Crack Initiation and Crack Growth as the Problem of Localized Instability in Microcrack Ensemble

Abstract
Statistical theory of defect evolution allows us to obtain non-linear kinetic equations for tensor parameter of microcrack density. Investigation of non-linear properties of kinetic equation showed the existence of specific type of self-similar solution at the developed stage of damage, which is characterized by explosion-like kinetics of the microcrack growth on the spectrum of spatial scales. The system behaviour is controlled by the type of attractor determining non-linear dynamics of failure evolution, the scale transition due to the failure cluster formation and topological regularities of fracture. The scale distribution of damage localization corresponds to the laws of the free energy release in solids with microcracks. The laws of spatial damage localization on various structural levels are defined by the non-linearity of the microcrack accumulation in the condition of intensive interaction of the defects. This leads to the multiscale generation of failure centers. The relation between typical non-linearity of damage kinetics and spatial failure localization is the theoretical background for the explanation of experimental results and numerical simulation of fracture in heterogeneous materials. Topological features of fracture development were investigated numerically using percolation model of failure cluster growth.