Fatigue-relevant stress field parameters of welded lap joints: pointed slit tip compared with keyhole notch

The notch stress intensity factor (NSIF) based analytical frame is applied to the slit tips (or weld roots) of welded joints with inclusion of the T-stress component. This T-stress can be determined from FE models evaluating the ligament stresses close to the pointed slit tip. An alternative analytical frame is presented for the corresponding keyhole notches based on analytical solutions from the literature, which are applied to the ligament stresses.
In the slit tip models, the mean local strain energy density (SED) with inclusion of the T-stress effect is determined analytically and numerically in comparison, using two different fatigue-relevant control radii,  R ₀= 0.28 mm and  R ₀= 0.15 mm, the former value well proven for thick-sheet welded joints made of structural steel. The latter smaller value is tentatively proposed for thin-sheet welded joints, in the direction suggested in the recent literature where a reduction of the microstructural support length for laser beam welds and resistance spot welds is recommended. The FEM-based and analytical stress concentration factors (SCF) for the lap joint keyhole model and also the SED values for the corresponding pointed slit tips are found to be in good agreement. The  J -integral consisting of the first and second component (the latter containing the T-stress) is compared with the corresponding SED values.     

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.     

Numerical and experimental applications of the least-squares method to determine mode-II stress intensity factors for double fillet welded lap joints

Due to its simplicity, the least-squares method provides an efficient means to evaluate the stress intensity factors (SIFs) of cracks in complicated structures. This paper demonstrates numerical and experimental applications of the least-squares method to study mode-II SIFs of double fillet welded lap joints. In the numerical application, double fillet welded lap joints with different geometric parameters, including overlap length, weld leg size, plate thickness and plate length, were systematically analysed by the finite-element method combined with the least-squares method. The computed SIF results were then employed to develop the general formulae of the shearing fracture mode (mode-II) stress intensity factors. To validate the numerical results, three double fillet welded lap joint specimens were tested by a non-contact optical experiment using a common digital camera and a proposed image processing scheme. The measured crack shearing displacements near the crack tip were substituted into the least-squares procedure to obtain the SIFs of the specimens. The numerical and experimental results were in good agreement with the existing numerical results for double fillet welded lap joints provided in the handbook (Murakami, 1987). The non-contact optical experiment makes the field measurement of SIFs possible, which is very useful for fracture analysis or fatigue evaluation of structures like steel bridges, naval structures and offshore structures.     

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.     

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.     

Application of two‐state M‐integral for analysis of adhesive lap joints

With the aid of the two‐state M‐integral and finite element analysis, the asymptotic solution in terms of the complete eigenfunction expansion is obtained for adhesive lap joints. The notch stress intensity is introduced to characterize the singular stress field near the notch vertex of adhesive lap joints. The proposed scheme enables us to extract the intensity of each eigenfunction term from the far field data without resort to special singular elements at the vertex. It turns out that a weak stress singularity is not negligible around the vertex when it exists in addition to the major singularity. For a thin adhesive layer, there exist two asymptotic solutions: one is the inner solution approaching the eigenfunction solution for the vertex at which the adherend meets with the adhesive and the other is intermediate solution represented by the eigenfunction series that would be obtained in the absence of the adhesive layer. An appropriate guideline for choosing the geometric parameters in designing the adhesive lap joints, particularly the overlap length or the size of the adhesive zone, is suggested from the viewpoint of minimizing the notch stress intensity. Copyright © 2001 John Wiley & Sons, Ltd.     

Out‐of‐plane singular stress fields in V‐notched plates and welded lap joints induced by in‐plane shear load conditions

When a crack or sharp notch is subjected to antisymmetric plane loading the Poisson's effect leads to the generation of a coupled out‐of‐plane singular mode. The latter was known to exist for problems with cracks for a long period of time; meanwhile this mode was largely ignored in theoretical studies of V‐shaped notches subjected to in‐plane loading as well as in practical fracture problems associated with such geometries. Only recently a characteristic equation describing the strength of the singularity of this mode was derived within the first order plate theory. Preliminary numerical investigations confirmed that a highly localized out‐of‐plane singular state linked to the transverse shear stress components does exist in the close vicinity of the notch tip with the singular behaviour as theoretically predicted. However, until now it is unclear how significant this mode is and whether it has to be taken into consideration in the stress analysis of engineering structures. This paper is aimed to discuss important features of this recently identified singular mode, out‐of‐plane singular mode, conduct a comprehensive three‐dimensional numerical study of a typical problem of a welded lap joint to investigate the contribution of this mode into the overall stress state in the close vicinity of the notch tip and discuss the implementation of these new results to the failure and integrity assessment of plate structures with sharp notches.     

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.     

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.     

State‐of‐the‐art review on extended stress intensity factor concepts

The stress intensity factor concept for describing the stress field at pointed crack or slit tips is well known from fracture mechanics. It has been substantially extended since Williams' basic contribution (1952) on stress fields at angular corners. One extension refers to pointed V‐notches with stress intensities depending on the notch opening angle. The loading‐mode‐related simple notch stress intensity factors K₁, K₂ and K₃ are introduced. Another extension refers to rounded notches with crack shape or V‐notch shape in two variants: parabolic, elliptic or hyperbolic notches (‘blunt notches’) on the one hand and root hole notches (‘keyholes’ when considering crack shapes) on the other hand. Here, the loading‐mode‐related generalised notch stress intensity factors K_1ρ, K_2ρ and K_3ρ are defined. The concepts of elastic stress intensity factor, notch stress intensity factor and generalised notch stress intensity factor are extended into the range of elastic–plastic (work‐hardening) or perfectly plastic notch tip or notch root behaviour. Here, the plastic notch stress intensity factors K_1p, K_2p and K_3p are of relevance. The elastic notch stress intensity factors are used to describe the fatigue strength of fillet‐welded attachment joints. The fracture toughness of brittle materials may also be evaluated on this basis. The plastic notch stress intensity factors characterise the stress and strain field at pointed V‐notch tips. A new version of the Neuber rule accounting for the influence of the notch opening angle is presented.     

Weight functions for the determination of stress intensity factor and T‐stress for semi‐elliptical cracks in finite thickness plate

This paper presents the application of weight function method for the calculation of stress intensity factors (K) and T‐stress for surface semi‐elliptical crack in finite thickness plates subjected to arbitrary two‐dimensional stress fields. New general mathematical forms of point load weight functions for K and T have been formulated by taking advantage of the knowledge of a few specific weight functions for two‐dimensional planar cracks available in the literature and certain properties of weight function in general. The existence of the generalised forms of the weight functions simplifies the determination of specific weight functions for specific crack configurations. The determination of a specific weight function is reduced to the determination of the parameters of the generalised weight function expression. These unknown parameters can be determined from reference stress intensity factor and T‐stress solutions. This method is used to derive the weight functions for both K and T for semi‐elliptical surface cracks in finite thickness plates, covering a wide range of crack aspect ratio (a/c) and relative depth (a/t) at any point along the crack front. The derived weight functions are then validated against stress intensity factor and T‐stress solutions for several linear and nonlinear two‐dimensional stress distributions. These derived weight functions are particularly useful for the development of two‐parameter fracture and fatigue models for surface cracks subjected to fluctuating nonlinear stress fields, such as these resulting from surface treatment (shot peening), stress concentration or welding (residual stress).     

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.     

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 assessment of laser stake‐welded T‐joints subjected to reversed bending

The paper investigates the fatigue strength of laser stake‐welded T‐joints subjected to reversed bending. The fatigue tests are carried out with the load ratio, R ≈ ?0.8. The experimental data is firstly analysed using the nominal stress approach and then by the J‐integral as the local fatigue strength parameter in the finite element (FE) assessment. The nominal stress approach demonstrated that the fatigue strength of the investigated T‐joints is lower than encountered for any other steel joint under reversed tensile loading. The results also showed that the fatigue strength of this joint under the load ratio R ≈ ?0.8 increases with respect to R = 0 bending by 22.6% in the case of the nominal stress approach and 13% in the case of the J‐integral approach. However, the slopes of the fatigue resistance curves for different load ratios appear very similar, suggesting that the load ratio has an insignificant influence to the slope. In contrast to the similar slopes, the scatter indexes were different. The nominal stress approach shows that the scatter index is 3.4 times larger for R ≈ ?0.8 than R = 0 bending. The J‐integral approach showed that the scatter index for R ≈ ?0.8 is only 67% larger than in the R = 0 case because the weld geometry is modelled in the FE analysis.     

Fatigue performance of adhesively bonded single lap joints with non‐flat sinusoid interfaces

The role of a sinusoid interface shape on the load bearing capacity and fatigue life of adhesively bonded single lap joints (SLJs) was investigated numerically and experimentally. Aluminium adherends with wavy interfaces were tested under both quasi‐static and fatigue loading conditions. The experimental results showed that the non‐flat SLJs were indeed much stronger than the conventional flat joints. In order to fully demonstrate the advantage of the non‐flat sinusoid SLJ over the conventional SLJ, comparative fatigue tests with different loading levels were performed to determine the durability performance of the SLJs with non‐flat interfaces. The experimental results revealed that the non‐flat SLJ had considerably higher fatigue life than the conventional lap joint.     

An extrapolation method to determine the effective notch stress in circular hollow section X‐joints

This paper presents an extrapolation method to determine the effective notch stress (ENS) on the weld toes of welded circular hollow section (CHS) X‐joints in‐line with the extrapolation method to determine the structural hot‐spot stress in existing design guidelines. This investigation verifies and extends the recently proposed ENS extrapolation scheme to CHS X‐joints, which elevates significantly the difficulty in generating a weld toe radius along the brace‐to‐chord intersection as required in existing guidelines. An extensive numerical study then investigates the ENS extrapolation for CHS X‐joints under three loading conditions, namely, the brace axial load, the brace in‐plane bending load, and the brace out‐of‐plane bending load. The numerical study derives a set of recommended extrapolation parameters that ensures accurate ENS estimation for each loading condition. This paper demonstrates that the proposed extrapolation method for the CHS X‐joints yields good agreement with the standard ENS calculation procedure described in the International Institute of Welding (IIW) guideline.     

Estimation of three‐dimensional stress intensity factor for structural ‘T’ details

Three‐dimensional (3D) opening mode stress intensity factors (SIFs) for structural steel‐welded ‘T’ details were investigated by the finite element method. A 3D shape‐dependent correction factor is proposed for semi‐elliptical surface cracks. The aspect ratio (a/c) of a semi‐elliptical crack plays a key role in the approximation of 3D‐SIF values, and in the present study, it was estimated for a 3D crack analysis. The estimated 3D‐SIF was determined through a correlation between the a/c ratio and the two‐dimensional SIF for semi‐elliptical cracks in the thickness direction adjacent to the web‐flange junction of a welded ‘T’. The resulting equation can be used to estimate the 3D‐SIF values from the two‐dimensional SIF without much ambiguity.     

Stress intensity factors for corner cracks in single‐edge notch bend specimen by a three‐dimensional weight function method

A three‐dimensional (3D) weight function method is employed to calculate stress intensity factors of quarter‐elliptical corner cracks at a semi‐circular notch in the newly developed single‐edge notch bend specimen. Corner cracks covering a wide range of geometrical parameters under pin‐loading and remote tension conditions are analysed. Stress intensity factors from the 3D weight function analysis agree well with ABAQUS‐Franc3D finite element results. An engineering similitude approach previously developed for the half‐elliptical surface crack in single‐edge notch bend specimen is also applied to the present corner crack configuration. The results compare well with those from the present weight function analysis.     

Stress intensity factors for surface cracks in single‐edge notch bend specimen by a three‐dimensional weight function method

Stress intensity factors for half‐elliptical surface cracks at a semi‐circular notch in a recently developed single‐edge notch bend specimen are determined for a wide range of geometrical parameters using a three‐dimensional weight function method. Two load cases of pin loading and uniform remote tension are considered. The results are in good agreement with abaqus/franc3d finite element analysis. It is found that the Ziegler–Newman engineering similitude approach (programmed into the Fatigue Crack Growth Structural Analysis life‐prediction code) produces good results for a wide range in a/c ratios. Expressions by multi‐variable curve fitting to the weight function results are presented for easy engineering applications.     

Calculation of mixed mode (I/II) stress intensities at sharp V‐notches using finite element notch opening and sliding displacements

In this paper, a simple, robust, and an efficient technique has been proposed for accurate estimation of mixed mode (I/II) notch stress intensity factors (NSIFs) of sharp V‐notched configurations using finite element notch opening and sliding displacements at the selected number of nodes along the notch flanks. Unlike the crack problems, displacement field is rarely employed in the notch problems due to complexities introduced by the presence of rigid body displacements. One of the main emphasis of the present work is to neatly bypass these rigid body displacements and develop a simple approach for accurate computation of the NSIFs so that it can be easily incorporated in the existing code. Several benchmark problems have been analyzed. The results obtained using the present method show excellent agreement with the solutions available in the literature. Some new results have also been reported in the present work.