Unidirectional fiber–polymer composites: Swelling and modulus anisotropy

The solvent swelling of unidirectional rubber–fiber composites was studied. The amount of matrix swelling was constrained to the extent that would be predicted from the thermodynamic theories of elasticity and polymer–solvent interaction. The geometry of swelling was found to be orthotropic in nature. A simple trigonometric function was derived to relate linear deformation due to swelling to the angle which the direction of its measurement makes with the fiber direction. The validity of the derivation was demonstrated experimentally. Considering swelling to be the imposition of tensile forces of equal magnitude in all directions, and considering a swelling‐induced linear deformation to be analogous to a tensile compliance, a simple set of relationships between elastic parameters and their direction of measurement was derived:\documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {\frac{1}{{E_\theta }} = \frac{{\cos ^2 \theta }}{{E_L }} + \frac{{\sin ^2 \theta }}{{E_T }}} \\ {G_\theta = G_{LT} } \\ {v_\theta = v_{LT} \frac{{E_\theta }}{{E_L }}} \\ {\eta _\theta = E\left( {\frac{1}{{E_T }} - \frac{1}{{E_L }}} \right){\rm }\cos \theta {\rm sin}\theta } \\ \end{array}$$\end{document} where E θ , G θ , v θ , and η θ are Young's modulus, shear modulus, Poisson's ratio, and the shear coupling ratio measured in a longitudinal transverse plane at an angle with the fiber direction, respectively, and E L , G LT , and θ LT are the longitudinal Young's modulus, the longitudinal transverse shear modulus, and the longitudinal transverse Poisson ratio, respectively. Further simplifying the case of combined transverse isotropy and special orthotropy was the conclusion that 1/ G LT = 1/ E T + (1 + 2 v LT )/ E L . The relationships for G and E were experimentally demonstrated.