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A new analysis technique for calculating the hardness, modulus, and contact area from indentation data obtained using pyramidal or conical indenters was formulated and compared with another commonly used technique. Experimental data using a Berkovich indenter to indent fused silica and tungsten were examined. In addition, finite element modeling results were used to examine the effectiveness of the analytical techniques when a wide range of materials properties was considered. The new technique relies on the slope of the loading curve rather than the indenter displacement as an input. It is shown that the new technique is far less affected by the deviation of the geometry of the indenter from its intended shape. This effect removes the necessity to have detailed descriptions of the precise tip geometry in some cases. The new technique does not reduce errors associated with pile up of material near the indenter.

I. INTRODUCTION

Instrumented indentation experiments have become an important tool for investigators to measure the mechanical properties of materials. A number of types of experiments can be used to highlight certain mechanical properties of interest. This paper will focus on some analytical techniques that are used to obtain the hardness, modulus, and contact area at peak load from the data obtained when a pyramid or conically shaped indenter is forced into the surface of a sample. The most commonly used technique to accomplish this was introduced by Oliver and Pharr1 and consists of the following five equations: P , Ac

(1)

h = hc + hs ,

(2)

P , hs = ⑀ Su

(3)

H=

冑

Su = ␤ Ac =

4 E 公Ac , ␲ r

兰共h 兲 c

.

(4) (5)

P ⳱ load, h ⳱ displacement beyond the point of contact, Su ⳱ the slope of the unloading curve, Er ⳱ the reduced modulus, H ⳱ hardness, ⑀ ⳱ epsilon (constant assumed to be 0.75), and ␤ ⳱ correction due to the lack of axial symmetry (constant assumed to be 1.034). 3202

http://journals.cambridge.org

J. Mater. Res., Vol. 16, No. 11, Nov 2001 Downloaded: 07 Dec 2014

The experimental inputs required for the analysis are the load on the indenter, the displacement of the indenter beyond the point of contact, and the elastic stiffness of the contact at the peak applied load. The elastic stiffness of the contact is generally obtained by either partially unloading the contact or by harmonically exciting the contact and studying its dynamic response. In addition, a detailed mathematical description of the geometry of the indenter is needed in the form of a function relating the cross-sectional area to the distance from its tip. Determining this area function can be difficult. Herein this commonly used technique will be referred to as the area function technique. Important limitations of the area function technique include potentially large errors associated with its application to data obtained from inhomogeneous samples or from materials that generate significant pile up of material at the perimeter of the indentation. Another problem is the accuracy of determining the point of contact. Any error