13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Сriticality of Damage-Failure Transitions under Dynamic and Fatigue Loading Oleg Naimark Institute of Continuous Media Mechanics UB RAS, 614013 Perm, Russia Corresponding author: naimark@icmm.ru Abstract Statistical theory of evolution of typical mesoscopic defects (microcracks, microshears) revealed specific type of criticality–structural-scaling transitions and allowed the development of phenomenology of damage-failure transition in solids with defects. The key results of statistically based phenomenology are the establishment of characteristic multiscale collective modes of defects responsible for damage-failure transitions under dynamic and fatigue loading. High resolution experiments and structural (SWFM and AFM) study in terms of scaling invariance supported the linkage of the evolution of these modes with material responses in large range of load intensity (dynamic crack propagation, fragmentation statistics, crack path under high cycle (HCF) and very high cycle (VHCF) fatigue) Keywords multiscale damage kinetics, collective modes of defects 1. Introduction The problem of fracture treated as a critical phenomenon represents one of the key problems of fundamental and applied physics of materials science. Experimental studies of material responses in a large range of loading rates show that the behavior of solids is intimately linked with the evolution of typical mesoscopic defects (microcracks, microshears). This characterizes generically solids under dynamic and fatigue loading, when the internal times of the evolution of ensemble of defects for different structural levels are approaching the characteristic loading times. Statistical theory of typical mesoscopic defects (microcracks, microshears) revealed specific type of criticality – the structural-scaling transitions and allowed the development of phenomenology of damage-failure transition based on the definition of non-equilibrium free energy of solid with defects. Multiscale aspects of damage-failure transition are analyzed to consider recent experiments on dynamic crack propagation, fragmentation statistics, scaling laws of fatigue. 1. Structural-scaling transitions in solid with defects Statistical theory of the evolution of typical mesoscopic defects (microcracks, microshears) allowed us to establish specific type of critical phenomena in solid with defects – structural-scaling transitions and to propose the phenomenology of damage-failure transition [1]. The key results of the statistical theory and statistically based phenomenology are the establishment of two order parameters responsible for the structure evolution – the defect density tensor ik p and the structural scaling parameter ( )3 0 R r δ= , which represents the ratio of the spacing between defects and characteristic size of defects. Non-equilibrium free energy F represents generalization of the Ginzburg-Landau expansion in terms of mentioned order parameters – the defect density tensor (defect induced deformation zz p p = in uni-axial case) and structural scaling parameter δ:
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