Fractal analysis of three-dimensional fracture surfaces in metals and ceramics

Three-dimensional images of fracture surfaces formed by different mechanisms were reconstructed by the computer-aided stereo matching method on metals and ceramics. The fractal dimension of the three-dimensional fracture surface was estimated by the box-counting method using the height data generated by the stereo matching method. The ductile fracture surface (stage I fatigue) had the larger fractal dimension compared with the brittle-type fracture surface (stage 11 fatigue) in a Cu-Be alloy. However, it was difficult to classify the type of fracture, namely, ductile fracture or brittle-type fracture, in different materials only by the fractal dimension of the fracture surface, since even fractal dimensions of brittle-type fracture surfaces exhibited different values with different materials, depending on the fracture mechanisms of materials. There was a good correlation between the results of the three-dimensional fractal analysis and those of the two-dimensional fractal analysis on materials. The value of the fractal dimension of the three-dimensional fracture surface depends not only on the size of the analyzed area but also on the algorithms of the fractal analysis. The fractal dimension estimated in a given length scale range can be correlated with specific microstructures in materials.