Calculating the Effective Mechanical Properties of Polymer Composites with Dispersed Particles Based on the Particle Size Distribution

Abstract

Development of adequate mathematic models of the mechanical properties of polymer composites with dispersed particles (PCDP) requires their verification. The following reasons complicate the verification of these mathematical models: lack of information on the mechanical properties of the transition layer at the boundary between the modified particle and the polymer; lack of information on the mechanical properties of the agglomerates that inevitably appear during the preparation of the PCDP. This study suggests a mathematical model for calculating effective mechanical properties (bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio) of the PCDP with encapsulated particles and verification of this model using PCDP samples with inclusions—nearly spherical dispersed aluminum oxide (Al₂O₃) particles that are not encapsulated and the particles encapsulated in a thin polymer shell. Equations for calculating the effective mechanical characteristics of these PCDPs are obtained. As demonstrated, the proposed model reliably provides the values of the bulk modulus, shear modulus, Young’s modulus and Poisson’s ratio of PCDPs with a small relative volume of dispersed submicron particles in the matrix.