PSI - Issue 34

Benjamin Möller et al. / Procedia Structural Integrity 34 (2021) 160–165 Author name / Structural Integrity Procedia 00 (2021) 000 – 000

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3. Fatigue assessment by notch stresses In order to evaluate notch stresses (von Mises and maximum principal stress hypotheses) based on 3d numerical simulations, 2d extruded finite element (FE) models using the reference radius of r ref = 0.05 mm at the relevant fatigue notch have been set up. For information on the parameters of the FE models for lap joints with I-shape seam welds and peel T-joints, it is referred to Möller et al. (2020). Supplementary, notch stresses have been evaluated from a representative FE model of lap joints with fillet welds on both sides using r ref = 0.05 mm at the weld toe radii, as shown in Figure 2(a). The remaining geometry parameters of the FE model have been defined according to the existing microsections (cf. Fig 1(b)). Both sheets of the lap joints are covered by at least four elements over the thickness. In the area of the welded joint, the mesh is refined towards toe radii of the fillet welds based on Baumgartner and Bruder (2013). For linear-elastic FE calculations, at least 24 quadratic elements distributed over 360° of a circle are recommended, according to Radaj et al. (2006). The modeled weld toe radii consist of eight elements distributed over an angular range of 28°, i.e. approx. 103 elements over a full circle would result. Brick elements with quadratic shape function and a ratio of two between length on circumference and length normal to the circumference are used. A Young’s modulus of E = 70 GPa and a Poission’s ratio of ν = 0.33 for both aluminum sheets – the additively manufactured and the conventionally manufactured – is applied in the linear-elastic material model.

Fig. 2. Results of the linear-elastic finite element simulation with stress concentration at the weld toe notch radius (von Mises stresses in MPa for a load of F = 100 N) of the laser beam welded lap joint with fillet welds.

In the FE simulation of the lap joint with fillet welds, the modeled clamping system on the fixed side is blocking the translatory degrees of freedom in the clamping area. At the other end of the specimen, the axial force is transferred to the specimen and the sheet metal is guided in the direction of force. Mounting of the specimens is not part of the simulation, so that angular misalignments are not considered. A linear-elastic simulation applying a unit force of 100 N is performed, since an experimental strain analysis does not show any geometrical non-linearity. A single load step from minimum to maximum loading is used to derive the notch stresses, since a comparison between experimentally – under quasi-static and cyclically loading – derived and numerically simulated strains at the sheet surfaces are in a good agreement. The simulation of the FE model represents the global stiffness of the experimental setup. The maximum notch stresses localize at the weld to radii, as it can be seen from the result of the simulation based on the von Mises stress hypothesis (vMSH) in Figure 2(b). In Figure 3, evaluated notch stress amplitudes  vM,a (at the weld toe location corresponding to the fatigue failure) versus the cycles to rupture N r are faced towards the results of lap joints with I-shape seam welds and peel T-joints as well as results of lap joints ( R = 0) from Kaufmann et al. (2000) and Störzel et al. (2012), respectively. The results of notch stresses based on the vMSH for lap joints with fillet welds exceed FAT 142 and even FAT 160 recommended for weld toe failure, assuming a slope of the design S-N curve of k = 5 in case of thin and flexible structures. The resulting notch stresses (vMSH) and fatigue lives are in the range of the results from Störzel et al. (2012). Notch stresses of both joint types with I-shape seam welds are in good agreement (scatter of T  = 1 : 1.44), showing fatigue failure from the notches in between the two sheets, i.e. to be categorized as ‘root notch’ failure . Recommended notch stress fatigue classes of FAT 160 and FAT 178 cannot be applied in a safe fatigue assessment,