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 fib er and particulate composites with interphases having nonhomogeneous e lastic properties in the radial direction. A multiphase generalized se lf-consistent (MGSC) model is applied for composites with multi-layere d fiber-matrix interphases using the transfer matrix method, In this m odel a transfer matrix is defined for each intermediate layer between an inclusion and the unknown effective medium and a total transfer mat rix is derived to relate the elastic field in the inclusion to that in the effective medium. In this form the solution for an arbitrary numb er 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 di rection, a transfer matrix for the inhomogeneous interphase is found u sing the solution of the governing differential equation of the elasti c field. An approximation to the transfer matrix is obtained for a thi n functionally-graded interphase. Also the spring approximation is con sidered. 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 t he composite transverse modulus is illustrated by numerical examples.