Effective elastic moduli of a composite containing rigid spheres at nondilute concentrations: A multiple scattering approach

Abstract

Based on the multiple scattering technique [K. F. Freed and M. Muthukumar, J. Chem. Phys. 69, 2657 (1978); 68, 2088 (1978); M. Muthukumar and K. H. Freed, J. Chem. Phys. 70, 5875 (1979)] previously applied to the study of suspensions of spheres and polymers, we propose an approach to the computation of the effective elastic properties of a composite material containing rigid, mono-sized, randomly dispersed, spherical particles. Our method incorporates the many-body, long-range elastic interactions among inclusions. The effective medium equations are constructed and numerically solved self-consistently. We have calculated the effective shear μ′ and Young E′ moduli, as well as the effective Poisson ratio σ′, as functions of the particle volume fraction Φ and of the Poisson ratio σ of the continuous phase. Comparisons with two sets of experimental data—glass beads in a polymer matrix and tungsten carbide particles in a cobalt matrix (Wc/Co)—and to a previous theoretical solution, are also presented. Our model can predict the effective Poisson ratio of the Wc/Co system for Φ⩽1 and for the glass/polymer system for Φ⩽0.5. In particular, the present work describes accurately composites with a high volume fraction of inclusions, where a percolation transition occurs. Very good agreement with the experimental data are obtained for E′ and μ′ when Φ⩽0.4, for both systems.