Fractal and Multifractal Characteristics of Propagating Cracks

Abstract
Specific features of crack propagation in random brittle materials are studied by means of lattice modelling. Emphasis of the investigation is on the analysis of the effect of spatial stochasticity in material properties' distribution on fracture characteristics. Local processes - evolution of ensembles of microdefects and its interaction with a crack- are introduced in terms of damage parameter and relevant evolution law. The influence of these processes on crack propagation is described as a crack-damage interaction : the criterion of local failure, causing the consequent crack growth, is introduced in the form of a critical damage value. Crack front morphology and time parameters of failure development are studied using the concepts of fractals and multifractals for three different cases of material's stochasticity (spatial randomness in properties' distribution). Characteristic features of energy release under crack growth are pointed out.