PSI - Issue 75

Jörg Baumgartner et al. / Procedia Structural Integrity 75 (2025) 538–545 Jo¨rg Baumgartner / Structural Integrity Procedia 00 (2025) 000–000

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Two assessments have to be performed: One for spot weld failure and one for failure in the sheet. The assessment of spot weld failure is, from a mechanical point of view, straightforward, as it uses section forces and moments in the bar element. However, these forces and moments cannot directly be used to determine the stresses in the sheet. A mechanical substitute model is used that consists of a metal sheet with the diameter of d a = 50 mm clamped on the outside. That diameter equals approx. 10 times the spot weld diameter d . Analytical formulae are used to calculate radial stresses for five cutting forces and moments: F x and F y , F z aswell as M x and M y . Whereas the approach is easily applicable, it has several drawbacks and a ”poor accuracy” [26]: • The assumption of d a = 10 × d of the mechanical substitute model is a simplification and does not represent the sti ff ness and deformation behavior in complex models. • Since only the radial stress is evaluated, the influence of all shear components is neglected. • Torque loading ( M z ) might also contribute to the damage, even though pure torque loading is not expected in structures with a huge number of spot welds. • The sti ff ness of the model is lower than that of 3D-model if sti ff ness or diameter of the bar element or neigh boring shell elements are not modified. The ideas of FESPOW have been develop further by adding beam elements in a radial pattern around the spot weld [21]. With this approach, the multiaxial stress states can be consider to a better extend; however, also the complexity of the model increases. The idea to model the fatigue critical notch at a spot weld with a reference radius was developed by Zhang [26]. The idea behind the approach is not connected to the reference radius of r = 1 mm with its FAT-class 225 [7]; furthermore, the derived notch stress can be interpreted as a value that is proportional to the stress intensity factor. Starting at spot welds, it was later used for the assessment of seam welds at thin sheets and a FAT-class of FAT630 was recommended [23]. This class is now included in the IIW-recommendations [3]. A benefit of notch stress is the possibility to assess multiaxial loading conditions by separating stresses normal to the weld and shear stresses [4, 1]. The interaction of normal and shear stress is assessed with the Gough-Pollard equation [6, 7]. Since the notches at a spot-weld have the characteristic of a crack, a lot of investigations have been conducted using fracture mechanics to assess the fatigue strength. The main di ffi culty in the assessment is the derivation of the stress intensity factor solution; i.e., an easy way to derive stress intensity factors (SIF). As input solutions, structural stress – in detail bending and membrane stress – is used to estimate the SIF [15, 9]. There also exists the possibility to calculate SIF directly with a Finite-Element model [10]; however, this approach cannot be used in industrial applications since it would consume too much time for setting up the models and too much resources to solve the models. As for the notch stresses, there exit various investigations that deal with the calculation of stress intensity factors for spot-welded structures under multiaxial loading. Here, not only the SIF under mode I loading, but also the SIF under mode II and mode III loading are evaluated [16, 27, 11]. As briefly introduced above, all three methods have in principle the possibility to assess multiaxial stress states. However, currently the structural stress based approaches are the most commonly used approaches to assess the fatigue strength of spot welds. The reason can be found in the simple models and fast calculation times. In addition, the main damage occurs in spot-welded structures due to mode I loading. Subsequently, in the majority of cases the assessment reliability is high. However, there are cases where shear, i.e., mode II loading dominates. In these cases, the assessment is non-conservative. So, in order to enhance the assessment reliability, a consideration of mode II and also mode III loading in the structural stress approaches would be beneficial. This can be achieved if notch stresses 2.3. Stress intensity factor for spot welds 2.4. Comparison of the approaches 2.2. Notch stress approach with radii smaller than 1 mm