Brittle-ductile transition and scale dependence: Fractal dimension of fracture surface of materials

The fractal dimension of fracture surfaces obtained within brittle-ductile transition regime is evaluated at various observation scales. Fracture surfaces are generated by the tensile fracture test. The brittle-ductile transition is accomplished by using the round-notched bar specimens with various notch radii, which cause the variation in stress triaxiality. The specimens are manufactured from mild steel, steel and cast-iron bar. The fracture model is identified according to the observation through scanning electron micrographs. The fractal dimension for ductile fracture surfaces is almost constant despite variations in observing scale and changes in stress triaxiality. Meanwhile, the fractal dimension on brittle fracture surfaces shows the different values for macroscopic and microscopic observing scales. This transition-like scale dependence of fractal dimension for brittle fracture surfaces is considered to reflect such a characteristic of the fracture i.e. its specific length in microscopic fracture mechanism. The existence of transition in fractal dimension with observing scale is considered to be an index, used to distinguish the ductile fracture surface from the brittle fracture one.