Theoretical Study On The Effective Conductivity And Elastic Properties Of Composites With Imperfect Interface

This thesis aims at obtaining effective mechanical properties as conductivity and linear transverse elastic properties of composites with imperfect interfaces characterized by the generalized imperfect interface model.The first goal of this thesis is to investigate the effective conductivities of a composite containing ellipsoidal inhomogeneity through the general imperfect interfaces. The general interface model of thermal conductivity is characterized by two jump relations. The first one reads that the temperature jump across an interface is proportional to the interfacial average of the normal heat flux and the second expresses that the normal heat flux jump across the interface is proportional to the local surface Laplacian of the interfacial average of the temperature. The well-known Kapitza’s resistance and highly conducting imperfect interface models can be referred as two extreme cases of the general interface model by letting the two scalar proportionality parameters equal zero respectively. The ellipsoidal harmonics and spheroidal harmonics for prolate and oblate configurations are utilized to express the temperature fields in the composites. The effective conductivities of a composite containing prolate, oblate inclusions with imperfect interface at the dilute and non-dilute concentration ratio are derived. The results are extended to compare with the reverent results obtained with Kapitza’s resistance and highly conducting imperfect interface models as a check. Numerical examples are carried out to illustrate some results.The second goal is using the generalized self-consistent method (GSCM) to obtain the closed-form estimates for the 5 elastic moduli of a transversely isotropic composite consisting of an isotropic matrix reinforced by unidirectional isotropic fibers of circular cross-section. The interfaces between the matrix and the fibers in this composite are taken to be imperfect and characterized by the general elastic isotropic model which includes as particular cases the widely used elastic spring-layer and membrane-type imperfect interface models. The displacement, strain and stress fields in an infinite homogeneous medium containing a composite cylinder with a general imperfect interface and subjected to each of 5 elementary remote uniform loadings are specified and used in deriving the estimates for the effective elastic moduli. These results extend and bridge the special relevant results reported in the literature for fiber-reinforced composites with imperfect interfaces characterized by the spring-layer or membrane-type imperfect interface model. Numerical examples are also presented to illustrate some results. At last, some conclusions are drawn.