Fatigue failure transition analysis in load‐carrying cruciform welded joints based on strain energy density approach

This paper details a study of the application of notch stress intensity theory to the fatigue failure mode analysis of the transition in load‐carrying cruciform welded joints. The weldment fatigue crack initiation point is difficult to predict precisely because it usually occurs in the vicinity of the weld toe or weld root. To investigate the relationship between fatigue failure location and the geometry of the weldments, we analysed the weld toe and root asymptotic notch stress fields were analysed using the notch stress intensity factors on the basis of the Williams' solution in Linear Elastic Fracture Mechanics (LEFM). Numerous configurations of cruciform joints of various plate thicknesses, transverse plate thickness, weld sizes and incomplete penetration size were used to investigate the location of the fatigue failure. The strain energy density (SED) surrounding the notch tip was introduced to unify the scalar quantity and preclude the inconsistency of the dimensionality of the notch stress intensity factors for various notch opening angles. The results of the investigation showed that the SED approach can be used to determine the transition zone for a variety of joint geometries. The validity of the SED criteria was verified by comparing the experimental results of this study with the complied results for load‐carrying cruciform welded joints reported in literature.     

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 of steel rollers with failure occurring at the weld root based on the local strain energy values: modelling and fatigue assessment

Weldments geometry with failures occurring at the weld toe or at the weld root cannot, by its nature, be precisely defined. Parameters such as bead shape and toe or root radius vary from joint to joint even in well-controlled manufacturing operations. The worst case configuration can be achieved by modelling as a sharp, zero radius, notch both the toe and the weld root. The intensity of asymptotic stress distributions obeying Williams’ solution is quantified by means of the Notch Stress Intensity Factors (NSIFs). For steel welded joints with failures originated from the weld roots, where the lack of penetration zone is treated as a crack-like notch, units for NSIFs are the same as conventional SIFs used in LEFM. The different dimensionality of NSIFs for different notch opening angles does not allow a direct comparison of failures occurring at the weld toe or at the weld root. In order to overcome the problem related to the variability of the V-notch opening angle, a simple scalar quantity, i.e. the value of the strain energy density (SED) averaged in the structural volume surrounding the notch tip, has been introduced. This energy is given in closed form on the basis of the relevant NSIFs for modes I, II and III. The radius R_c of the averaging zone is carefully identified with reference to conventional arc welding processes being equal to 0.28 mm for welded joints made of steel.The local-energy based criterion is applied here to steel welded rollers produced by Rulmeca and subjected to prevailing mode I (with failures at the weld root). The aim of the paper is firstly to describe the employed methodology for the fatigue assessment and secondly to show the first synthesis of fatigue data by means of local SED for a specific geometry.     

State‐of‐the‐art review on the local strain energy density concept and its relation to the J‐integral and peak stress method

The local average strain energy density (SED) approach has been proposed and elaborated by Lazzarin for strength assessments in respect of brittle fracture and high‐cycle fatigue. Pointed and rounded (blunt) V‐notches subjected to tensile loading (mode 1) are primarily considered. The method is systematically extended to multiaxial conditions (mode 3, mixed modes 1 and 2). The application to brittle fracture is documented for PMMA flat bar specimens with pointed or rounded V‐notches inclusive of U‐notches. Results for other brittle materials (ceramics, PVC, duraluminum and graphite) are also recorded. The application to high‐cycle fatigue comprises fillet‐welded joints, weld‐like shaped and V‐notched base material specimens as well as round bar specimens with a V‐notch. The relation of the local SED concept to comparable other concepts is investigated, among them the Kitagawa, Taylor and Atzori–Lazzarin diagrams, the Neuber concept of fictitious notch rounding applied to welded joints and also the J‐integral approach. Alternative details of the local SED concept such as a semicircular control volume, microrounded notches and slit‐parallel loading are also mentioned. Coarse FE meshes at pointed or rounded notch tips are proven to be acceptable for accurate local SED evaluations. The peak stress method proposed by Meneghetti, which is based on a notch stress intensity factor consideration combined with a globally even coarse FE mesh and is used for the assessment of the fatigue strength of welded joints, is also presented.     

Stress intensity factors for three‐dimensional weld toe cracks using weld toe magnification factors

In welded components, particularly those with complex geometrical shapes, evaluating stress intensity factors is a difficult task. To effectively calculate the stress intensity factors, a weld toe magnification factor is introduced that can be derived from data obtained in a parametric study performed by finite element method (FEM). Although solutions for the weld toe magnification factor have been presented, these are applicable only to non‐load‐carrying cruciform or T‐butt joints, due possibly to the requirement of very complicated calculations. In the majority of cases for various welded joints, the currently used weld toe magnification factors do not adequately describe the behaviour of weld toe cracks. In this study, the weld toe magnification factor solutions for the three types of welded joints such as cruciform, cover plate and longitudinal stiffener joints were provided through a parametric study using three‐dimensional finite elements. The solutions were formed with exponents and fractions that have polynomial functions in terms of a/c and a/t – that is, crack depths normalised by corresponding half crack lengths and specimen thickness. The proposed weld toe magnification factors were applied to evaluate the fatigue crack propagation life considering the propagation mechanisms of multiple‐surface cracks for all welded joints. It showed good agreement within a deviation factor of two between the experimental and calculated results for the fatigue crack propagation life.     

Fatigue assessment of high‐frequency mechanical impact (HFMI)‐treated welded joints subjected to high mean stresses and spectrum loading

The fatigue strength of welded joints can be improved with various post‐weld treatment methods. High‐frequency mechanical impact treatment is a residual stress modification technique that creates compressive residual stresses at the weld toe. However, these beneficial residual stresses may relax under certain loading conditions. In this paper, previously published fatigue data for butt and fillet welded joints subjected to high stress ratios and variable amplitude cyclic stresses were evaluated in relation to the current International Institute of Welding (IIW) recommendations on fatigue strength improvement and a proposed IIW design guideline for high‐frequency mechanical impact‐treated welded joints. The evaluation showed that the current IIW recommendations resulted in both non‐conservative and overly conservative fatigue strength estimations depending on the applied stress level, whereas the proposed fatigue assessment guideline fitted the current data well.     

Generalized stress intensity factors due to steady and transient thermal loads with applications to welded joints

This paper deals with the elastic and plastic stress fields induced by thermal loads in the vicinity of sharp V‐notch tips in plates. Under the hypothesis of steady‐state heat transfer and plane‐strain conditions, the thermal and mechanical problem requires the numerical solution of an ordinary differential equation (ODE) system, obtained by extending the ‘stress function approach’. The intensity of the stress distributions ahead of V‐notch tips can be expressed in terms of thermal notch stress intensity factors (thermal NSIFs), as for external loads. The problem becomes much more demanding in the presence of transient thermal loads. The residual asymptotic stress distribution arising from the solidification of a fusion zone during an arc welding process is obtained by considering different boundary conditions. An aluminium butt‐welded joint is analysed after having modelled the weld toe region as a sharp V‐notch. A finite element (FE) simulation of the welding process is carried out by means of SYSWELD code (version 2004.1) modelling the arc welding torch by means of Goldak's source. Near the weld toe, the intensity of the residual stress field is given in terms of elastic or elastic—plastic generalized NSIFs.     

Fatigue tests of notched specimens made from butt joints at steel

The weld toe as well as the weld root of joints acts as a geometrical notch, which decreases the fatigue strength of welded components. Local approaches used for fatigue assessment account for the local stress concentration when referring to the notch stress as a fatigue parameter. This applies also to the approaches based on the notch stress intensity factor like, for example, the averaged strain energy density, neglecting the actual notch radius and considering a sharp notch as a simplification. A uniform S‐N curve valid for different types of welded joints and failure locations was derived from re‐analyses of fatigue test results as documented in literature. The fatigue tests described in this paper aimed at validating that energy‐based S‐N curve by dedicated tests on artificially notched specimens. At first, four parameters were investigated in order to estimate their influence on the fatigue strength and to select appropriate notch geometries for the final step of the test campaign. The advantages of these tests are that both the exact notch geometry and the local stress range at the notch, including misalignment effects, were identified and considered in experimental data analysis. This paper presents the results of the rather comprehensive testing activities and comparisons with the design‐S‐N curve mentioned, yielding unexpected fatigue behaviour. This can be explained by the short crack propagation life.     

基于缺口应力法的焊接接头疲劳分析

等效缺口应力法作为焊接疲劳分析的一种局部方法,不仅克服了焊接结构名义应力难以确定和焊根结构应力无法定义的困难,而且能够反映焊接局部后处理对焊接接头疲劳强度的影响,因此近年来备受关注。该文建立了典型焊接接头的三维缺口应力模型,对焊趾根部的缺口应力集中系数进行了求解;通过对对接接头和纵向角接头在焊后未处理(AS-weld)和超声喷丸处理(UPT)两种状态下的疲劳试验数据进行分析处理,获得了两种焊接接头在缺口应力系统下统一的S-N曲线,并与目前国际焊接学会所推荐的具有相同存活率的疲劳寿命曲线(IIW:m=3,FAT=225)进行比较,结果表明,该曲线具有更高的疲劳等级和更低的斜度。     

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.     

Rib loading effects on weld root fatigue failure modes at rib‐to‐deck welded joint

The service life of orthotropic steel decks is dependent on the fatigue resistance of rib‐to‐deck welded joints, which is often tested using two kinds of experimental models in terms of the rib loading condition. Different weld root fatigue failure modes have been observed in the different models, but the role of rib loading remains unclear. This paper aims to clarify the effect of rib loadings on the weld root fatigue failure modes at rib‐to‐deck welded joints. The loadings are decomposed into the deck loadings and rib loadings according to the principle of superposition. Formulae of the weld root notch stress intensity factors and T‐stress under rib loadings are developed by multiparameter regression analysis and subsequently used for the local stress analysis. The fatigue failure modes determined from the local stress field agree well with the experimental results. The results reveal that the weld root failure modes depend on the rib loadings but are independent of the weld geometries. The averaged strain energy density (SED) that can capture both weld geometry and loading condition effects is used to correlate the fatigue test data of different weld root failure modes. The SED is capable of evaluating the fatigue strength of the rib‐to‐deck welded joint failed by different weld root failure modes with a narrow scatter band.     

FATIGUE ANALYSIS AND PREDICTION IN FILLET WELDED JOINTS IN THE LOW THICKNESS RANGE

Abstract— The paper reports the results of a comprehensive research project concerning fatigue life prediction in fillet welded joints. Geometry variables such as main plate thickness, radius of curvature at the weld toe and leg to leg distance were analysed in detail. Fatigue life computations were carried out for semi-elliptical cracks using appropriate FE techniques. The range of results covered several types of welded joints loaded in tension and in bending. A comparison of results was made using two methods of stress intensity determination. Experimental data was also obtained and that included measurements of weld toe radius, monitoring of crack shape and S-N curves. Correlation of results with the theoretical predictions gave generally good agreement. A set of fatigue design curves for fillet welded joints is proposed and in these the designer can introduce the geometry of the weldment.     

Kerbgrundkonzepte für die schwingfeste Auslegung von Aluminiumschweißverbindungen am Beispiel der naturharten Legierung AlMg4,5Mn (AW‐5083) und der warmausgehärteten Legierung AlMgSi1 T6 (AW‐6082 T6)

Fatigue design of aluminium welded joints by the local stress concept exemplarily shown on the naturally aged wrought aluminium alloy AW‐5083 and the artificially aged wrought aluminium alloy AW‐ 6082 T6 Local fatigue design concepts based on material‐ and microstructural‐related parameters, e.g. the microsupport‐concept, cannot be regarded as easily applicable. The investigations, which compared the micro‐support‐concept with the local stress concept with a fictitious notch radius r_f, were carried out with different types of MIG‐welded joints of the aluminium alloys AW‐5083 and AW‐6082 T6 under fully reversed and pulsating axial loading. The evaluation of the results showed that the local stress concept using the fictitious notch radius of r_f = 1.0 mm can be applied to aluminium welded joints from plates with thicknesses t ≥ 5 to 25 mm independently from the alloy and weld geometries (fully or partially penetrated butt welds, transversal stiffener). Master design curves are proposed for different stress ratios, i.e. R = ‐1, 0 and 0.5, which allow the consideration of residual stresses as well as load induced mean stresses. The results permit also the suggestion of Δσ = 70 MPa as FAT‐value for the IIW‐Fatigue Design Recommendations     

A simplified fatigue assessment method for high quality welded cruciform joints

The primary goal of this study was to develop an equation relating the geometric parameters to fatigue strength which can be used is routine design assessment. To attain this, the influence of local geometrical weld variations on the fatigue strength of non-load-carrying cruciform fillet welded joints were systematically studied using plane strain linear elastic fracture mechanics (LEFM). The effects of weld toe radius, flank angle and weld size were considered. Both continuous weld toe cracks and semi-elliptical toe cracks with alternate pre-existing defect depths were considered. A previously developed experimental crack aspect ratio development curve was used for assessing the growth of the semi-elliptical cracks using 2D FE models. A total of 152 experimental fatigue data points from six published studies of welded cruciform joints were evaluated. Details of the actual weld toe radius, flank angle and weld size were available for these joints. For the high quality welds evaluated, an assumed initial crack depth of 0.05 mm was found to correlate best with the experimental data. Of all the geometric parameters considered analytically, weld toe radius was found to have the most dramatic influence on fatigue life. A simple equation is proposed which relates welded joint fatigue strength to the ratio weld toe radius/plate thickness for high quality welds.     

Fatigue design of welded double‐sided T‐joints and double‐sided cruciform joints in steel marine structures: A total stress concept

Fatigue is a governing design limit state for marine structures. Welded joints are important in that respect. The weld notch stress (intensity) distributions contain essential information and formulations have been established to obtain a total stress fatigue damage criterion and corresponding fatigue resistance curve; a total stress concept. However, the involved weld load carrying stress model does not provide the required estimates and trends for varying geometry dimensions and loading & response combinations. A new one has been developed and performance evaluation for T‐joints and cruciform joints in steel marine structures shows that in comparison with the nominal stress, hot spot structural stress and effective notch stress concept based results up to 50% more accurate fatigue design life time estimates can be obtained. Taking advantage of the weld notch stress formulations, the effective notch stress concept performance has improved adopting a stress‐averaged criterion rather than a fictitious notch radius‐based one.     

On the slope of the fatigue resistance curve for laser stake‐welded T‐joints

The paper investigates the influence of highly localised stress distribution around the notch tips of the laser stake‐welded T‐joints to the slope of the fatigue resistance curve. The study considers experimental data of eight series involving joints under tension or bending loads. Various boundary conditions and plate thicknesses are considered. The stress distribution in the singularity‐dominated zone ahead of the notch tips is investigated by means of the finite element analysis. The aim is to relatively distinguish the stress distribution from one case to another. The growth rate of the elastic singular stress with respect to the distance from the tip is described by the dimensionless gradient. This gradient is equal to the slope of the linear stress‐distance function when presented in double‐logarithmic scale. The slope of the fatigue resistance curve varies approximately from 4 to 8. It is observed that the change of the slope can be closely associated with the gradient of the maximum principal stress evaluated in the plane that is orthogonal to the crack path. The orthogonal plane corresponds to the maximum principal stress direction. In contrast, there is a large scatter in the relation between the slope and the gradient evaluated in the commonly assumed crack plane. The study shows that the dimensionless gradient exhibits sensitivity towards plate thicknesses, local weld geometry and the loading condition.     

Experimental and analytical investigation of fatigue crack propagation of T‐welded joints considering the effect of boundary condition

T‐welded joints are commonly employed in ship and ocean structures. The fatigue failure of structure components subjected to cyclic loading always occurs in T‐welded joints because of the metallurgical differences, tensile residual stress fields and stress concentrations. The former researches about T‐welded joints fatigue have in common that the boundary condition needs to be taken into account as an influencing parameter to predict the crack propagation during cyclic loading. In this paper, the crack growth behaviour in T‐welded joint processed with Q345D steel (Pingxiang Iron & Steel Co., Ltd, Hukou, Jiangxi Province in China) under the fatigue loading was analysed via analytical model and verified via experiment. The results show that the influence of boundary condition should be considered in T‐welded joint structure during crack propagation in weld toe area. The correction factor concerning the effect of boundary condition and modified Paris' equation was proposed according to the experimental results and verified by the following repeated experiments.     

Anwendung des Kerbspannungskonzeptes auf die reale Geometrie von Schweißnahtenden

The process used to manufacture modern weld structures often lead to weld start and end points. Under cyclic loading, crack initiation occurs predominantly at the weld start. In particular, for special investigations into thin sheet structures, no approach for the determination of the fatigue life has been established thus far. Therefore, in this research, we have attempted to find a general approach for the assessment of weld ends using the notch stress concept. The primary aim was to obtain the real geometry of weld ends with high precision using a three dimensional scanner. We were able to find an idealised weld end model with the mean toe radius of r = 0,2 mm that provides almost the same notch stresses like the real geometry. The applied load cases were longitudinal and transverse tension as well as bending. The crack always occurs at the weld toe. The notch stress S‐N‐curve was derived from the fatigue life of the cyclic testing so that the assessment of weld ends is possible for the first time. Moreover, some conversion rules have been developed so that the idealised weld end geometry can be modelled with an arbitrary toe radius. Going one step further, some analyses have been performed regarding to unify the notch stress concept. The existing results of Olivier – who examined long welds with no start and end points – were re‐evaluated to unify the results of long regular welds with the local weld end under one scatter band. Using the scanned geometry a good agreement could be achieved. The use of an idealised model will be validated soon.     

A local strain method for the evaluation of welded joints fatigue resistance: the case of thin main-plates thickness

Current procedures for evaluating fatigue strength of welded structures may not be consistent with the real fatigue behaviour of welded joints. A local strain method for the prediction of the WELded joints FAtigue REsistance (WELFARE), by local strain measurements at the weld toe, was recently proposed on the basis of fatigue tests on more than 10 series of welded joints (T, cruciform, angular and butt joints) in structural steel, with 10–25 mm main‐plate thickness. This paper reports fatigue test results obtained from 30 cruciform and butt welded joints (3–5 mm thick) under two load ratios (0.1 and ?1) in order to extend the applicability of the method to thin welded joints.     

THE EFFECT OF UNDERCUT, MISALIGNMENT AND RESIDUAL STRESSES ON THE FATIGUE BEHAVIOUR OF BUTT WELDED JOINTS

Abstract— A mathematical model is developed to predict the effect of weld toe undercut, misalignment and residual stresses on the fatigue behaviour of butt welded joints subjected to zero-to-tensile loading. Linear Elastic Fracture Mechanics (LEFM), Finite Element Analysis (FEA) and superposition approaches have been used for the modelling. It has been found that an undercut at the toes of welded joints is one of the most important weld geometry parameters. The reduction of fatigue strength of welded joints with a weld toe undercut is at least twice that of joints without an undercut in comparison with flush-ground welded plate. A misalignment of 5% of plate thickness and an undercut of 2% of plate thickness are fairly representative for the lower boundary of S-N curves of butt joints. The improvement of fatigue limits by means of surface treatments is shown to be effective for both undercut and misaligned joints. This approach is practical for a "Fitness-for-Purpose" assessment of welded joints subject to fatigue conditions.