Error quantification in self-affine analysis of fracture surfaces

The theory of scaling processes is a toolbox suitable for the research of damage phenomena. In particular, correlation or self-affine analysis allows us to study the influence of microstructure and energy consumption mechanisms on crack nucleation and growth by topographical analysis of fracture surface morphology. It characterizes the topography of fracture surfaces with experimentally accessible parameters and relates it to process dynamics, allowing us to obtain governing equations. However, estimation of these parameters is not trivial at all; their currently available estimates are either contradictive or misguiding due to the inability to quantify the error of measurements or correlative behavior. In this research, we demonstrate that errors in self-affine analysis are easily quantified with relevant parameters such as the number of independent points in a correlated system and the discretization size per correlation length. Specifically, we study the influence of: (i) the finite-size effect; (ii) the profile's discretization; (iii) the effect of lateral correlation length; and (iv) the self-affine exponent on the accuracy of analysis. Finally, we demonstrate the applicability of the obtained methodology on real data of profiles at gigacycle fatigue fracture for measurements of the self-affine exponent and lateral correlation length. We found that the error in the self-affine analysis is often underestimated at least 8 times. We also give recommendations on how to estimate accuracy in self-affine analysis.