## 5 Experimental Verification  
### Test Specim and Procedure  
A HSLA steel Q550 plate/sheet and a welding wire ER70S-6 were chosen as materials for the experimental verification. The mechanical properties and chemical composition of the deposited metal and base metal are displayed in Table 1. The geometrical parameters of the fatigue specimen and the parent metal are illustrated in Figure 7.  
Figure 5: Schematic diagram of the three-tangent-circle methods. Figure 6: Design parameters of the fracture mechanics-based EFBC method. The given parameters were substituted into the realizing condition of EFBC, Equation (12). The critical design curve of the butt welds with a target life of 2 million stress cycles was hence obtained. The geometric discontinuity in a component would give rise to high local stress, which can be characterized by the stress concentration factor, \(K_{t}\), which is expressed as [34]:  
\[K_{t}=\sigma_{local}/\sigma_{nom} \tag{13}\]  
where \(\sigma_{nom}\) and \(\sigma_{local}\) denotes the nominal stress and the maximum local Von Mises stress, respectively. Besides, \(K_{t}\) is valid just for stress grades within the elastic scope. To decrease the stress concentration degree at the weld toe, a three-tangent-circle approach is applied to the critical design curve for geometric optimization. Finite element technique is used to acquire the maximal local Von-Mises stress. Abaqus 6.13 is chosen to carry out linear-elastic finite element analysis. Figure 8 shows the finite element model of the designed welded joint under a uniaxial traction in x direction. According to the symmetrical characteristic of the joint, only a quarter of the designed welded joint is calculated in a 2-D finite element analysis procedure. The Poisson ratio 0.3 and Young's modulus 210 GPa of ordinary steels are utilized for analysis. The geometrical characteristics are the same as those that are acquired through theoretic analysis. The coordinate origin is set at the weld toe of the critical curve. Eight-node biquadratic plane stress quadrilateral elements (CPS8) are employed for calculation. The global mesh scale is 0.5 mm. The overall number of nodes and elements used in the computations are 12,498 and 3972, respectively. 100 MPa is chosen as an initial tensile stress loaded at the end surface of the base metal, i.e., the left end of the FE models shown in Figure 8. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Material** & **Mn Wt.\%** & **Si Wt.\%** & **C Wt.\%** & \(\sigma_{B}\) (MPa) & \(\sigma_{y}\) (MPa) & \(\delta\)(\%)** \\ \hline Q550D & 1.74 & 0.022 & 0.05 & 777 & 678 & 20 \\ ER70S-6 & 1.49 & 0.84 & 0.07 & 543 & 438 & 29 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Chemical composition and mechanical properties of the parent and deposit metal. Figure 7: (**a**) Geometric parameters of the Q550 steel plate; (**b**) Geometric parameters of the fatigue specimen of welded joints. (Unit: mm). The simulation results of Mises stress filed in designed joints with different fillet radii are displayed in Figure 9. The Mises stress values along the elements marked red on Figure 8 and the calculated nominal stress are put into Equation (13) to compute the stress concentration factor. Figure 10 shows the influence of fillet radii on the variation of stress concentration factors of the welds. The outcomes show that, as the fillet radius \(r_{1}\) increases, the stress concentration factor \(K_{t}\) at the weld toe gradually goes down. \(K_{t}\) is 1.24373 while \(r_{1}\) decreases to 13 mm. Note that the extent of reduction in \(K_{t}\) turns low while \(r_{1}>11\) mm, so that \(r_{1}\) is determined to be 13 mm. \(r_{2}\) is set to be 9.8 mm, on the basis of the geometric relation in three tangent circles illustrated in Figure 5.  
Figure 11 displays the final design result of the EFBC butt welds. It can be seen that the critical curve adequately contained by the optimized design curve. Figure 8: FE models for the geometric optimization of the designed joints.