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Research Papers

# Aspects of Experimental Errors and Data Reduction Schemes From Spherical Indentation of Isotropic Materials

[+] Author and Article Information

Department of Mechanical Engineering,
University of Delaware,
Newark, DE 19711
e-mail: jpha@udel.edu

T. A. Bogetti

U.S. Army Research Laboratory,
Aberdeen Proving Ground,
Aberdeen, MD 21001
e-mail: travis.a.bogetti.civ@mail.mil

A. M. Karlsson

Department of Mechanical Engineering,
University of Delaware,
Newark, DE 19711
Washkewicz College of Engineering,
Cleveland State University,
Cleveland, OH 44115
e-mail: a.karlsson@csuohio.edu

This is a similar concept as used by previous researchers [32,37,40], with 36 coefficients required to describe the functions. As noted there, we are not striving to develop a relationship where the parameters have physical significance, but we are finding “fitting parameters” to accurately capture the response.

Alternatively, one shape function from depth-to-radius ratio of (hm/R)1 and two shape functions from depth-to-radius ratio of (hm/R)2 can be used. These results are omitted for brevity, since these gave almost the same condition number (for example, selecting Su and We from (hm/R)1 = 10% and Wt from (hm/R)1 = 40% gave almost same results as selection of Wt from (hm/R)1 = 10% and Su and We from (hm/R)1 = 40%).

The maximum experimental error in measuring shape functions from indentation testing has been reported to be within 5.1% [39,46].

Depth-to-radius ratio of 100% can be achieved by using a spherical indenter of sufficiently small radius, R. If R is large, cracking may ensue [37], invalidating the indentation analysis. Similarly, depth-to-radius ratio of 1% can be achieved by keeping R large. If R is small, the indentation depth will be small which will result in surface roughness effect [3] and size effect [47], invalidating the protocol.

Note that the combination (hm/R)1 = 1%, (hm/R)2 = 100% with shape function combination $(We2,Su1,We1)$ results in a condition number that is lower than the “best” dual conical indentation (shape function combination $(We2,Su1,We1)$ with half-angles 50 deg and 80 deg) as determined by the mentioned previous work [12].

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received September 24, 2013; final manuscript received April 28, 2014; published online May 15, 2014. Assoc. Editor: Georges Cailletaud.

This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Eng. Mater. Technol 136(3), 031005 (May 15, 2014) (8 pages) Paper No: MATS-13-1175; doi: 10.1115/1.4027549 History: Received September 24, 2013; Revised April 28, 2014

## Abstract

Sensitivity to experimental errors determines the reliability and usefulness of any experimental investigation. Thus, it is important to understand how various test techniques are affected by expected experimental errors. Here, a semi-analytical method based on the concept of condition number is explored for systematic investigation of the sensitivity of spherical indentation to experimental errors. The method is employed to investigate the reliability of various possible spherical indentation protocols, providing a ranking of the selected data reduction protocols from least to most sensitive to experimental errors. Explicit Monte Carlo sensitivity analysis is employed to provide further insight of selected protocol, supporting the ranking. The results suggest that the proposed method for estimating the sensitivity to experimental errors is a useful tool. Moreover, in the case of spherical indentation, the experimental errors must be very small to give reliable material properties.

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## Figures

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Fig. 2

Stress–strain relationship of a linear-elastic, power-law hardening plastic material

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