Analysis of Stress Intensity Factors in Semi-Elliptical and Semi-Circular Surface Cracked Plates

The present work proposes an open-form solution to calculate stress intensity factors (SIFs) from out-of-plane fracture modes (Mode I, II, and III) in structural steel rectangular plates containing surface cracks. These analytical methods are valuable for assessing structural integrity in components such as pressure vessels, bridges, and aircraft fuselages under complex loading. High-order meshing techniques within ANSYS enabled finite element method (FEM) simulations that validated the theoretical model. The study analyzes semi-elliptical and semi-circular surface cracks with depth-to-length ratios ≤ 0.5 under arbitrary 2D stress distributions. The employed weight function method evaluates SIFs under non-uniform loading with high predictive accuracy. The plate is assumed to be fully clamped along all edges. Results indicate that SIFs at the center of semi-elliptical cracks are approximately 25% higher than in semi-circular ones, with the opposite trend near the surface. An increase in the a/d ratio leads to higher SIFs, providing important input for damage-tolerant design. The derived expressions offer an efficient alternative to full-field FEM simulations in early-stage safety evaluations.