Determining The Contact Stiffness And Contact Area; The Power-Law Relation - Agilent Technologies Nano Indenter G200 User Manual

Determining the Contact Stiffness and Contact Area

The Power-Law Relation

Agilent Nano Indenter G200 User's Guide
From Equation 5 and Equation
hardness and elastic modulus from indentation load-displacement data,
one must have an accurate measurement of the elastic contact stiffness
(S) and the projected contact area under load (A).
One of the primary distinctions between IIT and traditional hardness
testing is the manner in which the contact area is derived. Rather than by
imaging, the area is established from an analysis of the indentation
load-displacement data.
The most widely used method for calculating the contact area was
developed by Oliver and Pharr. The Oliver-Pharr data-analysis
procedure begins by fitting the load-displacement data acquired during
unload to the power-law relation:
P is the load applied to the test surface, h is the resulting penetration, B
and m are empirically determined fitting parameters, and h
displacement after complete unloading (also determined by curve
fitting). The contact stiffness, S, is then established by analytically
differentiating Equation 8
penetration, h = h , or
max
S
Experience has shown that
adequate description of the entire unloading curve, especially for films
on substrates. It is thus prudent practice to determine the contact
stiffness by fitting only the upper portion of the unloading data; fitting
the upper 25 % to 50 % of the data is usually sufficient.
6, it is clear that in order to calculate the
m
 
P = B h h –
f
and evaluating at the maximum depth of
m 1 –
 
= Bm h h –
f
h =
Equation 8 does not always provide an
Theory 7
(8)
is the final
f
(9)
h
max
7-6