13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- V km s fw / 4 ≈ . Approaching of failure wave front velocity to the shock front velocity supports theoretically based result concerning the failure wave nature as “delayed failure” with the limit of “delay time” corresponding to the “peak time” in the self-similar solution [10]. a b Figure 8. a – The Taylor test data; b - Simulation of shock wave (S) and failure wave (F) propagation for different time [10]. Numerical simulation (Fig.8b) of damage kinetics describes the self-similar “blow-up” dynamics of damage-failure transition, supports the assumption concerning the failure wave mechanism as delayed failure with the delay time of the development of “peak regime” of “blow-up” dissipative structure. Time of the delay Dτ represents generally the sum of the induction time Iτ , that is the time of the formation of damage spatial distribution close to the self-similar profile, and the “peak time” Сτ , that is the time of “blow-up” damage kinetics. Steady-state regime of failure wave front propagation can be linked to the successive „resonance” activation of “blow-up” dissipative structures with characteristic “delay time” that is close to the “peak time” Сτ . 5. Scaling transitions and fatigue crack kinetics Damage kinetics according to Eq. 2 reveals the specific system behavior in the ranges of scaling parameter * δ δ δ < < C and C δ δ< when the defect density tensor ik p , influences on the correlation properties of defects on different spatial scales. The existence of two ranges of δ characterizes qualitative difference in relaxation mechanisms, which provide different dissipation ways: the orientation ordering and the formation of PSBs structures and the blow-up dissipative structures as the final stage of damage localization. The scenario of defect evolution in the range * δ δ δ < < C leads to the anomaly of the relaxation properties and, as the consequence, the energy absorbing. The high level of the structural relaxation time in the orientation metastability area in respect of the loading time ( ) 1− ≈ ε τ & l coupled with the self-similar features of structure rearrangement in the scaling transition regime explains the anomaly of the energy absorbing under cycle load starting from some characteristic level of strain. This stain corresponds to the saturation 0 5 10 15 20 25 30 0 0,5 1 1,5 2 2,5 3 3,5 4 s time μ , dis ce mm , tan
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