Analytical study of stress distributions due to semi-elliptic notches in shafts under torsion loading

Closed form solutions for the stress fields created by a semi-elliptic circumferential notch in an axisymmetric shaft under torsional loading are developed. The boundary value problem has been formulated by an approach using complex potential functions and the natural elliptic coordinate system. The solutions obtained for the shear stresses have a wide range of applicability, both in terms of the size and shape of the notches and the diameter of the shafts.