Elasticity-based locally-exact homogenization theory for three-phase composites considering the morphological effect of carbon fibers

Abstract

Elasticity-based locally-exact homogenization theory (LEHT) is further extended in this paper to investigate the mechanical behaviors of three-phase composites with orthotropic interlayer as well as circumferentially orthotropic (CO) and radially orthotropic (RO) carbon fibers that are determined by their morphological basal plane. Taking advantage of the Fourier series representations for displacements of each phase, in-plane and out-of-plane exact solutions are obtained for orthotropic media through rigorous mathematical derivations and the internal eigenvalue functions are directly solved within rectangular and hexagonal representative unit cells (RUCs) subjected to axial normal, transverse loading and axial shear loading, respectively. The balanced variational principle is applied to enforce periodical boundary conditions which ensures rapid convergence of displacement fields. The solutions of LEHT are verified with far-field Eshelby problems with good agreement and the morphological effects of fiber are investigated by comparing CO/RO properties and equivalent transversely isotropic (TI) parameters obtained from replacement scheme. Homogenized elastic moduli of RUCs with orthotropic interlayer are predicted through homogenization constitutive relations and compared to special extension of the composite cylinders approach and numerical results based on the asymptotic expansion homogenization method to demonstrate excellent correlation. Finally, the effects of orthotropic interlayer have been demonstrated and local stress distributions are obtained from a “top-to-down” procedure, illustrating constituents’ interactions from microscope perspective and identifying the possible crack initiations/propagations within microstructures.