Transversely isotropic moduli of two partially debonded composites

Abstract

The effective transversely isotropic moduli of two hybrid composites containing both partially debonded and perfectly bonded spheroidal inclusions are derived. In this derivation a fictitious, transversely isotropic inclusion is introduced to replace the isotropic, partially debonded one so that Eshelby's solution of a perfectly bonded inclusion could be used. [Eshelby, J. D. (1957). The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. LondonA241, 376–396]. Two types of debonding configuration are considered: the first type occurs on the top and bottom of the oblate inclusions and the second one exists on the lateral surface of the prolate inclusions. Albeit approximate, the method is simple and capable of providing explicit results for the five independent moduli in terms of the volume concentrations and aspect ratio of the partially-debonded and perfectly-bonded inclusions. The results are given for the spherical and various inclusion shapes. It is shown that, with spherical inclusions, the longitudinal Young's modulus E11 and axial shear modulus μ12 in type 1, and the transverse Young's modulus E22, plane-strain bulk modulus k23, and the axial and transverse shear moduli in type 2, can all be greatly affected by partial debonding. Examination on the influence of inclusion shape indicates that disc-shaped inclusions in the first type and prolate ones is the second type lead to stronger moduli reduction than spheres.