13th International Conference on Fracture June 16–21, 2013, Beijing, China -10- 7. Conclusion From polycrystalline modeling of pure copper coupled with a statistical study of the critical grains, we analyzed the mesoscopic responses of the multiaxial fatigue criteria, widely studied in the literature (Crossland, Matake and Dang Van). This statistical study allows us to introduce microstructural heterogeneities effect in the variability of the fatigue strength. The comparison between the mesoscopic predictions of these criteria and the macroscopic (original) ones shows that they are not conservative at the grain scale. Indeed the identification of macroscopic parameters of these criteria does not take into account variations of the strain field at the microstructure scale. The proposed method, based on extreme value statistics, consists in readjusting these parameters on the most critical grain computed from FE calculations. These critical grains are located in the tails of the aggregate response distributions. The determination of the different distributions allowed us to define a new mesoscopic threshold for the studied criteria. These thresholds are the average of the medians of the extreme value distributions related to the different loading conditions. These thresholds are different or similar to the macroscopic thresholds depending on the considered criterion. For Dang Van, the mesoscopic threshold is equal to the macroscopic value of the fatigue indicator parameter. At the opposite, for Crossland, the ratio between meso and macro thresholds is greater than 1.4. Matake criterion has a ratio of around 1.1. Finally, except for the biaxial loading with a phase shift of 90° where FIP median values are very different from one criterion to another, the mesoscopic thresholds is almost the same for all the loading conditions. Thus, these new mesoscopic thresholds can therefore be determined by applying a single loading case. References [1] H.V. Atkinson and G. Shi. Prog. in Mater. Sci., 48: 457-520, 2003. [2] M. Liao. Eng. Frac. Mech., 76: 668-680, 2009. [3] C. P. Przybyla, R. Prasannavenkatesan, N. Salajegheh, and D. L. Mc-Dowell. Int. J. of Fatigue, 32(3): 512-525, 2010. [4] C. P. Przybyla and D. L. McDowell. Int. J. of Plasticity, 26(3): 372-394, 2010. [5] L. Meric and G. Cailletaud. J. of Eng. Mater. and Tech., 113(1): 171-182, 1991. [6] C. Gérard, F. N’Guyen, N. Osipov, G. Cailletaud, M. Bornert, and D. Caldemaison. Comput. Mater. Sci., 46(3): 755-760, 2009. [7] C. Robert, N. Saintier, T. Palin-Luc, and F. Morel, Méca. et Indus., 209-214, 2011. [8] C. Robert, N. Saintier, T. Palin-Luc, and F. Morel, Mech. of Mater., 55: 112-129, 2012. [9] B. Crossland. Proceedings of the Inter.Conf. on Fatig. of Met., 138-149, London 1956. [10] T. Matake. Bulletin of the JSME, 141:257–263, 1977. [11] K. Dang Van, B. Griveau, and O. Message. Mech. Eng. Publi. London, 479-496, 1989. [12] P. Lukás and L. Kunz. Int. J. of Fatigue, 11(1): 55-58, 1989. [13] A.F. Jenkinson. Quaterly Journal of the Royal Meteorological Society, 81, 1955. [14] A. Hor, N. Saintier, C. Robert, T. Palin-Luc and F. Morel, 19TH European Conference on Fracture (ECF19), kazan (Russia), 2012.
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