Shafts with U-shaped circumferential grooves: design charts for stress concentration factors, radial displacement and Poisson’s ratio influence

Shafts with U-shaped circumferential grooves subjected to internal normal force and bending moment are investigated on the basis of finite element analysis. The classical problem of the Stress Concentration Factors (SCFs) identification is addressed. SCF charts are provided, adopting the maximum equivalent von Mises stress in the SCF definition. The discrepancy between the uniaxial SCFs extracted from the standard reference books and the multiaxial SCF obtained by finite element increases from 5% up to 20%. The intersections between the SCF curves are studied, which reveal a non-monotonic profile of the SCFs with respect to the outer and inner diameter ratio of the notched shaft. The radial displacement at the notch root is examined and design charts of ample validity and prompt access are compiled. It is found that the radial displacement sign and magnitude are largely dependent on the geometry of the notch. Furthermore, the strain and stress state of extremely shallow grooves are analysed and a critical discussion on their SCFs using the von Mises criterion is presented. The influence of the Poisson’s ratio is considered. A simplified method for the evaluation of a multiaxial SCF is proposed to account for the Poisson’s ratio effect. Thanks to the employment of few dedicated diagrams, the present method allows an accurate evaluation of the SCF for U-grooved shafts, when the Poisson’s ratio differs from the common 0.3 value.