PSI - Issue 57

Alberto Visentin et al. / Procedia Structural Integrity 57 (2024) 524–531 Alberto Visentin et al./ Structural Integrity Procedia 00 (2023) 000 – 000

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PSM, as described in Fig. 2. In the present investigation, a dedicated routine is presented in order to account for VA loadings according to the recent advancements of the PSM (Campagnolo et al. 2022). A single linear elastic FE analysis is required, wherein each unit load must be applied to the model using separate load step s (see Fig. 2). Then, the time-history of each applied load must be imported. Alternatively, in the case of uniaxial VA loading, the load spectrum can be input in place of the load time-history (see Fig. 2). Starting from the CAD geometry of the model, the developed PSM analysis tool accomplishes the following tasks in a fully automated way. a. Analyze the geometry of the model, in order to identify all sharp V-notches of the structure and evaluate individually the relevant notch opening angle 2α. b. Perform automated mesh generation by adopting 10-node tetrahedral elements and a proper element size in compliance with PSM requirements. c. Calculate the PSM-related coefficients (see (Meneghetti and Campagnolo 2020)) as a function of the notch opening angle 2α and material elastic properties, by using specifically developed polynomial expressions (Visentin et al. 2022b). d. After solving the FE analysis, define a properly oriented local coordinate system to retrieve the relevant peak stresses tied to mode I, mode II and mode III on each analysed node. In the case of FE meshes based on tetrahedral elements, the peak stresses on adjacent vertex nodes are automatically averaged according to (Meneghetti and Campagnolo 2020). e. Calculate mode I, mode II and mode III peak stress time-histories due to each individual load step, starting from the time-history of each applied load imported by the analyst. f. Sum the peak stress time-histories relevant to each applied VA load in order to define mode I, mode II and mode III peak stress time-histories accounting for the combination of all applied VA loadings. g. Apply the Rainflow cycle counting to obtain mode I, mode II and mode III peak stress spectra. h. Apply Palmgren-Miner LDR equivalency (Campagnolo et al. 2022), in order to obtain constant amplitude equivalent peak stress ranges Δ σ eq,peak, i ( i = I, II, III) (see Eq. (1)) i. Combine the calculated constant amplitude equivalent peak stress ranges into the equivalent peak stress range accounting for multiaxial VA local stresses, according to Eq. (1). j. Calculate the local biaxiality ratio λ , according to Eq. (3). k. Depending on the local biaxiality ratio λ, perform fatigue life estimation addressing the proper PSM -based fatigue design curve (Meneghetti and Campagnolo 2020). Eventually, the presented application allows to visualize the results as nodalequivalent peak stresses or expected fatigue life at the V-notch lines (i.e. the weld toes and weld roots) of the 3D FE model by means of contour plots over a wireframe view of the examined geometry (Fig. 2). In this way the analyst can easily single out and compare all different competing critical points in the structure. Moreover, the PSM application provides a dedicated toolbar specifically designed for results visualization and post-processing analyses (see Fig. 2). To illustrate the overall fatigue design procedure and prove its effectiveness, a case study taken from the literature is presented, where the PSM tool has been employed to analyze tube-to-flange welded joints subjected to both CA and VA uniaxial as well as multiaxial loadings. 3. Case study – Witt et al. (Witt et al. 2000; Yousefi et al. 2001), tube-to-flange joints Fatigue data concerning partial penetration tube-to-flange welded connections made of P460 fine-grained steel and tested under constant amplitude (CA) as well as variable amplitude (VA) pure bending, pure torsion and combined bending and torsion loadings have been re-analysed according to the PSM. CA fatigue tests were performed under pulsating (R = 0) and fully reversed (R = -1) bending, torsion and combined bending and torsion loadings. Combined bending and torsion loadings were applied in-phase ( ϕ = 0°) and out-of-phase ( ϕ = 90°), as well as with different frequency proportions (f T = f B , f T = f B /5 or f T = 5f B , where “T” and “B” refers to torsion and bending loads, respectively). A nominal biaxiality ratio Λ = Δτ/Δσ = 1 was adopted forall the tests. Moreover, additionalmultiaxial loading cases were obtained by combining a fully reversed (R = -1) bending loading and a constant torsional stress and vice versa, i.e. a fully reversed (R = -1) torsion loading and a constant bending stress. VA fatigue tests were performed under almost the same loading conditions employed in CA tests (more details in (Witt et al. 2000; Yousefi et al. 2001)) by adopting a standard Gaussian load spectrum (Haibach et al. 1976; Heuler et al. 2005) of 50000 cycles applied as a random load history (Fig. 3c). Additional multiaxial VA fatigue tests have been performed under fully reversed (R = - 1) combined bending and torsion “uncorrelated” loadings, where “uncorrelated” means that “the load