13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- structures approaches to the scale cL . Similar scenario of the “scaling transition” proceeds for the blow-up structures of different complexity to involve in the process of the final stage of damage localization the larger scales of material. The description of damage kinetics as the structural-scaling transition allowed the consideration of solid with defects as a dynamical system with spatial degrees of freedom (corresponding to the set of blow-up dissipative structures of different complexity). Stochastic behavior in this case can be linked with the dynamics of the critical state with the features of flicker noise, or 1 f - statistics. The systems reveal the so-called self-organized criticality (SOC) with universal behavior that is typical for the late state evolution of dynamic systems when the correlation will appear on all length of scales. The self-similar nature of mentioned collective modes associated with damage localization zones has the great importance in the case of dynamic loading, when the “excitation” of these modes can lead to the subjection of relaxation and failure to the dynamics of these modes. The examples for this situation are the transition from the steady-state to the branching regimes of crack propagation, qualitative change of the fragmentation statistics with the increase of the energy density imposed into the material. 2. Nonlinear crack dynamics. Crack branching The understanding of self-similar scenario of damage-failure transition stimulated our experimental study of crack dynamics for the explanation of mechanisms of transition from the steady-state to the branching regime, fragmentation statistics and failure wave phenomenon [2]. The stress field in the area of crack tip in the preloaded (by external stress σ) PMMA plate and the diagram “crack velocity V versus applied stress σ” are presented in Fig.1 according to the data of high speed framing with the usage REMIX REM 10-8 camera (time lag between pictures sμ 10 ). Three characteristic regimes of crack dynamics were established in the different ranges of crack velocity: steady-state С V V< , branching C V V> and fragmenting B V V> , when the multiply branches of main crack have the autonomous behavior (Fig.1, 2). Steady-state regime of crack dynamics is the consequence of the subjection of damage kinetics to the self-similar solution of the stress distribution at the crack tip (mechanically speaking to the stress intensity factor). Bifurcation point СV ( R СV V 0.4 ≈ where RV is the Rayleigh wave speed) corresponds to the transition to the regime, when the “second attractor” (with the symmetry properties related to the number of the blow-up dissipative structures) disturbs the steady-state regime due to the excitation of numerous new failure hotspots (the daughter cracks having the image of mirror zones on the fracture surface). The change of the symmetry properties of nonlinear system were studied under the recording of dynamic stress signal (polarization of laser beam) at the front of propagating crack in the point deviated on 4 mm from the main crack path. The corresponding phase portraits σ σ ~& for steady-state and branching regimes of crack dynamics are presented in Fig. 3 and confirmed the existence of two “attractors”, which subject the crack dynamics. The first attractor is related to the intermediate asymptotic solution for the stress distribution at the crack tip. The second attractor has
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