Wavelet-Based Multifractal Identification of Fracture Stages

Abstract

Because fracture phenomena are highly nonlinear and non-stationary, the classical analyzis of fracture lines development is not adapted for their characterization. Multifractal analysis is now increasingly used to characterize these irregular patterns. In this investigation, multifractal analyzis based on the continuous Wavelet Transform Modulus Maxima method (WTMM) is proposed to give a multifractal discrimination of the profile lines development at different fracture stages: fracture initiation, fracture propagation and final rupture. This multifractal analyzis makes it possible to take into account the local regularity of fracture profiles. The degree of these fluctuations is quantified by Holder exponent α, computed from WTMM coefficients of the signal. The proposed wavelet-based multifractal approach is mainly compared to standard multifractal one based on the box-counting method (BCM). We noted that WTMM describes reasonably well the scaling properties of fracture patterns distributions at three distinct fracture stages. The results suggest that parameters of the multifractal spectrum such as the capacity dimension D0, the average singularity strength α0, the aperture of the left side α0−αq and the total width (αmax−αmin) of the f(α) spectra may be useful as parameters characterizing the different fracture stages and mechanisms of elastomeric material.