Stochastic model of crack propagation in brittle heterogeneous materials

The explanation of experimentally observed phenomena of correlation of crack increments is required for consideration of stochastic crack propagation in structures and solids. The proposed model provides an explanation based on Brownian Motion with reflection from effective boundaries of a zone around main crack tip. The model is based on an assumption that there is a micro crack layer near the main crack tip, in which micro cracks are stabilized by inclusions. Main crack tip is advancing in surrounding micro crack layer with higher speed than the speed of boundaries of the micro crack layer, and it is assumed that there exists a positive probability for main crack tip to reflect from effective boundaries of its micro crack layer. The defined process is different from Reflected Brownian Motion in that only a fraction of crack paths get reflected. Results of stochastic Monte Carlo simulation for crack in infinite plate showed that crack trajectories are characterized, in general case, by quicker then linear growing variance, strong long range dependence and non-Normal distribution corresponding to non-Gaussian process. Questions related to usage of additional random parameters for case of long term loading and long term strength are also considered.