Torsional stress distributions in tubes with external and internal notches

Practical expressions useful to assess the elastic stress distribution in a torque loaded axisymmetric tube, weakened by circumferential U- and blunt V-shaped notches, are presented. The solution is obtained as an extension of a previous analytical solution valid for axisymmetric solid shafts. It accounts for the local geometry (notch tip root radius and notch opening angle) as well as for the global geometry (inner and outer diameter of the tube). Shear stress fields are written as a function of the shear stress at the notch tip. Varying global and local geometries, the obtained equations are compared with a large bulk of finite element results, showing a good agreement.