Modeling conical indentation in homogeneous materials and in hard films on soft substrates
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Yang-Tse Chengb) Materials and Processes Laboratory, General Motors Research and Development Center, Warren, Michigan 48090 (Received 11 August 2004; accepted 24 November 2004)
Dimensional analysis and finite element modeling were conducted to examine conical indentation in homogeneous materials and in hard films on soft substrates. In this paper, the solid materials modeled follow the incremental theory of plasticity with a von-Mises yield surface. The validity of the Oliver–Pharr method was examined. It was found that, for hard films on soft substrates, the Oliver–Pharr method is applicable only when the indentation depth is less than 10% of the film thickness. A linear relationship between the ratio of hardness to reduced modulus and the ratio of reversible work to total work was observed for conical indentation in homogeneous materials and in hard films on soft substrates. This relationship can be used to analyze instrumented indentation experiments.
I. INTRODUCTION
Instrumented indentation has become an important tool for characterizing the mechanical properties of films on substrates. The conventional view is that substrate properties can affect hardness measurement when the indentation depth is larger than 1/10 of the film thickness.1 Substrate effects are more pronounced for measuring elastic modulus of films.2 In the last two decades, there have been extensive research activities in extracting “film-only” properties from indentation at various depths.3–11 Since both hardness and modulus are calculated from the contact area, a method for accurate determination of the contact area for indentation measurements is essential. One of the most well known and widely adopted methods for analyzing instrumented indentation experiments was proposed by Oliver and Pharr.12,13 Specifically, they proposed that the contact depth (hop) can be determined from the load–displacement curves according to hop = hmax − ⑀
Fmax , S
(1)
a)
Address all correspondence to this author. Present address: Materials and Processes Laboratory, General Motors R&D Center, MS 480-106-224, Warren, MI 48090-9055. e-mail: [email protected] b) This author was an editor of this journal during the review and decision stage. For the JMR policy on review and publication of manuscripts authored by editors, please refer to http:// www.mrs.org/publications/jmr/policy.html. DOI: 10.1557/JMR.2005.0071 J. Mater. Res., Vol. 20, No. 2, Feb 2005
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where Fmax is the maximum indentation force, hmax is the indentation depth at Fmax, S is the initial unloading stiffness, and ⑀ is a constant that depends on the indenter geometry. For conical indenter: ⑀ ⳱ 0.72. It was found that, for indentation in homogeneous materials, the Oliver– Pharr method can accurately determine the contact area when sinking-in occurs, while it underestimates the contact area when piling-up occurs.14,15 Although Eq. (1) was derived for indentation in homogeneous materials, it has often been applied to films on substrates. Coated ma
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