Analytical and Numerical Modeling of Stress Intensity Factor in I-Shaped Cross Sections of Cracked Beams

In this paper, the stress intensity factor (SIF) in the opening mode I is investigated in cracked beams with the I-shaped cross sections under axial loading. In cracked cross sections, a couple is made due to shifting the two centroids, or in the other word due to a misalignment between the axes of the axial force. The analysis is carried out through two analytical and numerical approaches. In analytical approach, a mathematical model for SIF is proposed via the theory of the energy release rate in the region around the crack. This model is adapted by considering the moment of the couple. It is presented in two situations in terms of the crack location including the crack in a part of the flange, and the crack in the flange and a part of the web. In numerical approach, geometric and material characteristics and type of loading are modeled by using Abaqus software; then SIF values of the I-shaped cracked beam are determined. In the presented numerical solution, two methods of C-integral and X-FEM are employed to model the crack. The validity of proposed equations is confirmed by the comparison between the presented results of numerical and analytical approaches.