A notch stress intensity approach applied to fatigue life predictions of welded joints with different local toe geometry

In the Notch Stress Intensity Factor (N‐SIF) approach the weld toe region is modelled as a sharp V‐shaped corner and local stress distributions in planar problems can be expressed in closed form on the basis of the relevant mode I and mode II N‐SIFs. Initially thought of as parameters suitable for quantifying only the crack initiation life, N‐SIFs were shown able to predict also the total fatigue life, at least when a large part of the life is spent as in the propagation of small cracks in the highly stressed region close to the notch tip. While the assumption of a welded toe radius equal to zero seems to be reasonable in many cases of practical interest, it is well known that some welding procedures are able to assure the presence of a mean value of the weld toe radius substantially different from zero. Under such conditions any N‐SIF‐based prediction is expected to underestimate the fatigue life. In order to investigate the degree of conservatism, a total of 128 fillet welded specimens are re‐analysed in the present work by using an energy‐based N‐SIF approach. The local weld toe geometry, characterised by its angle and radius, has been measured with accuracy for the actual test series. The aim of the work is to determine if the N‐SIF‐based model is capable of taking into account the large variability of the toe angle, and to quantify the inaccuracy in the predictions due to the simplification of setting the toe radius equal to zero.     

From a local stress approach to fracture mechanics: a comprehensive evaluation of the fatigue strength of welded joints

This paper investigates the possibility of unifying different criteria concerned with the fatigue strength of welded joints. In particular, it compares estimates based on local stress fields due to geometry (evaluated without any crack-like defect) and residual life predictions in the presence of a crack, according to LEFM. Fatigue strength results already reported in the literature for transverse non-load-carrying fillet welds are used as an experimental database. Nominal stress ranges were largely scattered, due to large variations of joint geometrical parameters. The scatter band greatly reduces as soon as a 0.3-mm virtual crack is introduced at the weld toe, and the behaviour of the joints is given in terms of Δ K _I versus total life fatigue. Such calculations, not different from residual life predictions, are easily performed by using the local stress distributions determined near the weld toes in the absence of crack-like defects. More precisely, the analytical expressions for K _I are based on a simple combination of the notch stress intensity factors K ₁^N and K ₂^N for opening and sliding modes. Then, fatigue strength predictions, as accurate as those based on fracture mechanics, are performed by the local stress analysis in a simpler way.     

Reliability updating of welded joints damaged by fatigue

The paper introduces a probability-based fatigue assessment model for welded joints in steel bridges. The approach is based on a modelization of the fatigue phenomenon issued from the principles of fracture mechanics theory. The safety margin includes the crack growth propagation and allows us to treat fatigue damage in a general manner. Damaging cycles and non-damaging cycles are distinguished. The reliability calculus is performed by a FORM technique. The sensitivity study of the different parameters shows that some variables can be taken as deterministic. Applications are made on a welded joint ‘bottom plate/stiffener’ of a typical steel bridge. The model is then used for taking into account inspection results. A sensitivity analysis of different non-destructive inspection (NDI) methods is carried out for measuring their uncertainty levels. The different types of inspection results (no detection, detection with no measurement, detection with measurement) are analysed and a general methodology for updating reliability levels is given. The results show their ability to be inserted in a maintenance strategy for optimizing the next inspection time, the need to repair or to replace the joint, and, the eventual possibility of no action.     

Interim fatigue design recommendations for fillet welded joints under complex loading

Current fatigue design methods for assessing welded steel structures under complex combined or multiaxial loading are known to be potentially unsafe. This has led to a number of research projects over the past 10 years. Some progress has been made in developing better methods, but they are not yet suitable for general design. This paper presents an interim solution based on a review and analysis of relevant published data; all referring to fatigue failure from a fillet weld toe. These indicate that Eurocode 3/IIW S – N curve FAT80/3 (negative inverse slope of 3) is suitable for combined normal and shear stresses acting in phase, and possibly for out-of-phase (i.e. non-proportional loading) bending and shear if the shear stress is not due to torsion. However, a shallower curve FAT80/5 is necessary for out-of-phase torsion and bending or tension. Both curves are used in conjunction with the nominal maximum principal stress range occurring during the loading cycle.     

Fatigue strength of steel and aluminium welded joints based on generalised stress intensity factors and local strain energy values

Weld bead geometry cannot, by its nature, be precisely defined. Parameters such as bead shape and toe radius vary from joint to joint even in well-controlled manufacturing operations. In the present paper the weld toe region is modelled as a sharp, zero radius, V-shaped notch and the intensity of asymptotic stress distributions obeying Williams’ solution are quantified by means of the Notch Stress Intensity Factors (NSIFs). When the constancy of the angle included between weld flanks and main plates is assured and the angle is large enough to make mode II contribution non-singular, mode I NSIF can be directly used to summarise the fatigue strength of welded joints having very different geometry. By using a large amount of experimental data taken from the literature and related to a V-notch angle of 135°, two NSIF-based bands are reported for steel and aluminium welded joints under a nominal load ratio about equal to zero. A third band is reported for steel welded joints with failures originated from the weld roots, where the lack of penetration zone is treated as a crack-like notch and units for NSIFs are the same as conventional SIF used in LEFM. Afterwards, in order to overcome the problem related to the variability of the V-notch opening angle, the synthesis is made by simply using a scalar quantity, i.e. the mean value of the strain energy averaged in the structural volume surrounding the notch tips. This energy is given in closed form on the basis of the relevant NSIFs for modes I and II and the radius R_C of the averaging zone is carefully identified with reference to conventional arc welding processes. R_C for welded joints made of steel and aluminium considered here is 0.28 mm and 0.12 mm, respectively. Different values of R_C might characterise welded joints obtained from high-power processes, in particular from automated laser beam welding. The local-energy based criterion is applied to steel welded joints under prevailing mode I (with failures both at the weld root and toe) and to aluminium welded joints under mode I and mixed load modes (with mode II contribution prevailing on that ascribable to mode I). Surprising, the mean value of ΔW related to the two groups of welded materials was found practically coincident at 2 million cycles. More than 750 fatigue data have been considered in the analyses reported herein.     

Prediction of fatigue life of metallic structures with welded joints using automatic learning systems

Welded metallic joints are prone to fatigue damage, which may lead to sudden and catastrophic structural failure. In this research, fatigue failures of metallic structures with welded joints are analyzed using an approach based on automatic learning technology. A database of physics-based parameters, including material properties, loading histories, and stresses around potential cracking sites, is constructed based on experimental results and numerical analyses. Various automatic learning tools are used to search for the mathematical formulas and data patterns embedded in the database. The obtained rules and formulas can be used to support design of welded metallic structures. This approach provides a new way to locate fatigue-prone areas, predict fatigue lives, and may lead to designs of more fatigue resistant structures. It complements the classical deterministic and statistical fatigue failure predictions.     

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.     

A method of determining geometric stress for fatigue strength evaluation of steel welded joints

This paper presents a new method for evaluating the geometric or structural stress in welded constructions. The method is based on the computed stress value 1-mm below the surface in the direction corresponding to the expected crack path. The total stress distribution along the crack path direction is considered to be the sum of the geometric stress caused by the structural geometry change and the non-linear local stress produced by the weld itself. Linear elastic fracture mechanics is used to correlate the total stress based crack propagation life and the local stress based crack propagation life to explain the geometric stress evaluated 1-mm below the surface. Validity of the method is further verified by analyzing fatigue test results for several typical welded joints reported in literature. When compared to the surface extrapolation technique for structural hot spot stress evaluation, the proposed method has the additional advantage in that it is able to account for the size and thickness effect observed in welded joints.     

Fatigue assessment of welded structures: practical aspects for stress analysis and fatigue assessment

Analysis of welded structures still remains a challenge for the analyst and in fact cannot be considered as fully solved for practical applications. For many years, a large international aggregation of researchers has developed methods to assess fatigue behaviour of welded structures. Nowadays many suggestions and methods exist to estimate fatigue life of welded structures with respect to nominal, structural, notch stress or fracture mechanics approaches. All of them are still under improvement. The high motivation and many activities of experts in the International Institute of Welding (IIW) group of researchers is a good demonstration of the complexity and need for analysis methods in that field. The purpose of this paper is to provide some discussion on selected methods available. Both authors are giving lectures to transfer methods to industrial applications. It is their experience that a large amount of knowledge has been developed although proper applications require some grading and comments on the use of those methods. This paper should give some comments and recommendations for the practical application of a selection of methods already available. A hierarchical two‐step procedure for the assessment of large welded structures will be described and recommended. Also benchmark results are presented on a sample structure for sake of comparison of a few selected methods. Finally a presentation of results obtained by application of selected methods on real structures in comparison with fatigue lives from experiments will be presented. The methods selected within the paper cover the approaches for modelling, structural analysis and assessment of welded structures using finite element analysis (FEA) and stress based concepts for fatigue life estimation.     

Unique fatigue threshold and growth properties of welded joints in a tensile residual stress field

The fatigue threshold and high growth rate region properties were investigated on several kinds of welded joints. These properties became unique in spite of the variation of steels (ferrite-pearite, martensite, austenite), welding method, heat input and stress ratio. It was revealed that the unique properties occurred from the fully opened fatigue crack due to the tensile residual stresses. Based on these results, the equation of the fatigue crack growth curve for the design and inspection of welded structures was proposed. It is also suggested that the inducement of compressive residual stress at the fatigue critical zone is effective in improving the fatigue properties of welded structures.     

A new damage parameter for fatigue life predictions under local strain analysis

A new damage parameter is proposed for fatigue life prediction using a local stress-strain approach. This parameter has a physical energy basis, and makes it possible to obtain the same accuracy as, and better life assessments than, the well-known Smith et al parameter using significantly less calculation time for load history treatment. Comparisons of life predictions obtained using the proposed parameter with experimental results and other predictions are presented.     

A notch stress intensity approach to assess the multiaxial fatigue strength of welded tube-to-flange joints subjected to combined loadings

Full penetration T butt weld joints between a tube and its flange are considered, subjected to pure bending, pure torsion and a combination of these loading modes. The model treats the weld toe like a sharp V‐notch, in which mode I and mode III stress distributions are combined to give an equivalent notch stress intensity factor (N‐SIF) and assess the high cycle fatigue strength of the welded joints. The N‐SIF‐based approach is then extended to low/medium cycle fatigue, considering fatigue curves for pure bending and pure torsion having the same slope or, alternatively, different slopes. The expression for the equivalent N‐SIF is justified on the basis of the variation of the deviatoric strain energy in a small volume of material surrounding the weld toe. The energy is averaged in a critical volume of radius R_C and given in closed form as a function of the mode I and mode III N‐SIFs. The value of R_C is explicitly referred to high cycle fatigue conditions, the material being modelled as isotropic and linear elastic. R_C is thought of as a material property, independent in principle of the nominal load ratio. To validate the proposal, several experimental data taken from the literature are re‐analysed. Such data were obtained by testing under pure bending, pure torsion and combined bending and torsion, welded joints made of fine‐grained Fe E 460 steel and of age‐hardened AlSi1MgMn aluminium alloy. Under high cycle fatigue conditions the critical radius R_C was found to be close to 0.40 mm for welded joints made of Fe E 460 steel and close to 0.10 mm for those made of AlSi1MgMn alloy. Under low/medium cycle fatigue, the expression for energy has been modified by using directly the experimental slopes of the pure bending and pure torsion fatigue curves.     

Thickness effects on the fatigue strength of welded steel cruciforms

Over 100 fatigue tests were conducted on high strength welded steel (HSLA-80) cruciforms of different thickness. Tests were conducted under both constant and random amplitude axial loads to characterize thickness effects on fatigue strength. Specimens were similar in size, except for the thickness which was varied between four nominal values. Examination of both experimental and analytical results (obtained using linear cumulative damage and Rayleigh approximation) indicates thicker specimens exhibit lower fatigue lives under both constant and random amplitude loadings. These results, when compared with the commonly used ‘fourth root rule' thickness correction formula, indicate the latter to be generally conservative, particularly at low stress levels.     

Combined effect of strength & sheet thickness on fatigue behaviour of resistance spot welded joint

Fatigue performance of spot welded lap shear joint is primarily dependent on weld nugget size, sheet thickness and corresponding joint stiffness. Two automotive steel sheets having higher strength lower thickness and lower strength higher thickness are resistance spot welded with established optimum welding condition. The tensile‐shear strength and fatigue strength of lap shear joint of the two automotive steel sheets are determined and compared. Experimental fatigue life of spot welded lap shear joint of each steel are compared with predicted fatigue lives using different stress intensity factor solutions for kinked crack and spot weld available in literature. Micrographs of fatigue fractured surfaces are examined to understand fracture micro‐mechanisms.     

Probabilistic fatigue crack growth analysis of spot‐welded joints

This paper presents a probabilistic fatigue crack growth life prediction methodology for spot‐welded joints under variable amplitude loading history. The loading is multi‐axial and is obtained from transient response analysis of a vehicle model using finite‐element analysis. A three‐dimensional (3D) finite element model of a simplified joint with four spot welds is developed, and the static stress analysis of this joint is performed. Then the fatigue crack inside the base material sheet is modelled as a surface crack. Probabilistic crack growth model is combined with the stress analysis result to develop a probabilistic fatigue crack growth life prediction methodology for spot welds. This new method is implemented with MSC/NASTRAN and MSC/FATIGUE and is useful for the reliability assessment of spot‐welded joints against fatigue crack growth.     

Probabilistic prediction of high cycle fatigue reliability of high strength steel butt‐welded joints

The aim of this paper is to develop a probabilistic approach of high cycle fatigue (HCF) behaviour prediction of welded joints taking into account the surface modifications induced by welding and the post‐welding shot peening treatment. In this work, the HCF Crossland criterion has been used and adopted to the case of welded and shot peened welded parts, by taking into account the surface modifications which are classified as follows: (i) the compressive residual stresses, (ii) the surface work‐hardening, (iii) the geometrical irregularities and (iv) the superficial defects. The random effects due to the dispersions of: (i) the HCF Crossland criterion material characteristics (ii) the applied loading and (iii) the surface modifications parameters are introduced in the proposed model. The HCF reliability has been computed by using the ‘strength load’ method with Monte Carlo simulation. The reliability computation results lead to obtain interesting and useful iso‐probabilistic Crossland diagrams (PCD) for different welding and shot peening surface conditions. To validate the proposed method, the approach has been applied to a butt‐welded joint made of S550MC high strength steel (HSS). Four types of specimens are investigated: (i) base metal (BM), (ii) machined and grooved (MG) condition, (iii) As welded (AW) condition and (iv) as welded and shot peened (AWSP) condition. The comparison between the computed reliabilities and the experimental investigations reveals good agreement leading to validate the proposed approach. The effects of the different welded and post‐weld shot peened specimen's surface properties are analysed and discussed using the design of experiments (DoE) techniques.     

Discussion on local approaches for the fatigue design of welded joints

Design of welded structures under fatigue is governed by two conflicting requirements: to minimize weight without compromising structure safety. Any theoretical and/or numerical approaches are necessarily based on some simplifying assumptions which, because of the complexity of fatigue phenomena, could miss some aspects involved in the real structure behaviour. On the other side, experimental approaches provide direct information on structure behaviour. In view of this, the paper will underline the importance of experimental observations and practical procedures to evaluate the stress/strain magnitude that could lead some components to unsafe working conditions. Experimental approaches may greatly support designers in all industrial applications where fast and reliable responses are strongly needed.