Improved stress concentration factors for circular shafts for uniaxial and combined loading

Stress concentration factors (SCF) related to specific geometries, loadings and stress quantities can be calculated efficiently using approximate equations. Those relations are typically based on metamodeling via the results of linear elastic analyses. Existing equations for the, technically speaking, very important circular shafts with shoulder fillets or U-shaped notches under bending, torsion or tension/compression can be appropriated, for example, from the DIN 743-2 : 2012-12. Using these relations requires compliance with underlying constraints and assumptions. For example, equations from that code do not provide SCFs larger than 6 and refer only to the maximum principle stress. Furthermore, DIN 743-2 : 2012-12 does not provide SCFs for combined loading, i. e. simultaneous bending, torsion and tensile/compressive loading. This paper presents new and improved equations based on sampling computational finite element simulations and subsequent regression analyses. Multiple improvements could be achieved: The six equations for circular shafts with shoulder fillets or U-shaped grooves derived from DIN 743-2: 2012-12 were simplified down to two equations. Despite this simplification, the new equations have been generalized for combined loading and include SCFs larger than 6 as well. Choosing between various equations for each type of loading is no longer necessary. Only one equation for each of the two basic geometries is needed. Moreover, two further equations which refer to von Mises equivalent stress have been added. Although the new equations are easier to handle and allow for an estimation of stress concentration factors larger than 6, the accuracy of the new equations is higher than the accuracy of DIN 743-2 : 2012-12 when compared to SCFs derived from finite element simulation as reference values.