On the interpretation of the fractal character of fracture surfaces

Abstract

To examine the usefulness of the fractal concept in quantitative fractography, a series of classical fracture surfaces, namely transgranular cleavage, intergranular fracture, microvoid coalescence, quasicleavage and intergranular microvoid coalescence, are analyzed in terms of fractal geometry. Specifically, the five brittle and ductile fracture modes are studied, from three well characterized steels (a mild steel, a low-alloy steel and a 32 wt% Mn-steel) where the salient microstructural dimensions contributing to the final fracture morphology have been measured. Resulting plots of the mean angular deviation, and Richardson (fractal) plots of the lineal roughness, as a function of the measuring step size, are interpreted with the aid of computer-simulated fracture-surface profiles with known characteristics. It is found that the ranges of resolution, over which the fractal dimension is constant, correspond to the pertinent metallurgical dimensions on the fracture surface, and thus can be related to microstructural size-scales.