An Extended Annular Coated Inclusion Model with Imperfect Interfaces

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Interactions between the nanoinclusion and polymer matrix in nanoparticlereinforced polymer nanocomposites result in an interphase region with different properties than the bulk polymer. This polymer interphase and complicates micromechanical predictions of effective properties and may have a large influence on the overall nanocomposite properties. Recently the Annular Coated Inclusion model has been formulated in terms of appropriate single-inclusion auxiliary problems following the procedure of Benveniste, such that the components of the dilute strain concentration tensor can be determined analytically for coated spherical and coated cylindrical geometries. These solutions then available to be directly implemented within standard micromechanical models. This framework can be extended by implementing a spring-layer model incorporated within the Annular Coated Inclusion framework to evaluate the impact of an imperfect interface on these micromechanics model predictions. To verify the accuracy of the approach for the spherical inclusion case, the interfacial stresses predicted by the proposed model are shown to be identical to classical analytical results, while the effective composite elastic modulus predictions closely agree with results generated by a thin-soft interphase model. Lastly, one can show that the imperfect interface model can be extended for non-dilute particle concentrations via iterative solution of the appropriate auxiliary problems. In this manner, one can determine the stress fields within the composite as a function of the spring-layer interface model parameters in a way that accounts for the impact of particle-particle interactions on the composite response. The stress distributions for cases of both shear and uniaxial loading agree closely with a corresponding Finite Element analysis which highlights the utility of the proposed approach.