Elsevier

Acta Materialia

Volume 70, 15 May 2014, Pages 249-258
Acta Materialia

A method for measuring the contact area in instrumented indentation testing by tip scanning probe microscopy imaging

https://doi.org/10.1016/j.actamat.2014.02.036Get rights and content

Abstract

The determination of the contact area is a key step in deriving mechanical properties such as hardness or an elastic modulus by instrumented indentation testing. Two families of procedures are dedicated to extracting this area: on the one hand, post-mortem measurements that require residual imprint imaging, and on the other hand, direct methods that only rely on the load vs. penetration depth curve. With the development of built-in scanning probe microscopy imaging capabilities such as atomic force microscopy and indentation tip scanning probe microscopy, last-generation indentation devices have made systematic residual imprint imaging much faster and more reliable. In this paper, a new post-mortem method is introduced and further compared to three existing classical direct methods by means of a numerical and experimental benchmark covering a large range of materials. It is shown that the new method systematically leads to lower error levels regardless of the type of material. The pros and cons of the new method vs. direct methods are also discussed, demonstrating its efficiency in easily extracting mechanical properties with enhanced confidence.

Introduction

Over the last two decades, the instrumented indentation technique (IIT) has become widely used to probe the mechanical properties of samples of virtually any size or nature. However, the intrinsic heterogeneity of the mechanical fields underneath the indenter prevents the determination of any straightforward relationships between the measured load vs. displacement curve and any expected mechanical properties as would be the case for tensile testing. Many models have been published in the literature in order to enable the measurement of properties such as elastic modulus, hardness or various plastic properties. Despite their diversity, most of these models rely heavily on the accurate measurement of the projected contact area between the indenter and the sample’s surface. Existing methods dedicated to estimating the true contact area can be classified into two subcategories: direct methods, which rely on the sole load vs. displacement curve [1], [2], [3], and post-mortem methods, which use additional data extracted from the residual imprint left on the sample’s surface. For example, Vickers, Brinell and Knoop hardness scales rely on post-mortem measurements of the geometric size of the residual imprint. However, in the case of Vickers hardness, the contact area is only estimated through the diagonals of the imprint; the possible effect of piling-up or sinking-in is then neglected. Other post-mortem methods use indent cross-sections to estimate the projected contact area [4], [5]. In the 1990s, the development of nanoindentation led to a growing interest in direct methods because they do not require time-consuming post-mortem measurement of micrometer- or even nanometer-scale imprints, typically using atomic force microscopy (AFM) or scanning electron microscopy (SEM). The uncertainty level with direct measurements remains high, mainly because of the difficulty of predicting the occurrence of piling-up and sinking-in. Oliver and Pharr considered this issue as one of the “holy grails” in IIT [2]. Recent developments in scanning probe microscopy (SPM) using indentation tips (ITSPM) have attracted new interest in post-mortem measurements. Indeed, ITSPM allows systematic imprint imaging without manipulating the sample or facing repositioning issues to determine the imprint to be imaged. Nevertheless ITSPM imaging suffers from drawbacks when compared to AFM: it is slower, and it uses a blunter tip associated with a much wider pyramidal geometry and a higher force applied to the surface while scanning. While the latter may damage delicate material surfaces, the former will introduce artifacts. Nonetheless, these artifacts will not affect the present method. In addition, ITSPM only allows for contact mode imaging; non-contact or intermittent contact modes are not possible. As a consequence, only the techniques based on height images can be used with ITSPM and there is a need for new methods as very recently reviewed by Marteau et al. [6]. This paper introduces a new post-mortem procedure that relies only on the height image and is therefore valid for most types of SPM images, including ITSPM. In this paper, a benchmark based on both numerical indentation tests as well as experimental indentation tests on properly chosen materials to span all possible behaviors is first introduced. Then, the existing direct methods are reviewed and a complete description of the proposed method is given. These methods are then confronted using the above-mentioned benchmark and the results are finally discussed.

Section snippets

Numerical and experimental benchmark

A typical instrumented indentation test features a loading step where the load P is increased up to a maximum value Pmax, then held constant in order to detect creep, and finally decreased during the unloading step until contact is lost between the indenter and the sample. A residual imprint is left on the initially flat surface of the sample. During the test, the load P as well as the penetration of the indenter into the surface of the sample h is continuously recorded and can be plotted as

Direct methods

Direct methods rely only on the load vs. penetration curve (P,h) to determine the contact height hc using equations given in Table 4. Let us recall that hc<h in the case of sinking-in (as seen in Fig. 2) and hc>h for piling-up. Three direct methods are investigated in this paper:

  • DN

    The Doerner and Nix method [1] was one of the first to be published (along with similar work done by Bulyshev et al. [28]) and provided the basic relationships later improved by the two other methods.

  • OP

    The Oliver and

FEM benchmark results

The four methods are compared to the numerical benchmark and their ability to accurately compute the contact area Ac is tested. The results focus on the relative error e between Ac and the contact area predicted by each method. Note that a 10% relative error on the contact area means roughly a 10% relative error in the hardness but only 5% in the elastic modulus (see Eq. (4)). The results are plotted in Fig. 6, Fig. 7 for constitutive equations CE1 and CE2, respectively, and a summary of the

Conclusion

We have proposed a new procedure to estimate the indentation contact area based on the residual imprint observation using height-based images produced by SPM. This area is the key component of instrumented indentation testing for extracting mechanical properties such as hardness or elastic modulus. For the estimation of this contact area, the method has been compared with three widely used direct methods. We have showed, by means of an experimental and numerical benchmark covering a large range

Acknowledgements

The authors would like to thank the Brittany Region for its support through the CPER PRIN2TAN project and the European University of Brittany (UEB) through the BRESMAT RTR project. V.K. also acknowledges the support of the UEB (EPT COMPDYNVER).

References (35)

  • D. Beegan et al.

    Thin Solid Films

    (2004)
  • X. Zhou et al.

    Mater Sci Eng A

    (2008)
  • I.N. Sneddon

    Int J Eng Sci

    (1965)
  • J.-L. Bucaille et al.

    Acta Mater

    (2003)
  • M. Dao et al.

    Acta Mater

    (2001)
  • M.N.M. Patnaik et al.

    Acta Mater

    (2004)
  • C.A. Schuh et al.

    Acta Mater

    (2007)
  • V. Keryvin

    Acta Mater

    (2007)
  • H. Ji et al.

    Scr Mater

    (2006)
  • Y. Yokoyama et al.

    Acta Mater

    (2008)
  • M.F. Doerner et al.

    J Mater Res

    (1986)
  • W.C. Oliver et al.

    J Mater Res

    (2004)
  • J.-L. Loubet et al.

    J Lubr Technol

    (1984)
  • J. Marteau et al.

    Scanning

    (2014)
  • A.C. Fischer-Cripps

    Nanoindentation

    (2011)
  • A.E.H. Love

    Q J Math

    (1939)
  • M.T. Hanson

    J Appl Mech

    (1992)
  • Cited by (0)

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