Multiscale wavelet-based analysis and characterization of fretting fatigue damage in titanium alloys

Wavelet analysis is used to rationalize information at various scales in several branches of science, including particle physics, biology, electrical engineering, fluid mechanics, and medicine. However, this powerful technique has not been applied extensively to characterize structures of materials, fretting damage for the present case, even though many critical questions could be addressed. In particular, the following unsolved problems are considered in this paper: (a) The first problem deals with the quantitative characterization of fretted surfaces in a Ti-6A1-4V alloy. This is investigated by analyzing profilometric digital images of fretted surfaces obtained in a range of magnifications. Wavelet analysis of the data is able to identify, by examining the wavelet coefficients, dominant length scales as those regions in scale-space where the energy of the wavelet transform and/or peaks of local concentration dominate. For the range of magnifications examined, i.e. from 1.25× to 100×, the ̃20× magnification is identified as the one with the most useful information. (b) An alternative procedure is employed for the second use of wavelets which deals with the non-uniformity of the contact regions. Wavelet analysis is employed to identify partially slipping regions, which result in the "pattern" of the fretted surface morphology.