Saint-Venant torsion of orthotropic bars with rectangular cross section weakened by cracks

• We analyze the torsion problem of a rectangular bar with a screw dislocation.
• Bar is governed by the Saint-Venant torsion theory.
• We use the dislocation distribution technique for analysis of curved cracks.
• By enhancing crack length the stress intensity factor of crack tip is increased.
• We specify boundary of plastic region around crack tip.

The solution to problem of a Volterra-type screw dislocation in an orthotropic bar with rectangular cross section is first obtained by means of a finite Fourier cosine transform. The bar is under axial torque which is governed by the Saint-Venant torsion theory. The series solution is then derived for displacement and stress fields in the bar cross section. The dislocation solution is employed to derive a set of Cauchy singular integral equations for the analysis of curved cracks. The solution to these equations is used to determine the torsional rigidity of bar and the stress intensity factors (SIFs) for the tips of the cracks. Several examples of a single straight crack and an arc-crack are solved. Furthermore, the interaction between two cracks is studied. Finally, the stress components around an inclined edge crack tip are used to define the boundary of the plastic region employing von Mises yield criterion.