A generalized cycle counting criterion for arbitrary multi-axial fatigue loading conditions

Abstract

In this article, a generalized cycle counting criterion applicable for both uniaxial and arbitrary multi-axial loading conditions is presented. This criterion consists of two parts: (1) an effective fatigue damage parameter definition in either stress or strain space and (2) a fatigue cycle definition corresponding to maximum damage possibly attained by the fatigue damage parameter within a given loading history. After discussing its mathematical and mechanics basis, we first provide a rigorous proof that the proposed generalized cycle counting criterion yields exactly the same results as the rainflow counting method under uniaxial variable amplitude loading conditions. Then, its applications in multi-axial fatigue are demonstrated by presenting a series of closed-form solutions of both the fatigue damage parameter and number of cycles for a general harmonic loading history of three independent traction stress components on a crack plane. The validity of the new generalized cycle counting criterion is demonstrated by its ability to correlate available fatigue test data in the literature. These new developments also provide a more refined physical and mechanics basis for the recently proposed path length–based cycle counting method developed by the same authors for performing cycle counting of variable amplitude multi-axial loading histories.