Conventional Vickers and true instrumented indentation hardness determined by instrumented indentation tests

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Ju-Young Kima) Materials Science, California Institute of Technology, Pasadena, California 91106

Chan-Pyoung Park, Hyun-Uk Kim, and Dongil Kwon Department of Materials Science and Engineering, Seoul National University, Seoul 151-744, Korea (Received 16 September 2009; accepted 18 November 2009)

We evaluate Vickers hardness and true instrumented indentation test (IIT) hardness of 24 metals over a wide range of mechanical properties using just IIT parameters by taking into account the real contact morphology beneath the Vickers indenter. Correlating the conventional Vickers hardness, indentation contact morphology, and IIT parameters for the 24 metals reveals relationships between contact depths and apparent material properties. We report the conventional Vickers and true IIT hardnesses measured only from IIT contact depths; these agree well with directly measured hardnesses within 6% for Vickers hardness and 10% for true IIT hardness. I. INTRODUCTION

The fundamental advantage of instrumented indentation testing (IIT) over conventional hardness testing is that mechanical properties such as elastic modulus,1–15 tensile properties,16–29 and hardness can be measured by analyzing the indentation force–depth curve and without observing the residual indentation marks. However, elastoplastic deformation of materials around the indenter, i.e., plastic pileup or sink-in,30–37 makes it difficult to determine the true contact depth in the loaded state. A contact depth can be determined by taking into account the response of two major materials to an indentation, elastic deflection from the initial sample surface, and plastic pileup/sink-in around the indenter.30–37 The elastic deflection depth (hd) is given by the widely used Oliver and Pharr method3,12: Pmax ; ð1Þ S where Pmax and S are the maximum indentation force and initial unloading stiffness, respectively, and e is a geometrical constant (0.75 for a conical indenter). However, the plastic pileup and sink-in cannot be expressed as an analytical equation because the plastic deformation underneath the indenter is far more complex than elastic deflection. Many studies30–37 have been performed to evaluate the contact depth, taking into account the plastic pileup/ hd ¼ e


Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2010.0045 J. Mater. Res., Vol. 25, No. 2, Feb 2010

sink-in of a sharp indenter. From extensive finiteelement analysis (FEA) work on a wide range of elastoplastic materials, Cheng and Cheng13,25,30 proposed to measure elastic modulus and hardness without determining the contact area directly by correlating these properties and the indentation work ratio. Alcala et al.,35 using FEA, suggested a relationship between strain-hardening exponent n and pileup/sink-in height. Cheng and Cheng also suggested a correction parameter f, the ratio of contact depth (hc) to maximum indentation depth (hmax), and showed that f is given by the product of a function of the strain-hardening exponent n and the ratio of yield strength t