PSI - Issue 82

118 Sigbjørn Tveit et al. / Procedia Structural Integrity 82 (2026) 112–118 S. Tveit et al. / Structural Integrity Procedia 00 (2026) 000–000 7 for all materials as goes from 0° to 90° . For the generalized format that accounts for the effect of the shear stress fatigue limit !" , there appears to be a dependency between the predicted increase of the fatigue limit due to the phase shift and the shear stress fatigue limit ratio !" !" ⁄ . The largest relative increase (32.0 %) was seen for mild steel ( !" !" ⁄ =0.583 ), and the smallest increase (20.0 %) was seen for 3%C cast iron ( !" !" ⁄ =0.949 ). It is also worth noting that for stress angle = 45° , the original and the generalized formulations appear to coincide at phase angle = 90° . Besides this, the differences between the two formats are moderate for the stress angles = 45° and 67.5° , and only becomes considerable when = 22.5° . 4. Conclusion The efficacy of the continuum mechanics fatigue model to predict the infinite fatigue limits for out-of-phase combinations of shear and normal stresses was examined for four different materials: mild steel, hard steel, duraluminum, and 3%C cast iron. The model performed well when the stress angles were 22.5° and 67.5° , but for mild steel, hard steel and duraluminum, it overestimated the fatigue limits when the stress angle was 45° as the phase shift angle approached 90° . On the other hand, the behavior of the 3%C cast iron was well captured when applying the generalized format proposed by Tveit et al. (2025). The study confirms the previous indication that the continuum mechanics fatigue model cannot fully capture the complexities of out-of-phase loading, and that further research is needed to address these limitations. The experimental data was limited to bending-torsion fatigue tests that allowed us to directly compare fatigue limits in pure bending and pure torsion, without considering the stress-gradient effect. Developing an enhanced model formulation demands additional experimental evidence, but tests on out-of-phase combinations of bending and torsion are scarce in the literature. Because of this, future investigations should account for the stress-gradient modification by Ottosen et al. (2018) to facilitate the use of experimental data obtained by push-pull and torsional loading References Hänel, B., Haibach, E., Seeger, T., Wirthgen, G., Zenner, H., 2003. FKM-guideline - Analytical strength assessment of components in mechanical engineering, Forschungskuratorium Maschinenbau eV (FKM), Research Association for Mechanical Engineering, Frankfurt. Kouhia, R., Ottosen, N.S., Ristinmaa, M., Rubio Ruiz, A., Holopainen, S., Saksala, T., 2025. Modelling of anisotropic high-cycle fatigue of metals. 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