Diffraction of Elastic Waves by a Spherical Inclusion with an Anisotropic Graded Interfacial Layer and Dynamic Stress Concentrations

Scattering of compressional waves in multiphase metal matrix composites containing spherical particles with spherically isotropic graded interfacial layers is investigated using a state-space approach. A continuous transition from the particle to the matrix with the change of volume fraction of one of the constituents is assumed to exist across the thickness of the interphase zone. A simplified multilayer model for the interphase complications including both anisotropy and inhomogeneity is considered. Taylor’s expansion theorem is employed to solve a modal state equation leading to a global transfer matrix that directly links the boundary conditions at the outer surface of the interface layer to those at the inner surface. Numerical calculations reveal the important effects of interphase anisotropy and inhomogeneity on the total scattering cross section and dynamic stress concentrations for a moderately wide range of frequencies and interface layer thicknesses.