A multiaxial fatigue failure criterion considering the effects of the defects

An endurance criterion is proposed which aims at capitalizing the advantages of both fracture mechanics and of energetic or stress-based approaches. As a matter of fact, fracture mechanics based approaches allow building probabilistic criterions by introducing the statistic distributions of defects sizes, positions and orientations. On the other hand, stress-based approaches allow building multiaxial failure and life criterions. However, as shown by the diagram of Kitagawa and Takahashi [Kitagawa H, Takahashi S. Applicability of fracture mechanics to very small cracks. In: ASM Proceedings of 2nd International Conference on Mechanical Behaviour of Materials, Metalspark, Ohio. 1976, pp. 627–631], none of these approaches applies over the whole range of possible defects dimensions. For large defects, fracture mechanics concepts apply and the fatigue limit is deduced from the threshold stress intensity factor and the defect size. There is usually a threshold below which the sensitivity of the fatigue limit to the defect size becomes negligible. In that domain, Linear Elastic Fracture Mechanics (LEFM) overestimates the fatigue limit and stress-based approaches are more pertinent. In the present paper, the LEFM framework is used, defects are assumed to be cracks. The size effect exhibited by Kitagawa and Takahashi [Kitagawa H, Takahashi S. Applicability of fracture mechanics to very small cracks. In: ASM Proceedings of 2nd International Conference on Mechanical Behaviour of Materials, Metalspark, Ohio. 1976, pp. 627–631] is accounted for through the T-stress parameter, which is the first non singular term in the asymptotic development of the stresses at crack tip. The proposed criterion is a non-propagation criterion based on a critical distortional elastic energy in the crack tip region. The use of an energetic criterion ensures the consistency with endurance criterion. The specificity of our approach lies in the calculation of the distortional energy using the displacement fields of LEFM which ensures the consistency with fracture mechanics.