This study investigates the fatigue behaviour of welded tube-to-tube steel joints subjected to non-proportional (NP) multiaxial loading induced by frequency- and phase-shifts. A comprehensive test campaign consisting of 125 fatigue tests were performed under different combinations of axial and torsion loading. Including 45 NP frequency-shifted multiaxial tests with four different frequency ratios ( f σ Hz : f τ Hz of 1 : 2 , 1 : 1 . 25 , 1 . 25 : 1 and 2 : 1 ) and 43 NP phase-shifted multiaxial tests with four unique phase angle distributed over seven series ( ϕ σ ° : ϕ τ ° of 0 : 10 , 0 : 45 , 0 : 90 , 10 : 0 , 45 : 0 , 90 : 0 and 0 : 180 ). Additionally, 13 proportional multiaxial tests and 24 pure axial (tension/compression) and torsion tests were conducted. The results show that frequency-induced NP loading has little effect on the S-N curve slope, but it significantly reduces the strength coefficient, resulting in a parallel downward shift of the S-N curve. Phase-shifted NP loading likewise results in only minor slope variations, but the parallel shift in fatigue life follows a distinct phase-dependent trend, with the largest reduction occurring at 90 ° . To evaluate fatigue life prediction accuracy, several conventional assessment methods were examined, including the Palmgren–Miner linear damage rule and rainflow counting using von Mises, maximum principal and maximum shear stress formulations. These approaches failed to capture the additional damaging effects from NP loading. Among the evaluated design codes, IIW, DNV, ASME, FKM and BSI, the ASME method provided the best overall performance. An experimentally derived method has been developed to account for out-of-phase loading conditions involving frequency- and phase-shifts, based on a straightforward fitting of experimental S-N data. • Frequency-shifted NP loading gives a uniform 62% fatigue-life reduction. • Phase-shifted NP loading shows a phase-dependent 15%–77% life reduction. • No conventional fatigue assessment could predict the NP reduction. • NP fatigue factor: descriptor of uniform and phase-dependent life reductions.
Winther et al. (Sun,) studied this question.