Fractal Analysis of the Microstructure of Model Composites as a Tool for Digital Materials Science

The paper presents the results of a fractal analysis of model composites with different volume fractions, sizes and shapes of dispersed-phase particles as part of the physicochemical engineering of materials. Models of composites with a random distribution of spherical and rod-shaped particles of various sizes and aspect ratios in the matrix, as well as models with particles segregated along grain boundaries, are proposed and substantiated. Computational experiments were performed to determine the fractal dimension of model composites, and a specific variation in fractal dimension depending on the geometry of the dispersed phase was demonstrated. Characteristic regions in the relationship between fractal dimension and dispersed-phase particle size were identified; these regions are consistent with the conventional classification of particles into ultramicro-, micro-, submicro-, and nanoscale size ranges. The calculated fractal-dimension values for the model composites are consistent with literature data for experimentally obtained composite samples. Optimal dispersed-phase particle sizes required to achieve target fractal-dimension values associated with the performance characteristics of composite materials are proposed. To decrease the fractal dimension of a composite, particles in the micro-size range (0.6–1.5 μm) are preferable, whereas to increase the fractal dimension, particles in the nanoscale range (<0.1 μm) should be used. It is shown that particle segregation along grain boundaries leads to a decrease in fractal dimension. Changes in the aspect ratio of rod-shaped particles were found to cause fluctuations in fractal dimension and, consequently, in composite properties. The numerically obtained results on the effect of dispersed-phase particle size, shape, and concentration on the fractal dimension of composites can be used to describe real composite systems. The results of the computational experiment for different dispersed-phase geometries provide a basis for controlling fractal dimension and properties in the physicochemical engineering and synthesis of new composite materials with desired performance characteristics.