13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- Let us to introduce the following dimensionless variables t l ap , 0 n n / n , /(Ea) , h h /(V a) , taking into account the fact that the initial defect (submicrocrack) concentration near specimen surface is in one or two order high then in the bulk of specimen [6] ( bulk sur n n ) and the difference in boundary conditions we can write the equation (18) for sur V , bulk V as m 2 0 m 2 sur m p p 1 h p p n , (19) m 2 0 m 2 bulk m p p p p n . (20) Under one dimension loading the stress is equal for both representative volumes and can be written as cos 0 . The numerical solutions of equations (19,20) are presented in figure 2. a) b) Figure 2. Defect induced strain evolution near specimen surface (1) and in the bulk of 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 increasing of defect density near specimen surface (Fig.2a). 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 bulk of specimen (Fig. 2b). The calculation of critical times corresponding the blow-up of defect accumulation allows us to determine the S-N of the material which describes the two possibilities of fatigue crack initiation. The materials constants l ,a, p ,n ,h,V 0 0 p were selected to describe the two stage S-N curve experimentally obtained by C. Bathias and P. Paris for 2023-T3 aluminum alloy [6]. The numerical result presented in figure 3. The S-N curve has dual form. First branch describes the ordinary surface fatigue crack
RkJQdWJsaXNoZXIy MjM0NDE=