Fractal character of fracture surfaces of metals

Abstract

In this review, the fractals in the fractography is described, using brittle fracture surfaces of chromium and molybdenum, and stress corrosion cracking surfaces of SNCM 439 steel. It is emphasized that the quantitative fractography at the atomic region is opened, combining scanning tunneling microscopy with fractal geometry.

Fractal analysis of the heat treatment response for multiphase Al alloys

“…"Fractals" were introduced by Mandelbrot et al 1 , being a non-Euclidean geometry theory used to describe the irregularity in nature. Fractal analysis has been used for the study of distributions and microstructural changes of systems with discontinuities, mainly through the use of the fractal dimension (D f ).…”

“…(1) indicates that the fractal dimension is determined by plotting N(δ) against δ in a log-log scale.…”

Acoustic Nonlinearities Produced by a Single Macroscopic Fracture in Granite

“…The same statistical description applies to fractures in metals and ceramics (7,8), suggesting that the results reported here for fractures in rock may have wider application to other fractured materials.…”

Fractal Approach to Alternating Current Impedance Spectroscopy Studies of Carbon Nanotubes/Epoxy Polymer Composites

“…The fractal geometry is a mathematical concept that describes objects of irregular shape. It has been used to analyze different objects in various scientific and technological branches since their description by Mandelbrot (Mandelbrot et al, 1984). Application of the fractal concept for the prediction of the physical properties of composites has demonstrated that the fractal dimension is related to the dielectric relaxation process (Hopkins et al, 2011;Lira-Olivares et al, 2000).…”