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

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4. Constitutive property calculation: Finally, constitutive material properties are derived from hardness values. The following key points are addressed in this procedure: • Elements located outside the boundaries of the hardness map (i.e., outside the ROI) are assigned to the BM material properties, identified as the BM homogeneous region. These elements are not involved in this procedure, which helps to reduce computational costs. • The hardness map is essentially a 2D representation ( − plane) and does not provide data in the third dimension ( − direction). The developed algorithm assigns the same material properties to elements with identical centroid coordinates in the − plane, while the − coordinate (in the transverse direction) may differ. Consequently, element-specific material properties are transferred from the hardness data to the front surface of the ROI (at , , = 0) and remain consistent along the transverse − direction. • In cases where elements have differing centroids and − coordinates, the algorithm assigns material properties through local interpolation based on neighboring elements. The developed algorithm then generates a set for each element, assigning specific material properties, and subsequently assigns a corresponding section. This section assignment retrieves the mechanical and hydrogen-related parameters from the input data. As a result, the ROI of the current benchmark contains 42,080 distinct sets, each associated with specific flow stress-strain data. Fig. 3-a) illustrates the assignment of element-specific material properties within the ROI. The mechanical properties have been assigned to each element based on data obtained from the hardness map HV10 (proof load of 10), c.f. Fig. 1-b). Considering the mean HV10 in the WM region, the corresponding yield stress is approximately 600 MPa. However, the heterogeneity extends beyond the mechanical properties to also include hydrogen-related parameters. To accurately incorporate heterogeneous hydrogen properties, such as hydrogen concentration and diffusivity, the BM, HAZ and WM regions, must first be geometrically identified and mapped into the numerical model. They are clarified by fusion lines, which serve as boundaries between regions with distinct material properties. The fusion lines are constructed by interpolating segmented paths that connect manually selected reference points on the hardness map, automatically processed using a Python script. As shown in Fig. 1, each fusion line (blue coloured) is defined by approximately one hundred data points, leading to a precise representation of the weld fusion boundary. Since these points are initially recorded as pixel-based − and − coordinates, they must be converted into the appropriate physical coordinate system for numerical implementation. To achieve this, a scale factor should be applied, translating pixel-based measurements into millimetres. At this stage, the weld centre is set as the reference coordinate, c.f. Fig. 1-a). The output data are the corresponding , coordinates and HV values for each indentation. Based on the fusion line data, the HAZ and WM regions are geometrically defined with corresponding boundaries. Elements are assigned to HAZ, WM, or BM based on centroid location, with overlaps resolved by volume fraction. Hydrogen-related properties are applied to each set, c.f. Fig. 3-b). 4. Computational Damage Modeling Numerical damage simulations were performed using the material properties reported in Table 1. The BM yield stress was determined as 455 MPa through experimental tensile testing. Two configurations were considered: a homogeneous model, where the NRB sample consists entirely of the BM, and a heterogeneous model, reflecting the actual sample extraction shown in Fig. 1-a), with element-specific properties assigned as described in Section 3.2. Reference simulations under air conditions were conducted to evaluate material degradation. The resulting force/elongation curves are presented in Fig. 4. Here, HMG and HTG denote homogeneous and heterogeneous models, respectively. The simulations employ the CGM to capture the ductile damage behaviour of the material, with damage parameters calibrated and validated in (Depraetere et al., 2021).

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