Bulk Modules of Three-Phase Composites with Spherical Inclusions

Abstract

In order to theoretically estimate the bulk modulus of granular composite materials (concretes: consisting of a binder and fine and coarse aggregates), the proposed model of the representative unit cell of a 3-phase concrete (with spherical gravel inclusion) is replaced by two 2-phase models: sand mortar (binder + sand) and concrete (mortar + gravel). The research paper substantiates the transition from the use of the Voigt – Reuss "fork" formulas (two models of 2-phase composites) to the generalized Voigt – Reuss "fork" formulas in cell models of 3-phase composites. A numerical and graphical analysis of the generalized formulas is made using the example of one of the possible subsets of 3-phase concretes. The graphic images of the Voigt – Reuss "forks" (of the analyzed subset of 3-phase composites) are characterized by their greater diversity in comparison with traditional images (in 2-phase composites). In this work, to choose out from the multitudes of possible compositions (3-phase composite) of the studied subset of 2-phase composites the authors employ and recommend for practical use the multistep dichotomy method.