PSI - Issue 31

M.L. Larsen et al. / Procedia Structural Integrity 31 (2021) 70–74 M.L Larsen, V. Arora, H.B. Clausen/ Structural Integrity Procedia 00 (2019) 000–000

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3.2. Results The optimization algorithm searches for the lowest damage by changing the weld direction of the initial FE model. In Fig. 3, the results of the optimization are shown for each of the four investigated fatigue criteria. The damage in the welds original 0֯ orientation is given together with the optimized angle and final damage. The damage is found based on the Palmgren-Miners law using linear damage accumulation see e.g. Pedersen (2016). The results from the optimization are as expected, with a total rotation of the weld to the allowed 45 degrees for the IIW and EC3 approach, as these methods assumes the most damage from the normal stresses. As the applied loading is uniaxial in the x-direction, rotating the weld 45 degrees results in minimized normal stresses and maximized shear stresses in the direction normal to the weld. The IIW and EC3 predicts the same damage for the original 0֯ weld orientation. For the optimized weld, however, the EC3 criterion estimates around half the damage compared to the IIW criterion. This is due to the formulation of the two criteria’s being different considering the exponents of the shear and normal stresses. In the case of uniaxial normal stresses perpendicular to the weld toe, the shear stress is zero, resulting in the same damage from the two criteria. When shear stresses are introduced, i.e. in all other planes than 0, the criteria will produce different results.

(a) IIW 0֯ damage: 0.151 Optimized: 45֯ damage: 0.064

(b) EC3 0֯ damage: 0.151 Optimized: 45֯ damage: 0.036

(c) Findley 0֯ damage: 0.148 Optimized: N/A damage: 0.148

(d) MWCM 0֯ damage: 0.202 Optimized: N/A damage: 0.202

Fig. 3. Optimized weld orientations using the developed optimization framework and various fatigue criteria.

As seen from Fig. 3, the Findley and MWCM criteria do not provide optimized orientations of the weld. This is due to the critical plane approach, which searches and maximizes the critical damage based on all possible planes, as seen schematically in Fig. 4. As the FE models in this paper are based on shell elements without any geometric modelling of the welds and as the nominal stress approach is used, no stress concentration will add to the stresses at the weld. Thus, the critical plane approaches predict the same damage, even when rotating the welds, as seen in Fig 4 because the critical plane will not change. Thus, it can be concluded that the critical plane approaches should only be used with other stress estimation methods, such as the structural hot-spot stress approach or the notch stress approach for optimization. Another benefit of using the structural hot-spot stress approach or the notch stress approach is the fact that only a single S-N curve for the normal stress and shear stress needs to be considered. In the case of the optimization using the criteria from the standards, the rotation of the weld would principally change the relevant S-N curves. I.e. in the case of stresses more parallel to a weld, another S-N curve is recommended in the standards compared to the case of