Fractal Dimension of Grain-boundary Fracture for Characterization High-temperature Fracture in Heat-resistant Alloys

The fractal dimension of the grain-boundary fracture, D(f), (2<D(f)<3), which represents the fracture surface pattern with grain-boundary microcracks in three-dimensional space, is proposed for characterization of high-temperature fracture in materials. The value of D(f) as well as its two dimensional value, D(fp) (the fractal dimension of the grain-boundary fracture surface profile, 1<D(fp)<2), was estimated in the length scale range more than about one grain-boundary length using the height data of fracture surfaces of heat-resistant alloys obtained by the stereo matching method. The value of D(f) increased with increasing fractal dimension of the grain-boundary surface profile (D(GB), 1<D(GB)<2) in the specimens of the HS-21 alloy ruptured at 1089 K. Both rupture life and creep ductility increased with increasing value of D(f) in these specimens. Similar results were obtained by the two-dimensional fractal analysis on other specimens of cobalt-base, nickel-base and iron-base heat-resistant alloys. Creep fracture process including the growth of the main creep crack was examined by the fractal analysis using the fractal dimension map (FDM, a color-coded map) on the surface notched specimens. The result of the fractal analysis was compared with that of the FRASTA (fracture surface topography analysis) in the Inconel X-750 alloy. The fractal analysis used in this study is more convenient and more advantageous than the FRASTA, and is widely applicable to the investigation of high-temperature fracture in materials.