O. Plekhov et alii, Frattura ed Integrità Strutturale, 35 (2016) 414-423; DOI: 10.3221/IGF-ESIS.35.47 422 ln ln f N a b , (8) where 0 0 1 m b sur m h p a dp n p p , is a loading frequency. C ONCLUSION umming up the results of structural investigation of iron samples we can make several conclusions. The increase of the number of cycles leads to the dilatation of iron samples. The dilatation can be caused by initiation of new dislocations, micro voids and cracks. The hydrostatic weighing shows that the maximum of dilatation is observed in the middle part of the sample. The decrease of diameters of samples П1, П2 show the decrease of Young`s modulus and dilatation. The crack in the sample П3 doesn’t allow us to find the change in the dilation and elastic properties. The observed dilatation in the samples П1 и П2 shows the initial stages of micro voids and micro cracks formation in the volume of the sample and initiation of crack under surface. The investigation of crack opening evolution and elastic properties of the samples also supports these results. The small size and high concentration of microvoids and microcracks allow us to propose a statistical description of microcrack evolution in metals under cyclic loading and introduce a new thermodynamic variable – defect induced strain. The new variable gives a natural description of thermodynamics of metals with microcracks and allows us to describe the interaction of plasticity and failure processes. This model coupled with a description of nonlocal effect in the defect ensemble. This gives us a key parameter for the description of defect kinetics in the volume of the sample and near its surface under cyclic loading. Based on the developed model the new equation for defect kinetics in the volume of the specimen and near its surface has been proposed. The surface was considered as a physical object with high concentration of incomplete atomic planes and other defects of different nature. It allows us to explain the difference in the defect kinetics far and close to the specimen surface and describe the damage to fracture transition both in the volume of the specimen and near its surface. It was shown 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 volume of the specimen. It leads to the shift of the location of the crack initiation from the surface to the volume of the specimen. The developed theoretical model describes the important role of the specimen surface and its physical state in the process of the defect accumulation under cyclic loading. This model proposes a physical mechanism of the shift of the crack initiation location from the specimen surface to its volume that experimentally observed under VHCF regime (cyclic loading with small stress amplitude). It is interesting to note that the best experimental verification of the model could be carried out on the base of the structural investigation of microcrack accumulation in the fine grain metals (materials with high concentration of initial submicrocracks) under VHCF regime. A CKNOWLEDGMENTS he work was supported by the Ministry of education and science of the Russian Federation (contract No 02.G25.31.0068 of 23.05.2013 as part of measures for implementation of the Presidential decree of the Russian Federation government No 218). R EFERENCES [1] Zhu, X., Shyam, A., Jones, J.W., Mayer, H., Lasecki, J.V., Allison, J.E., Effect of microstructure and temperature on fatigue behavior of E319-T7 cast aluminum alloy in very long life cycles, Int. J. Fatigue, 28 (2006) 1566-1571. [2] Bathias, C., Paris P., Gigacycle Fatigue in Mechanical Practice, Taylor & Francis, (2004) 328. S T

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