New methods of analyzing indentation experiments on very thin films
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Nicholas X. Randall CSM Instruments, Needham, Massachusetts 02494
Joost J. Vlassaka) School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138 (Received 3 September 2009; accepted 17 December 2009)
Indentation experiments on thin films are analyzed by using a rigorous solution to model elastic substrate effects. Two cases are discussed: elastic indentations where film and substrate are anisotropic and elastoplastic indentations where significant material pileup occurs. We demonstrate that the elastic modulus of a thin film can be accurately measured in both cases, even if there is significant elastic mismatch between film and substrate.
I. INTRODUCTION
In materials research and nanotechnology, instrumented indentation has evolved into a powerful tool for probing the mechanical response of a material at the micrometer and nanometer length scales. Applications are widespread, ranging from metals and ceramics to polymers and biomaterials.1–3 A number of material properties can be deduced from the measured load-displacement (P–h) curve,1–3 although proper interpretation of the experimental results requires an accurate model of how the material interacts with the indenter. Sometimes direct imaging of the indentations may be required as well.4–9 One problem of technological interest that comes back time and again is how to measure the properties of a very thin film on a substrate using indentation techniques. Substrate effects in indentation experiments are well known, but a robust procedure for evaluating the substrate effect quantitatively and for extracting intrinsic film properties remains elusive. Often indentations are limited to less than 10% of the film thickness to avoid substrate effects. This rule of thumb does not work well, if there is a large elastic mismatch between film and substrate10,11—especially so if the film is stiffer than the substrate.11,12 Furthermore, for thin films the indentation depth required to avoid the substrate effect is so small that it is difficult if not impossible to obtain any meaningful experimental results. Extensive theoretical and experimental efforts have been devoted to understanding the role of the substrate in modeling the overall contact response and in the interpretation of experimental data.10–21 A recent review on this subject is given in Refs. 22 and 23. Among these efforts, Yu et al. a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2010.0095
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http://journals.cambridge.org
J. Mater. Res., Vol. 25, No. 4, Apr 2010 Downloaded: 11 Mar 2015
solved the axisymmetric contact problem for a layered elastic half-space,16 providing results that generalize Sneddon’s well-known equation for a monolithic material.24 Yu’s solution has been used for analyzing elastoplastic indentations subject to various restrictions.17,19 In this paper, we proceed along this line of development and revisit two familiar scenarios where Yu’s analysis can be applied in a novel and simple way. We begin with a
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