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Research Papers

Nanoindentation of Compliant Substrate Systems: Effects of Geometry and Compliance

[+] Author and Article Information
Thao D. Nguyen1

Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218vicky.nguyen@jhu.edu

J. D. Yeager, D. F. Bahr

School of Mechanical and Materials Engineering, Washington State University, Pullman WA, 99164

D. P. Adams

 Sandia National Laboratories, Albuquerque, NM 86185

N. R. Moody

 Sandia National Laboratories, Livermore, CA 94550

1

Corresponding author.

J. Eng. Mater. Technol 132(2), 021001 (Jan 12, 2010) (7 pages) doi:10.1115/1.4000230 History: Received April 19, 2009; Revised July 22, 2009; Published January 12, 2010; Online January 12, 2010

Nanoindentation is widely used to characterize the mechanical and interfacial properties of thin film systems. However, the effects of substrate compliance on the indentation response of compliant substrate systems are not well understood. This paper investigates the effects of the large compliance mismatch between the film and the substrate and of the film thickness for model systems using nanoindentation tests, finite element simulations, and an analytical model based on a classical plate-bending solution. The results showed that for displacements less than the film thickness and for ratio of the substrate to film modulus less than 100. The indentation force-displacement response exhibits a linear relationship that can be predicted accurately by the linear plate-bending model. The effective stiffness depends linearly on the film thickness and also on the substrate and film moduli. For larger displacements, the indentation response exhibits the scaling relationship of the nonlinear plate-bending model.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of the plate-bending model. The film and substrate are modeled as an infinite plate on an elastic half space.

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Figure 2

Finite element geometry of indentation of a thin stiff film on a compliant substrate.

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Figure 3

The force-displacement curves comparing: (a) different strain-rates for the 200 nm W/PS system and (b) different residual film stresses for 200 nm W/PS system at 0.01/s.

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Figure 4

The force-displacement curve comparing different film thickness for the (a) W/PS system and (b) W/FS system.

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Figure 5

The force-displacement curves comparing the results of nanoindentation experiments (Exp) and FE simulations (Sim) for 100 nm and 200 nm W/PS systems.

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Figure 6

(a) Finite element simulation results for the 100 nm film W/PS system. (b) The indentation stiffness for W/PS systems of different film thicknesses comparing experiments, FE simulations, and the plate-bending model.

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Figure 7

The effective modulus from finite element simulations of (a) tungsten film systems with different substrate moduli and (b) polystyrene substrate systems with different film moduli. The effective stiffness measured from experiments and calculated from the linear plate-bending model is plotted also for comparison.

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Figure 8

Nondimensional force-displacement curves from finite element simulations of (a) W/PS systems with different film thicknesses hf, (b) hf=100 nm tungsten film systems with different substrate moduli, (c) polystyrene substrate systems with hf=100 nm thick films of different moduli, and (d) hf=100 nm W/PS system for different indenter radius Ri.

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