A path-dependent cycle counting method for variable-amplitude multi-axial loading

Abstract A path-dependent maximum range (PDMR) cycle counting method is presented in this paper for performing fatigue evaluation of engineering components under variable-amplitude and arbitrary multi-axial conditions. For a given multi-axial time history, PDMR method can be used to reliably extract the following parameters that are important for modeling multi-axial fatigue damage: (a) Path-independent reference effective stress or strain ranges which are defined as distances in a mapped stress or strain space. (b) Path-dependent effective stress or strain ranges which are defined as path lengths in completing the corresponding reference stress or strain ranges in an incremental sense in the same stress or strain space. (c) Histogram of both path-independent reference effective stress or strain ranges and their corresponding path lengths that can be consistently used to measure out-of-phase induced fatigue damage in arbitrary multi-axial loading. The effectiveness of PDMR method has been validated by its ability in correlating multi-axial fatigue data available in the literature. Its fracture mechanics basis is also illustrated. Under uniaxial loading conditions, PDMR method recovers exactly the same rainflow counting results.