Constitutive Modeling of Crosslinked Nanotube Materials

*† ‡ § ** A non-linear, continuum-based constitutive model is developed for carbon nanotube materials in which bundles of aligned carbon nanotubes have varying amounts of crosslinks between the nanotubes. The model accounts for the non-linear elastic constitutive behavior of the material in terms of strain, and is developed using a thermodynamic energy approach. The model is used to examine the effect of the crosslinking on the overall mechanical properties of variations of the crosslinked carbon nanotube material with varying degrees of crosslinking. It is shown that the presence of the crosslinks has significant effects on the mechanical properties of the carbon nanotube materials. An increase in the transverse shear properties is observed when the nanotubes are crosslinked. However, this increase is accompanied by a decrease in axial mechanical properties of the nanotube material upon crosslinking. arbon nanotube (CNT) composite materials have the potential to provide order-of-magnitude increases in stiffness-to-weight and strength-to-weight ratios relative to current materials used for aerospace structural applications. These properties are especially important in the design and development of ultra-light-weight aircraft such as new classes of Unmanned Aerial Vehicles (UAVs), in which the primary requirements are those associated with long-duration, high-altitude flights. To facilitate the development of CNT-based materials for this purpose, constitutive relationships must be developed that predict the bulk mechanical properties of the materials as a function of the molecular structure. Within the past few years, considerable effort has been expended to synthesize CNT/polymer composites that take advantage of CNT properties by enhancing the load transfer between the CNTs and the adjacent polymer molecules. 1-9 One approach to achieving this is to form chemical bonds between CNTs and adjacent polymer molecules (functionalization). Despite the potential increase in load transfer that follows from functionalization with respect to the load transfer that occurs without the presence of a chemical bond, it has been recently demonstrated that functionalization itself can measurably affect the structure and mechanical properties of CNTs, 10,11 which can, in turn, ultimately alter or perhaps degrade the bulk mechanical properties of CNT/polymer composite materials. As an alternative approach to increasing load transfer efficiency between the CNT and surrounding polymer, NASA Langley Research Center has recently developed a material in which single-walled CNTs are covalently bonded together (crosslinked) with the chemical linking agent 1,3-bis(4-aminophenoxy-4’benzoyl)benzene (1,3-BABB). In this material, the short, organic linker units allow for direct CNT-to-CNT load transfer, therefore, possibly allowing for improved overall mechanical properties with respect to pure CNT-based materials and CNT/polymer materials in which the CNTs are functionalized to the polymer only. Since it is expected that the bulk mechanical properties in this new class of materials are expected to be affected by intrinsic and sometimes subtle changes in the molecular structure, a multi-scale modeling approach must be developed to allow for accurate design of materials and provide the constitutive relationships necessary for macro-scale analysis methods. The objective of the present paper is to develop non-linear constitutive models for these crosslinked CNT materials and to examine the influence of crosslink density on the overall, continuum-level elastic properties. Following a brief description of the materials, the equivalent-continuum modeling approach is described in detail. * Staff Scientist, National Institute of Aerospace. Senior Member, AIAA.