Abstract: Existing test results show that during non-proportional cyclic loading, the continuous rotation of principal strain axis in cyclic deformation leads to actuation of multi-slip systems which hinder the forming of stable dislocation substructures inside the material. As a result, the material show additional hardening upon non-proportional cycling. The increased cyclic hardening by non-proportional loading reduces the fatigue life. Therefore, with the analysis for the state of the strain on the critical plane of the thin-walled cylindrical specimen, a new damage parameter for multi-axial fatigue is proposed by means of von-Mises criterion based on the critical plane approach. In addition, the effects of the mean stress on the fatigue life are analyzed as well. The new damage parameter considers maximum shear strain range and normal strain range on the critical plane, and the effect of the additional cyclic hardening caused by the non-proportional loading on the fatigue life is taken into account as well. It is convenient for engineering application because of no material constants in this parameter. The predicted multi-axial fatigue lives of the materials studied (steel 45, S460N steel, 1045HR steel, Haynes 188 alloy and GH4169 alloy) by using the proposed damage model are found in good agreement with experimental results.

Key words: Additional cyclic hardening, Critical plane approach, Life prediction, Multiaxial fatigue, Proportional and non-proportional loading