13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- defects. The second part of the paper devoted to the thermodynamic description of deformation process. Based on the results of solution of the statistical problem we introduce a new thermodynamic variable and derive the constitutive equation for metals with submicrocracks. In the last part the proposed constitutive equation applied for the description of defect kinetics near specimen surface and in the bulk. The model allows us to describe the shift of crack initiation location from the specimen surface to the bulk and numerically obtain dual S-N curve for 2023 T3 aluminum alloys. The discuses about physics of the investigated process and proposition for father experimental verification of the model presented in conclusion. 2. Statistical description of damage accumulation in metals The data obtained from systematic studies of defects evolution, carried out at Physical technical institute named after A.F. Ioffe RAS shows that the volume defects (submicrocracks with characteristic size about 0.1 mkm) play the important role in deformation process [3]. These defects emerge at the early stage of deformation and effect on the microplasticity and failure processes. The same situation could be observed under cyclic loading. The best materials for the experimental proofing of this hypothesis are the fine grain metals which contained the high concentration of volumes defects (micropores) after manufacturing procedures (equals channel pressing). The value, geometrically representing the real microcracks with allowance made for a variety of their shapes, sizes and arbitrary orientations as well as or the crack initiated material loosening, can be introduced in terms of the dislocation theory [4]. The dislocation loop D, bounding the surface S , where the displacement vector undergoes a finite increment equal the Burgers vector b, is characterized by the tensor of the dislocation moment i k S b . The sum of N dislocation loops, which is equivalent to a microcrack, introduces the tensor of dislocation moment of a microcrack: N l 1 l k l i l ik S b , s (1) where l is the vector of a normal to the surface S of the 1-th loop. Small sizes and multiple character of microcrack nucleation as well as size and orientation distributions of microcracks permit averaging of their parameters over elementary volume to obtain the macroscopic tensor p n s , ik ik (2) where n is a concentration of microcracks. A solution of equation (2) was presented in [4]. The solution depends on structural parameter and defect concentration n. Figure 1 presents two solutions of the equation (2) for 1.1 and different values of initial defect concentration (curves 1,2). To describe a real deformation process which characterized by the growth of defect concentration we propose that the representative material volume rV contains 0 r nV defects
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