Quantitative characterization of fracture surface of full lamellar TiAl under high temperature creep and fatigue conditions on the basis of fractal concept

Abstract

Previously, we proposed the method of clarification of the relationship between fractal dimension and observational scale. This method enables us to characterize a representative length of fracture surface. In this paper, as a general extension of this method, the concept of the space distribution on the locality of fractal dimension, that is, the characteristics of multi‐fractal, was proposed to characterize fracture surfaces quantitatively. It enables us to clarify the morphological distribution of fracture unit by changing the observational area. Using the concept of the space distribution on the locality of multi‐fractal, critical value of the representative length of observational region, x^* _C which shifts to the self similarity and the asymptotic coefficient to self similarity, α₂ were observed. Using these values as characterizing parameters of a fracture surface, the possibility on the quantitative estimation of fracture unit depending on various material structures was assured. From the view point of self similarity, x^* _C was found to correspond the minimum size of grains. It is in good agreement with experimental result. From the results mentioned above, the concept of the space distribution on the locality of multi‐fractal was found to be useful for the quantitative characterization of the fracture surfaces and material structures.