Analysis of different boundary condition models for study of wave scattering from fiber–matrix interphases

Abstract

In this paper different approximate boundary conditions (BC) describing a thin fiber–matrix interphase are used to study ultrasonic wave scattering from a multiphase fiber embedded in a solid matrix. To facilitate the analysis of scattering from a multilayered fiber, a matrix differential equation is derived for elastic fields in a cylindrical medium with radially-dependent properties. From this equation the transfer matrix for each intermediate layer between the fiber core and matrix, relating the stress and displacement fields on the inner and outer boundaries of the layer, is obtained. To describe the effect of the interphase the first- and second-order asymptotic and the spring boundary conditions are derived using an asymptotic expansion of the transfer matrix for a thin fiber–matrix interphase. Analysis performed for different models of spring boundary conditions shows the advantage of preserving the interphase gap connected by springs versus the spring BC defined on an infinitely thin interface, after eliminating the interphase layer and filling the remaining gap by matrix or fiber material. In the last two cases the geometry of the system changes due to change of the scattering surface radius, leading to error in the scattering amplitude. Numerical examples are given for scattering cross sections of longitudinal and shear waves from a multiphase SiC fiber in titanium. It is shown that the spring BC can be used to represent a thin interphase layer with elastic moduli smaller than those of the fiber.