The Research On The Equivalent Viscoelastic Continuum Micromechanics For Polymer Based Nanocomposites

The so-called polymer based nanocomposites is the polymer/layered silicate nanocomposite with layered silicate as its dispersed phase that produced by using the special method of intercalating polymerization and melt intercalating. Layered silicate mainly comes from the natural montmorillonite, so that it is also called polymer/clay nanocomposites, which is the most hopeful polymer nanocomposite that can be produced by industrialization and have attracted most research works.The research of equivalent viscoelastic continuum micromechanics is a front task of the mechanics in nowadays. It belongs to multiscale, hierarchical, multi-realm intersected, macro/micro conjoint, and most difficult research realm. The aim of which is to find the effective viscoelastic properties and the constitutive relations for macro (large scale) homogeneous materials. The basic ideal is homogenization. We may control individual constituents and corresponding distributions in order to optimize performance. A few per cent volume fraction of layered silicate can remarkably improve many overall properties of nanocomposites. Presently, the development of micromechanics for elastic materials is relatively ripeness. However, for viscoelastic materials, especially for nonlinear viscoelastic nanocomposites, the research works are just now starting. Thus, the research of this program has important scientific and practical sense.The matrix of polymer based nanocomposites is linear viscoelastic or nonlinear viscoelastic material. Its microstructure is heterogeneity hierarchical structure. Aside the enhance phase of nano-/micron-scale, there may be other inclusions, holes, micro cracks, fibers and crystals, etc. The so-called multiscale is the theoretical and computational realm that includes the continuum bodies, molecule particles and quanta with different size-scales and time-scales. Since the continuum micromechanics cannot be applied directly into the nanoscale, we may determine the"equivalent particle","equivalent representative volume element", which possesses equivalent size and equivalent properties, by the equality of the inter-atom potential calculated by molecule dynamics and the strain energy of continuum mechanics, together with the observations by using wide-angle X-ray diffraction (WAXS) and transmission electron microscope. If we replace the"particle"in traditional continuum micromechanics with"equivalent particle", than we obtain the"equivalent continuum micromechanics".The novel achievements of this paper are: 1. The concepts of"equivalent representative volume element"and"equivalent particle"are proposed. In virtue of the calculation methods of"classical elastic continuum micromechanics"the overall effective elastic properties for polymer based nanocomposites are predicted. Some comparisons with the already known theoretical models and the experimental results are shown. The numerical results are good in agreement with the experimental results and the above theoretical predictions.2. Final explicit analytical formulae for predicting the equivalent transversely isotropic elastic modulus tensor and the equivalent transversely isotropic viscoelastic relaxation modulus tensor of the intercalated"equivalent particle"are obtained, which provide the basis for the calculation of the overall effective properties of nanocomposites further. The final explicit analytical formulae in the time domain derived here make it convenient to estimate the influence of all the material parameters of micro-structural details on the overall properties of the nanocomposite, which provide the basis for optimization of the material performance.3. A new rheological model theory with derivatives of fractional order is proposed;"A simple and practical fractional exponential model"and"the correspondence principle in micromechanics"and its applications in polymer based nanocomposites have been proposed.4. By means of the"correspondence principle in micromechanics"the overall effective viscoelastic properties for polymer based nanocomposites with random distributed equivalent particles of different microstructure types are calculated. A new method, which calculates the overall effective viscoelastic properties for every instant by the instantaneous elastic properties in that instant, has been proposed. So that we can use the original elastic finite element program directly; the overall effective elastic and viscoelastic properties for polymer based nanocomposites with exfoliated type, intercalated type, and exfoliated and intercalated mixed type microstructures are predicted and the calculated results are satisfactorily in agreement with the experimental results.5. By using an entirely different ideal of the classical correspondence principle, two elasticity recovery correspondence principles for solving the nonlinear viscoelastic problems are proposed.6. Applications of"the elasticity recovery principle"in polymer based nanocomposites are discussed; a new method for finding the instantaneous curve in the theory of nonlinear viscoelasticity has been proposed; the power law type nonlinear viscoelastic crack-tip fields are obtained. According to the experimental data of the modified polypropylene and polymer based nanocomposites, the solution of the crack-tip stress, strain fields for these materials, are obtained.The above achievements of this paper provide the basis for the further research of polymer based nanocomposites engineering, which have wide application prospects.