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Lateral Contact Stiffness and the Elastic Foundation

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Abstract

A model for the lateral contact stiffness for an elastic foundation was developed. The model was evaluated using a low force and low contact pressure microtribometer capable of performing indentation and reciprocated sliding experiments. The slope of lateral force versus the lateral displacement was used to fit the shear modulus. When complementary elastic indentation measurements are made to determine the composite modulus of the elastic foundation, there is sufficient data to fit elastic modulus, shear modulus, and Poisson ratio for these thin films. Using these models, the elastic properties for a thin (~65 μm) vertically aligned multiwall carbon nanotube film were evaluated. The experiments were performed with a silicon nitride indenter (radius = 1.6 mm) over a range in loads from 100 to 800 μN. The resulting values of the elastic modulus, shear modulus, and Poisson ratio were E = 429 kPa, G = 156 kPa, and ν = 0.37, respectively.

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Abbreviations

A c :

Contact area

b :

Contact radius

C :

Resistance to deformation

d :

Indentation depth

Δx :

Lateral deformation

E :

Elastic modulus

E′:

Composite elastic modulus

F f :

Friction force

F n :

Normal force

G :

Shear modulus

k c :

Lateral contact stiffness

ν :

Poisson’s ratio

R :

Indenter radius

t :

Thickness

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Acknowledgments

Financial support for this study was provided through an AFOSR-MURI Grant FA9550-04-1-0367. We are also indebted to Profs. Linda Schadler and P. M. Ajayan and the Rensselaer Nanotechnology Center for many helpful discussions regarding MWNT films and for providing numerous samples to our laboratory over the years.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, 32611, USA

    Daniel J. Dickrell III & W. G. Sawyer

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  1. Daniel J. Dickrell III
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  2. W. G. Sawyer
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Correspondence to W. G. Sawyer.

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Dickrell, D.J., Sawyer, W.G. Lateral Contact Stiffness and the Elastic Foundation. Tribol Lett 41, 17–21 (2011). https://doi.org/10.1007/s11249-010-9666-5

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