Issue 35

O. Plekhov et alii, Frattura ed Integrità Strutturale, 35 (2016) 414-423; DOI: 10.3221/IGF-ESIS.35.47 421 As a result we can consider the surface as negative source with infinite capacity which has a great influence on the defect evolution. This influence can be described by the value of constant h in the boundary condition (4). There are two limiting cases for Eq. (4). The first case is 0    p S h p . It means the surface is the sink of infinite capacity and this condition can be used for the description of defect evolution close to specimen surface ( sur V ). The second case is 0 0       p S p h D x . The surface is closed for the defect diffusion. This condition can be used for the description of the defect evolution in the volume of the specimen ( bulk V ). Let us introduce the following dimensionless variables   p t l a , 0 /   n n n , / ( )    Ea , / ( )   h h V a , taking into account the fact that the initial defect (submicrocrack) concentration near specimen surface is one or two order higher than in the volume of the specimen (    sur bulk n n ) and there is the difference in boundary conditions, we can write the Eq. (4) for sur V , bulk V as     2 2 0 1        m sur m m p n p p h p  , (5)   2 2 0     m bulk m m p n p p p  . (6) Under one dimension loading the stress is equal for both representative volumes and can be written as   0 cos     . The numerical solutions of Eqs. (5,6) are presented in Fig. 8. a) b) Figure 8 : Defect induced strain evolution near specimen surface (1) and in the volume of the specimen (2) for high (a) and small stress amplitudes (b) . At high stress amplitude the initial defect concentration plays the main role and leads to the sharp increase of the defect density near specimen surface (Fig.8a). The blow-up regime of defect accumulation can be considered as damage to fracture transition and can manifest the emergence of macroscopic crack. At small stress amplitude the defect diffusion and defect annihilation on specimen surface lead to the low defect growth near specimen surface and blow-up regime of defect accumulation can be observed in the volume of the specimen (Fig. 8b). In the case of proposed approximation the critical time in the Eq. (6) can be estimated as follows     0 0 1        m f b b sur m h p t dp n p p . (7) To describe the full S-N curve we have to use several Eqs. (5) with different values ,   h n which could be connected with initial heterogeneity of materials. The Eq. (6) gives the traditional representation of S-N curve in Basquin form