FRACTAL AND SCALING PHENOMENA ON FRACTURE AT MICRO-SCALES

A simple numerical model is proposed to investigate the fracture owing to the coalescence of numerous microcracks, in which the spatial nucleation of a microcrack is simulated through a random distribution, and the coalescence of two microcracks is determined using a critical condition in accordance with the load-sharing principle. As the number density of nucleated microcracks increases, stochastic coalescence occurs, and finally, a newly nucleated microcrack triggers a catastrophic failure. Simulation results show that fracture profiles exhibit fractal (self-affine) characteristics with a universal roughness exponent, but the critical damage threshold is sensitive to details of the model. The spatio-temporal distribution of nucleated microcracks in the vicinity of critical failure exhibits a power-law behaviour, which implies that the system is in a self-organized critical state.