PSI - Issue 75

J. Havia et al. / Procedia Structural Integrity 75 (2025) 43–52 Havia et al. / Structural Integrity Procedia (2025)

47 5

Y

Fig. 5. a) ¼-symmetry model of FE model with either pure membrane (Fx) or bending (Mz) loading cases, and local notch geometries of b) Case 1, c) Case 2, and d) Case 3. e) Structural stress components at reference the location

Two different load cases were needed to solve the fatigue notch factors for membrane ( k f,m ) and bending ( k f,b ) loadings. This was necessary as the DED-detail causes both structural membrane and bending stress concentrations at the fatigue critical location. These factors were solved by applying both pure axial membrane ( F x ) or bending load ( M z ) at the end of the specimen and extracting the structural stress components ( k s ) through-the-thickness (Niemi et al., 2018) at the weld toe. When both structural stress components were acquired under both pure membrane and bending loading conditions, and the effective notch stress ( σ k ,FEA ) was extracted from the same model. Following pair of equations can be used to solve k f,m and k f,b .

k k

k k k k



+

    = =

  

f,m s,m,m nom f,b s,b,m nom k,FEA,m

(1)

k k



+

f,m s,m,b nom f,b s,b,b nom k,FEA,b

where, σ nom is the nominal stress corresponding, k s,m,m/b are membrane and k s,b,m/b are bending structural stress concentration factors under either pure membrane and bending loading, respectively, and σ k ,FEA,m/b are corresponding effective notch stresses. The third analysis for each model was necessary to capture the actual stress distribution of membrane and bending components. In this model, the rotation of the end of plate was constrained similar to the experimental test setup (clamping constraint), allowing development of the secondary stresses at the support. However, various discrepancies, e.g., simplifications on the FE- ’ boundary conditions, angular misalignment caused by DED-process, and straightening effect of specimen due to clamping, cause differences between the FEA and the experiment. All these factors can be assumed to have an influence on the bending component of the specimen. Additional bending was estimated using a stress modification factor ( η ) that represents the combined effect of all known and unknown imperfections. This approach is based on an assumption that the ratio of nominal stress to stress at reference location (SG location) should be the same in the FE model and in the experiment. The method is presented schematically in Fig. 5e. Factor η can be calculated with following equation:

ref,SG ref,FEM  





+

(2)





nom

nom

where, σ ref,SG/FEM are stresses at the reference location in the specimen or FE model, and σ nom is the corresponding applied nominal stress. The ENS stress range for each specimen can be calculated for the following equation: ( ) ENS f,m s,m nom f,b s,b nom k k k k      =  + +  (3)