Halpin-Tsai equations mechanical properties

The effect of polymer-filler interaction on solvent swelling and dynamic mechanical properties of the sol-gel-derived acrylic rubber (ACM)/silica, epoxi-dized natural rubber (ENR)/silica, and polyvinyl alcohol (PVA)/silica hybrid nanocomposites was described by Bandyopadhyay et al. [27]. Theoretical delineation of the reinforcing mechanism of polymer-layered silicate nanocomposites has been attempted by some authors while studying the micromechanics of the intercalated or exfoliated PNCs [28-31]. Wu et al. [32] verified the modulus reinforcement of rubber/clay nanocomposites using composite theories based on Guth, Halpin-Tsai, and the modified Halpin-Tsai equations. On introduction of a modulus reduction factor (MRF) for the platelet-like fillers, the predicted moduli were found to be closer to the experimental measurements. 

Various composite models such as parallel model, series model, Halpin-Tsai equation, and Kerner s model can be used to predict and compare the mechanical properties of polymer blends [43-45]. For the theoretical prediction of the tensile behavior of PMMA/EMA blends, some of these models... 

Generally, the two simplest and most common models for the mechanical properties of fiber reinforced composites are the rule of mixtures and the Halpin-Tsai equations [71]. The computational methods for the investigation of CNTs and CNT-filled composites can be categorized into two classes continuum methods and atomistic methods [31]. 

The Halpin-Tsai equation (Halpin 1969) expresses the mechanical properties of a composite in terms of those of the filler and the matrix. Modifications of the Halpin-Tsai model to better describe clay-fiUed nanofiber composites have recently been reported by Ramakrishna et al. (2006). 

The Halpin-Tsai equations and the Mori-Tanaka model are the most used to predict mechanical properties of composites. The Halpin-Tsai equations predict stiffness of the unidirectional composites as a function of aspect ratio. In this model, the longitudinal stiffness and transverse engineering moduli are expressed in the following general form ... 

Although there is enormous variability in mechanical properties because of local concentration and isotropy variation, the Halpin-Tsai model has been shown to provide reasonably good approximations of the elastic modulus of randomly distributed CNT-based nanocomposites [322,323]. The Halpin-Tsai model (Equations 5.7, 5.8) is specifically for glassy matrix polymers, but it has also shown to be fairly effective for semicrystalline polymers as well [324]. 

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