PSI - Issue 71

Shreebanta Kumar Jena et al. / Procedia Structural Integrity 71 (2025) 103–110

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phase case, as discussed earlier. Additionally, the location of the maximum damage plane remains fixed for in-phase conditions at different time instant. However, the location of the maximum damage plane is revolving continuously along the periphery of the hole between 45 ° and 90 ° at different time instants in a given cycle for 90 ° out-of-phase condition. Because of this, damage is getting concentrated over a small material volume in case of in-phase condition whereas for 90 ° out-of-phase condition damage is getting dispersed over a larger material volume. Further, though the rotation of principal strain/ stress planes exists at material point (as indicated in Fig. 6(b)) for remote 90 ° out-of-phase condition, yet, this additional hardening effect is not prominent at such a small equivalent strain amplitude. Thus, for notched tube specimen crack initiation is due to the competition between the magnitude of the equivalent strain amplitude and additional hardening effect and it is observed that the fatigue crack initiation event is mainly dictated by the magnitude of equivalent strain amplitude. Therefore, the fatigue life under remote in-phase condition is smaller than that of remote out-of-phase condition, as shown in Fig. 7 (b) and Fig. 7 (c). In Fig. 7 (b), test fatigue life in case of 90 ° out-of-phase loading while subjected to remote equivalent strain amplitude of 0.075% is significantly higher than its in-phase counterpart due very less amplification in equivalent stain amplitude at the hole tip when axial and torsional strain amplitudes acting separately as compared to that of when they are acting combined. However, promising cyclic plasticity models Arora et al (2021) & Vibhanshu et al. (2023) are required to accurately simulate material behavior in a finite element framework under remote out-of-phase condition to quantify the increase in stress value owing to rotation of principal directions.

(a)

(b)

(c) Fig. 7. Effect of proportional/ non-proportional conditions on fatigue life for tube (a) without hole, subjected to uniform in-phase and 90 ° out-of-phase axial-torsion condition, (b) with hole, subjected to remote in-phase and 90 ° out-of-phase axial-torsion condition for a given hole diameter of 5.5mm and (c) for a given remote equivalent strain amplitude of 0.1%