Computational Simulation of Composites Reinforced by Planar Random Fibers: Homogenization and Localization by Unit Cell and Mean Field Approaches

Abstract

The linear thermoelastic and thermophysical behavior of a short fiber reinforced composite material with planar random fiber arrangement is investigated by advanced numerical and analytical micromechanical methods. On the one hand, finite element based multi-fiber unit cells are introduced that contain 40-50 short fibers in arrangements approximating 2D random orientation distributions. On the other hand, the same fiber arrangements are investigated by an extended Mori-Tanaka mean field approach that can handle both statistical and discrete descriptions of the fiber orientations. Within the Mori-Tanaka scheme average microfields are extracted for individual fibers, and finite-length cylindrical reinforcements are modeled via averaged dilute concentration tensors that are evaluated numerically by finite element analysis. Homogenization and localization are performed for a metal matrix composite consisting of copper, reinforced by 21 vol% of carbon fibers that closely approximate a planar random arrangement. Simulation results on the macroscopic and microscopic linear elastic, thermoelastic, and thermal conductivity responses obtained by the two approaches are compared and excellent agreement is found.