Effect of Inclusion Morphology on the Coefficient of Thermal Expansion in Filled Polymer Matrix

Abstract

The paper presents both analytical and experimental work towards reducing the thermal expansion of polymer-matrix materials for cryogenic composite tank applications. In a cryogenic composite tank, large thermal strains develop through the thickness of the tank laminate due to the mismatch in the coefficient of thermal expansion between reinforcing fibers and the polymer matrix. Excessive thermal strains can cause microcracks in the matrix and inter-ply delamination, leading to leakage of the fluid contained by the tank. Therefore, methods for reducing the thermal expansion of the matrix are highly desirable. Addition of inclusions (e.g., nano-particle reinforcements) that are much stiffer than the matrix is an effective means to reduce thermal expansion of the matrix. The paper presents an analytical model to predict the effective thermal expansion of a polymer matrix reinforced with such inclusions. The model is validated through comparison with thermal- expansion tests on a new, toughened-epoxy matrix material with various concentrations of nanofiber reinforcement. The model is further used to investigate the effect of inclusion morphology, shape, and aspect ratio on the thermal-expansion behavior of the matrix. These analyses indicate (as expected) that high-aspect-ratio, low-CTE inclusions provide the greatest reduction in matrix thermal expansion. Nomenclature α1 = coefficient of thermal expansion in the longitudinal direction of the ellipsoidal inclusion α2, α3 = coefficient of thermal expansion in the transverse direction of the ellipsoidal inclusion {αf} = vector defining the orthotropic coefficients of thermal expansion of the inclusion {αm} = vector defining the isotropic coefficient of thermal expansion of the matrix {αc} = vector defining the orthotropic coefficient of thermal expansion of the filled matrix