Is Fractal dimension a true quantifier of microstructure?

Abstract

Self-similarity, a phenomenon described as fractal, is observed in nature and manmade things. In medical image and signal analysis, fractal dimension, the quantifier of fractal geometry, has been used extensively as diagnostic tool. In materials research, it is possible to quantify microstructures of materials by fractal dimension. How ever, it is often argued whether fractal dimension is a true quantifier of microstructure. This report presents a systematic investigation on morphological analysis as well as computation of fractal dimensions using synthetic and real microstructural images. Results of creep-fatigue damage in Ni based super alloy and pitting damage in Aluminum alloy have been presented to show the correlation between fractal dimension and conventional morphological parameters