PSI - Issue 57

Jacques BERTHELLEMY et al. / Procedia Structural Integrity 57 (2024) 872–903 J. Berthellemy / Structural Integrity Procedia 00 (2023) 000 – 000

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However, after1987 others decided for usual smaller bridges to use the tables from the Eurocodes project without modifying the stresses using finite element analysis. The correct FEM methods to compute the stress concentration factors are presented below and we will see how they can be crucial in ensuring durability.

2. Evaluation of fatigue details using the “hot spot method” 2.1 Principes of the calculation method

The calculation presented are realized using Code_Aster, an Open Source Software developed by EDF, R & D [8]. This software has been externally tested and approved in several countries (France, UK, China) for applications in the nuclear industry. The process uses Code_Aster's CALC_FATIGUE operator. The model is completely volumetric. The mesh is a non structured mesh made of tetrahedrons obtained with GMSH. As recommended for Code_Aster, the tetrahedrons are never very different from regular platonic tetrahedrons in the area of the hot spots. This mesh also conforms with the recommendations of December 2008 of IIS-IIW (International Institute of The extrapolation of the recommendations of December 2008 of the IIS-IIW is carried out industrially for all the tetrahedrons using the GMSH [10] smoothing function of the results instead of using the more complex but similar extrapolation process required in [9] to evaluate the structural stress. This process was already tested and successfully applied to solve many problems. It produces very good results, in particular for fatigue categories of detail between 36 and 71 MPa with the hot spot method. The point with of the strongest probability of crack initiation along a cut is determined using the signed von Mises criterion as scalar function in order to determine the probability of crack initiation during one cycle of stress variation. During this cycle presented in Fig. 5, a time varying factor is applied to the set of stresses that constitute the loading and for instance for the longitudinal stress  , the amplitude of stress is of 50 MPa which means in other words that the  stress range is of 100 MPa. Welding) [9]. In the areas of the hot spots, the size of the sides of the 3D-volume mesh is 4 mm. In each tetrahedral element, the stresses are calculated by Code_Aster at the Gauss point.

Figure 5 : History of stress variation that is used to evaluate the crack initiation probability (Stress Range 100 MPa = 2 x amplitude)

Along a rounded cutting line, the von Mises function avoids us to have to look for the governing principal stress. The quality of the cut is assumed to be 125 MPa and Code_Aster presents directly as a result the probability of crack initiation.