More singular? Self-similar dynamics of damage localization and instability in dynamic fracture

Dynamic fracture instability is studied for three characteristic statements: dynamic crack propagation, dynamic fragmentation and failure wave initiation to combine theoretical interpretation and “in-situ” high resolution experimental data for dynamically loaded quasi-brittle materials (PMMA, glasses, ceramics and fused quartz). Specific type of criticality (the structural-scaling transitions) was established in solid with defects in terms of two structural variables: defect density tensor (defect induced strain) and structural scaling parameter. Two critical values for structural scaling parameter were found that separate characteristic nonlinearity of free energy release in damage kinetic equation that allowed one to establish specific self-similar solution (blow-up dissipative structures) responsible for final stage of damage localization and crack initiation. The set of spatial scales of damage localization (that has the image of mirror zones) and corresponding “incubation” time follow from the self-similar solution as the “eigen-values” of non-linear problem. Different scenario of instability of dynamic fracture in mentioned experiments were analyzed as nonlinear dynamic problem in the presence of two self-similar solutions (two attractors): intermediate asymptotical solution for stress field in crack process zone (as the basement for stress intensity factor) and the set of blow-up self-similar solutions for damage localization kinetics playing the role of collective modes of damage localization. Theoretically predicted flicker noise temporal-spatial statistics was found in dynamic experiments for fused quartz and ceramic rod fragmentation combined with fracto-luminescence recording and analysis of fragment statistics. Resonance excitation of blow-up modes allowed explanation of self-similar pattern of multiple spall kinetics (“dynamic branch” under spall) due to “resonance” excitation of blow-up damage localization kinetics.