Study of anisotropy in polydispersed 2D micro and nano-composites by Elbow and K-Means clustering methods

A new two-dimensional polydisperse model for testing multiphase composites is developed. The verification of the model is carried out based on the microstructure of two composites obtained in the ex-situ and in-situ techniques produced in the Friction Stir Processing (Al–Si–Cu/SiCp) and the Self-propagating High temperature Synthesis (Al/nano-TiCp). The examined microstructure is considered on macro-, meso- and micro- levels. Besides the reinforcement phase distribution concentration, an anisotropy coefficient κ is calculated for every meso-cell. It is the cumulative vector parameter that characterizes the spatial two-point correlation of inclusions. In particular, κ determines the principal axes of the effective conductivity tensor over a meso-cell. The anisotropy spatial distribution ϰ(x) is introduced as the discrete function of values κ calculated over meso-cells centered at the point x. This new distribution ϰ(x) accumulates the geometrical information of the considered microstructure. A computational experiment is designed and carried out in order to study the influence of the reinforcement phase redistribution on the anisotropy. Therefore, it adequately describes the anisotropy of fields in composites modeling thermal and electric conductivity, diffusion, and elastic antiplane deformation. The results of the computational experiments are analyzed using the Elbow and K-Means clustering machine learning algorithm. The detailed analysis is carried out to divide the data set into up to 5 clusters. A research hypothesis concerning the criterion of isotropy of the distribution of reinforcing phase particles in the composite structure is formulated.