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.     

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 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.     

Fatigue crack initiation assessment of welded joints accounting for residual stress

The impact of residual stresses on the fatigue crack initiation life of welded joints is evaluated by the finite element method. The residual stresses of nonload‐carrying cruciform joints, induced by welding and ultrasonic impact treatment, are modelled by initial stresses, using the linear superposition principle. An alternative approach of using modified stress‐strain curves in the highly stressed zone is also proposed to account for the residual stress effect on the local stress‐strain history. An evaluation of the fatigue crack initiation life of welded joints based on the local strain approach is carried out. The predicted results show the effect of residual stresses and agree well with published experimental results of as‐welded and ultrasonic impact treated specimens, demonstrating the applicability of both approaches. The proposed approaches may provide effective tools to evaluate the residual stress effect on the fatigue crack initiation life of welded joints.     

FATIGUE LIFE PREDICTION OF WELDED JOINTS—A RE-ASSESSMENT

Abstract— Fatigue life prediction of welded joints needs an accurate and exhaustive theoretical Fracture Mechanics characterization of weld toe crack propagation. The method proposed by Albrecht et al. leads rapidly to accurate solutions of the LEFM δK-parameter. However, non-LEFM short crack behavior within the notch (weld toe) plastic zone must be taken into account. Available information on notch fatigue is surveyed, and practical cases where short crack growth is likely to occur are identified. Based on an elastoplastic finite element analysis, the LEFM validity limits and errors resulting from the misuse of LEFM in fatigue life prediction are quantified.     

Stress intensity factors in spot welds

This paper looks at stress intensity factors of cracks in resistance spot welded joints. Stress intensity factors have been used in the past to predict fatigue crack propagation life of resistance spot welds. However, the stress intensity factors from all previous work was based on assumed initial notch cracks at the nugget, parallel to the sheets. Physical evidence shows, however, that fatigue cracks in spot welds propagate through the thickness of the sheets rather than through the nugget. In this work, stress intensity factors of assumed notch cracks and through thickness cracks in tensile shear (TS) and modified coach peel (MCP) specimens were determined by the finite element method. The finite element results from the assumed notch cracks were compared with the results in the literature and were found to be in agreement with the results from Zhang’s equations [Int. J. Fract. 88 (1997) 167]. The stress intensity factors of assumed notch cracks were found to be different from those of through thickness cracks. To date, no analytic equations for stress intensity factors of through thickness cracks in spot welds have been published. In the current work, simple equations are proposed to estimate the K_I and K_II values of through thickness cracks in TS and MCP specimens.     

Stress intensity factors in spot welds

This paper looks at stress intensity factors of cracks in resistance spot welded joints. Stress intensity factors have been used in the past to predict fatigue crack propagation life of resistance spot welds. However, the stress intensity factors from all previous work was based on assumed initial notch cracks at the nugget, parallel to the sheets. Physical evidence shows, however, that fatigue cracks in spot welds propagate through the thickness of the sheets rather than through the nugget. In this work, stress intensity factors of assumed notch cracks and through thickness cracks in tensile shear (TS) and modified coach peel (MCP) specimens were determined by the finite element method. The finite element results from the assumed notch cracks were compared with the results in the literature and were found to be in agreement with the results from Zhang’s equations [Int. J. Fract. 88 (1997) 167]. The stress intensity factors of assumed notch cracks were found to be different from those of through thickness cracks. To date, no analytic equations for stress intensity factors of through thickness cracks in spot welds have been published. In the current work, simple equations are proposed to estimate the K_I and K_II values of through thickness cracks in TS and MCP specimens.     

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.     

Stress intensity factor solutions for estimation of fatigue lives of laser welds in lap-shear specimens

Fatigue behavior of laser welds in lap-shear specimens of high strength low alloy (HSLA) steel is investigated based on experimental observations and two fatigue life estimation models. Fatigue experiments of laser welded lap-shear specimens are first reviewed. Analytical stress intensity factor solutions for laser welded lap-shear specimens based on the beam bending theory are derived and compared with the analytical solutions for two semi-infinite solids with connection. Finite element analyses of laser welded lap-shear specimens with different weld widths were also conducted to obtain the stress intensity factor solutions. Approximate closed-form stress intensity factor solutions based on the results of the finite element analyses in combination with the analytical solutions based on the beam bending theory and Westergaard stress function for a full range of the normalized weld widths are developed for future engineering applications. Next, finite element analyses for laser welded lap-shear specimens with three weld widths were conducted to obtain the local stress intensity factor solutions for kinked cracks as functions of the kink length. The computational results indicate that the kinked cracks are under dominant mode I loading conditions and the normalized local stress intensity factor solutions can be used in combination with the global stress intensity factor solutions to estimate fatigue lives of laser welds with the weld width as small as the sheet thickness. The global stress intensity factor solutions and the local stress intensity factor solutions for vanishing and finite kinked cracks are then adopted in a fatigue crack growth model to estimate the fatigue lives of the laser welds. Also, a structural stress model based on the beam bending theory is adopted to estimate the fatigue lives of the welds. The fatigue life estimations based on the kinked fatigue crack growth model agree well with the experimental results whereas the fatigue life estimations based on the structural stress model agree with the experimental results under larger load ranges but are higher than the experimental results under smaller load ranges.     

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.     

基于失效评定图(FAD)研究含疲劳裂纹T型圆钢管节点的安全性

失效评定曲线(FAD)常用来评价焊接结构在出现裂纹后的安全性,为了验证这种曲线在评价焊接管结构在节点部位出现疲劳裂纹后安全性的适用性,采用实验测试和有限元分析的方法研究了3个含疲劳裂纹的T型管节点试件在静力作用下的极限承载能力及破坏过程。3个T型管节点试件首先进行疲劳实验在焊趾处产生表面裂纹,然后通过在支管端部施加轴向拉力作用检测节点的破坏过程。基于自行开发的含表面裂纹T型管节点的有限元网格自动产生程序以及ABAQUS分析软件,研究了在管节点破坏过程中表面裂纹最深点的应力强度因子大小,并通过实验的荷载-位移曲线确定了T节点试件的塑性极限承载力。在这些结果的基础上,验证了FAD在评价含疲劳裂纹的焊接管节点安全性方面的适用性。研究结果标明:FAD在评价含疲劳裂纹管节点的安全性方面是安全可靠的,但偏于保守。     

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.     

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.     

Fatigue crack growth analyses of offshore structural tubular joints

This study investigated various aspects of a fatigue crack growth analysis, ranging from the stress intensity factor solutions to the simulation of a fatigue crack coalescence process of a tubular joint weld toe surface flaw. Fracture mechanics fatigue crack growth analyses for offshore structural tubular joints are not simple, because of the difficulty to calculate the stress intensity factors due to their geometric complexity. The fully mixed-mode stress intensity factors of nine weld toe surface cracks of an X-shaped tubular joint under tension loading were calculated by detailed three-dimensional finite element analyses. Using these stress intensity factor solutions, a fatigue crack growth study was performed for the X-joint until (the crack surface length grew to two times the tube thickness. Through this study, the crack shape change during the fatigue crack propagation was investigated in detail. Fatigue life calculations were also performed for a range of crack geometries using the stress intensity factor solutions of the nine flaws. These calculations indicate that the natural fatigue crack growing path for a crack is its quickest growing path. The study demonstrated that detailed fracture mechanics fatigue analyses of tubular joints can be practical using the finite element method.     

Fatigue life prediction based on crack closure for 6156 Al-alloy laser welded joints under variable amplitude loading

A fatigue prediction approach is proposed using fracture mechanics for laser beam welded Al-alloy joints under stationary variable amplitude loading. The proposed approach was based on the constant crack open stress intensity factor in each loading block for stationary variable amplitude loading. The influence of welding residual stress on fatigue life under stationary variable amplitude was taken into account by the change of crack open stress intensity factor in each loading block. The residual stress relaxation coefficient β = 0.5 was proposed to consider the residual stress relaxation for the laser beam welded Al-alloy joints during the fatigue crack growth process. Fatigue life prediction results showed that a very good agreement between experimental and estimated results was obtained.     

Fatigue life estimation of ultrasonic spot welded Mg alloy joints

Lightweight magnesium alloys are increasingly used in automotive and other transportation industries for weight reduction and fuel efficiency improvement. The structural application of magnesium components requires proper welding and fatigue resistance to guarantee their durability and safety. The objective of this investigation was to identify failure mode and estimate fatigue life of ultrasonic spot welded (USWed) lap joints of an AZ31B-H24 magnesium alloy. It was observed that the solid-state USWed joints exhibited a superior fatigue life compared with other welding processes. Fatigue failure mode changed from interfacial failure to transverse-through-thickness crack growth with decreasing cyclic load level, depending on the welding energy. Fatigue crack initiation and propagation occurred from both the notch tip inside the faying surface and the edge of sonotrode indentation-footprints due to the presence of stress concentration. A life prediction model for the spot welded lap joints developed by Newman and Dowling was adopted to estimate the fatigue lives of the USWed magnesium alloy joints. The fatigue life estimation, based on the fatigue crack growth model with the global and local stress intensity factors as a function of kink length and the experimentally determined kink angle, agreed fairly well with the obtained experimental results.     

Fatigue strength of laser beam welded automotive components made of thin steel sheets considering size effects

The applicability of and the quality of assessment using the nominal stress, structural stress and notch stress approaches for calculating the fatigue strength of laserbeam welded components made of thin steel sheets has been investigated. For this purpose, the fatigue lives of a longitudinal carrier, an injector and two tube-flange specimens have been determined by tests under constant amplitude loading. Fatigue cracks initiated at sharp root notches on all of these components. While the nominal stress is derived by theory of structural mechanics, the determination of structural and notch stresses is performed using 3D finite element models and solid elements. The structural stress is derived by an extrapolation of surface stress to the fatigue critical notch and the notch stresses by rounding the sharp root notch with a reference radius of r_ref = 0.05 mm. For all of the concepts used, the endurable stresses have been compared to the design SN-curves recommended by the International Institute of Welding (IIW).On comparing the quality of assessment of the different concepts, the notch stress approach shows the highest scatter. The highest endurable notch stresses occur in specimens with crack initiation at weld ends. These specimens have a very small highly loaded weld length. The lowest endurable stresses are determined for specimens with a long, equally loaded weld. The reason for these findings can be explained by statistical size effects. For an improved fatigue assessment, an easily applicable method is introduced, which takes into account the highly stressed weld length.     

Stresses and stress intensities at notches: ‘anomalous crack growth’ revisited

In this paper, a new notch stress estimation scheme is presented within the context of conventional finite element solutions. The estimation method is based on a separation of an actual notch stress state into two parts. One part is a far-field stress in the form of membrane and bending components that satisfy far-field equilibrium conditions, and the other is a self-equilibrating part that provides an effective measure of the notch stress state. The self-equilibrating part can be directly related to notch geometry and captured using a rather coarse finite element model. The singular stress behavior at an arbitrary notch is then described by a closed form solution formulated using the self-equilibrating part of the stress state for a small crack emanating from a notch. The corresponding stress intensity factor solutions are then presented by considering both the far-field stress (also called structural stress) and self-equilibrating notch stress. The stress intensity solutions are formulated using existing solutions for typical simple crack geometry. One important feature of the notch stress and stress intensity solutions is that the current solutions not only capture the singular characteristics as the notch tip is asymptotically approached, but also recover the far-field (or nominal) stress state.Finally, the effectiveness of the present notch stress estimation scheme is demonstrated by using a series of well-known short crack growth data exhibiting ‘anomalous growth’. It has been found that, for instance, the anomalous growth discussed in, for example, Fat Eng Mat Struct 6 (1983) 315; Eng Fract Mech 29 (1988) 301; as well as Surface Crack Growth: Models, Experiments, and Structures (1990) 333, can be unified with long crack data as straight lines, without resorting crack closure considerations. As a result, a two-stage crack growth model is proposed within the context of K-dominant crack growth. The first stage is dominated by the notch-induced self-equilibrating part of the stress state and the second stage is dominated by the equivalent far-field stress state or structural stresses that satisfy equilibrium conditions and can be effectively computed in a mesh-insensitive manner. The implications of these findings on fatigue growth rate data generation and fatigue life predictions will also be discussed.     

Modellierung des Ermüdungsrisswachstums in Schweißverbindungen unter Berücksichtigung von Schweißeigenspannungen

The present paper contains research results determined within the framework of a project called IBESS (?Integrale Bruchmechanische Ermittlung der Schwingfestigkeit von Schweißverbindungen“) by the Materials Mechanics Group of the Technische Universität Darmstadt [1]. Aim is to calculate the fatigue life of welded joints by taking into account the effect of residual stresses and the influence of the weld toe geometry. Here, the fatigue life is regarded as period of short fatigue crack growth. Two and three dimensional finite element models, with cracks as initial defects, are constructed for this purpose. Fatigue crack growth analyses are performed by using the node release technique together with the finite element program ABAQUS. The welding residual stresses as well as the plasticity induced crack closure effects are considered. Structural calculations are performed in order to introduce residual stress fields in finite element models. The calculated compressive residual stress field matches the measured one especially in the weld notch area. The effective cyclic J‐integral (ΔJ_eff) is used as crack tip parameter in a relation similar to the Paris equation for the calculation of the fatigue life. For this purpose, a Python code was written for the determination of ΔJ_eff at every crack length phase. The calculated fatigue lives were compared with experimental data and a good accordance between both results was achieved. The impact of welding residual stresses on ΔJ_eff as well as on the fatigue life during short crack growth was investigated. As expected, results revealed that at lower stress amplitude, a compressive residual stress field is favorable to the fatigue life, whilst a tensile residual stress field is unfavorable. The influence of residual stresses can be neglected only for large load amplitudes.     

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.