Fractal Characteristics of Fracture Surfaces

Quantitative fractography is often used to study material failure mechanisms. During calculation of surface or profile roughness parameters, the magnification used in obtaining fractographic data is found to influence the value of the parameters. Fractal geometry has been developed into a tool capable of defining surface and profile topography without sensitivity to magnification, and several studies have related fractal dimension (DF) to other physical or mechanical properties. In this study, we obtained the fractal dimension of profiled fracture surfaces of one glass and three proprietary dental porcelains. The fracture toughness (K1c) of these materials was also measured using the indentation-strength method. Results show the surfaces to be fractal. No quantitative relationship between fractal dimension and toughness was found. Differences in K1c were demonstrated between some materials. It is postulated that the size range within which fractal dimension can be defined as constant is dependent on the toughening mechanism, and that the relationship between KIc and DF cannot be identical for all materials.