In this paper, a path-dependent maximum range (PDMR) multi-axial cycle counting method is presented for performing fatigue life assessment of engineering components under general variable-amplitude multi-axial loading conditions. The PDMR method has two distinct features: (a) multi-axial cycle counting, in which the cycle counting is conducted in an equivalent stress or strain space, and (b) explicit loading path dependency. For uniaxial loading data, the PDMR and the ASTM standard Rainflow methods both generate the same counting results. The path-length, a function of both normal and shear stress components on a critical crack plane, is proposed as a fatigue damage parameter for ductile materials. PDMR can be applied to welded structures, in which the crack plane is usually known in advance, as well as to non-welded structures, in which the critical plane approach can be implemented into PDMR to determine both the fatigue crack orientation and the associated fatigue damage. The effectiveness and robustness of the PDMR method have been validated by its ability to correlate nominal stress and Battelle structural stress fatigue data including pure-bending, pure-torsion, in-phase, and out-of-phase loading conditions for welded tube-to-flange steel structures. The relationship between the data correlations based on nominal stress and Battelle structural stress for these loading conditions is illustrated. Finally, one-parameter and two-parameter equivalency approaches for PDMR operation are also introduced and discussed.

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