Multiaxial fatigue: An overview and some approximation models for life estimation

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Additive manufacturing of fatigue resistant materials: Challenges and opportunities (2017, background): “Variation of FS damage parameter with plane orientation under in-phase (IP) and 90 out-of-phase (OP) axial–torsion loadings at the same strain levels [80].”
Fatigue of additive manufactured Ti-6Al-4V, Part II: The relationship between microstructure, material cyclic properties, and component performance (2020, background): “Even in parts under uniaxial loading conditions, the stress state may be biaxial or multiaxial due to complex geometries, residual stresses, and stress concentrations [23].”
A Review on Fatigue Life Prediction Methods for Metals (2016, methodology): “For the multiaxial fatigue life prediction, critical plane approaches linked to the fatigue damage of the material can be found in literature; these approaches are based either on the maximum shear failure plane or on the maximum principal stress (or strain) failure plane [190].”
Multiaxial fatigue behavior of wrought and additive manufactured Ti-6Al-4V including surface finish effect (2017, methodology): “Thus, among other reasons [24], more slip planes are active during non-proportional loading, as compared to under proportional loading, where only two planes experience maximum shear stress and strain [25].”