Method for quantitative evaluation of stretched zone width using two-dimensional local Hurst exponent

Abstract

Fractal analysis has been widely used to characterize the fracture surface. It has been recognized that the local Hurst exponent, which is based on the concept of the self-affine fractal, is useful to detect the transition point of the fracture surface. In order to calculate the local Hurst exponent, a high-resolution profile is needed. The measurement of this profile, however, requires considerable time and effort, which thus makes it difficult to calculate all the profiles of the fracture surface and arrive at a detailed evaluation of the features of the fracture surface. In the present study, we propose a new method of calculating the two-dimensional local Hurst exponent, which can be used to evaluate the features of the fracture surface using the local Hurst exponent. To investigate the validity of the two-dimensional local Hurst exponent, our calculations were applied to grayscale images in which the stretched zone was observed and the width of the stretched zone (SZW_c) was measured. The SZW_c calculated by the two-dimensional local Hurst exponent and that detected by human observation were found to be in good agreement. We thus conclude that the two-dimensional local Hurst exponent is a useful means of detecting the transition point of the fracture surface.