Fractal analysis of crack paths into innovative carbon-based cementitious composites

Fractal geometry has been widely used in literature to characterize the mechanical behaviour of quasi-brittle materials. In this work, innovative cementitious composites with carbon-based pyrolyzed micro-aggregates were tested until complete fracture and their fracture behaviour was studied in the light of fractal geometry. Images of the crack paths across the tested specimens were acquired by Scanning Electron Microscopy (SEM) and their fractal dimension was calculated via the box counting method. Results show that the pyrolyzed micro-aggregates, characterized by high strength and stiffness due to their significant carbon content, are able to alter the crack path by increasing its tortuosity, thus inducing toughening mechanisms in the cementitious composites. This favourable behaviour is explained by means of fractal geometry: it is found that, the greater the fractal dimension of the crack path, the higher the fracture energy.