PSI - Issue 71

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

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(b) Fig. 6. Time variations of measured equivalent strain values, maximum principal strain under remote (a) in phase and (b) 90 ° out-of-phase axial-torsion conditions For the time instant (t=c) when remote axial is maximum, the peak strain is maximum at hole tip along =0° location. At this instant, no such strain peaking exists by virtue of remote torsional strain. Hence, no such strain field interaction takes place for 90 ° out-of-phase conditions as it happens for in-phase axial-torsion conditions. Due to this reason, the localized peak equivalent strain amplitude is comparatively higher for remote in-phase axial-torsion conditions. Further, a material point (Fig. 6(a)) is considered near the hole tip. The direction of maximum principal strain is measured using DIC and denoted for remote in-phase and out-of-phase conditions. Fig. 6(b) shows that the principal strain direction remains fixed for remotely applied in-phase condition, whereas it rotates for remote out-of-phase condition. 4.2. Test fatigue life for proportional/ non-proportional conditions The test fatigue lives under proportional and non-proportional conditions are compared for tube without hole [Arora et al., PhD Thesis] and tube with hole (present study) in Fig. 7(a) and Fig. 7 (b)/(c), respectively. It is well understood that the material degradation mechanism in case of multiaxial loading condition is mainly governed by three factors (i) location of the maximum damage plane (ii) magnitude of equivalent strain amplitude (iii) additional hardening effect. Fatigue crack initiation event for multiaxial loading condition is mostly dictated by the competition between these two governing parameters that is magnitude of equivalent strain amplitude and addition hardening effect. When unnotched tube specimens subjected to same set of axial and torsional strain amplitudes, then it is observed that test fatigue life in case of non-proportional loading condition is lesser than that of proportional loading condition. This is because, in case of non-proportional loading condition additional material hardening takes place owing to rotation of principal stress/ strain directions as reported by Arora et al. (2016). This in turn results in amplification of stress amplitude leading to higher material damage in case of nonproportional loading. Also, fatigue damage at a material point is primarily a function of strain amplitude and maximum value of stress over a cycle, as brought out by critical plane model Arora et al. (2019) / various strain energy density models Arora et al. (2019,2020), Gupta et al. (2011) and Liao et al. (2018). However, the location of the maximum principal damage plane remains fixed for both the loading conditions. Hence, in case of unnotched tube specimen additional hardening has a dominating effect than that of the magnitude of the equivalent strain amplitude on fatigue crack initiation event. This in turn results in lesser test fatigue life for 90 ° out-of-phase as compared to in-phase loading condition. However, when tube specimens with hole subjected to same set of remote axial and torsional strain amplitudes, it has been observed that test 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) which is contrary to results of unnotched tube specimens .This is because under same strain controlled remote loading condition, the localized strain amplification is relatively higher for remote in-phase condition compared to remote 90 ° out-of-