Effective stiffness of wavy aligned carbon nanotubes for modeling of controlled-morphology polymer nanocomposites

The mechanics of nano-scale fiber reinforced polymer matrices are investigated using an analytical reduction and finite element modeling to consider the effect of waviness of the reinforcing carbon nanotubes (CNTs). Nanofiber-reinforced polymer matrices are of significant interest as structural materials in and of themselves, and particularly as hybridized matrices within bulk polymer-matrix composites containing standard microndia. fibers, e.g., carbon fiber reinforced plastics (CFRP) that are used extensively in aerospace applications. Here, a representative volume element (RVE) of aligned, continuous, and wavy CNTs in a polymer matrix is modeled to deduce the waviness effects on the elastic properties of the aligned-CNT polymer nanocomposite (A-PNC) as a function of the properties of the reinforcing fibers (CNTs), including CNT type and degree of waviness. Experimental modulus data as a function of CNT volume fraction for an A-PNC RVE using an aerospace-grade thermoset epoxy is used to highlight the importance of waviness and the axial vs. bending stiffness contributions of the CNTs to RVE stiffness. Straightforward implementation for single- and multi-walled CNTs improves upon prior work that considers the filaments to have a solid, rather than hollow, cross section. The derivation of effective axial and bending stiffness for the CNT filaments utilizes proper modulus-thickness pairs for investigating more complex cases. Waviness is noted to be the dominant morphological feature controlling the elastic response of such PNCs, effectively significantly reducing stiffness relative to rule of mixtures predictions. Future work will focus on modelexperiment correlation with in-progress experimental work to characterize the full, nonisotropic, constitutive relation for A-PNCs.