Establishing a protocol for measurements of fractal dimensions in brittle materials

Many techniques have been used to measure the fractal dimension of brittle fracture surfaces. The purpose of this study was to create a protocol for obtaining the fractal dimension using a simplified optical technique for comparison to reported procedures. Four classes of ceramic materials were used in this study: baria silicate (a glass-ceramic), silicon nitride (a fine grain polycrystalline ceramic), zinc selenide (a large grain polycrystalline ceramic), and silicon (a single crystal ceramic). Contours were produced in perpendicular and parallel planes to the fracture surface using three techniques: slit-island (parallel), profile technique (perpendicular), and crack indentation technique (perpendicular). These contours were then analyzed using a method first introduced by Richardson. The slit-island technique produced statistically greater fractal dimensional increments, ranging from 0.08 to 0.28 for all the materials, than either the profile technique (0.01 to 0.03) or the indentation technique (0.02–0.05). This difference is due in part to the fact that many brittle fracture surfaces are self-affine objects and not self-similar objects. A list of recommendations for a protocol and sources of error for this technique are presented in the appendices.