Fractal Analysis and Fractography: What Can we Learn that’s New?

Abstract

The tenets of fractography are well known. The principles of fractal geometry have been applied to fracture surfaces for several decades. How these two fields can be used in a synergistic manner eludes many. The key element in discovering that a fracture surface is fractal is that the features we observe with the naked or aided eye also occur at the atomic scale! Thus, we should be able to interpret the mirror, mist and hackle boundaries in terms of atomic bond breaking. I will present a consistent hypothesis for relating the bond breaking process at the atomic scale to the features we all observe on the fracture surface of materials. I suggest these can be related through one equation: 2 = E a0 D*, where  is the fracture energy, E is the elastic modulus, a0 is a characteristic dimension related to the structure of the material, and D* is the fractal dimensional increment. In turn, D* = c/r1 for which c is the crack size and r1 is the mirror mist boundary radius. Thus, the energy expended in fracture at the atomic scale is encoded on the fracture surface features we observe. The novel combination of fractography, fracture mechanics and fractal geometry can be combined to create a powerful tool for forensic analysis, research investigations and production analyses.