A multiaxial incremental fatigue damage formulation using nested damage surfaces

Multiaxial fatigue damage calculations under non-proportional variable amplitude loadings still remains a quite challenging task in practical applications, in part because most fatigue models require cycle identification and counting to single out individual load events before quantifying the damage induced by them. Moreover, to account for the non-proportionality of the load path of each event, semi-empirical methods are required to calculate path-equivalent ranges, e.g. using a convex enclosure or the MOI (Moment Of Inertia) method. In this work, a novel Incremental Fatigue Damage methodology is introduced to continuously account for the accumulation of multiaxial fatigue damage under service loads, without requiring rainflow counters or path-equivalent range estimators. The proposed approach is not based on questionable Continuum Damage Mechanics concepts or on the integration of elastoplastic work. Instead, fatigue damage itself is continuously integrated, based on damage parameters adopted by traditional fatigue models well tested in engineering practice. A framework of nested damage surfaces is introduced, allowing the calculation of fatigue damage even for general 6D multiaxial load histories. The proposed approach is validated by non-proportional tension-torsion experiments on tubular 316L stainless steel specimens.