Models for some mechanical properties of particulate-filled composite materials

Abstract

In this project, we have used various kinds of computational and analytical models to study the mechanical properties of particulate filled composite materials. We have also applied the effective medium theory (EMT) to some theoretical models to study this kind of material. Firstly, we have applied finite element analysis to a single cylindrical cell model, a single spherical cell model and statistical cylindrical cell model. The aim is to verify the results obtained by others. The material we studied was the glass-bead filled epoxy-resin composite material. Young's modulus and Poisson's ratio for various volume fractions of fillers were obtained. The results matched quite well with those obtained previously by others. Secondly, we have carried out a statistical analysis on the spherical cell model. The results were satisfactory and showed large corrections to those from the single spherical cell finite element model, especially at high volume fractions. We have also investigated the influence of stress field interaction by considering a single cylinder containing two equal-sized spherical fillers. The results are used to explain why the statistical spherical cell model can give large correction to those results from the single spherical cell model. Finally, we have applied EMT to the lower bound derived in Christensen's book [Christensen, 1979] and have solved the equations numerically. The results were satisfactory when compared with experimental data. We have also applied EMT to the equations of Christensen's three-phase model [Christensen, 1979]. The results we obtained showed large improvement to those obtained by a direct application of the equations. During the project, we have written a program for the simulation of three-dimensional Gibb's hard-core point process. The distributions of the half-interparticle distances obtained from the program matched quite well with theoretical prediction [Pamela, 1988]. The program is listed in Appendix I. Maxwell's equation for the effective dielectric constant of spherical cell containing a spherical filler was re-derived in Appendix II. Application of EMT to Maxwell's equation was used to predict the dielectric constant of metal-coated particulate-filled composite. Satisfactory results were found. Statistical analysis was used to multi-phase Landau-Lifschitz's model and equation was derived for the effective dielectric constant of the sphere-filled composite material. The results showed improvement to the Maxwell's equation. They were listed in appendix III.