13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- under cyclic loading. The high concentration of these defect experimentally observed in fine grain metals after equals channel pressing allows us to propose the fine grain metals as model materials for verification of the theoretical predictions obtained in this work. The small size and high concentration of submicrocracks in metals, the existing of their size and orientation distributions allows us to develop a statistical description of microcrak evolution in metals under cyclic loading and introduce a new thermodynamical variable – defect induced strain. The new variable gives a natural description of thermodynamics of metals with microcracks and allows one to describe the interaction of plasticity and failure processes. The combination of statistical description of microcrack ensemble with stochastic consideration of defect initiation process allows us to describe the effect of initial nucleus concentration of the deformation process. This model coupled with a description of nonlocal effect in the defect ensemble gives us a key parameter for the description of defect kinetics in the bulk and near specimen surface under cyclic loading. Based on the developed model the new equation for defect kinetics in the bulk and near specimen surface have been proposed. The surface was considered as a physical object with high concentration of incomplete atomic planes and other defect of different nature. It allows us to explain the difference in the defect kinetics far and close to specimen surface and describe the damage to fracture transition both in the bulk and near specimen surface. It was show that the stress amplitude can influence on the location of macro fatigue crack initiation. At small stress amplitude the defect induced strain reaches an equilibrium value near specimen surface due to the defect diffusion and annihilation processes. It can be considered as an infinite fatigue life but in this case there is possibility of blow-up regime of defect kinetics in the bulk of specimen. It leads to the shift of location of crack initiation from the surface to the bulk of specimen. These two modes of crack initiation leads to dual form of S-N curve of materials. The calculated S-N curve has a good quantitative agreement with experimental data obtained by C. Bathias and P. Paris for 2023-T3 aluminum alloy [6]. Each part of the dual S-N curve has the traditional Basquin representation. The micromechanical model allows as to propose the link of macroscopic parameters a,b with defect accumulation kinetics and used the experimentally determined S-N curve for the estimation of microscale model variables. The developed theoretical model describes the important role of specimen surface and its physical state in the process of defect accumulation under cyclic loading. This model proposes a physical mechanism of the shift of crack initiation location from specimen surface to the bulk that experimentally observed under gigacyclic fatigue (cyclic loading with small stress amplitude). It is interesting to note that the best experimental verification of the model could be carried out based on the structural investigation of microcrack accumulation in fine grain metals (materials with high concentration of initial submicrocracks) under gigacyclic fatigue. Acknowledgements This work was carried out during the stay of first author at the department DuMAS I2M (Bordeaux, France). The authors sincerely thank prof. T. Palen-Luc and prof. N. Saintier for his hospitality and fruitful discussions. The work is partly supported by grant of President of the Russian Federation for support of young Russian scientists and leading scientific schools (MD-2684.2012.1) and RFBR (grant N 11-01-00153).
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