Correlation between Fractal Dimension and Areal Surface Parameters for Fracture Analysis after Bending-Torsion Fatigue

Abstract

This paper investigates the fracture surface topography of two steel and aluminum alloys subject to bending-torsion fatigue loadings, as well as their susceptibility to fatigue performance and failure mechanisms. Using fracture surface topography data analysis, elements with different geometries were elaborated. A correlation between the fractal dimension, other selected parameters of surface topography such as areal Sx, and fatigue loading conditions was found. Distinctions in particular regions of cracks were also recognized through proving the correctness and universality of the total fracture surface method. The influence of fatigue loading parameters on the surface topography of fatigue fractures was demonstrated. For the analyzed cases, results show that the fractal dimension and standard surface topography parameters represent a correlation between them and loading conditions. As a single parameter, the appropriate loading ratio cannot be outright calculated with fractal dimension, but can be estimated with some approximation, taking into account additional assumptions.

Keywords

• fracture
• surface topography
• fractal dimension
• bending-torsion fatigue
• steel
• aluminium alloy