Annular Coated Inclusion model and applications for polymer nanocomposites – Part II: Cylindrical inclusions

• Published in: Mechanics of materials 2016-10, Vol.101, p.50-60
• Main Authors: Wang, Z., Oelkers, R.J., Lee, K.C., Fisher, F.T.
• Format: Article
• Language: English
• Subjects: Annular; Coating effects; Inclusions; Interphase; Mathematical analysis; Mathematical models; Micromechanics; Modelling; Nano composites; Polymer-matrix composites (PMCs); Strain concentration; Tensors
• ISSN: 0167-6636; 1872-7743
• DOI: 10.1016/j.mechmat.2016.07.005

•An Annular Coated Inclusion (ACI) model for cylindrical geometry is proposed.•Analytically determines the dilute strain concentration tensor via auxiliary problems.•Orientational averaging addresses inclusions with known orientational distributions.•Predictions of ACI model benchmarked by Finite Element Analysis.•Model is used to interpret experimental data with randomly oriented inclusions. This work provides an analytical solution for the unknown components of the dilute strain concentration tensors for coated cylindrical inclusions, which can be directly implemented into traditional micromechanical models to predict the effective mechanical properties of composites with coated cylindrical/fibrous inclusions. Comparison of the predictions of the proposed model with predictions based on the standard Mori-Tanaka (MT) approach shows that differences between the models are largest when the annular interphase region is softer than the matrix material. A two-dimensional finite element (FE) analysis is then used to benchmark the transversely isotropic composite behavior captured in the proposed model. Using standard orientational averaging approaches, the effective moduli of composites with randomly oriented cylindrical inclusions are predicted and compared to experimental results for polymer nanocomposites described in the literature, providing insight into the utility of the approach. In addition, by providing an analytical solution to the dilute strain concentration tensor, the proposed methodology would allow one to connect the average stress and strain fields in the constituent phases to known macroscopic fields. The proposed model may be particularly useful as a guide to evaluate the impact of various strategies that seek to tailor the properties of the interphase region in nanocomposite materials. [Display omitted]