PSI - Issue 75

S.S. Penkulinti et al. / Procedia Structural Integrity 75 (2025) 1–9 Author name / Structural Integrity Procedia (2025) 5 where is the maximum value of the FIP found on the surface of the defect, and Σ the applied loading amplitude. The post-processing procedure described previously corresponds to a local analysis of the stress fields since the value only corresponds to the Gauss point where stresses are maximum, commonly designated as the hotspot . Several authors have demonstrated that this type of approach leads to conservative predictions of the fatigue strength, as for example the studies of Karolczuk et al. (2008) or Morel et al. (2009). These works highlighted that the stress/strain gradients surrounding the hotspot should also be considered for a proper prediction. To do so, one possibility is to average the stresses over a small volume centered on the Gauss point at which the FIP value is assigned, in the framework of the critical distance theory (Susmel 2008). This volume usually corresponds to a sphere of radius which was set to 6µm in the present study, based on previous work on additively manufactured Ti64 (Vayssette et al. 2019). This type of post-processing will be designated as non-local analysis in what follows. 2.4. Numerical strategy to study the effect of loading orientation For each defect and loading type, different loading directions have been considered. To do so, rotation is applied to the macroscopic applied stress tensor , leading to a rotated stress tensor ′ corresponding to equation (6). ′ = ( , , ) ( , , ) (6) where is a rotation matrix parameterized with the Euler angles ( , , ) (see Bunge (1982) for the Euler angle definition). It worth noting that this rotation corresponds to the application of three subsequent rotations, as described in equation (7). The rotated tensor ′ can then be written as a linear function of 6 independent elementary macroscopic stress tensors (see equation (8)) which are designated as in what follows, where  is an index corresponding to the Voigt notation. The expressions of these 6 elementary tensors are provided in equation (9). ( , , ) = ( ) ( ) ( ) (7) ′ =∑ ′ 6 =1 (8) = [ 1 0 0 0 0 0 0 0 0 ] ; =[ 0 0 0 0 1 0 0 0 0 ] ; =[ 0 0 0 0 0 0 0 0 1 ] (9) ( ) corresponding to these elementary macroscopic loadings have been computed, so that the local stress field ′( ) corresponding to the rotated loading ′ can be assembled using equation (10) using the superposition principle. ′( ) = ∑ ′ ( ) 6 =1 (10) This decomposition of the rotated stress tensor makes possible to use only 6 elementary FE computations per defect to assess the local stress fields for any loading direction, so that the considerations of multiple loading direction does not raise heavy computational cost. Thus, for each loading type and each defect, 8125 loading directions have been considered by varying between 0° and 360°, between 0° and 180°, and between 0° and 360°, all with an increment of 15°. = [ 0 0 0 0 0 1 0 0 0 ] Therefore, for each defect, the local stress fields 0 1 0 ] ; =[ 0 0 1 0 0 0 1 0 0 ] ; =[ 0 1 0 1 0 0

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