Evaluation of the effective elastic properties of long fiber reinforced composites with interphases

The present paper predicts the effective elastic properties of long fiber reinforced composites which have transversely isotropic material behavior. It is assumed that there is a periodic microstructure, which can be taken by homogenization as a representative volume element (RVE) for the composite. A three phases (fibers, matrix and interphases between fibers and matrix) RVE is applied to study the effects of the interphase on the effective elastic properties of composites. By using the periodicity boundary conditions and the average field theory, the effective elastic properties of composites are evaluated on the basis of hexagonal and square fiber arrangement. Considering the orthotropic material behavior of composites with square fiber arrangement, a rotational average procedure which leads to the transversely isotropic stiffness matrix of composites with square fiber arrangement is developed. The effective elastic properties derived from hexagonal and square fiber arrangements combining with the rotational average procedure are compared, and the discrepancies are present. Effects of the volume fraction and stiffness of the interphase on the effective elastic properties are discussed. The present results are in good agreements with other existing results.