-based multiaxial fatigue criterion proposed by Carpinteri and Spagnoli for smooth and notched structural components is extended to the fatigue assessment of welded joints under in- and out-of-phase loadings. The applicability of this criterion, expressed in terms of nominal stresses, to the fatigue life prediction of welded specimens is investigated by using experimental data available in the literature.     

Four stress analysis strategies to use the Modified Wöhler Curve Method to perform the fatigue assessment of weldments subjected to constant and variable amplitude multiaxial fatigue loading

The present paper investigates the different ways of using the Modified Wöhler Curve Method (MWCM) to perform the fatigue assessment of steel and aluminium welded joints subjected to in-service variable amplitude (VA) multiaxial load histories. Thanks to its specific features, the above critical plane approach can efficiently be applied in terms of both nominal, hot-spot, and local quantities, that is, by using any of the stress analysis strategies suggested by the Design Recommendations of the International Institute of Welding (IIW). The MWCM can efficiently be used also along with the so-called Theory of Critical Distances applied in the form of the Point Method (PM). The accuracy of the different formalisations of the MWCM investigated in the present paper was systematically checked against a large number of experimental results taken from the literature and generated by testing, under VA biaxial nominal loading, welded samples having different geometries. Such a systematic validation exercise allowed us to prove that our multiaxial fatigue criterion is successful in designing welded joints against VA multiaxial fatigue, this holding true independently from both definition adopted to calculate the necessary stress quantities and complexity of the assessed load history.     

A novel engineering method based on the critical plane concept to estimate the lifetime of weldments subjected to variable amplitude multiaxial fatigue loading

This paper summarizes an attempt at proposing a new engineering method suitable for estimating the fatigue lifetime of steel‐ and aluminium‐welded connections subjected to variable amplitude multiaxial fatigue loading. In particular, the proposed approach is based on the use of the so‐called Modified Wöhler Curve Method (MWCM), i.e. a bi‐parametrical critical plane approach, whose accuracy has been checked so far solely in addressing the constant amplitude multiaxial fatigue problem. In order to extend the use of our criterion to variable amplitude situations, the critical plane is suggested here as being determined by taking full advantage of the maximum variance concept, that is, such a plane is assumed to be the one containing the direction along which the variance of the resolved shear stress reaches its maximum value. The main advantage of such a strategy is that the cycle counting can directly be performed by considering the shear stress resolved along the maximum variance direction: by so doing, the problem is greatly simplified, allowing those well‐established cycle counting methods specifically devised to address the uniaxial variable amplitude problem to be extended to those situations involving multiaxial fatigue loading. The validity of the proposed methodology was checked by using two different datasets taken from the literature and generated by testing both steel and aluminium tube‐to‐plate welded connections subjected to in‐phase and 90° out‐of‐phase variable amplitude bending and torsion. This new fatigue life assessment technique was seen to be highly accurate allowing the estimates to fall within the calibration scatter bands not only when the constants in the governing equations were calculated by using the experimental uniaxial and torsional fully reversed fatigue curves, but also when they were determined by using the reference curves supplied, for the investigated geometry, by the available standard codes. These results seem to strongly support the idea that, thanks to its peculiar features, our method can be considered as an effective engineering approach capable of performing multiaxial fatigue assessment under variable amplitude loading which fully complies with the recommendations of the available standard codes.     

Fatigue assessment of metallic components under uniaxial and multiaxial variable amplitude loading

In the present paper, the fatigue lifetime of metallic structural components subjected to variable amplitude loading is evaluated by applying 2 different multiaxial high‐cycle fatigue criteria. Such criteria, proposed by some of the present authors, are based on the critical plane approach and aim at reducing a given multiaxial stress state to an equivalent uniaxial stress condition. In particular, the procedure employed by both criteria consists of the following 3 steps: (1) definition of the critical plane; (2) counting of loading cycles; and (3) estimation of fatigue damage. Finally, the previous criteria are validated by comparing the theoretical results with experimental data related to smooth metallic specimens subjected to uniaxial and multiaxial variable amplitude loading.     

The multiaxial weld root fatigue of butt welded joints subjected to uniaxial loading

In this study, the fatigue strength of inclined butt welds subjected to a proportional multiaxial stress state generated by uniaxial loading is studied in nominal and local stress concepts. The local methodologies studied included principal stress hypothesis, von Mises stress hypothesis and modified Wöhler curve method. Nominal methodologies included modified Gough–Pollard interaction equation, the design equation in Eurocode3 and the interaction equation in DNV standard. Results are evaluated along with data published in relevant literature. It is observed that both local and nominal stress assessment methods are able to estimate multiaxial fatigue strength. No obvious difference in fatigue strength is observed in the nominal stress concept, but the notch stress concept is able to capture a decrease in fatigue strength in shear‐dominated joints. It is concluded that modified Wöhler curve method is a suitable tool for the evaluation of fatigue strength in joints dominated by both normal and shear stresses.     

On the use of nominal stresses to predict the fatigue strength of welded joints under biaxial cyclic loading

In this paper, the modified Wöhler curve method proposed by Susmel and Lazzarin is employed to predict the fatigue life of welded connections subjected to biaxial cyclic loading. This criterion is reformulated here in order not to take into account the mean stress effect, as suggested by several design codes (at least when welded connections are not completely stress relieved). The accuracy of the proposed method in fatigue lifetime estimation was evaluated by using a number of data sets taken from the literature. The modified Wöhler curve method was applied in terms of nominal stresses and was calibrated using the uniaxial and torsional fatigue curve determined by reanalysing the experimental data, as well as using the standard fatigue curves of the Eurocode 3. The proposed approach was seen to be successful, giving multiaxial fatigue life predictions located within the widest scatter band related either to uniaxial or to torsional data, independently of both out‐of‐phase angle and load ratio value. Finally, the accuracy of the modified Wöhler curve method was compared to the one obtained by applying the procedure suggested by the Eurocode 3: the proposed criterion is demonstrated to be much more accurate and reliable than the standard one.     

Fatigue behaviour of tubular AlMgSi welded specimens subjected to bending–torsion loading

This paper is concerned with an experimental and numerical study of the fatigue behaviour of tubular AlMgSi welded specimens subjected to biaxial loading. In‐phase torsion–bending fatigue tests under constant amplitude loading were performed in a standard servo‐hydraulic machine with a suitable gripping system. Some tests in pure rotating bending with and without steady torsion were also performed. The influence of stress ratio R and bending–torsion stress ratio were analysed. Correlation of the fatigue lives was done using the distortion energy hypothesis (DEH), based on the local stresses and strains. The applicability of the local strain approach method to the prediction of the fatigue life of the welded tubular specimens was also investigated. Static torsion has only a slight detrimental influence on fatigue strength. The DEH (von Mises criterion) based on local stresses in the weld toes was shown to satisfactorily correlate fatigue lives for in‐phase multiaxial stress–strain states. The stress–strain field intensity predictions were shown to have less scatter and are in better agreement with the experimental results than the equivalent strain energy density approach.     

A NOTCH INTENSITY FACTOR APPROACH TO THE STRESS ANALYSIS OF WELDS

In the context of linear elastic stress gradients that are present in welded joints, a stress field approach based on notch stress intensity factors is presented with the aim of describing stress distributions in the neighbourhood of weld toes, since fatigue strength is dependent on such distributions. This paper summarizes the analytical fundamentals and gives an appropriate definition of the parameters for stress components under opening and sliding modes. Then, by comparing the expected results with those obtained by numerical analysis, the contributions of the symmetric and skew-symmetric loading modes are quantified for different geometries, and summarized into concise expressions which also take into account the influence of the main geometrical parameters of the welded joint. The range of validity and the application limits of this field approach in the presence of weld toe radii are discussed. Finally, a synthesis of experimental fatigue strength data based on the new field parameters is reported.     

The peak stress method applied to fatigue assessments of steel and aluminium fillet-welded joints subjected to mode I loading

The aim of this work is to present an engineering method based on linear elastic finite element (FE) analyses oriented to fatigue strength assessments of fillet‐welded joints made of steel or aluminium alloys and subjected to mode I loading in the weld toe region where fatigue cracks nucleate. The proposed approach combines the robustness of the notch stress intensity factor approach with the simplicity of the so‐called ‘peak stress method’. Fatigue strength assessments are performed on the basis of (i) a well‐defined elastic peak stress evaluated by FE analyses at the crack initiation point (design stress) and (ii) a unified scatter band (design fatigue curve) dependent on the class of material, i.e. structural steel or aluminium alloys. The elastic peak stress is calculated by using rather coarse meshes with a fixed FE size. A simple rule to calculate the elastic peak stress is also provided if a FE size different from that used in the present work is adopted. The method can be applied to joints having complex geometry by adopting a two‐step analysis procedure that involves standard finite element (FE) models like those usually adopted in an industrial context. The proposed approach is validated against a number of fatigue data published in the literature.     

Fatigue strength improvement of longitudinal fillet welded out-of-plane gusset joints using air blast cleaning treatment

Blast cleaning treatments are used widely in newly built steel structures to clean forged surfaces and increase the adhesive properties of subsequent coatings. On the other hand, the beneficial effects of a blast cleaning treatment, which are similar to shot peening, on the fatigue strength of welded steel structures are not considered in the fatigue design procedure. In this study, fatigue tests were carried out on as-welded and blast-treated longitudinal fillet welded out-of-plane gusset joints subjected to three different cyclic loading conditions: uniaxial tension, out-of-plane bending and in-plane bending stress cycles. The effect of the blast cleaning treatment on the fatigue strength of the gusset joints was studied. The fatigue tests showed that the blast cleaning treatment increased the fatigue strength of the gusset welded joints, particularly at the lower stress range. A 19% increase in fatigue strength at 2 million cycles and 66% increase in fatigue limit could be realized using the blast cleaning treatment.     

Multiaxial fatigue life assessment of welded structures

Welded structures, such as welded pressure vessel components subjected to multiaxial cyclic loading, are particularly susceptible to fatigue damage. In this paper, a new path-length-based effective stress range is proposed to assess the fatigue life of weld joints under multiaxial fatigue loading. The path-length measure, a function of both normal and shear components on a critical crack plane, has a solid root in classic fracture mechanics and its application is validated by correlating nominal fatigue data including pure-bending, pure-torsion, in-phase, and out-of-phase loading. Path-Dependent Maximum Range (PDMR), a unique general-purpose fatigue life assessment package for multiaxial variable-amplitude loading, is introduced in this paper. Finally, the application of PDMR to multiaxial fatigue life assessment of complex loading cases is also discussed.     

EFFECT OF AN ELASTIC-PLASTIC SHOCK WAVE PART A: ON THE FATIGUE STRENGTH OF WELDED JOINTS

Fatigue data for welded joints subjected to an explosion treatment (ET) were obtained using rotary bending fatigue specimens. The fatigue fracture surfaces were observed by SEM and the dislocation morphologies by TEM. Mechanical properties have been quantitively studied by considering elastic and plastic shock wave characteristics. The test results indicate that the fatigue strength of welded joints subjected to ET is apparently improved due to the action of elastic or plastic stress waves while the ductility of the welded joints, i.e., reduction in area, is greatly increased.