Micromechanical Nanocomposites Modeling

Tucker et al. [50] prepared an application review of different classes of micromechanical models. The authors remarked that Halpin-Tsai equations [46] are the most widely used, but the Mori-Tanaka type models [45] give the best results for large aspect ratio fillers. 

The direct use of these models for nanoreinforced composites is questionable due to the significant scale difference. The development of nanoscale continuum theories that integrate continuum mechanics theories with the nanoscale molecular structure has aroused a greater interest. These modeling techniques are referred to as nanoscale mechanics or molecular structural mechanics in the literature, and they link the interatomic potentials of atomic structure to the continuum level of materials [64]. 

Mechanical Characterization of Nanocomposites under Static Loading 

Mechanical characterization under static loading of polymer-based nanocomposites has been widely studied in order to evaluate the influence of nanofiller content, dispersion, geometry, orientation, interfadal adhesion quality, and others on their mechanical performance. Layered silicates and CNTs are the most studied reinforcing agents in polymers due to their large aspect ratio and mechanical properties, but in the past decade particulate nanofillers such as sUica or functionalized graphene (FG) have received special interest. 

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In the present work, the micromechanics-based model presented by Anoukou et al. [7,8] is applied to formulate the effective viscoelastic response of polyamide-6/clay nanocomposites, experimentally tested in a previous work [6]. 

A micromechanics-based model recently proposed by Anoukou et al. [7,8] was adopted in the present investigation to develop a pertinent model for describing the viscoelastic response of polyamide-6-based nanocomposite systems. Comparisons between the results from the micromechanical model and experimental data were considered for nanocomposites reinforced with modified and unmodified montmorillonite clay. Reasonable agreement between theoretical predictions and experimental data was noticed, the discrepancies being attributed to both uncertainties in the input data and a possible effect of reduced chain segment mobility in the vicinity of clay nanoplatelets. 

CNTs have extremely high stiffness and strength, and are regarded as perfect reinforcing fibers for developing a new class of nanocomposites. The use of atomistic or molecular dynamics (MD) simulations is inevitable for the analysis of such nanomaterials in order to study the local load transfers, interface properties, or failure modes at the nanoscale. Meanwhile, continuum models based on micromechan-ics have been shown in several recent studies to be useful in the global analysis for characterizing such nanomaterials at the micro- or macro-scale. 

The analytical expressions of micromechanics are generally most accurate at low volume fractions of the filler phase. The details of the morphology become increasingly more important at higher volume fractions. This fact was illustrated by Bush [64] with boundary element simulations of the elastic properties of particulate-reinforced and whisker-reinforced composites. The volume fraction at which such details become more important decreases with increasing filler anisotropy, as was shown by Fredrickson and Bicerano [60] in the context of analytical models for the permeability of nanocomposites. 

At present nanocomposite pol5rmer/organoclay studies attained very big wide spreading. However, the majority of work done on this theme has mainly been of an applied character and theoretical aspects of the polymer s reinforcement by organoclays have been studied much less. In this chapter we describe a multiscale micromechanical model. 

Since the assumption of uniformity in continuum mechanics may not hold at the microscale level, micromechanics methods are used to express the continuum quantities associated with an infinitesimal material element in terms of structure and properties of the micro constituents. Thus, a central theme of micromechanics models is the development of a representative volume element (RVE) to statistically represent the local continuum properties. The RVE is constracted to ensure that the length scale is consistent with the smallest constituent that has a first-order effect on the macroscopic behavior. The RVE is then used in a repeating or periodic nature in the full-scale model. The micromechanics method can account for interfaces between constituents, discontinuities, and coupled mechanical and non-mechanical properties. Their purpose is to review the micromechanics methods used for polymer nanocomposites. Thus, we only discuss here some important concepts of micromechanics as well as the Halpin-Tsai model and Mori-Tanaka model. 

The stiffness of polymer-based composite systems depends on numerous factors such as the stiffness of constituents, the volume fraction of each component, and the size, shape and orientation of reinforcements. As a whole there are three distinct types of polymer composites continuous fibre-reinforced polymer composites, short fibre-reinforced polymer composites, and polymer nanocomposites. Theoretical models based on micromechanical models are well developed and provide an adequate representation of composite stiffness. These micromechanical models are formulated based on assumptions of continuum mechanics. However, for nanocomposite materials, with fillers of size approximately 1 nm compared to the typical carbon fibre diameter of 50 tm, the rules and requirements for continuum... 

Another mode of natural nanocomposites reinforcement degree description is micromechanical models application, developed for pol5mier composites mechanical behavior description [1, 37-39]. So, Takayanagi and Kemer models are often used for the description of reinforcement degree on composition for the indicated materials [38, 39]. The authors of Ref. [40] used the mentioned models for theoretical treatment of natural nanocomposites reinforcement degree temperature dependence on the example of PC. 

Boutaleb, S., Zairi, F., Mesbah, A., Nait-Abdelaziz, M., Gloaguen, J.M., Boukharouba, T. Lefebvre, J.M. Micromechanical modelling of the yield stress of polymer-particulate nanocomposites with an inhomogeneous interphase. Procedia Engineering 1 (2009), pp. 217-220. 

Sheng, N., Boyce, M.C., Parks, D.M. etal. (2004) Multiscale micromechanical modeling of polymer/clay nanocomposites and the effective clay particle. Polymer, 45, 487-506. 

Sheng N, Boyce M C, Parks D M, Rutledge G C, Abes J J and Cohen R E (2004) Multiscale Micromechanical Modeling of Polymer/Clay Nanocomposites and the Effective Clay Particle, Polymer 45 487-506. 

Micromechanical Modeling of the Effective Viscoelastic Response of Polyamide-6-based Nanocomposites Reinforced with Modified and... 

Polymer/clay nanocomposites, micromechanical modeling, structure-property... 

Polymer-based nanocomposites have been widely developed over the last two decades due to their highly specific mechanical properties compared to conventional polymer-based microcomposites [1], The reinforcement mechanism in nanocomposites may be attributed to the strong inter-particle and particle-matrix interactions due to the large specific surface area. Among this recent class of materials, the most intensive researches are focused on polymer-based nanocomposites reinforced with inorganic montmorillonite clay, and especially on their synthesis and characterization. However, their micromechanical modeling has been less investigated so far. 

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