Analytical Solution of the Dilute Strain Concentration Tensor for Coated Spherical Inclusions, and Applications for Polymer Nanocomposites

摘要

There is considerable interest in using various nanoparticles to create multifunctional polymer nanocomposite materials with enhanced properties. Due to the large amount of surface area available within the nanocomposite, the effects of non-bulk polymer in the vicinity of the nanoinclusion, with different properties than the bulk polymer, can complicate micromechanical predictions of effective properties. Several micromechanical approaches require one to calculate the dilute strain concentration tensor, for which elegant solutions are available for separate, physically distinct ellipsoidal inclusion geometries using the well-known Eshelby tensor. However, the actual physical geometry of the interphase region is an annular coating layer in which case these elegant solutions are not readily available. In this work, the general coated inclusion problem is formulated for the case of a spherical inclusion,such that the components of the dilute strain concentration tensors for both the inclusion and the interphase/coating region are analytically determined,from which they canthen be directly implemented within standard micromechanical models. Comparison of the results of the proposed model with predictions based on the originalmultiphase Mori-Tanaka approach show that differences between the models are largest when the annular interphase region is softer than the matrix material, attributed to the ability of the proposed model to capture the “stress-shielding effect” in the case of the softer annular interphase. Moreover, the comparison for the soft-interphase case reveals that the overall nanocomposite stiffness calculated by the proposed method is less sensitive to the increasing volume fraction of inclusion than the traditional multiphase Mori-Tanaka model. However, for cases where the interphase material is stiffer than the matrix, the results of the Annular Coated Mori-Tanaka model and the Multiphase Mori-Tanaka model are surprisingly similar. It is anticipated that the proposed model will be particularly useful in evaluating the impact of chemical functionalization techniques and other strategies that seek to tailor the properties of the interphase region in these materials. The extension of this approach for cylindrical coated-inclusion geometry, with application for nanotube and nanorod inclusions, is currently under development.