Mathematical Modeling Buckingham's Theorem and Optimization Technique on Mechanically Alloyed Nanocomposite Materials

Abstract

This research work is focused to develop and investigate the mathematical linear and non-linear modelling techniques for mechanically alloyed nanocomposites materials. These conventional and non-conventional artificial intelligent models could predict the both physical and mechanical properties of some nanocomposites materials. The conventional techniques such as dimensional analysis using Buckingham -theory, regression analysis and its hybrid approach; and non-conventional approaches like neural networks, fuzzy theory and adaptive fuzzy theory have addressed through this research work. The most significant input parameters which would affect the mechanical alloying processes, namely, milling time (t, min), ball-to-powder ratio (B), milling speed (N, rpm), ball size (D, mm), percentage of reinforcement (R, %) sintering temperature (T, K), sintering time (ts, min) and consolidation pressure (P, MPa) can be used for the various models. The various responses as physical and mechanical properties to be used are crystallite size (d, nm), bulk hardness (H, MPa), bulk density (ρ, kg/m3 ), tensile strength (σy , MPa), matrix particle size (Z, μm), compressive strength (σu, MPa), and percentage of elongation (e, %). Through this research work, we can select an optimum input parameter as per our required output properties, predicting the physical and mechanical behavior of nanocomposites and select the best linear & non-linear methods.