Quantitative Analysis of Brittle Fracture Surfaces Using Fractal Geometry

Abstract

Fractal geometry is a non‐Euclidean geometry which has been developed to analyze irregular or fractional shapes. In this paper, fracture in ceramic materials is analyzed as a fractal process. This means that fracture is viewed as a self‐similar process. We have examined the fracture surfaces of six different alumina materials and five glass‐ceramics, with different microstructures, to test for fractal behavior. Slit island analysis and Fourier transform methods were used to determine the fractal dimension, D, of successively sectioned fracture surfaces. We found a correlation between increasing the fractional part of the fractal dimension and increasing toughness. In other words, as the toughness increasing the fracture surface increases in roughness. However, more than just a measure of roughness, the applicability of fractal geometry to fracture implies a mechanism for generation of the fracture surface. The results presented here imply that brittle fracture is a fractal process; this means that we should be able to determine processes on the atomic scale by observing the macroscopic scale by finding the generator shape and the scheme for generation inherent in the fractal process.