The fractal dimension of grain-boundary fracture in high-temperature creep of heat-resistant alloys

The fractal dimension of the grain-boundary fracture in high-temperature creep was estimated by the vertical section method on several creep-ruptured specimens of the cobalt-nickel- and iron-based heat-resistant alloys. Grain-boundary microcracks linked to the fracture surface were also taken into account in the present analysis by the box-counting method. In the specimens containing many grain-boundary microcracks linked to the fracture surface, the fractal dimension of the grain-boundary fracture was larger in the scale range of more than about one grain-boundary length than in the scale range less than this length. Thus, there was a cross-over in the fractal dimension of the grain-boundary fracture at about one grain-boundary length in these specimens. In the specimens containing much fewer microcracks, there was no clear cross-over in the fractal dimension of the grain-boundary fracture with regard to the scale of the analysis, irrespective of creep-ductility and grain-boundary configuration of the specimens. The fractal dimension of the grain-boundary fracture was generally larger in specimens with serrated grain boundaries than in specimens with straight grain boundaries in these heat-resistant alloys, because the fractal dimension of the grain boundary and the number of the grain-boundary microcracks were larger in the former specimen. The fractal dimension of the grain-boundary fracture did not tend to converge to unity when the scale of the analysis approached the specimen size. The inclusion of near-specimen size data with regard to the scale of the analysis did not affect the fractal dimension of the grain-boundary fracture in these alloys. Thus, the grain-boundary fracture in the creep-ruptured specimens exhibited a fractal nature, at least in the scale range below specimen size, although there was a cross-over in the fractal dimension of the grain-boundary fracture in specimens containing a large number of grain-boundary microcracks.