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.     

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.     

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.     

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.     

Cruciform fillet welded joint fatigue strength improvements by weld metal phase transformations

Arc welding typically generates residual tensile stresses in welded joints, leading to deteriorated fatigue performance of these joints. Volume expansion of the weld metal at high temperatures followed by contraction during cooling induces a local tensile residual stress state. A new type of welding wire capable of inducing a local compressive residual stress state by means of controlled martensitic transformation at relatively low temperatures has been studied, and the effects of the transformation temperature and residual stresses on fatigue strength are discussed. In this study, several LTTW (Low Transformation‐Temperature Welding) wires have been developed and investigated to better characterize the effect of phase transformation on residual stress management in welded joints. Non‐load‐carrying cruciform fillet welded joints were prepared for measurement of residual stresses and fatigue testing. The measurement of the residual stresses of the three designed wires reveals a compressive residual stress near the weld toe. The fatigue properties of the new wires are enhanced compared to a commercially available wire.     

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.     

Fatigue strength assessment of partial and full‐penetration steel and aluminium butt‐welded joints according to the peak stress method

In fatigue design of welded joints, the local approach based on the notch stress intensity factors (NSIFs) assumes that the weld toe profile is a sharp V‐notch having a tip radius equal to zero, while the root side is a pre‐crack in the structure. The peak stress method (PSM) is an engineering, FE‐oriented application of the NSIF approach to fatigue design of welded joints, which takes advantage of the elastic peak stresses from FE analyses carried out by using a given mesh pattern, where the element type is kept constant and the average element size can be chosen arbitrarily within a given range. The meshes required for the PSM application are rather coarse if compared with those necessary to evaluate the NSIFs from the local stress distributions. In this paper, the PSM is extended for the first time to butt‐welded joints in steel as well as in aluminium alloys, by comparing a number of experimental data taken from the literature with the design scatter bands previously calibrated on results relevant only to fillet‐welded joints. A major problem in the case of butt‐welded joints is to define the weld bead geometry with reasonable accuracy. Only in few cases such geometrical data were available, and this fact made the application of the local approaches more difficult. Provided the local geometry is defined, the PSM can be easily applied: a properly defined design stress, that is, the equivalent peak stress, is shown (i) to single out the crack initiation point in cases where competition between root and toe failure exists and (ii) to correlate with good approximation all analysed experimental data.     

Review of the fatigue strength of welded joints based on the notch stress intensity factor and SED approaches

Several approaches exist for the fatigue strength assessment of welded joints. In addition to the traditional nominal stress approach, various approaches were developed using a local stress as fatigue parameter. In recent times, the N-SIF based approaches using the notch stress intensity at the weld toe or root have been developed. Based on this, the more practical strain energy density (SED) and the Peak Stress approaches were proposed. This paper reviews the proposed design S–N curves of the N-SIF and SED approaches questioning in particular the consideration of misalignment effects, which should be included on the load side of local approaches in order to consider them individually in different types of welded joints. A re-analysis of fatigue tests evaluated for the effective notch stress approach leads to slight changes of the design S–N curves and of the radius of the control volume used for averaging the SED at the notches. Further, on purpose fatigue tests of artificially notched specimens show that the fatigue assessment using a single-point fatigue parameter might be problematic because the crack propagation phase, being part of the fatigue life, is strongly affected by the stress distribution along the crack path that may vary considerably between different geometries and loading cases.     

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.     

THE EFFECT OF MISALIGNMENT ON THE FATIGUE STRENGTH OF WELDED CRUCIFORM JOINTS

Abstract— The effect of axial misalignment on the fatigue strength of load-carrying transverse cruciform welded joints was investigated using experimental and fracture mechanics methods. Where failure occurred by cracking from the weld toe, misalignment significantly reduced the fatigue strength. The reduction could be predicted using a nominal stress concentration factor (SCF). Misalignment had less effect where failure was due to cracking through the weld metal; an expression was deduced for the SCF in this case. For fracture mechanics assessments, an expression for an effective stress intensity factor using the SCF and stress intensity factors for aligned welds was shown to agree with the finite element (FE) results. Predictions of the effect of misalignment using the FE results agreed with experimental data. Misaligned transverse load-carrying cruciform joints should be assessed for fatigue failure from the toe using the same SCF as for a butt weld with the same misalignment. For failure through the throat, an alternative expression for the SCF is recommended. Fracture mechanics assessments of misaligned joints should be carried out using an effective stress intensity factor derived from the SCF and stress intensity factors for aligned joints. These recommendations are now incorporated in British Standard PD 6493:1991.     

Local strain energy density and fatigue strength of welded joints under uniaxial and multiaxial loading

In the notch stress intensity approach to the fatigue assessment of welded joints, the weld toe is modelled as a sharp V-notch and the local stress distributions in plane problems are given on the basis of the relevant mode I and mode II notch stress intensity factors (N-SIFs). These factors quantify the magnitude of asymptotic stress distribution obeying Williams’ solution. If the V-notch opening angle at the weld toe is constant and the mode II is not singular, the mode I N-SIF can be directly used to summarize the fatigue behaviour of welded joints. In all the other cases, varying the V-notch angle or including multiaxial loading conditions (where typically both Mode I and Mode III stress distributions are singular), the synthesis can be carried out on the basis of the mean value of the strain energy density over a well-defined volume surrounding the weld toe or the weld root. By using this scalar quantity, two fatigue scatterbands are obtained for structural steels and aluminium alloys, respectively. The material-dependent radius R_C of the control volume (area) is carefully identified with reference to conventional arc welding processes.Sometimes the weld toe radius is found to be very different from zero. The local strain energy approach can be extended as it stands also to these cases, providing a gradual transition from a N-SIF-based approach to a K_t-based approach.     

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.     

Fatigue behaviour of welded joints with cracks, repaired by hammer peening

Rehabilitation of a welded structure, which involves repair of cracked joints, is achieved when the local treatment for repair gives a fatigue strength in the joint equal or above the fatigue strength of the uncracked original detail. If the treatment is properly applied the rehabilitation of the detail is assured, and the nature of the weld toe improvement methods can produce a joint, after repair, with a fatigue strength and residual life greater than the initial detail. The paper presents the results obtained on a fatigue study on the rehabilitation of non‐load carrying fillet welded joints loaded in bending at the main plate and with fatigue cracking at the weld toes of the attachment in the main plate and though the plate thickness. Residual stresses were measured at the surface, with X‐ray diffraction. The residual stresses induced by hammer peening at the weld toe were found to be greater along the longitudinal direction of the plate than in the transverse direction. The peak residual stresses near the weld toe were found to be close to yield in compression, justifying the great benefit of hammer peening. Results of a derived gain factor, g, in fatigue life were obtained as a function of the crack depth repaired by hammer peening.     

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 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.     

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.     

Improving fatigue life for aluminium cruciform joints by weld toe grinding

The increase of fatigue life in aluminium cruciform joints by weld toe grinding was the focus of the current study. The test data are presented by both a nominal stress range approach and by the more refined structural and notch stress range approaches. The influence of the weld toe angle, weld leg length and weld toe radius on the structural and notch stress concentration factor (SCF) was systematically studied by means of finite element analysis. Experimental data based on 18 pieces of as-welded and 13 pieces of weld toe-ground specimens made of 12 mm thick plates showed a significant improvement in fatigue life in aluminium by grinding the weld toe and confirmed the permitted improvement in fatigue life by design codes.     

Gigacycle fatigue data sheets for advanced engineering materials

Gigacycle fatigue data sheets have been published since 1997 by the National Institute for Materials Science. They cover several areas such as high-cycle-number fatigue for high-strength steels and titanium alloys, the fatigue of welded joints, and high-temperature fatigue for advanced ferritic heat-resistant steels. Some unique testing machines are used to run the tests up to an extremely high number of cycles such as 10¹⁰ cycles. A characteristic of gigacycle fatigue failure is that it is initiated inside smooth specimens; the fatigue strength decreases with increasing cycle number and the fatigue limit disappears, although ordinary fatigue failure initiates from the surface of a smooth specimen and a fatigue limit appears. For welded joints, fatigue failure initiates from the notch root of the weld, because a large amount of stress is concentrated at the weld toe. The fatigue strength of welded joints has been obtained for up to 10⁸ cycles, which is an extremely high number of cycles for large welded joints. The project of producing gigacycle fatigue data sheets is still continuing and will take a few more years to complete.     

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。     

A study of fatigue crack growth from artificial corrosion pits at welded joints under complex stress fields

The paper studies the effects of artificial corrosion pits and complex stress fields on the fatigue crack growth of full penetration load‐carrying fillet cruciform welded joints with 45° inclined angle. Parameters of fatigue crack growth rate of welded joints are obtained from S‐N curves under different levels of corrosion. A numerical method is used to simulate fatigue crack growth using different mixed mode fatigue crack growth criteria. Using polynomial regression, the crack shape correction factor of welded joints is fitted as a function of crack depth ratios. Because the maximum circumferential stress criterion is simple and easy to use in practice, fatigue crack growth rate is modified using this criterion. The relationship of effective stress intensity factor, crack growth angle and crack depth is studied under different corrosion levels. The simulated crack growth path obtained from the numerical method is compared with the actual crack growth path observed by fatigue tests. The results show that fatigue cracks do not initiate at the edge or bottom of pits but at the weld toes where the maximum stress occurs. The artificial corrosion pits have little effect on the effective stress intensity factor ranges and crack growth angle. The fatigue crack growth rates of welded joints with pits 1 and 2 are 1.15 times and 1.40 times larger than that of the welded joint with no pit, respectively. The simulated crack growth path agrees well with the actual one. The fatigue life prediction accuracy using the modified formulation is improved by about 18%. The crack shape correction factor obtained using the maximum circumferential stress criterion is recommended being used to calculate fatigue life.