Length scale dependence in elastomers – comparison of indentation experiments with numerical simulations

Published Date

19 August 2016, Vol.98:201–209, doi:10.1016/j.polymer.2016.06.020

Title 

Length scale dependence in elastomers – comparison of indentation experiments with numerical simulations

• Author 

• Nitin Garg
• Chung-Souk Han ^,
• Farid Alisafaei ^1,

• Department of Mechanical Engineering, University of Wyoming, Laramie, WY 82071, USA

Received 24 March 2016. Revised 25 May 2016. Accepted 7 June 2016. Available online 11 June 2016.

Highlights

• •
  Indentation size effects in elastomers are analyzed with a couple stress theory implemented in a finite element (FE) approach.
• •
  The FE simulations were performed for both conical indenter tips at various indentation depths and spherical indenter tips of various tip radii.
• •
  Good agreement has been found in experiments and simulations corroborating the notion of higher gradient dependent deformation in elastomers.

Abstract

Probing depth dependent deformation at nano- and micrometer length scales has been observed in indentation experiments of polymers. Unlike in metals, where size effects are observed in plastic deformation and are attributed to geometrically necessary dislocations, the origin of size dependence in polymers is not well understood. As classical continuum theories are unable to describe such phenomena, higher order gradient theories have been developed to capture such size dependent deformation behavior. The present study adopts the penalty finite element approach for a couple stress elasticity theory under axisymmetric conditions to numerically simulate and analyze the probing depth dependent deformation. Polydimethylsiloxane (PDMS) and natural rubber have been used as model materials to analyze the depth dependent deformation at different probing depths. Simulations were performed on PDMS using spherical indenter tips of different radii to show the influence of strain/rotation gradients on elastic modulus. To capture the experimentally observed increase in hardness with decreasing probing depth, simulations applying a conical indenter tip were performed and compared with experimental data.

Graphical abstract

Keywords

• Polymers
• Nanoindentation
• Length scale dependent deformation
• Finite elements

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• ∗ 
  Corresponding author. Dept. 3295, University of Wyoming, Laramie, WY 82071, USA.

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