Fractal character of fracture surfaces and boundary values of toughness in a simple ceramic-ceramic system

Eight ceramic-ceramic composites with a common matrix but reinforcement of different size and/or morphology have been characterized by fracture mechanics testing, and their fracture surfaces quantitatively analyzed by means of computer-aided scanning electron microscopy. The fracture surfaces were found to obey approximately a fractal rule over about four orders of magnitude in the range investigated between the submicrometre and the millimetre scales. Therefore, each fracture surface could be characterized in terms of a single numerical parameter, i.e. its fractal dimension ξ. A simple proportionality relationship between the measured toughness value (the work of fracture) and the fractal dimension of its fracture surface also could be established. Finally, some insight has been gained into predicting the boundary values of toughness for the present ceramic-ceramic system, based on fractal concepts.