A Semi-Empirical Methold to Characterize Effective Elastic Moduli of Components in Binary Composite Materials

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Abstract
The paper describes a semi-empirical method to obtain average elastic energy densities of components in a composite environment with any particulate geometry. The average elastic bulk and shear energy densities of components in two phase composite materials are expressed in terms of effective bulk and shear moduli, average strains squared of the composite material, and the volume fractions of the components. These energy densities are obtained by assuming that the effective elastic, bulk, and shear moduli of the composite materials are known. Therefore, the present analysis is semi-empirical. Numerical calculations of an aluminum matrix, reinforced by silicon-carbide (SiC) randomly oriented in the metallic composite material, are performed by using the effective bulk (K) and shear (μ) moduli of the composite material, measured by the ultrasonic technique. Measured K and μ and component energy densities at various volume fractions of SiC are compared with results obtained for spherical inclusions, using expressions derived by previous investigators. The comparisons of K and μ with those of the spherical inclusions are reasonable. At various volume fractions, comparisons of the average energy densities of components obtained by the present method with those of spherical inclusions using analytically obtained K and μ agree reasonably within 50% of SiC. The deviations are increased in the region of high concentration of SiC. The analysis in the paper could be applied to an investigation of the effect of particle geometries on the strengthening of components in the composite. Another application is numerical stress analysis to find local effects in the composite environment, since the properties of the components are required as input data.