Analysis of thermo-mechanical incompatibility of fullerenes with polymer matrices of composites

Abstract

Unique strength and rigidity properties of carbon nanotubes and fullerenes do them very perspective reinforcing admixtures into composites produced on the basis of polymeric and metallic matrices. It is established that even relatively small their dopes into composites can essentially enlarge physico-mechanical characteristics of polymers. At the same time, comparatively low value of the linear thermal expansion coefficient of carbon nanomolecules results in the possibility of the emergence of the internal mechanism of the additional intrastructural stresses origination in the polymer conditioned due to thermomechanical incompatibility of the composite fractions. To examine this possibility, the theoretical modelling of the thermomechanical deforming of the considered heterogeneous structures under thermal change action was carried out. In doing so, the fullerenes were simulated as a thin elastic shell with adduced (effective) thickness, elasticity modulus, Poissonn’s coefficient and linear thermal expansion coefficient, the polymer matrix was supposed to be a homogeneous elastic medium with the prescribed parameters of thermoelasticity. The system of constitutive ordinary differential equations was deduced, which described the thermoelastic stress-strainedstate of the elastic fragment chosen for consideration. These equations solutions were deduced in the closed form for the case when the system temperature changed in. Fenolformaldegid, epoxy rezin, polycarbonate, polyamide, polystirol, polyester, and polypropylene, possessing increased values of the linear thermal expansion coefficients, were chosen as the matrix materials. With these initial data, the values of the fullerene radial displacements were calculated for two magnitudes of the sphere radius. It is demonstrated that owing to the high value of the fullerene effective elasticity modulus, the thermal deflections of its wall poorly depend on the properties of the encompassing matrix and practically are equal to its free thermal displacements. The thermal stresses of the polymer matrices have the largest values in the zones of the interface surfaces and they decrease proportionally to cube of the radial coordinate, so, the damages provoked by them have localized character.