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.     

Local fatigue strength parameters for welded joints based on strain energy density with inclusion of small-size notches

A fatigue strength parameter for (seam-)welded joints is presented which is based on the averaged elastic strain energy density (SED) criterion applied to full circle and semicircular ‘control volumes’, the latter centred by the expected crack path. The parameter is applicable both at weld toes and weld roots, at least in the medium-cycle and high-cycle fatigue range where elastic conditions are prevailing. Based on a rectangular slit-plate model representing the weld root and analysed by the finite element method, the effect of the following influencing conditions is investigated: tension loading (mode 1) and shear loading (mode 2), slit-parallel tension loading acting on a rounded slit tip, pointed slit tip versus small-size key-hole at the slit tip, semicircle and narrow sector versus full circle or full sector SED evaluations, distortional SED versus total SED under plane strain conditions. The following conclusions are drawn from the numerical results. The SED approach should be based on the full circle or full sector evaluation of the total SED, with R₀ = 0.28 mm for steels. In cases of a markedly unilateral angular SED distribution, the semicircle evaluation centred by the expected crack path is more appropriate. The use of small-size reference notches instead of pointed notches provides no advantage. The endurable remote stresses for fatigue-loaded welded joints according to the SED approach are well in correspondence with those according to the fictitious notch rounding approach. High accuracy of the results can already be achieved with a rough meshing at the pointed notches.     

Relationships between local and structural stress in the evaluation of the weld toe stress distribution

This paper deals with the problem of determining, by proper stress analyses, the stress fields near arc-welded joint toes and the use of such distributions in fatigue strength predictions. In particular, the relationships between the local stress field and the structural (geometrical) stress field are investigated under the hypothesis that highly stressed zones remain under linear elastic conditions.

The local stress distribution is given for different joints in terms of the relevant notch stress intensity factors (NSIFs), having modelled their weld beads like re-entrant sharp corners. The structural stress distribution is, in contrast, the stress field linearly distributed through the thickness of the welded plates (and sometimes on the plate surfaces), beyond the zone affected by local effects due to the beads. The aim of the proposed methodology is to provide an explicit link between NSIF values and structural stress at a well-defined distance from the weld toe. Such a distance is chosen equal to the main plate thickness.

The expressions obtained allow a direct comparison with the well-known “hot-spot stress” approach; it is demonstrated that there are circumstances of practical interest in which the usual hot-spot stress (which is the simple linear extrapolation at the weld root of the structural field) is not able to predict accurately the fatigue behaviour of the joints, whereas the combination of structural field and NSIF-based field is more advantageous.

The complete methodology can be simplified for rapid calculations involving weldments of different types. Some examples are also reported and discussed.     

Evaluation of nominal and local stress based approaches for the fatigue assessment of seam welds

In the context of the German joint research project “Applicability of fatigue analysis methods for seam welded components”, fatigue tests were performed by five universities and institutes on welded components, welded parts of larger structures as well as component-like samples of weld details. The sheet thickness t was in the range 1 mm ? t ? 20 mm. The welding parameters for all test coupons and structures tested were chosen according to the industrial production process. Based on the data acquired, nominal, structural and notch stress approaches were analysed with regard to applicability and quality of assessment. The actual weld geometry except the real notch radii was taken into account within the notch stress approach. For the notch radii various values, the reference radii 0.05, 0.3 and 1 mm, were applied.Experimental and numerical results for welded steel components are presented.Approximately equivalent scatter ranges were obtained when applying the various approaches based on the current state of the art. It should be noted that both the nominal and the structural stress approaches are limited in their application compared to the notch stress approach. A comparison of the scatter bands obtained for the various approaches is subject to limitations because it was necessary, in each case, to use different test series as the basis for determining the scatter bands.     

The effect of an elliptical inclusion on a crack

The interaction between an elliptical inclusion and a crack is analyzed by body force method. The investigated stress field is simulated by superposing the fundamental solutions for a point force applied at a point in an infinite plate containing an elliptical inclusion. Based on numerical results, effects of the inclusion shape on the crack tip stress intensity factor are discussed. It is found that for small cracks emanating from a stress-higher point on the inclusion interface the stress intensity factors are mainly determined by the stresses, occurring at the crack starting point before the crack initiation, and the inclusion root radius, besides the crack length. However, for the cracks occurring in a stress-lower region around the inclusion, it is difficult to characterize the effect of the inclusion geometry on the stress intensity factors of small cracks by the inclusion root radius alone. This revised version was published online in July 2006 with corrections to the Cover Date.     

A structural stress definition and numerical implementation for fatigue analysis of welded joints

A mesh-size insensitive structural stress definition is presented in this paper. The structural stress definition is consistent with elementary structural mechanics theory and provides an effective measure of a stress state that pertains to fatigue behavior of welded joints in the form of both membrane and bending components. Numerical procedures for both solid models and shell or plate element models are presented to demonstrate the mesh-size insensitivity in extracting the structural stress parameter. Conventional finite element models can be directly used with the structural stress calculation as a post-processing procedure. To further illustrate the effectiveness of the present structural stress procedures, a collection of existing weld S-N data for various joint types were processed using the current structural stress procedures. The results strongly suggests that weld classification based S-N curves can be significantly reduced into possibly a single master S-N curve, in which the slope of the S-N curve is determined by the relative composition of the membrane and bending components of the structural stress parameter. The effects of membrane and bending on S-N behaviors can be addressed by introducing an equivalent stress intensity factor based parameter using the structural stress components. Among other things, the two major implications are: (a) structural stresses pertaining to weld fatigue behavior can be consistently calculated in a mesh-insensitive manner regardless of types of finite element models; (b) transferability of weld S-N test data, regardless of welded joint types and loading modes, can be established using the structural stress based parameters.     

A parametric fracture mechanics study of welded joints with toe cracks and lack of penetration

The existing design rules give quite general guidelines to the fatigue assessment of different types of welded joints. The goal of this investigation was to give designers some tools, which would allow more precise assessment of the effect of dimensional variations on the fatigue strength. Therefore the fatigue behaviour of 12 common types of welded joints has been studied parametrically. Two-dimensional (2D) finite element models of the joint were made and evaluated using plane strain linear elastic fracture mechanics (LEFM) calculations. The as-welded condition was assumed with the result that no crack initiation period was considered and stress ranges were fully effective. A maximum tangential stress criterion with the Paris’ crack growth law was used to predict the growth rate and direction of root and toe cracks under mixed mode K_I-K_II conditions. The effects of weld size and joint dimension ratios on the fatigue strength were systematically studied. In addition to tensile loading, bending and combined tension/bending moment loading in both directions are examined for positive and negative mean stress.     

Fatigue strength and fatigue fracture mechanism of three-sheet spot weld-bonded joints under tensile–shear loading

This paper deals with fatigue behavior of three-sheet spot weld-bonded (SWB) joints to investigate the influence of adhesive bonding on fatigue strength and fracture mechanism. From the results of tensile–shear fatigue tests, the fatigue strength of the SWB joint was higher than that of the spot welded (SW) joint. For fatigue behavior in the SWB joint, debonding between a steel sheet and adhesive propagated from an edge of bonded area to a nugget edge, and a fatigue crack initiated at the nugget edge. It was concluded that the delayed fatigue crack initiation at the nugget edge in the SWB joint resulted in the fatigue strength improvement of SW joint.     

Fatigue resistance of MAG welded steel elements

The present paper describes the results of a research programme carried out to assess the fatigue properties of MAG (Metal Active Gas) welded elements, built in Fe510 D1 steel. Tests on both small and large specimens were carried out to evaluate the effects, on fatigue resistance, of the residual stresses produced by the welding process. The joints examined were butt welded and longitudinally welded. Crack propagation tests were also carried out on welded plates. The data available, together with results taken from the literature, allowed us to analyse the fatigue test results on the basis of the methodologies of Fracture Mechanics; by calibrating the initial defects using the results of the tests carried out on small specimens, a good prediction of the fatigue resistance of large specimens was obtained.     

The Peak Stress Method applied to fatigue assessments of steel tubular welded joints subject to mode-I loading

The paper presents the practical aspects involved in structural design of tubular joints mainly employed in roller coasters manufacturing. Different design standards, commonly adopted in fatigue assessments, are considered and compared. Then some constant amplitude fatigue test results concerning typical tubular welded joints are presented. Finally the experimental results and additional test data taken from the literature are compared with the theoretical estimations based on the Peak Stress Method, which has been recently conceived and proposed as a simplified, application-oriented version of the well known Notch-Stress Intensity Factor approach. The results indicate that the Peak Stress Method is suitable to estimate the fatigue life up to crack initiation of tubular welded joints subject to mode-I loading.     

Fatigue of high strength steel joints welded with low temperature transformation consumables

In the present paper constant (CA) and variable amplitude (VA) fatigue testing have been carried out on out-of plane gusset fillet welded high strength steel joints. The joints were welded with conventional weld filler material and martensitic low transformation temperature weld filler, LTT, in order to study the influence of the residual stress on the fatigue strength. Residual stress measurements were carried out close to the weld toe using X-ray diffraction technique in order to study the relaxation due to VA fatigue. The residual stress showed different level of relaxation depending on the VA spectrum loading used. The LTT joints show 40% increase in mean fatigue strength compared to the conventional joints in CA. The LTT joints show 12% increase in mean fatigue strength compared to the conventional joints. The LTT joints show 33% increase in mean fatigue strength in CA compared to VA testing. However, the improvement of the fatigue strength is less significant in variable amplitude testing mainly due to the relaxation of the compressive residual stresses.     

Fatigue analysis of non-load-carrying fillet welded cruciform joints

The goal of this investigation was to study the effect of local geometrical variations of the weld on the fatigue strength. Therefore the fatigue behaviour of non-load-carrying cruciform fillet welded joint under tensile loading has been studied parametrically. Several two-dimensional (2D) finite element models of the joint were analysed using plane strain linear elastic fracture mechanics (LEFM) calculations in order to get the magnification function M_k. A maximum tangential stress criterion was used to predict the crack growth direction under mixed mode K_I-K_II conditions. The derived M_k solution was then applied both for continuous weld toe cracks and also for semi-elliptical toe cracks at the deepest point of the crack front. An experimental crack aspect ratio development curve was used for propagating semi-elliptical cracks. The as-welded condition was assumed with the result that no crack initiation period was considered and stress ranges were fully effective. The Paris crack growth law was used to predict the growth rate. The effects of weld toe radius, flank angle and weld size on the fatigue strength were systematically studied. Finally, predicted fatigue strength values corresponding to different assumed crack sizes were compared with the available test results.     

Fatigue strength assessment of laser stake-welded T-joints using local approaches

This study investigates the applicability of local stress- and energy-based approaches to the fatigue strength assessment of laser stake-welded T-joints. The T-joint has two crack-like notches with infinitesimal tip rounding on each side of the weld. The local approaches used are fictitious tip rounding of 1 and 0.05 mm and the approaches that assume zero rounding within this study, namely the stress intensity factor, the average strain energy density and the J-integral.It is shown that the slopes of the fatigue resistance curves vary between 4 and 8 under different loading conditions imposed on the joint. The slope value exhibits a linear relation with the dimensionless gradient of the maximum principal stress evaluated at the critical notch tip. The same linear relation between the slope and the gradient is valid for all approaches. Because of the slopes, which differ from the usual 3, the agreement of the T-joints with other steel joints is obtained at five million load cycles. The exception is the fictitious rounding concept of 0.05 mm, in which case the recommended design S–N curve with a slope of 3 appears overly conservative in a high-cycle regime.     

Durability of welded aluminium extrusion profiles and aluminium sheets in vehicle structures

Different approaches - the nominal stress, structural hot spot stress and notch stress approach - to analyse the fatigue strength of welded structures made from wrought aluminium alloys were studied. Experimental and numerical investigation was carried out for this purpose on detail specimens and components. The results shown here were generated during the research project “Extrusion profile and sheet metal structures of wrought aluminium alloys in vehicle construction” [1].The studies show that due to the existing guidelines, welds on structures made from aluminium alloys are sometimes designed very conservatively. It is possible to optimise and reliably design welded joints of thin sheet structures by applying the notch stress approach using the reference radius r_ref = 0.05 mm and the reference SN curves derived here.     

New Developed Welding Electrode for Improving the Fatigue Strength of Welded Joints

A new welding electrode, low transformation temperature electrode (LTTE), was introduced in this paper. It was described in design principle, mechanics, chemical compositions of their deposited metal and manufacturing methods. It was proved that the best transformation starting temperature from austenite to martensite of the deposited metal of LTTE was at about 191℃ and it was obtained by adding alloying elements such as Cr, Ni, Mn and Mo. The microstructure of the weld metal of the LTTE was low carbon martensite and residual austenite. The compressive residual stress was induced around the weld of the LTTE and the -145 MPa in compression could be obtained in middle of weld metal. The fatigue tests showed that the fatigue strength of the longitudinal welded joints welded with the LTTE at 2×106 cycles was improved by 59% compared with that of the same type of welded joints welded with conventional E5015 and the fatigue life was increased by 47 times at 162 MPa. It is a very valuable method to improve th     

Acoustic emission imaging of shear failure in large reinforced concrete structures

The averaged value of the strain energy density over a well-defined volume is used to predict the static strength of U-notched specimens under mixed-mode conditions due to combined bending and shear loads. The volume is centered in relation to the maximum principal stress present on the notch edge, by rigidly rotating the crescent-shaped volume already used in the literature to analyse U- and V-shaped notches subject to mode I loading. The volume size depends on the ultimate tensile strength σ _u and the fracture toughness K _IC of the material. In parallel, an experimental programme was performed. All specimens are made of polymethyl-metacrylate (PMMA), a material which exhibits quasi-brittle behaviour at -60°C. Good agreement is found between experimental data for the critical loads to failure and theoretical predictions based on the constancy of the mean strain energy density over the control volume.     

Strain energy-based evaluations of plastic notch stress intensity factors at pointed V-notches under tension

An analytical study is carried out on the existing link between elastic and plastic notch stress intensity factors at pointed V-notches in plates under tension.The frame is developed on the basis of the elastic and plastic energy concentration factors of the notch defined here as the ratio between the local and the nominal strain energy densities. The link varies under plane stress and plane strain conditions. The local strain energy density is evaluated over a control volume drawn by the energy contour lines ahead of the notch and allows plastic notch stress intensity factors to be predicted on the basis of an ideally linear elastic analysis, both under small and large scale yielding.     

STRESS CONCENTRATION FACTOR FORMULAE WIDELY USED IN JAPAN

Abstract— This report presents a brief outline of three papers on stress concentration factor formulae, which have been frequently referred to in Japanese technical literature. Most well known is a book entitled "Stress Concentration" [1] while Refs [2,3] have often been quoted for cases of fillet joints. The stress concentration factor covered in this report is the so-called theoretical, elastic stress concentration factor. A discussion on plastic stress concentration factors is not in the scope of this report.