PSI - Issue 75

S.S. Penkulinti et al. / Procedia Structural Integrity 75 (2025) 1–9 Author name / Structural Integrity Procedia (2025)

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3. Results and discussion 3.1. Fatigue strength anisotropy for uniaxial loading (R = -1) The stress tensor corresponding to the macroscopic loading amplitude for the uniaxial case is given by equation (11). = [ 0 0 0 0 0 0 0 0 1 ] (11) When a rotation ( , , ) is applied to this stress tensor, the final rotation corresponding to the Euler angle has no impact on the rotated stress tensor ′ , as the loading direction coincide with the final rotation axis . Consequently, for this specific loading case, the rotated loading directions can be fully described by the and angles. This makes possible to visualize the results on a surface response involving spherical coordinates, consisting of the points of coordinates Σ ( , ). ( , ) , where ( , ) is the loading direction corresponding to the angles ( , ) and defined by equation (12), and Σ ( , ) the corresponding fatigue strength obtained from the computations. = [ ( ) ( ) ( ) ( ) ( ) ] (12) For each pair of angles ( , ) , the fatigue strengths from the 25 LoF defects have finally been averaged in order to build a surface response corresponding to the mean fatigue strength associated to the whole defect population. This surface response is provided in Fig. 3 for the case of local analysis. From this figure one can observe that the fatigue strength is not sensitive to the angle and that it is fully governed by the polar angle . The minimum fatigue strength corresponds to =0° , which corresponds to a loading direction aligned with the building direction and would therefore corresponds to a vertical sample. On the other hand the maximum fatigue strength is obtained with =90° , which would correspond to a horizontal sample. One can assess an anisotropic factor defined as the ratio between the maximum and minimum fatigue strengths (see equation (13)).

Fig. 3: Evolution of the mean fatigue strength associated to the LoF defect population with respect to the loading direction (illustrated with the red vector) - Local analysis (from Penkulinti et al. (2025))