Effective Elastic Moduli of Fiber-Reinforced Polymer Matrix Composites Filled with Nanoparticle

Effective moduli of fiber-reinforced polymer matrix composites filled with nanoparticle considering the effect of linear change of interphase are presented in this paper. The three-phase inclusion problem for matrix-interface-particle is equivalent to the Eshelby two-phase inclusion problem. According to the result of the Eshelby inclusion problem, the effective modulus tensor of unit cell of equivalent particle is derived. The effective moduli of equivalent matrix are given based on Mori-Tanaka method. Using two fundamental equation of micromechanic theory, the three-dimensional bridged formulation of unidirectional composites is derived. The quantitative relationship between the macroscopic elastic parameters and the structural parameters of the fiber-reinforced polymer composites filled with nanoparticles is investigated. Effects of the thickness of interfacial layer, the particle size and the volume fraction of nanoparticles on the effective elastic moduli of the composites are also discussed.