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Numerical analysis of different methods to calculate residual stresses in thin films based on instrumented indentation data

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Abstract

In this work, different methods to estimate the value of thin film residual stresses using instrumented indentation data were analyzed. This study considered procedures proposed in the literature, as well as a modification on one of these methods and a new approach based on the effect of residual stress on the value of hardness calculated via the Oliver and Pharr method. The analysis of these methods was centered on an axisymmetric two-dimensional finite element model, which was developed to simulate instrumented indentation testing of thin ceramic films deposited onto hard steel substrates. Simulations were conducted varying the level of film residual stress, film strain hardening exponent, film yield strength, and film Poisson’s ratio. Different ratios of maximum penetration depth hmax over film thickness t were also considered, including h/t = 0.04, for which the contribution of the substrate in the mechanical response of the system is not significant. Residual stresses were then calculated following the procedures mentioned above and compared with the values used as input in the numerical simulations. In general, results indicate the difference that each method provides with respect to the input values depends on the conditions studied. The method by Suresh and Giannakopoulos consistently overestimated the values when stresses were compressive. The method provided by Wang et al. has shown less dependence on h/t than the others.

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Acknowledgments

The authors acknowledge FAPESP (São Paulo Research Foundation) for Grant No. 2007/04731-9 and CNPq (National Council of Technological and Scientific Development) for Grants 303780/2008-8, 150966/2009-1, and 141259/2007-8.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Polytechnic School of the University of São Paulo, 05508-900, São Paulo, Brazil

    Carlos Eduardo Keutenedjian Mady

  2. Department of Mechanical Engineering, Polytechnic School of the University of São Paulo, 05508-900, São Paulo, Brazil

    Sara Aida Rodriguez

  3. Research Group of Fatigue and Surface, Mechanical Engineering School, Universidad del, Valle, Cll 13 No 100-00, Cali, Colombia

    Sara Aida Rodriguez

  4. Department of Mechanical Engineering, Polytechnic School of the University of São Paulo, 05508-900, São Paulo, Brazil

    Adriana Gómez Gómez

  5. Faculty of Engineering of Pontificia, Universidad Javeriana Cali, Cll 18 No. 118-250, Cali, Colombia

    Adriana Gómez Gómez

  6. Department of Mechanical Engineering, Polytechnic School of the University of São Paulo, 05508-900, São Paulo, Brazil

    Roberto Martins Souza

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  1. Carlos Eduardo Keutenedjian Mady
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  2. Sara Aida Rodriguez
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  3. Adriana Gómez Gómez
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  4. Roberto Martins Souza
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Correspondence to Carlos Eduardo Keutenedjian Mady.

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Keutenedjian Mady, C.E., Rodriguez, S.A., Gómez, A.G. et al. Numerical analysis of different methods to calculate residual stresses in thin films based on instrumented indentation data. Journal of Materials Research 27, 1732–1741 (2012). https://doi.org/10.1557/jmr.2012.166

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  • DOI: https://doi.org/10.1557/jmr.2012.166

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