Halpin-Tsai model tensile moduli

A number of micro-mechanical models have been developed over the years to predict the mechanical behavior of particulate composites [23-2. Halpin-Tsai model has received special attention owing to better prediction of the properties for a variety of reinforcement geometries. The relative tensile modulus is expressed as... 

The Halpin-Tsai model [49] is most widely used in the fiber composites industry to predict the tensile modulus of unidirectional composites as a function of aspect ratio. The Halpin-Tsai model can deal with a variety of reinforcement geometries, including discontinuous filler reinforcement such as fiber-like or flake-like fillers. The Young s modulus of a composite material in the Halpin-Tsai model is proposed as... 

Jonoobi et al. (2010) studied mechanical properties of CNF reinforced PLA composites. The tensile strength and modulus were improved with increased nanofiber contents. The modulus of the PLA was increased from 2.9 to 3.6 GPa with the addition of 5 wt% nanofibers, a 24 % increase. Similarly, a 21 % increase in tensile strength was observed for nanocomposites compared to neat PLA. On the other hand, strain to failure of nanocomposites was decreased with increase in nanofiber content. Classical models of Halpin-Tsai and Krenchel were used to compare the predicted theoretical data with the experimental data. It was found that experimental data were nearer the predicted value of Krenchel than Halpin-Tsai, which was a confirmation of the random distribution of nanofibers in the matrix, as hypothesized by Krenchel, rather than aligned in longitudinal direction, as hypothesized by Halpin-Tsai. 

It can be seen that, with regard to the pure matrix, the elastic modulus, tensile strength and strain at break increase with nanotube loading. On the other hand, the addition of 10 MWNTs impart to the matrix a higher level of reinforcement than 10 phr of carbon black. Many factors could potentially explain the superior reinforcing efficiency of carbon nanotubes and among them, the filler aspect ratio is expected to play an important role in the mechanical response of the composite. Experimental data can be usefully compared to theoretical model predictions, especially those of Guth [71] and Halpin-Tsai [72]. 

X-ray diffraction measurements were used to determine the orientation of talc and lead carboxylate fillers in plasticised PVC extrudates. Correlations between the extrusion conditions (draw ratio and temperature), the development of filler particle orientation and the tensile properties of the plasticised PVC were studied. The presence of fillers enhanced Young s modulus and this was predicted well by the model developed by Halpin and Tsai. The extrudates were stretched above and below the gel-liquid transition temperature of PVC (about 205C). Above this temperature, the PVC could be stretched more and the tensile results indicated that the crystallites which were surrounded by more flexible chains were more oriented. 24 refs. 

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