PSI - Issue 57

Gustav Hultgren et al. / Procedia Structural Integrity 57 (2024) 428–436 Hultgren & Barsoum / Structural Integrity Procedia 00 (2023) 000 – 000

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failure in the as-welded side. The weld geometry and idealisation are extracted for all specimens using the commercial 59 quality assurance system Winteria®. 60 2.1. Simulating the exact weld geometry 61 A pre-processing of the local weld geometry recreates the topography of the weld surface based on the individual 62 scanned sections of the weld and the trajectory of the laser scanner on the robotic arm. Any drift in the scanning path 63 trajectory is cancelled out using affine transformations, and erroneous data is filtered out to not influence the results. 64 The remaining geometry that extends out from the scanned zone is added based on the nominal dimensions and the 65 measured angular distortion. A meshing scheme then builds the model, element by element and exports it as a meshed 66 model. This model is imported into ANSYS, where the boundary conditions are applied according to Hultgren et al. 67 (2023). The surface stress state at the weld and its close proximity is then used to determine the unique properties of 68 the individual weld through the probabilistic evaluation presented below. 69 3. Fatigue strength assessment using the true weld geometry 70 This section summarises the probabilistic framework in Hultgren et al. (2023), used to determine the sectional 71 stress component. These results are the basis for the later comparison with the analytical stress concentration 72 expressions from the literature. 73 3.1. Probabilistic evaluation 74 The interaction between different local highly stressed regions along the weld seam and their combined effect on 75 the fatigue strength of the complete joint is studied using the Weakest-link theory, which combines the failure 76 probability at each location to determine the failure probability of the complete structure according to, 77 78 The local failure probability of each sub-area dA in the fatigue-critical region is determined based on the local Signed 79 von Mises stress criterion that is calculated using the simulated stress fields, Papuga et al. (2012), 80 ( ) ( ) ( ) 2 2 2 SvM 1 1 2 2 3 1 3 1 =sign(I ) 2         − + − + − . (2) 81 The distribution shape parameter,  , and the characteristic fatigue life, 0  , define the two-parameter Weibull 82 cumulative distribution function that has proven to be a good representation of experimental fatigue data. The latter 83 of the two is stress level dependent and is thus formulated to follow the Basquin relation, 84 1 m EM 0 ref 6 exp 2 10 n c    −     =          . (3) 85 This characteristic stress curve utilises a reference stress value ref  for two million cycles as the fatigue strength value, 86 the Basquin slope exponent m , the number of cycles n , and the exponential value of the ratio between the Euler- 87 Mascheroni constant EM c and the distribution shape parameter. The size effect of the highly stressed region is scaled 88 towards a reference area 0 A , used as the nominal size of the region where the detailed information of the weld 89 geometry is measured. 90 The only variable parameter of the integrand in Eq.(1) over the area domain is the stress component that varies 91 over the surface. Substituting the integral over the Signed von Mises stress criterion with an equivalent stress equ  92 does therefore simplify the expression further, 93 94 The equivalent stress can either be determined by integrating the stress over the complete domain at once or divided 95 into discrete sections along the weld that defines the influence of the local geometry. The latter does then use the 96 sectional stress components sec  to determine the equivalent stress equ  , 97 SvM 0  0 1 exp = − − . A f A  dA p                (1) equ 0  1 exp = − − f p                . (4)