An Analytical Procedure for the Prediction of the Stress-Strain State in Notches under Multiaxial Fatigue

Abstract

This work presents an analytical procedure for estimating elastic-plastic stresses and strains in notched shafts subjected to synchronous non-proportional torsional and tensile cyclic loading. The specification of the equivalent stress concentration factor is firstly accomplished. Neuber’s rule in conjunction with the assumed material law provides the relation between the applied loading and the equivalent stress and strain. Principal stresses and strains yield from the corresponding equivalent values incorporating Hencky’s equations. The transformation of the principal stresses and strains to the appropriate coordinate system yields the final result. For the assessment of the analytical procedure, notch stress-strain results from several finite element analyses of an axisymmetric cylindrical shaft with a circumferential groove subjected to multiaxial synchronous fatigue loading are presented. A satisfactory agreement between the analytical and numerical results is observed.