Composite Laminates Performance Enhancement by Nanoparticles Dispersion: an Investigation on Hybrid Nanocomposites pp. 287-339
Authors: Antonio F. Avila, Universidade Federal de Minas Gerais, Department of Mechanical Engineering, NanoComposites Research Group, Belo Horizonte, Brazil
Abstract: The composite performance can be measured by employing different approaches. One common strategy applied is considered the composite mechanical properties. As explained by Daniel and Ishai , mechanical properties can be evaluated taking in consideration stiffness or strength. The composite materials stiffness evaluation has been investigated since the late 1950´s when Eshelby proposed the ellipsoidal inclusion model. According to Eshelby , an ellipsoidal inclusion causes a perturbation into the region surrounded by this inclusion. By applying variational calculus and the energy theorem, Eshelby proposed a model capable of predict the composite material effective property. Hashin and Strikman  a couple of years later proposed a mathematical model take can be applied to fibrous composites also derived from the principle of energy and variational calculus. Their model also known as composite cylinder assemblage (CCA) was able to predict the upper and lower bounds for the main stiffness constants, i.e. Young´s modulus, shear modulus, bulk modulus, and Poisson´s ration. Hashin and Rosen  extended the previous work described by Eshelby , Hashin and Strikman  and compared their predictions with experimental data with very good accuracy. They even suggested that CCA model upper and lower bounds predictions define the optimal range for composite design. Experimental tests and validations of CCA model were extensively performed by Whitney and Riley , Hashin [6-8] and different researchers [9,10]. In some cases, differences between the CCA model predictions and experimental data obtained were attributed to experiments variations. The large majority of the academic community employs the variational calculus predictions as a benchmark for different models validation. However, the off-axis shear modulus calculation was a point of weakness. It was only in 1979 that, Lo and Christensen  proposed a liable alternative for this elastic modulus. According to Christensen , the model was a complement of the work developed by Hashin and his colleagues. Another very reliable work into elastic moduli calculation, based into Eshelby work, is the Mori and Tanaka model . Although the analytical predictions were very accurate, the models were limited to unidirectional composites.