Mechanics of cnt turfs modeling experiments and characterization
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P max. Load ( P ). 0.2 P max. 0. 10. 20. 30. 40. time (sec). 1. 0.1. Tangent modulus (GPa). 0.01. 0. 2000. 4000. Indentation depth (nm). Mechanics of CNT Turfs: Modeling, Experiments and Characterization. Grant Number: CMMI-0856436, PI – Sinisa Dj. Mesarovic

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Mechanics of CNT Turfs: Modeling, Experiments and Characterization

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Mechanics of cnt turfs modeling experiments and characterization


Load (P)

0.2 Pmax






time (sec)



Tangent modulus (GPa)





Indentation depth (nm)

Mechanics of CNT Turfs: Modeling, Experiments and Characterization

Grant Number: CMMI-0856436, PI – Sinisa Dj. Mesarovic

David F. Bahr, David P. Field, Coralee McCarter, Anqi Qiu, Hina Malik, Harish RadhakrishnanSchool of Mechanical and Materials Engineering, Washington State University, Pullman WA 99164

  • Introduction

  • Exceptional mechanical and thermal properties of carbon nanotubes (CNTs) qualify them for many potential applications.

  • CNTs grown on a substrate form aturf – intertwined, mostly nominally vertical tubes, cross-linked by adhesive contact (van der Waals bonded) and few bracing tubes.

  • Deformation of the structure affects thermal and electrical properties.

  • Mechanical behavior of the turf is dependent of nanoscale topological parameters characterized by

    • Density

    • Average curvature

    • Contact between tubes

  • Deduce mechanical behavior using:

    • Experiments

      • Load-depth response

      • Spatial variation of properties

    • Computational models

      • Continuum model

      • Discrete model

  • No statistical variation of elastic properties across the turf surface

  • Using thermo-compression bonding the turf is inverted and the properties of the inverted turf are measured

  • A discrete model of a CNT turf is generated using a controlled random walk algorithm to obtain a turf structure with desired density and initial curvature

  • CNTs are discretized using length-constrained elastica finite elements

  • Equations of motion are integrated using the Verlet technique and the constraint equations are solved using a technique similar to the SHAKE algorithm [Rykeart et. al., J. Comp. Phys. 1977]

  • Periodic boundary conditions are employed to model infinitely wide turfs and tube interactions are based on Lennard Jones force law

Figure: Percentile distribution of the (a) elastic modulus (b) hardness

  • Elastic modulus and hardness measurements of the inverted turf are identical to the original turf.

  • SEM images of the surface reveal identical morphology with original turf.

  • Density of turf remains unchanged after inversion (order of 50 / mm2)

Figure: SEM image of a CNT turf


Figure: (a) & (b) Random walk generation of the turf structure using different parameters. (c) Side view showing the periodic BC’s

True Stress (Pa)

  • Independent parameters

    • - Length of CNTs per unit volume

    • - Thickness of the tube

  • Stiffness of turf scales as

  • Nanoindentation experiment reveal the deformation of the turf under moderate strains is reversible

  • In situ compression tests on a cluster of CNTs reveal the primary mechanism of deformation is due to bending of the tubes

  • Tubes in contact remain in contact after unloading revealing no sliding of contacts

True Strain

Figure: Sum of angles technique to measure the average curvature

  • Measurement of the average curvature of turfs

    • Sum of angles technique

    • - Interpolating the CNTs (splines, hermite curves)


  • Depth sensing experiments to measure the tangent modulus show an exponential decay of an order of magnitude with increasing depth

Figure: Flat punch indentation of turf samples using periodic boundary condition. (a) relaxed configuration (b) deformed configuration. Load-depth curves from (c) simulation of turfs with different densities (d) experiments (inset) cooridinated buckling of turf columns

Figure: CNT cluster geometry before and after TEM compression

  • Computational Modeling

  • Under moderate strains, can the turf be modeled using an continuum material model? The compressive behavior of the turf is similar to an elastomeric foam.

  • Continuum finite element model of the turf:

    • Turf modeled using elastomeric foam model with zero Poisson’s ratio

    • Kelvin-Voigt relaxation

    • Interaction between turf and indenter modeled using Lennard-Jones type force law

  • Conclusions

  • Mechanical Behavior of turfs are dependent on micromechanical parameters characterized by density and average curvature

  • Nanoindentation experiments reveal a foam like response under moderate strains

  • Spatial variation of mechanical properties is negligible

  • Continuum model of the turf can accurately represent the mechanical behavior under moderate strains

  • Load-depth curves from discrete model reveal qualitative agreement with experiments under uniform compression

  • Spatial variation of the mechanical response is analyzed by indentating at various points on the surface of the turf


This work has been funded by the NSF grant #CMMI-0856436

The authors also acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources that have contributed to the research results reported.

Figure: (a) Load-depth curves from experiments and FE results (inset) indentation mechanism (b) Loading profile

Figure: (a) Location of the indentation experiments (b) Load-depth response of two turf samples using a Berkovich tip.

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