Numerical Verification of Stress Intensity Factors at Semielliptical Surface Cracks at the Weld Toe of Cruciform Joints

In linear elastic fracture mechanics, stress intensity factors quantify crack tip stresses. Hobbacher developed formulas for welded details, using the stress magnification factor M_k for semielliptical surface cracks. These formulas are critical for calculating residual lifetimes and inspection intervals of welded steel bridges. This paper systematically reviews Hobbacher's formulas and introduces refined expressions. A validated finite element model of a semielliptical surface crack in a plate forms the basis for analyzing cruciform joints with directly and indirectly loaded welds. Stress intensities at the deepest and surface points are determined and compared with existing formulas. The study also investigates the influences of parameters such as weld angle and weld throat thickness on stress intensity. Results show that Hobbacher's formulas are conservative at the deepest point, overestimating M_k by up to 44%. Correction factors and regressions are derived for both the deepest and surface points, aiming to enhance stress intensity factor accuracy.