PSI - Issue 79

D. Marhabi et al. / Procedia Structural Integrity 79 (2026) 34–52

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Kakuno and Marhabi criterion are given fairly optimistic forecasts (slightly non-conservative). 11. CONCLUSIONS The over-energy analysis enables us to take into account the effect of shear stress leading the mechanical component to the small crack. Consequently, the following results are obtained concerning the threshold stress:  The study using an over-energy method predicts the shear stress leading to the small crack.  The small crack and shear stress are in good agreement with Kitagawa plot.  The Bazant Low representation include well the shear stress. Hence, considerations of shear stress fatigue analysis may help the damage-tolerant design. The Multiaxial Fatigue Criterion including Shear Stress is established. We have been able to define the field of application for various criteria and comparing them with statistical analysis. Further investigations will aim to validate these results by experimental processes and microscopic observations. [1] A. Banvillet, T. 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(1976) Applicability of Fracture Mechanics to Very Small Cracks or the cracks in the early stage. Proceeding of the second Int. Conf. on Mechanical behaviour of Materials, American society for metals, Metal Park, OH, Vol. 2, pages 627-631. [7] Bazant, Z.P. (1997) Scaling of quasi brittle fracture: asymptotic analysis. Int. J. Fracture, Vol. 83, n°1, p. 19-40. [8] Tanaka, K. Nakai, Y. Yamashita, Y. (1981) Fatigue Growth Threshold of Small Cracks. Int. J. Fracture, Vol. 17, n°5, pages 519-533. [9] Livieri, P. Tovo, R. (2004) Fatigue Limit Evaluation of Notches, Small and Defects: An Engineering Approach, Fatigue & Fracture of Engineering Materials& Structures. Vol. 27, p. 1037-1049. [10] Brand, A. Flavenot, J.F. (1989) Technological Data on Fatigue, CETIM Publications (Senlis-Nantes-St Etienne) [11] De Leiris, H. (1969) Triaxialité des contraintes et critére de non-fragilité. Bulletin d'Association Technique Maritime Aéronautique, pages 481-491. [12] Chamat, A. Abbadi, M. Gilgert, J. 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(2019) Modélisation de l’influence des défauts de surface sur le Comportement en fatigue de nuances d’acier innovants PhD. (205 pages) University Clermont-Ferrand,.France. [22] Chamat, A. (2005) Prévision de la durée de vie en fatigue des roues ferroviaires sous solicitations multiaxiale proportionnelles et non proportionnelles, (147 pages) PhD thesis, University P. Verlaine, Metz, France. [23] B. Webern, B. (1999) Fatigue multiaxiale des structures industrielles sous chargement quelconque, PhD. thesis, INSA-Lyon, France. [24] Dubar, L. (1992) Multiaxial fatigue of Steels, Passage of the endurance to the limited endurance and taking into account of geometrical accidents PhD thesis. ENSAM Bordeaux, France. 12. REFERENCES