A Theory for the Effect of Mean Stress on Fatigue of Metals Under Combined Torsion and Axial Load or Bending

TLDR

The study introduces a rational theory that treats alternating shear stress as the primary fatigue driver while accounting for mean (static) stresses on the critical shear plane in combined torsion–axial or bending loading. It investigates how the cycle’s maximum stress affects the permissible alternating stress and the orientation of the critical shear plane for a specified fatigue life. The theory’s predictions align with experimental fatigue data, showing weak mean‑stress effects for torsion and stronger effects for bending in ductile metals, while both torsion and bending exhibit strong mean‑stress influence in cast irons.

Abstract

The concept that alternating shear stress is the primary cause of fatigue with the normal stress on the critical shear plane as an influencing factor has been developed for the case of mean (or static) stresses superimposed on combinations of torsion and axial load or bending. The influence of the maximum stress of the cycle of stress on the allowable alternating stress for a given number of cycles and on the orientation of the critical shear plane is explored. The predictions of the theory are consistent with the known trends of fatigue data both for ductile metals and cast irons. The theory explains the fact that the influence of mean stress is weak for torsion and stronger for bending of ductile metals, but strong for both torsion and bending of cast irons. As far as is known this is the first rational theory for the influence of mean stress.