On the constant parameters of Halpin-Tsai equation

- By combining the Mori-Tanaka (MT) and Laminated Analogy (LA) methods, a new model (MT-LA) was presented.
- The MT-LA calculates the elastic modulus of the randomly oriented composites, like nanotube or graphene nanocomposites.
- Using the MT-LA, it was proved that the so called constant coefficient of Halpin-Tsai (HT) method is a variable and not a constant.
- It was found that this coefficient depends on the volume fraction and the stiffness ratio of the matrix to reinforcement.

The Halpin-Tsai method is a well-known technique to calculate the stiffness of composites reinforced by micro and nano particles. In this method, first the longitudinal and transverse moduli of composites are calculated. Then, the elastic modulus of randomly oriented composites is obtained using an equation contains a constant coefficient. This coefficient is assumed to be constant and independent of the matrix and reinforcement properties. The aim of the present research is to calculate this coefficient with an analytical model and show that it depends on the matrix and reinforcement properties. In this regard, an analytical method called the Mori-Tanaka laminated analogy (MT-LA) was developed which is able to calculate the elastic modulus of the randomly-oriented composites. Comparing the result of the MT-LA method with that of the Halpin-Tsai equation, the coefficient of Halpin-Tsai equation was obtained. It was shown that this coefficient is not constant and depends on the volume fraction and the stiffness ratio of the matrix to reinforcement. Finally, using this new coefficient, equations are presented which are able to compute the elastic modulus of both platelet and fibrous randomly oriented composites. Using the mechanical properties of the carbon nanotube (CNT), graphene sheet (GS) and the polymer, the elastic moduli of nanocomposites were calculated. The results were compared with experimental data available in the literature. It was shown that more accurate results were achieved by using this new coefficient in the Halpin-Tsai equation.