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.     

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 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.     

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.     

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.     

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.     

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.     

Fatigue strength assessment of Invar alloy weld joints using the notch stress approach

The aim of this study investigated the fatigue strength of Invar alloy weld joints. Invar steel (Fe-Ni 36%) is widely used in the primary and secondary barriers of membrane-type liquified natural gas (LNG) containment vessels. The fatigue test was carried out for two different types of welded joints with raised edge specimens and with overlap joint specimens based on the nominal and notch stress approaches. The thickness of the Invar plate is less than 1.5 mm, so the notch stress approach with r_ref = 0.05 mm was applied. Our evaluation of the results in terms of the FAT value and the slopes of the design curves are compared with steel, aluminum, and magnesium weld joints in accordance with International Institute of Welding (IIW) recommendations.     

A strain energy based damage model for fatigue crack initiation and growth

A strain energy based fatigue damage model is proposed which uses the strain energy from applied loads and the strain energy of dislocations to calculate stress-life, strain-life, and fatigue crack growth rates. Stress ratio effects intrinsic to the model are discussed, and parameterized in terms of the Walker equivalent stress and a fatigue crack growth driving force. The method is then validated using a variety of different metals with strain-life data and fatigue crack growth rate data available on the SAE Fatigue Design & Evaluation subcommittee database.     

The effects of multiple overloads and absorbed hydrogen on the fatigue strength of notched steel specimens

It is well known that earthquakes can damage structures and machinery. After an earthquake, those components, which have been obviously damaged are scrapped and replaced, and most of the components which have not been obviously damaged will continue to be used even after earthquakes. However, as will be shown, the earthquake may have severely impaired the fatigue strength of such components by introducing unfavourable residual stresses and short cracks at stress raisers. In addition, if such components should contain hydrogen, an increasingly possible scenario for the hydrogen economy in the future, then it is shown that the loss of fatigue strength can be even greater. This paper explores the extent of fatigue degradation due to overloads and to absorbed hydrogen. It was shown that generation of small crack and tensile residual stress imposed by overloads caused substantial decrease of residual fatigue strength compared with that in the initial state. It was also shown that hydrogen enhanced more reduction. Hydrogen enhanced reduction in two ways. The crack generated by overloads grew deeper in hydrogen charged material. In addition to this, the reduction of ΔK_th also occurred in hydrogen charged material. These two factors worked together to reduce the residual fatigue strength after multiple overloads.     

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

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

Fatigue assessment of high strength leaf springs based on the FKM guideline

Analytical fatigue strength calculations based on the FKM guideline have been performed for hot tapered and stress‐shot‐peened high‐strength leaf spring specimens subjected to three‐point fatigue bending. The ultimate tensile strength of the decarburized specimens' surface has been approached by means of Rockwell‐C hardness measurements, and used as input for the approximation of its fatigue limit and mean stress sensitivity. Surface roughness and residual stress measurements were performed to take account for the technological life influencing factors. Fatigue tests at a constant mean stress and various stress amplitude levels were performed to determine the specimens' S–N curve and validate the calculation's accuracy. Comparison of calculated with experimentally determined fatigue lives, though satisfactorily, pinpoints the necessity for more accurate implementation of the stress‐shot‐peening process within the FKM guideline.     

A finite-volume-energy based approach to predict the static and fatigue behavior of components with sharp V-shaped notches

The paper presents an energetic approach useful to predict of the static and fatigue behavior of components weakened by sharp re-entrant corners. Despite the fact that stresses and strain energy density tend toward infinity at the point of singularity, the energy in a small volume of material surrounding the notch tip has obviously a finite value and such a value is thought of as the entity that controls the failure. The energy, averaged in a volume of radius R (which depends on the material properties), is a precise function of the Notch Stress Intensity Factors and is given in closed form for plane stress and plane strain conditions, the material being thought of as isotropic and linear elastic. The method is validated taking into account experimental data already reported in the literature, concerning both static tests carried out on polymethyl metacrylate (PMMA)and Duraluminium specimens and fatigue tests on welded joints and notched components in structural steels. As a matter of fact, the method proposed here is the re-formulation, on one hand, of some recent area/volume criteria (in which averaged values of the maximum principal stress are used to predict component fatigue limits) and, on the other, of N-SIF-based criteria, where the Notch Stress Intensity Factors are thought of as the parameters that control static and fatigue failures.     

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.     

Calculation of transient strain energy release rates under impact loading based on the virtual crack closure technique

This paper describes an interface element to calculate the strain energy release rates based on the virtual crack closure technique (VCCT) in conjunction with finite element analysis (FEA). A very stiff spring is placed between the node pair at the crack tip to calculate the nodal forces. Dummy nodes are introduced to extract information for displacement openings behind the crack tip and the virtual crack jump ahead of the crack tip. This interface element leads to a direct calculation of the strain energy release rate (both components G_I and G_II) within a finite element analysis without extra post-processing. Several examples of stationary cracks under impact loading were examined. Dynamic stress intensity factors were converted from the calculated transient strain energy release rate for comparison with the available solutions by the others from numerical and experimental methods. The accuracy of the element is validated by the excellent agreement with these solutions. No convergence difficulty has been encountered for all the cases studied. Neither special singular elements nor the collapsed element technique is used at the crack tip. Therefore, the fracture interface element for VCCT is shown to be simple, efficient and robust in analyzing crack response to the dynamic loading. This element has been implemented into commercial FEA software ABAQUS^® with the user defined element (UEL) and should be very useful in performing fracture analysis at a structural level by engineers using ABAQUS^®.     

Tensile failure of concrete at high loading rates: New test data on strength and fracture energy from instrumented spalling tests

For the numerical prediction of the response of concrete structures under extreme dynamic loading, like debris impact and explosions, reliable material data and material models are essential. TNO-PML and the Delft University of Technology collaborate in the field of impact dynamics and concrete modelling. Recently, TNO-PML developed an alternative Split Hopkinson Bar test methodology which is based on the old principle of spalling, but equipped with up-to-date diagnostic tools and to be combined with advanced numerical simulations. Data on dynamic tensile strength and, most important, on fracture energy at loading rates up to 1000 GPa/s are obtained. The paper describes the test and measurement set-up, presents the new test data and the analysis of the test results. In addition, a rate-dependent softening curve is given which is based on the integrated findings so far.     

Evaluation of the overload effect on fatigue crack growth with the help of synchrotron XRD strain mapping

The overload retardation effect on fatigue crack growth rate (FCGR) in titanium alloy Ti-6Al-4V is studied. Synchrotron X-ray diffraction strain mapping of near-crack tip regions of pre-cracked fatigued samples is used to determine the effective stress intensity factors experienced by the crack tip. The effective stress intensity factor values are computed by finding the best match between the experimental strain maps and linear elastic fracture mechanics (LEFM) predictions. The dependence of the effective stress intensity factor, K, on the applied load is plotted, and an interpretation of the overload retardation effect is proposed. The present approach permits to reconcile the traditional LEFM fatigue crack propagation prediction and the experimental measurement of strain fields.     

Multiaxial fatigue of V‐notched steel specimens: a non‐conventional application of the local energy method

The paper deals with the multi‐axial fatigue strength of notched specimens made of 39NiCrMo3 hardened and tempered steel. Circumferentially V‐notched specimens were subjected to combined tension and torsion loading, both in‐phase and out‐of‐phase, under two nominal load ratios, R=?1 and R= 0, also taking into account the influence of the biaxiality ratio, λ=τ_a/σ_a. The notch geometry of all axi‐symmetric specimens was a notch tip radius of 0.1 mm, a notch depth of 4 mm, an included V‐notch angle of 90° and a net section diameter of 12 mm. The results from multi‐axial tests are discussed together with those obtained under pure tension and pure torsion loading on plain and notched specimens. Furthermore the fracture surfaces are examined and the size of non‐propagating cracks measured from some run‐out specimens at 5 million cycles. Finally, all results are presented in terms of the local strain energy density averaged in a given control volume close to the V‐notch tip. The control volume is found to be dependent on the loading mode.     

Modeling and fatigue assessment of weld start‐end locations based on the effective notch stress approach

The present paper contains a methodology for modeling and life assessment of fatigue loaded welded components providing distinct weld start and end locations. The proposed methodology follows the IIW recommendation regarding modeling and finite element meshing of weld toe and root by means of an effective notch radius and uses the corresponding Wöhler curve (FAT class) to assess the durability. Geometrical singularities and, therewith, numerical discontinuities, can be overcome especially when 3D weld root problems are treated. The fatigue life assessment is performed on the basis of normal stresses acting at the failure‐critical weld toe and root locations. Comprehensive experimental database containing stress and fatigue life results derived from motor truck's hypoid rear axles providing complex 3D welds subject to vertical, longitudinal, and torsional loading is used to verify the calculation accuracy of the proposed methodology. The agreement between experimentally determined and calculated fatigue results is satisfactory.