Determining Equi-Biaxial Residual Stress and Mechanical Properties From the Force-Displacement Curves of Conical Microindentation

[+] Author and Article Information
J. Yan

Department of Mechanical Engineering, University of Delaware, Newark, DE 19716-3140

X. Chen

Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027-6699

A. M. Karlsson1

Department of Mechanical Engineering, University of Delaware, Newark, DE 19716-3140karlsson@udel.edu

It is not practical to measure a at maximum load. The elastic recovery upon unloading can be significant for materials with large σyE, and the elastic recovery also increases with increasing residual compression (4). Therefore, measuring the contact radius after unloading (e.g., through a surface scan) may lead to substantial errors.

Note that none of these parametric combinations were used in generating Fig. 2.

Extending the proposed method to any other shape of the indenter is straightforward, but omitted for brevity.


Corresponding author.

J. Eng. Mater. Technol 129(2), 200-206 (Jun 19, 2006) (7 pages) doi:10.1115/1.2400280 History: Received April 05, 2006; Revised June 19, 2006

An alternative, improved method to determine mechanical properties from indentation testing is presented. This method can determine the elastic modulus, yield strength and equi-biaxial residual stress from one simple test. Furthermore, the technique does not require the knowledge of the contact area during indentation, a parameter that is hard to determine for highly elastic material. The evaluation technique is based on finite element analyses, where explicit formulations are established to correlate the parameter groups governing indentation on stressed specimens.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Schematic of instrumented indentation with a sharp indentation: (a) indentation on a homogeneous, isotropic semi-infinite substrate; (b) typical force-displacement curves obtained from an indentation experiment; and (c) conical indentation on a specimen with equi-biaxial in-plane residual stress

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Figure 2

Example of the axisymmetric mesh, including boundary conditions. The indenter is shown for maximum indentation depth.

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Figure 3

The dimensionless functional forms based on the finite element simulations (a) contact stiffness, Ψ, (b) work of indentation, Π, and (c) unload work, Ω; the error between fitting functions and the functional forms (d) contact stiffness, Ψ, (e) work of indentation, Π, and (f) unload work, Ω. The error is determined by (fitted−FEresults)∕FEresults

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Figure 4

Schematic of the process flow of reverse analysis

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Figure 5

Comparison between the material properties predicted from reverse analysis and the input parameters used in numerical indentation experiments for imaginary materials

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Figure 6

Error sensitivity analysis with 2%, 5%, and 10% error (a) in contact stiffness and (b) in indentation work: the reverse analysis is compared with input parameter from FE-simulations (squares) and the unperturbed analysis (circles)



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