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

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    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 R(0) = 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

    Fatigue assessment of welded joints under slit-parallel loading based on strain energy density or notch rounding

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    Three types of welded joints exhibiting weld roots with slit-parallel tensile stresses combined with predominant mode 2 loading are assessed with regard to their fatigue strength based on the strain energy density (SED) concept in comparison to the fictitious notch rounding (FNR) concept: the butt weld joint with permanent backing plate, the fillet-welded single-sided attachment joint and the fillet-welded double-sided lap joint. This mainly numerical analysis extends a more fundamental previous investigation of the authors. The common feature of these joints is the markedly one-sided angular distribution of the SED or notch stress at the slit tip of the weld root. The main geometrical influencing parameters, plate thickness ratio and joint face width ratio, are varied systematically for a main plate thickness of 10 mm. The effect of slit closure is considered where the effect may occur. Fatigue-effective stress concentration factors are determined. Corresponding endurable structural membrane stresses are given based on Lazzarin's uniform (W) over bar -N curve on the one hand (SED approach) and based on the endurable notch stress for the reference radius rho(Gamma) = 1 mm in the parallel to W recommendations on the other hand. Finally a welded sandwich panel joint is considered. for which some fatigue test data are available. Sufficiently accurate results can already be achieved by the SED approach using an extremely coarse FE mesh

    Verifiche a fatica di giunti saldati mediante criteri locali: Un confronto tra il criterio basato su un raggio di raccordo fittizio e il criterio della densità di energia di deformazione in un volume finito

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    The aim of the paper is to demonstrate the close correspondence between two local approaches to assess the fatigue strength of welded joints: Radaj's approach based on fictitious notch rounding and a recently proposed approach based on the local strain energy density (SED) averaged over a given control volume. This volume surrounds the weld root or weld toe, both modelled as sharp (zero radius) V-notches with different opening angles. The two approaches are applied to load carrying and nonload carrying cruciform joints and the theoretical fatigue notch factors Kf are compared. The SED averaged over the control volume is determined from finite element models with very fine meshes, as typically designed to evaluate the intensity of the asymptotic stress distributions, and also from coarse meshes, showing a surprisingly good correspondence. This fact is surely of interest in view of possible applications of the SED method to components of complex geometry

    Fatigue design of welded joints by local approaches: Comparison between fictitious notch rounding and strain energy averaging

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    The paper demonstrates the close correspondence between two local approaches to assess the fatigue strength of welded joints: Radaj's approach based on fictitious notch rounding and a recently proposed approach based on the local strain energy density (SED) averaged over a given control volume. This volume surrounds the weld root or weld toe, both modelled as sharp (zero radius) V-notches with different opening angles. The two approaches are applied to load carrying and non-load carrying cruciform joints and the theoretical fatigue notch factors Kf are compared. The SED averaged over the control volume is determined from finite element models with very fine meshes, as typically designed to evaluate the intensity of the asymptotic stress distributions, and also from coarse meshes, showing a surprisingly good correspondence

    Fictitious notch rounding concept applied to V-notches with root holes subjected to in-plane shear loading

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    The fictitious notch rounding concept is applied here for the first time to V-shaped notches with root hole subjected to in-plane shear loading. The fictitious notch radius is determined as a function of the real notch radius, the microstructural support length and the notch opening angle, at first using the normal stress criterion in combination with the maximum tangential stress criterion for finding the crack propagation angle. Two analytical methods have been developed resulting in closed form expressions for the multiaxiality factor s. Finally, for comparison, the factor s is determined also on a purely numerical basis by iteration of FE-models. © 2011 Elsevier Ltd

    Generalised Neuber concept of fictitious notch rounding

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    The microsupport effect at sharp notches subjected to high-cycle fatigue can be described according to Neuber by averaging the maximum notch stress in a small material volume (microsupport length ρ*) at the notch root (radius ρ). The averaged stress may be expressed by the maximum stress of a corresponding notch of an enlarged, fictitious radius, ρf = ρ + sρ*, where s is the microsupport factor. The status of Neuber's concept within his general theory of notch stresses is reviewed, followed by more recent theoretical and application-relevant developments. The theoretical developments refer to the notch angle dependency of the support factor, to its value for pointed versus rounded notches and to in-plane shear loading with out-of-bisector crack propagation. The application developments refer to the fatigue assessment of welded joints. © 2013 Elsevier Ltd. All rights reserved

    Fictitious notch rounding concept applied to sharp V-notches: Evaluation of the micro structural support factor for different failure hypotheses. Part I: Basic stress equations

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    With the aim to perform a comprehensive and accurate evaluation of the microstructural support factor of sharp V-notches (Neuber's notch rounding concept), in Part I of this contribution, the indispensable theoretical tools, especially the basic stress equations, are reconsidered and amended in respect of accuracy of results. First, the analytical solution derived by Neuber [Neuber H. Kerbsparmungslehre. 2nd ed. Berlin: Springer-Verlag; 19581 for sharp rounded V-notches with an arbitrary flank angle under tension loading is considered. The equation of the normal stress has been obtained with the restriction to the notch bisector. Using the Airy stress function suggested by Neuber, this solution is extended to the region outside the notch bisector, and the complete stress field is derived in this manner. A comparison between Neuber's solution, a more recent solution due to Filippi et al. [Filippi S, Lazzarin P, Tovo R. Developments of some explicit formulas useful to describe elastic stress fields ahead of notches in plates. Int J Solids Struct 2002;39:4543-65] and highly accurate FE results is performed. Filippi's equations which include Williams' solution [Williams ML. Stress singularities resulting from various boundary conditions in angular corners on plates in tension. J App] Mech 1952;19:526-8] for pointed V-notches, are shown to be superior
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