ANALYSIS OF DIFFERENT BOUNDARY-CONDITION MODELS FOR STUDY OF WAVE SCATTERING FROM FIBER-MATRIX INTERPHASES

In this paper different approximate boundary conditions (BC) describin g a thin fiber-matrix interphase are used to study ultrasonic wave sca ttering from a multiphase fiber embedded in a solid matrix. To facilit ate the analysis of scattering from a multilayered fiber, a matrix dif ferential equation is derived for elastic fields in a cylindrical medi um 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 bo undaries of the layer, is obtained. To describe the effect of the inte rphase the first- and second-order asymptotic and the spring boundary conditions are derived using an asymptotic expansion of the transfer m atrix for a thin fiber-matrix interphase. Analysis performed for diffe rent models of spring boundary conditions shows the advantage of prese rving the interphase gap connected by springs versus the spring BC def ined on an infinitely thin interface, after eliminating the interphase layer and filling the remaining gap by matrix or fiber material. In t he last two cases the geometry of the system changes due to change of the scattering surface radius, leading to error in the scattering ampl itude. Numerical examples are given for scattering cross sections of l ongitudinal and shear waves from a multiphase SiC fiber in titanium, I t is shown that the spring BC can be used to represent a thin interpha se layer with elastic moduli smaller than those of the fiber. (C) 1997 Acoustical Society of America.