Effective medium theory of composite elastic properties

This thesis attempts to establish a method based on simple ideas for the calculation of the elastic moduli of a composite material in terms of the moduli of its constituents and the volume composition. The method was originally used previously in the study of dielectric permittivity of binary mixtures. It employs the concept of an effective medium and is called an effective medium theory (EMT). EMT is extended in this thesis to deal with the moduli of spherical particulate-filled composites where a coupled set of two EMT equations are formulated. These are solved exactly in the limiting cases of composites with rigid and soft fillers. For the general case of spherical filler of arbitrary moduli, only non-closed form solutions are obtained. Then the study of the elastic moduli of a unidirectional fibre composite is attempted, where a couple set of five EMT equations for the five engineering constants emerge. These are solved exactly in this thesis. Finally, using these results, the elastic moduli of random fibre composite are studied by averaging over orientation.; Throughout the theory development, experimental data taken from the existing literature are used to check the correctness or not of the calculation. Comparison is also made with results from other theories such as those of Kerner and Mackenzie for particulate-filled composites and of Hashin and Halpin-Tsai for fibre composites. In the cases investigated in this thesis, the EMT results seem to indicate that they are able to give a good description of data and sometimes better than other theories. Also, the EMT results all fall within the appropriate Hashin bounds.