13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- characteristic scales: the scale of the process zone Pz L and the correlation length sc l that is the scale when the correlated behavior of defect induced roughness has started [13]. a b Figure 9: a –roughness scaling in the process zone; b – “fish eye” area of damage localization under VHCF (fine grain titanium) Assuming incomplete self-similarity in the variables ( ) 0 sc K E l Δ → , 0 sc Pz l L → and the definition of the effective stress intensity factor ( ) eff sc PZ K K l L β α Δ =Δ the kinetics of fatigue crack path reads ( ) ( ) sc eff sc dl dN l K E l α = Δ , (5) where the exponent α and β are the parameters related to the intermediate asymptotic dependence of crack rate on the stress intensity range. There is important case of the fatigue crack advance near-fatigue threshold when the scale of the process zone has the limit Pz sc L l → , the effective stress intensity factor range eff KΔ is approaching to the value KΔ and Eq.5 has the form ( ) ( ) sc sc dl dN l K E l α = Δ This form is similar to the equation proposed by Hertzberg [14] for sc l b→ , where b is the Burgers vector. Generally, in the limit of small scales sc l b≈ the application of stress intensity factor conception is problematic and numerous multiscale mesodefects interaction and corresponding scaling laws must be introduced [15]. This situation is characteristic for the fatigue of fine grain materials and especially for Very High Cycle Fatigue, when the stage of crack nucleation is dominated in the life time. The image of fracture surface of fine grain titanium (grain size ~300nm) in the condition of VHCF (number of cycles ~1010) is shown in Fig.9b and revealed the “fish eye” image and the large “process zone” occupying fracture surface area in the bulk of specimen. NNew View image of process zzone
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