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Micromechanical experiments, image analysis, and theoretical modeling revealed that local failure events and compressive stresses of vertically aligned carbon nanotubes (VACNTs) were uniquely linked to relative density gradients. Edge detection analysis of systematically obtained scanning electron micrographs was used to quantify a microstructural figure-of-merit related to relative local density along VACNT heights. Sequential bottom-to-top buckling and hardening in stress–strain response were observed in samples with smaller relative density at the bottom. When density gradient was insubstantial or reversed, bottom regions always buckled last, and a flat stress plateau was obtained. These findings were consistent with predictions of a 2D material model based on a viscoplastic solid with plastic non-normality and a hardening–softening–hardening plastic flow relation. The hardening slope in compression generated by the model was directly related to the stiffness gradient along the sample height, and hence to the local relative density. These results demonstrate that a microstructural figure-of-merit, the effective relative density, can be used to quantify and predict the mechanical response.

We report the mechanical behavior of vertically aligned carbon nanotube films, grown on Si substrates using atmospheric pressure chemical vapor deposition, subjected to in situ large displacement (up to 70 lm) flat-punch indentations. We observed three distinct regimes in their indentation stress-strain curves: (i) a short elastic regime, followed by (ii) a sudden instability, which resulted in a substantial rapid displacement burst manifested by an instantaneous vertical shearing of the material directly underneath the indenter tip by as much as 30 lm, and (iii) a positively sloped plateau for displacements between 10 and 70 lm. In situ nanomechanical indentation experiments revealed that the shear strain was accommodated by an array of coiled carbon nanotube "microrollers," providing a low-friction path for the vertical displacement. Mechanical response and concurrent deformation morphologies are discussed in the foam-like deformation framework with a particular emphasis on boundary conditions.

Motivated by a model that qualitatively captured the response of vertically aligned carbon nanotube (VACNT) pillars in uniaxial compression, we consider the uniaxial tensile response of a class of compressible elastic-viscoplastic solids. In Hutchens et al. ["Analysis of Uniaxial Compression of Vertically Aligned Carbon Nanotubes," J. Mech. Phys. Solids, 59, pp. 2227-2237), Erratum 60, 1753-1756] an elastic viscoplastic constitutive relation with plastic compressibility, plastic non-normality, and a hardening-softeninghardening hardness function was used to model experimentally obtained uniaxial compression data of cylindrical VACNT micropillars. Complex deformation modes were found in uniaxial compression, which include a sequential buckling-like collapse of the type seen in experiments. These complex deformation modes led to the overall stress-strain signature of the pillar not being of the same form as the input material hardness function. A fundamental question that motivates exploring the deformation of this class of materials-both experimentally and theoretically-is how to extract the intrinsic material response from simple tests. In this study we explore the relation between the input material response and the overall stress strain behavior in uniaxial tension using the constitutive framework of Hutchens et al. A simple one-dimensional analysis reveals the types of instability modes to be expected. Dynamic, finite deformation finite element calculations are carried out to explore the dependence of diffuse necking, localized necking, and propagating band deformation modes on characteristics of the hardness function. Attention is devoted to uncovering implications for obtaining intrinsic material properties of complex hierarchical structures; for example, vertically aligned carbon nanotubes (VACNTs), from uniaxial tension experiments.

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