Modelling the elastic stiffness of nanocomposites using interphase models

This report describes mathematical modelling of the elastic stiffness of nanocomposites, which in this context is referred to as particles of nano-size included in a polymer matrix, i.e. particles with one dimension of nanometre size. The main motivation for this work was to establish mathematical models for calculating the elastic properties of different nanocomposites, which then can be included in a “model toolbox” for future applications and for improved understanding of this type of materials. In this study, it is assumed that micromechanics models and continuum mechanics theory can be applied in the modelling. In this report, an interphase model found in the literature is considered. The interphase is defined as the layer surrounding the particle, which has different elastic properties compared to the neat matrix (and the particle). Such models can thus be applied for describing changes in the polymer structure due to the inclusions, the bonding properties between the particle and the matrix, as well as the stiffness increase for the composite as a function of particle volume fraction. Only spherical particles are included in the interphase model considered. Extensions of the model that include other spheroidal inclusion shapes than spheres are therefore presented. With the introduction of non-spherical inclusions, random orientation of the particles is also relevant. Stiffness expressions are presented for including randomly oriented spheroidal inclusions. The general two-phase Mori-Tanaka, described and analyzed in more detail in another recent FFI report, is included for comparison. The composite elastic stiffness calculated by the interphase model and the two-phase Mori- Tanaka model is found to agree well for different spheroidal inclusion shapes and orientations. The composite stiffness calculations from using the interphase model are also compared with experimental data for two different nanocomposites. Based on a very brief and initial analysis, the model calculations are observed to agree well with the experimental data. Hence, the significant stiffness increase for some composites, especially for low volume fractions, may be explained by interphase effects. A more thorough and detailed analysis than presented in this report can be found in a recent paper by the author (submitted to journal in March 2015). Future studies should consider other factors th