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.

Analysis of 3D Random Al<SUB>18</SUB>B<SUB>4</SUB>O<SUB>33</SUB> Whisker Reinforced Mg Composite Using FEM and Random Sequential Adsorption

“…The main idea of the method for modeling RVE to represent a real composite behavior is to find a globally homogeneous medium equivalent to the original composite, where the strain energy stored in both systems is approximately the same. 10) As pointed out by several researchers, [9][10][11][12] a RVE should be typical of the whole composite microstructure and contains a sufficient number of inclusions for the apparent overall properties to be effectively independent of the boundary condition. In this point of view, this study focused on the statistical homogeneity of the effective elastic modulus (Young's modulus) of the model to be statistically representative of the composite.…”

“…For these reasons, the modeling of composites with a periodic boundary condition has been intensively studied in the case of particle and short fiber reinforced composites. [10][11][12] However, using periodic conditions and the RSA algorithm, it was confirmed that the volume fraction of random whiskers in the RVE could not exceed about 9%, because of the geometrical jamming limit. Therefore, the present study adopted nonperiodic boundary conditions to describe the complex microstructures of the high aspect ratio random whiskers.…”

“…Therefore, the finite element method (FEM) has been extensively employed to determine the effective material properties of short fiber and particle reinforced composites. [7][8][9][10][11][12] Numerous studies have been reported on the effective modulus and overall stressstrain responses of these composites using representative unit cell 7,8) and 2D/3D microstructure [9][10][11][12] models. Most of these models were constructed using representative volume elements (RVEs), which were selected to reflect the actual microstructures of the composite.…”

“…Kari et al 10) employed FE analysis to investigate the effect of the volume fraction and fiber aspect ratio on a random short SiC fiber reinforced metal matrix composite (MMC). Boehm et al 11) and Duschbauer et al 12) studied an MMC reinforced by random short fibers using a periodic unit cell model, which was developed by the random sequential adsorption (RSA) 14) scheme. The results of these studies showed the capability and advantage of FE analysis in the simulation of composite materials, not only for predicting the effective modulus, but also for the local field characterization and overall stress-strain response analysis.…”

Modeling of the thermal conductivity and thermomechanical behavior of diamond reinforced composites

“…Such unit cells, which are a well-established micromechanical tool for studying the behavior of discontinuously reinforced composites [23,24,25,26], can provide highly detailed predictions on the microscopic gradient, flux, stress and strain fields in complex microgeometries, but pose much higher requirements in terms of analyst's time and computational power compared to mean field methods.…”