Fractal model to predict the crack roughness effect on the local bending compliance of circular shafts

In this paper the local compliance due to a transverse fractal crack in a shaft under pure bending is investigated. In a fractal crack, the surface is considered irregular and it is characterized by the presence of nonuniformities at different scales. Therefore, the crack surface can be modeled as a fractal surface with fractal dimension D. An analytical model for the compliance coefficient is presented with and without the effect of the surface roughness. The results obtained shows that as the dimension of the fractal surface increases the compliance increases as well. It is shown that this behavior conforms well with existing experimental results.