Theory 7
Agilent Nano Indenter G200 User’s Guide 7-23
The area function is a curve fit to (h
c
, A(E
r
)) data. The purpose of the
indenter area function calibration is to determine the best fit to the
experimental data. The fitting process is the same, regardless of how the
data were obtained.
The ideal area function for a Berkovich tip is A = 24.56d
2
. The fitted
form follows:
(30)
The Parabolic (first) term provides the ideal form. The Linear (second)
term provides for perfect rounding at the apex. This is the ideal form for
a spherical tip. Later terms may or may not be necessary
More constants may provide a smaller c
2
but at the sacrifice of physical
relevance and applicability of the resulting fit. The fit may behave in
unexpected ways between data points, or outside the range of data
included in the fit.
If all terms are constrained to be positive, the fit may be reliably used
over any displacement range. Otherwise, the fit (and the tip) should only
be used within the displacement range for which it was determined.
Area Function Summary
1 The indenter area function is an experimentally determined function,
A
= f(d), which relates the distance from the apex along the axis of
the diamond (d) to the cross-sectional area at that distance (A).
2 If the indenter area function is known, one can calculate the contact
area for any known contact depth, A = f(h
c
).
3 The indenter area function is a best-fit to a series of (h
c
, A) data
points. For these data points, A is calculated assuming the modulus
of the material is known.
4 A variety of test methods are available for generating the
experimental data necessary for determining an area function (ISO
14577, CSM, or Express Test). These procedures are described in
detail
"Frame Stiffness and Area Function Calibration" on page 235
in Chapter 6, "Commonly Used Procedures".
Am
o
d
2
m
1
dm
2
d
12
m
3
d
14
m
4
d
18
+++++=
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