## Structural Hot-Spot Stress Evaluation Approach
### IIW Surface Stress Extrapolation Methods  
This method is based on the extrapolation of surface stress at the specified locations. The structural stress component acting normally to the weld-toe is the main cause of fatigue crack initiation in the welded component. This normal stress can be determined through strain measurements at different reference points and then extrapolated to the weld-toe for the evaluation of SHSS. For the better estimation of stresses, strain rosettes are recommended instead of uniaxial strain gauges, especially when the direction of principal stresses is unknown. Otherwise, FEA can be used for the evaluation of SHSS. There are several formulations available on the positioning of reference points from the weld-toe, but the recommendations given by ECSC (European Coal and Steel Community) and CIDECT (Comite International pour le Developpement et l'Etude de la Construction Tubulaire) [16; 17] are adopted, because these are applicable to both tubular and non-tubular joints. These studies are summarized in IIW recommendations [1; 3].  
After the advancement in computational analysis, the finite element-based models are preferred today for the evaluation of SHSS. Normally, linear stress extrapolation (LSE) is used for the determination of SHSS at the weld-toe, but if the increase in stress is highly non-linear near the weld-toe, then the quadratic stress extrapolation (QSE) method is preferred. For LSE, two reference points are used, while three or more reference points are required for the QSE method [1]. The distance of the reference points from the weld-toe normally depends upon the plate thickness (\(t\)). According to IIW recommendations, two reference points at 0.4\(t\) and 1.0\(t\) or 0.5\(t\) and 1.5\(t\) from the weld-toe can be used in LSE method for the finer and coarser mesh, respectively. While, for QSE, three reference points are recommended at a distance of 0.4\(t\), 0.9\(t\), and 1.4\(t\) from the weld-toe, respectively. The detail of these methods according to IIW recommendations is shown in Figure 1.  
In this study, both linear and quadratic stress extrapolation are implemented on an RD joint of the OSD specimen. After the evaluation of stresses at specified reference points, the following equations are used for the calculation of SHSS. If the linear extrapolation is performed using stresses \(\sigma_{0.4t}\) and \(\sigma_{1.0t}\) located at a distance \(0.4t\) and \(1.0t\) from the weld-toe, respectively, the following expression is used, and SHSS is abbreviated as LSE 410.  
\[LSE\ 410=1.67\sigma_{0.4t}-0.67\sigma_{1.0t} \tag{1}\]  
If linear extrapolation is performed using stresses \(\sigma_{0.5t}\) and \(\sigma_{1.5t}\) located at a distance \(0.5t\) and \(1.5t\) from the weld-toe, respectively, the following expression is used, and SHSS is named LSE 515.  
\[LSE\ 515=1.5\sigma_{0.5t}-0.5\sigma_{1.5t} \tag{2}\]  
Additionally, for quadratic stress extrapolation (QSE), \(\sigma_{0.4t}\), \(\sigma_{0.9t}\), and \(\sigma_{1.4t}\) stresses are used located at a distance of \(0.4t\), \(0.9t\), and \(1.5t\) from the weld-toe, respectively, and the following equation is used.  
\[QSE=2.52\sigma_{0.4t}-2.24\sigma_{0.9t}+0.72\sigma_{1.4t} \tag{3}\]