Application of fractal geometry to damage development and brittle fracture in materials

Abstract

This article represents a first attempt to apply the concepts of fractal geometry to damage development in materials. Two extremes of material behavior were considered. In the case of unstable brittle propagation of microcracks, application of fractal geometry and weakest link statistics lead to the well-known Weibull distribution for fracture stress. The Weibull slope (shape parameter) is equal to twice the fractal dimension of the flaw distribution. For the case of stable microcrack growth, a number of simplifying assumptions led to a closed-form expression for the change in effective modulus with an increment of damage. Although an oversimplification, this latter analysis illustrates the potential value of fractal geometry in modeling damage development. Future work will be directed towards developing these initial results further.