Numerical analysis of different methods to calculate residual stresses in thin films based on instrumented indentation d
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ra Aida Rodriguez Department of Mechanical Engineering, Polytechnic School of the University of São Paulo, 05508-900, São Paulo, Brazil; and Research Group of Fatigue and Surface, Mechanical Engineering School, Universidad del, Valle, Cll 13 No 100-00 Cali, Colombia
Adriana Gómez Gómez Department of Mechanical Engineering, Polytechnic School of the University of São Paulo, 05508-900, São Paulo, Brazil; and Faculty of Engineering of Pontificia Universidad Javeriana Cali, Cll 18 No. 118-250 Cali, Colombia
Roberto Martins Souza Department of Mechanical Engineering, Polytechnic School of the University of São Paulo, 05508-900, São Paulo, Brazil (Received 7 October 2011; accepted 8 May 2012)
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 5 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.
I. INTRODUCTION
The correlation between residual stresses and data from instrumented indentation testing (IIT) has been the subject of a significant number of publication in the past 15 years. In general, these publications may be divided into analysis on how residual stresses affect the load– displacement curve (also called the direct method) and analysis on how to calculate the value of residual stress based on instrumented indentation data (inverse method). A. Effects of residual stress on IIT
Contributions toward the analysis of the effects of residual stresses on instrumented indentation data may be found in the works by Tsui et al.1 and Bolshakov et al.2 In the first case,1 results initially confirmed a trend published a)
Address all correspondence to this author. e-mail: [email protected], [email protected] DOI: 10.1557/jmr.2012.166 1732
J. Mater. Res., Vol. 27, No. 13, Jul 14, 2012
http://journals.cambridge.o
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