Effective indenter radius and frame compliance in instrumented indentation testing using a spherical indenter

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

Ingeun Kang and Dongil Kwon Department of Materials Science and Engineering, Seoul National University, Seoul 151-744, Korea (Received 31 January 2009; accepted 22 June 2009)

We introduce a novel method to correct for imperfect indenter geometry and frame compliance in instrumented indentation testing with a spherical indenter. Effective radii were measured directly from residual indentation marks at various contact depths (ratio of contact depth to indenter radius between 0.1 and 0.9) and were determined as a function of contact depth. Frame compliance was found to depend on contact depth especially at small indentation depths, which is successfully explained using the concept of an extended frame boundary. Improved representative stress-strain values as well as hardness and elastic modulus were obtained over the entire contact depth.


Instrumented indentation testing (IIT), which measures penetration load and depth continuously, is widely used to evaluate mechanical properties at microscales1–16 because it is a simple procedure that is relatively nondestructive and easy to use on small scales. In IIT, elastic modulus (a measure of resistance to elastic deformation) and hardness (a measure of resistance to plastic deformation) are generally evaluated by analyzing the indentation load-depth curve without observing the residual indentation marks.3 IIT has also been applied to evaluate flow properties,17–30 residual stress,31–33 and fracture toughness.34–37 Corrections for imperfect indenter geometry and frame compliance play a critical role in the accuracy of IIT, because the real indenter geometry is not ideal and the measured displacement is not the same as the penetration depth of indenter due to frame compliance when the instruments do not use the surface reference for depth sensor. Oliver and Pharr3 suggested a general correction method for the imperfect geometry of a sharp Berkovich indenter and frame compliance in which an area function is given by 1=4 Ac ¼ 24:5h2c þ C1 hc þ C2 h1=2 c þ C3 hc

þ    þ C8 h1=128 c




Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2009.0358 J. Mater. Res., Vol. 24, No. 9, Sep 2009


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where Ac is the contact area, hc is the contact depth, and C1 through C8 are constants correcting for imperfect indenter geometry that are usually determined by fitting points of contact area versus contact depth obtained for a standard sample. In the Oliver-Pharr method, the inverse of measured total stiffness Stotal is given by the sum of frame compliance Cframe and the inverse of sample stiffness Ssample as pffiffiffi p 1 1 pffiffiffiffiffi : ð2Þ ¼ Cframe þ ¼ Cframe þ Stotal Ssample 2Er Ac Here Er is the reduced modulus expressed by   1  n2i 1 ð1  n2 Þ þ ¼ ; Er E Ei


where E and v are the elastic modulus and Poisson’s ratio of the sample and Ei and vi are the elastic modulus and Poisson

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