The sharpness of a Berkovich indenter
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Precise calibration of the indenter shape is an important procedure in nanoindentation analysis since the indenter geometry enters directly into the most common methods of data analysis in this type of testing. Not only is the geometry required to be known with some precision, but also the sharpness of the tip, especially in the case of pyramidal indenters, is important for the use of indenters for testing hardness in thin film specimens—the most common application of nanoindentation. In this paper, a method of determining the area function and tip radius for a Berkovich indenter is described. It is shown that the tip radius estimated from the area function data is in reasonable agreement with a direct measurement using a calibrated atomic force microscope. It is shown that subjective decisions about tip radius may lead to unjustified rejection of a tip for hardness measurement. A new criterion for tip quality is presented in terms of tip radius and specimen material properties.
I. INTRODUCTION
E.S. Berkovich introduced his three-sided pyramidal indenter in 1951.1 The original Berkovich indenter was designed to have the same ratio of actual surface area to indentation depth as a Vickers indenter and had a face angle of 65.0333 . Since it is now customary to use the mean contact pressure as a definition of hardness in scientific work, Berkovich indenters usually used in research work are designed to have the same ratio of projected area to indentation depth as the Vickers indenter in which case the face angle is 65.27 . The equivalent cone angle (which gives the same area to depth relationship) is 70.296 . As attention has moved to thin films, often less than 100 nm thickness, it is important to not only be able to fabricate a pyramidal indenter with a radius small enough to induce plastic deformation at low loads, but it is also necessary to be able to characterize the indenter shape at this scale so as to make absolute measurements of elastic modulus and hardness using conventional instrumented indentation analysis techniques. Because indenters are not perfectly sharp, it is common practice to represent the rounding at the tip of the indenter and other departures from ideal geometry by an equation known as the area function. The area function gives the contact area as a function of the contact depth and usually contains constant terms derived from experiments on reference specimens of known elastic modulus, fused silica being the most common reference. a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2010.0111 J. Mater. Res., Vol. 25, No. 5, May 2010
Oliver and Pharr2 originally expressed the area function in the following form: 1=4 A ¼ 24:5h2c þ C1 hc þ C2 h1=2 c þ C3 hc þ . . .
:
ð1Þ
This equation usually provides a good fit to the experimental data over a wide range of contact depths as long as sufficient experimental data on the reference specimen is taken. The first term represents the area at large penetration depths where the effect of the tip ro
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