Novel application of fractal analysis in refractory composite microsturctural characterization

Abstract

Fractal geometry theory implied in a composite surface topographic analysis as a means of explanation of the structural characteristics has hardly been reported so far. This paper proposes a new method of roughness peaks curvature radii calculation and its application to the refractory composite surface tribological analysis. Fractal geometry method is introduced via calculation of asperity radius, by introducing a fractal concept of curvature radii of surfaces, depending on the observation scale and also numerically depending on horizontal lines intercepted by the investigated profile. The dependence of the calculated radii on the fractal geometry of the studied curves was established and the notion of peak was mathematically formulated. The efficiency of the method was tested by simulations of fractal curves described by Brownian motions. Microstructural investigations were carried out using a scanning electron microscope. The correlation between microstructure and properties of the investigated refractory composite, based on fractal geometry and contact surface probability, has been developed. Using the fractals of the contact surfaces of grains, a reconstruction of microstructure configuration, as grain shapes or inter-granular contacts, has been successfully performed. Obtained results indicated that fractal analysis of contact surfaces of different shapes was very important for the prognosis of refractory composite properties and behavior. The morphology of composite grains and surfaces highlighted the validity of developing new structure analytical methods based on different grain shape geometries. The novel approach to the investigation of refractory composite characteristics was successfully conducted, as a result introducing fractal identification as a means of evaluating and predicting material performances.