Effect of Foreign Inclusions on Properties of Solids

Approximate expressions are given for the elastic properties of heterogeneous solids made of inclusions imbedded in a matrix with dissimilar properties and for the upper and lower limits of elastic properties for a case of rigid inclusions. Experimental results are presented on properties of epoxy-alumina composites. The results of the approximate theory are compared to theoretical results based on rigorous mathematical approaches, to existing experimental data, and to experimental results obtained by the author. In all cases, a good agreement is found to exist. A comparison between experimental and theoretical results on Young's modulus is given for heterogeneous solids with inclusion-to-matrix moduli ratios of 3.4, 7, 17, 25, 32, 69, and 100. To allow for tailor making of new composites, the inter-dependence between properties of composites and their constituents has been generalized through a selection of convenient parameters and is presented graphically. The approximate results are shown to be simple, relatively accurate, and quite suitable for engineering computations of the elastic properties of heterogeneous solids.