Evaluation of the Effective Mechanical Properties of a Particle-Reinforced Polymer Composite with Low-Modulus Inclusions

Adequate mathematical models of the mechanical properties of particle-reinforced polymer composites (PRPCs) require verification, which is difficult to do for at least the following reasons: lack of information on the mechanical characteristics of the transition layer formed at the modified particle–polymer interface, and lack of information about the mechanical characteristics of agglomerates that inevitably form during PRPC fabrication. This paper proposes a mathematical model for calculating the effective mechanical properties (bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio) of PRPCs with encapsulated filler particles. The model is verified on PRPC specimens with inclusions in the form of air bubbles. Simplified equations are derived for calculating the effective mechanical properties of PRPCs with low-modulus inclusions in the form of air bubbles. It is shown that the proposed model provides reliable estimates of the bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio of PRPCs at a small relative volume of submicron-sized filler particles in the matrix.