PSI - Issue 71

Shreebanta Kumar Jena et al. / Procedia Structural Integrity 71 (2025) 34–41

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A typical tube model along with its mesh and boundary condition to simulate remote pure torsion condition has been shown in Figure 6 (a). The h-type (reducing the size of the element by keeping the element order the same) and p-type (increasing the order of the element by keeping the size of the element same) of mesh refinement studies have also been performed to simulate remote pure axial/torsional and in-phase axial torsional conditions on unnotched tube specimens. In Figure 6(a), E 1 and E 2 show the pin locations of the extensometer; the extensometer; E 1 and E 2 would displace along the axial/circumferential direction of the tube for pure axial/torsion conditions. Good agreement between the cyclic saturated hysteresis loop obtained from the test and FE simulation confirms the suitability of the Chaboche material model parameter under different loading conditions, as shown in Figures 6 (b), (c) & (d). 3. Fatigue test investigation on notched tube This section aims to highlight the limitations in the existing test methodology and the importance of the need for pretest FE analyses on notched tube specimens before carrying out the actual tests. Subsequently, strain-controlled tests performed under cyclic remote pure axial & pure torsion conditions will also be discussed here. 3.1. Limitations in existing notched fatigue test methodology The test methodologies available in literature for notched fatigue tests have been performed on different notch dimensions (different gradient conditions) while subjected to the same remote loading condition. This in turn results in different peak equivalent strain amplitudes at the notch tip due to different strain amplification factors, as shown in Figure 7(a). (a) (b) Figure 7 (a) Same remote loading condition resulting different peak equivalent strain amplitude (test methods in literature) (b) Different remote strain amplitude applied to achieve same peak strain amplitude (Proposed test methodology) Therefore, present test methodology brings out the combined effect of strain gradient and peak equivalent strain on fatigue crack initiation life instead of the individual one. However, before carrying out the actual test, if it is preceded by detailed pretest FE analyses where the remote displacement field is so adjusted that it will result same peak equivalent strain amplitude for different notch diameters as shown in Figure 7(b). This small modification in the present test methodology, where the actual test has been carried out in conjunction with pretest FE analyses, will be able to bring out the individual effect of peak equivalent strain and strain gradient on fatigue crack initiation life. 3.2. Need of pretest FE analyses To bring out the individual effects of strain gradient and peak equivalent strain amplitude on fatigue crack initiation life, the need for pretest FE analyses has been realised before conducting actual tests. Pretest FE analyses comprise modelling of tube specimens with one-sided thickness holes (two different hole diameters of 3 mm and 8 mm) using 20-node brick elements and using a full integration scheme. Typical FE models of notched tubes along with their mesh & boundary conditions subjected to remote pure axial and torsion loading conditions are shown in Figure 8 (a) and Figure 8 (b), respectively. In the close proximity region of the hole, very fine mesh was adopted to capture the strain/stress gradients accurately, whereas the coarse-meshing option was opted for at a faraway location. Additionally, a mesh convergence study has also been carried out for the model tube geometry shown in Figure 8(d). These displacement/angle-of-twist-controlled FE analyses have been carried out in such a manner that the equivalent peak strain amplitude at the notch tip for different hole diameters is maintained nearly equal. This peak equivalent strain amplitude at the notch tip has been achieved by controlling the axial displacement and angle of twist at the remote location.