MECHANICS OF INDENTATION - Nanoindentation with Biological Applications - page 131

Figure 5-6. Elastic-plastic indentation responses for a Berkovich on fused silica glass,
illustrating the three parameters taken directly from the load-displacement ( P - h ) response
for Oliver-Pharr 1 analysis: h max , P max , S .

In Eq. 5-12 the contact area ( A c ) appears, where the contact area is the
projected area calculated from the contact displacement ( h c ) via a
calibration function of the form A c = A c ( h c ). In Eq. 5-9 , it was assumed
for both a four-sided and a three-sided pyramid that the indenter was
infinitely sharp. However, in reality the tip is blunt at small indenter
depths as a pyramid cannot be made perfectly sharp. The probe therefore
approximates a sphere at some small contact depth h c . The hardness is re-
defined as H c = P max / A c ( h c ) where the relationship between contact depth
and contact area is often taken as a summed polynomial of the form

C k h 1/2 (k-1) A c ( h c ) = C 0 h c 2 + (5-13)

k = 1

in which the coefficients C i are determined by calibration. Other
functional forms are possible, such as the physically-meaningful 14 :

A c ( h c ) = (π tan 2 ψ ) h c 2 + 4 R π h c + 4 R 2 π cot 2 ψ (5-14)