Correlation functions for predicting properties of heterogeneous materials. III. Effective elastic moduli of two-phase solids

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Abstract
The Beran‐Molyneux bounds on the effective bulk modulus and the McCoy bounds on the effective shear modulus of a statistically homogeneous and isotropic heterogeneous material require a knowledge of several three‐point correlation functions. These correlation functions are contained within integrals which must be evaluated. Both sets of bounds are here evaluated for two‐phase materials, using the correlation functions developed in Paper II of this series. The method of evaluation includes a simplification of the integrals containing the correlation functions and a numerical evaluation of the simplified integrals. The resultant bounds are compared with experimental data on the effective shear modulus of three two‐phase systems: aluminum‐lead, iron‐lead, and tungsten‐lead. The bounds are also compared with the less restrictive Hashin‐Shtrikman bounds which do not require any knowledge of correlation functions. It is shown that both sets of bounds are a significant improvement over the Hashin‐Shtrikman bounds, and that they are in agreement with existing experimental data.