PSI - Issue 77

Behzad Vasheghani Farahani et al. / Procedia Structural Integrity 77 (2026) 424–431 Behzad V. Farahani et al./ Structural Integrity Procedia 00 (2026) 000–000

427

4

≈ 3.21 ∙ = 1 1 . 07+ ( 350 / ) 4 . 8 = ∙ / = / ′ =0.002/ 1−0 . 95 /

( / )

(1) (2) (3) (4) (5)

=2.4+2.9 /

(6) Within all these parameters, the true stress-strain data can be derived using the constitutive model of Ramberg and Osgood (Ramberg & Osgood, 1943): = + ′ � � (7) An explicit procedure to derive Ramberg–Osgood parameters ( , , , and ′ ) from data was applied as: 1. is determined by using Eq (1); 2. / is calculated from using Eq. (2); 3. is then obtained as Eq. (3); 4. is calculated as Eq. (4); 5. ′ is determined as Eq. (5); 6. Finally, is derived from / using Eq. (6). Notice that material heterogeneity has been confined to variations in yield strength, while the strain hardening exponent ( ) was kept constant across all studied regions as proposed in (Hertelé et al., 2015). This assumption ensures that differences in mechanical response are primarily driven by yield strength variations. It led to simplifying the numerical model while still capturing the essential effects of weld heterogeneity. 3.2. Numerical implementation Considering an NRB-R6 specimen, a 3D numerical model has been built, as validated by Depraetere et al. (Depraetere et al., 2021). It must be noted that the center of the sample (notch) is set as the reference coordinate, c.f. Fig. 1-a). This numerical model is generated using an in-house Python script integrated within the ABAQUS® finite element software package (version 6.23). The object-oriented scripting approach enables efficient preparation, execution, and postprocessing with minimal user intervention. Since the sample is symmetrical along the central plane, it allows for the consideration of only half of the model. The numerical model comprises 54,119 nodes and 49,280 linear hexahedral elements of type C3D8T. The element size in the notched region is defined as =0.2 , following the methodology validated by Depraetere et al. (Depraetere et al., 2021). A dedicated element set was created for the region of interest (ROI), which represents the heterogeneous zone. The ROI is defined based on the dimensions of the hardness map (as shown in Fig. 1-b) but can be adjusted to meet specific model requirements. Additionally, two separate element sets represent the BM homogeneous regions outside the ROI. The ROI itself contains 42,080 C3D8T elements. Fig. 2 illustrates the procedure outlined in the following steps: 1. Element centroid determination: Each finite element centroid (denoted as ' ') located in the ROI is identified. 2. Coordinate mapping: The ( , ) -coordinates of this centroid are linked to the corresponding position of the indentations in the hardness map. 3. Hardness estimation: Hardness values are estimated using barycentric interpolation within a triangle formed by the three nearest hardness measurement points (denoted as , , and ). This triangle is generated through Delaunay triangulation (Dwyer, 1987) of hardness indentation grids.

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