A unified scheme for prediction of effective moduli of multiphase composites with interface effects. Part I: Theoretical framework

In this part of the two-part paper, we present a unified theoretical framework to predict the effective moduli of multiphase composites containing spherical particles or cylindrical fibres with various interface effects. This framework is based upon a replacement procedure and the generalized self-consistent prediction of the effective moduli. However, both of the replacement procedure and the generalized self-consistent prediction are different from the conventional ones in that the former is implemented in terms of an energy equivalency condition to calculate the elastic constants of the equivalent particles or fibres, and the latter is based upon the Eshelby equivalent inclusion method in an average sense for the three-phase configuration. Using this replacement procedure, the expressions for the moduli of the spherical particles and cylindrical fibres with the linear-spring interface effect, the interface stress effect and the interphase model are presented. It is shown in a companion paper (Part II) that this scheme, together with the decoupled formulas for the generalized self-consistent prediction of the effective moduli of multiphase composites, can give simple and accurate predictions of the effective moduli.