Stress field equations for U and blunt V-shaped notches in axisymmetric shafts under torsion

Analytical solutions are developed for the stress fields induced by circumferential U- and blunt V-shaped notches in axisymmetric shafts under torsion, with a finite value of the notch root radius. The boundary value problem is formulated by using complex potential functions and the real boundary notch shape. Shear stress components are then written as a function of the maximum shear stress evaluated at the notch tip. Considering different global and local geometries the obtained equations are compared with a large bulk of finite element results, showing a very good agreement. Due to their reduced complexity, such equations turn out to be particularly useful in practice.