Generalized self-consistent model for composites with functionally graded and multilayered interphases. Transfer matrix approach

This paper reports calculations for the transverse shear moduli of fiber and particulate composites with interphases having nonhomogeneous elastic properties in the radial direction. A multiphase generalized self-consistent (MGSC) model is applied for composites with multi-layered fiber-matrix interphases using the transfer matrix method, In this model a transfer matrix is defined for each intermediate layer between an inclusion and the unknown effective medium and a total transfer matrix is derived to relate the elastic field in the inclusion to that in the effective medium. In this form the solution for an arbitrary number of interphasial layers resembles the simplicity of the GSC solution for a two-phase composite. To determine the transverse shear modulus of the composite with continuously varied interphases in the radial direction, a transfer matrix for the inhomogeneous interphase is found using the solution of the governing differential equation of the elastic field. An approximation to the transfer matrix is obtained for a thin functionally-graded interphase. Also the spring approximation is considered. The approximate results for the transverse shear modulus are compared with those for the functionally-graded interphase discretized into multilayered homogeneous interphasial layers when the MGSC model can be used directly. The effect of the inhomogeneous interphase on the composite transverse modulus is illustrated by numerical examples.