This dissertation investigates the applicability and usefulness of applying Fractal mathematics and to the fracture of brittle particulates in Fluid Energy Mill devices, and in particular quantifying the resulting power law particle size distributions, examining the Surface Fractal Dimension of milled particulates, and relating the Izod Impact Strength values of composites of polypropylene and Calcium carbonate particulates which are large un-milled, small milled, as well as small and produced by the simultaneous milling and coating with nano-silica to the Surface Fractal Dimension of the impact fracture surfaces.

First, the dissertation examines the behavior of un-coated and micron-sized wax pre-coated particulates in a specially designed Single-event Fluid Mill (SEFM), which is utilized to represent (for each pass) the Elementary Breakage Events in the Fluid Energy Milling process, and analyze the results in terms of the Fractal Theory.

The results establish that brittle milled particulates have self-similar shape to the original particulates, which points to the self-similarity property of fractals. Particle size distribution (PSD) of milled particulates obeys Power Law expression. This allows the analysis of size reduction efficiency and specific kinetic energy of particulates during SEFM milling using fractal methods. For modeling the surface structure of particles by a fractal surface at various scales, Atomic Force Microscopy and the Gwyddion 2.25 software are used to measure the surface fractal dimension (Ds) of raw and ground particles. The results show that the surface fractal dimensions of CaCO3 and KCl particles are independent of scale or grinding. This is a strong indication that the fracture process is self-similar. The surfaces of CaCO3 and KCl particles are modeled very well by fractal surfaces. For the materials of CaCO3 and KCl, a relationship between the macro-mechanical property and the micro-structure is built. The fractal dimension of the fracture surface increases with energy per unit surface area for fracture.

The dissertation also investigates the fractal behavior of the following Polypropylene (PP) based polymer composites performance during impact testing and establishes a quantitative relationship between the evolution of microstructure and fracture macro-mechanical properties by fractal theory. The results show that the Izod impact strength increases, as the fractal dimension of composite's impact-fractured surface increases.

PP is compounded with large un-milled , small milled, as well as small and produced by the simultaneous milling and coating with nano-silica Calcium carbonate at the 10 and 20 wt% levels. The Izod impact strengths of the composites are obtained and their values are related to their Surface Fractal Dimension. The results establish an excellent relationship, strongly indicating that increasing fracture surface roughness shows more inter-particle ligaments in the composites resulting tougher materials.