Quantitative Analysis of Three-dimensional Fatigue Fracture Surface Reconstructed by Stereo Matching Method

Abstract

Three-dimensional geometry of a fatigue fracture surface in a Cu-Be alloy (the grain diameter is about 24 μm) was reconstructed by the stereo matching method based on the coarse-to-fine method. The fractal dimensions of the contours and of the fracture surface profiles extracted from the reconstructed image were then estimated by the box-counting method in the scale length range smaller than about one grain-boundary length (about 14 μm). The mean value of the fractal dimension of the contours was about 1.238, and was close to that of the actual fracture surface profiles in the plane in parallel with the crack growth direction (about 1.210) (in the parallel direction) and in the plane perpendicular to the crack growth direction (about 1.190) (in the perpendicular direction). Thus, the stereo matching method can reproduce the three-dimensional image of the complex fracture surface. However, the mean value of the fractal dimension of the reconstructed fracture surface profiles (about 1 128 in the parallel direction and about 1.146 in the perpendicular direction) was a little smaller than that of the actual fracture surface profiles, since there were microstructural features such as overhang, debris and microcracks on the fatigue fracture surface, which were only partly reproducible by the stereo matching method. Nevertheless, the geometrical information about a given fracture surface in a wide area can be obtained by the three-dimensional fracture surface reconstruction and analysis. Combination of three-dimensional and two-dimensional analyses may lead to the further understanding of the geometrical features of fracture surfaces and the fracture mechanism in materials. The fractal dimension was found to be a useful index not only for characterizing fracture surfaces but also for comparison of the result of three-dimensional image reconstruction with the actual fracture surface morphology.