A dual triangular pyramidal indentation technique for material property evaluation
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Jin Haeng Lee Research Reactor Mechanical Structure Design Division, Korea Atomic Energy Research Institute, Daejeon 305-353, Republic of Korea
Felix Rickhey and Hyungyil Leea) Department of Mechanical Engineering, Sogang University, Seoul 121-742, Republic of Korea (Received 26 September 2014; accepted 12 February 2015)
In this study, a method using dual triangular pyramidal indenters is suggested for material property evaluation. First, we demonstrate that the load–depth curves and the projected contact areas from conical and triangular pyramidal indentations are generally different. Nonequal projected contact areas of two indenters and nonplanar contact line of Berkovich indenter are the main sources of different indentation characteristics of two indenters. For this reason, an independent approach to the triangular pyramidal indentation is needed. With finite element (FE) indentation analyses for various materials, we investigate the relationships between material properties, indentation parameters, and load–depth curves. Based on the FE solutions, we suggest mapping functions for evaluating material properties from indentations by two triangular pyramidal WC indenters, which differ in their centerline-to-face angles. Elastic modulus, yield strength, and strain hardening exponent are obtained with an average error of ,3%.
I. INTRODUCTION
Tensile and compression tests have long been used to obtain material properties. However, there are limitations in terms of specimen preparation and equipment when it comes to the application to micro/nano materials. On the other hand, by indentation tests, unlike tensile or compression tests, we can predict and measure material properties from load–depth curves by applying micro/nano indentation to micro/nano materials or the part in use. For these reasons, there have been many studies on instrumented indentation tests.1–3 The loading curves from self-similar indenters, e.g., conical and pyramidal indenters, generally follow Kick’s law4: P ¼ C ht 2
;
ð1Þ
where P, ht, and C are indentation load, indentation depth, and Kick’s law coefficient, respectively. To obtain material properties of a given material from an indentation test, there should be a one-to-one match between the load–depth curve obtained from an indentation test and its material properties. However, equal load–depth curves can Contributing Editor: George Pharr a) Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2015.67 J. Mater. Res., 2015
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be obtained for different materials due to the self-similarity of sharp indenters.5,6 Previous studies7,8 tried to solve this problem by using the concept of representative strain eR, which changes with the half-included angle of the indenter. Most of the reverse analysis methods are based on the concept of eR introduced by Tabor.9 With Eq. (2), Dao et al.7 found that stress–strain curves having the same C exhibit the same true stress at eR 5 0.033 for sharp indentation. n E rR
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