Characterization of grain-boundary configuration and fracture surface roughness by fractal geometry and creep-rupture properties of metallic materials

Abstract

Grain-boundary configuration in heat-treated specimens and fracture surface roughness in creep-ruptured specimens of several kinds of metallic material were quantitatively evaluated on the basis of fractal geometry. Correlations between the fractal dimension of grain boundary, that of fracture surface profile, the creep-rupture properties and the fracture mechanisms of the alloys are discussed. In heat-resistant alloys, the fractal dimension of a nominally serrated grain boundary was always larger than that of a straight grain boundary in the same alloy. The relative importance of the ruggedness of grain boundaries was estimated by the fractal dimension difference between these two grain boundaries. There was a quantitative relationship between the increase of the fractal dimension of the grain boundary and the improvement of rupture ductility and rupture strength owing to grain-boundary serration in the alloy. A similar correlation was also found between the increase in the fractal dimension of the fracture surface profile and the improvement of the creep-rupture properties, since in some cases the fractal dimension of the fracture surface profile was correlated with that of the grain boundary. Both grain boundary and fracture surface profile were assumed to exhibit a fractal nature between one grain boundary length (upper bound) and an interatomic spacing (lower bound). In carbon steels with ferrite-pearlite structure, according to the increase in pearlite volume fraction, the rupture ductility decreased and the fracture mechanism changed from transgranular fracture in pure iron and low-carbon steels to intergranular fracture at ferrite-pearlite grain boundaries in medium-carbon steels, and further to intergranular fracture at pearlite grain boundaries in high-carbon steels. The correspondence between the fractal dimension of the grain boundary and that of the fracture surface was confirmed in ruptured specimens of ferrite-pearlite steels when the grain boundary was the fracture path.