Effect of interphase layers on the overall elastic and conductive properties of matrix composites. Applications to nanosize inclusion

For a composite with thin interface layers between inclusions and the matrix, the effective elastic properties and the effective conductivity (thermal or electric) are almost unaffected by the layers, provided (1) the layer thickness is much smaller than the inclusion sizes and (2) the contrast between the properties of the layers and either of the phases is not overly high. For composites with nanoparticles, the interface thickness may be comparable to the particle sizes. Therefore, the effect of interfaces on the overall properties may be substantial. The controlling parameters are (1) the ratio of the interface thickness to particle sizes and (2) variability of the properties across the interface thickness. Explicit expressions constructed in the present work show that the overall elastic/conductive properties are affected, mostly, by the interface thickness (normalized to the size of the core particle) and are much less sensitive to the extent of the variation and its exact character. Similarities and differences between the elasticity and the conductivity problems are discussed.