Continuum analysis of carbon nanotube array buckling enabled by anisotropic elastic measurements and modeling

For the first time, carbon nanotube (CNT) forests are fully characterized as transversely isotropic continuum material. Each of the five independent elastic constants is experimentally obtained using a combination of nanoindenter-based uniaxial compression and shear testing, in situ SEM compression, and digital image correlation (DIC) of vertically and laterally oriented CNT microstructure columns. Material properties are highly anisotropic, with an axial modulus (165-275 MPa) that is nearly two orders of magnitude greater than the transverse modulus (2.5-2.7 MPa) and the out of plane shear modulus (0.8-1.6 MPa). The Poisson's ratios along three mutually orthogonal axes, measured directly by simultaneous in situ DIC evaluation of axial and transverse strain, are found to be similarly anisotropic (ν₁₂ = 0.35, ν₂₃ = 0.1, ν₂₁ = 0.005). A Timoshenko beam model is then developed to accurately predict the critical buckling stress of the vertically oriented columns using a subset of these anisotropic properties and considering inelastic column buckling. These results show that the critical bucking stress of CNT microstructures vary predictably with geometry and that continuum models with appropriate material constants may be applied to analyze CNT microstructures and evaluate their stability for many applications.