STRESS DISTRIBUTIONS FOR V-SHAPED NOTCHES UNDER TENSILE AND BENDING LOADS

Abstract— An analytical solution has been proposed recently by the authors to describe, with a unified approach, the stress fields in the neighbourhood of sharp cracks, V-shaped notches and re-entrant corners in plates subjected to remote tensile loading. In the present paper, the above solution is revised and extended, by also determining the relevant displacement fields and the degree of accuracy of the solution for both the longitudinal and transverse stress fields. Afterwards, since the stress field depends on the type of loading, the circumferential principal stress component is modified to account for bending in fatigue life predictions, while the radial principal stress is almost negligible in this case. The analytical results are compared with finite element values obtained for different geometries loaded under tensile or bending conditions, as well as with other closed-form solutions. The new expressions seem to give better stress estimates than the currently available approximate solutions, whether analytical or numerical, when the opening angle of the re-entrant corner is equal to or greater than π/2. Hence they should represent a good starting point to describe stress distributions induced by stress raisers with large and well defined opening angles such as shafts with shoulder fillets, gears and weldments.