Optics11 CHIARO NANOINDENTER, User Manual, Page: 41 / 65

41
𝐸
∗
represents the effective Young’s modulus, 𝑅
𝑖
is the spherical tip radius, S is the slope at maximum
indentation ,and ℎ
𝑚𝑎𝑥
and ℎ
𝑟
are the maximum indentation depth and final contact depth,
respectively. In order to optimize the retrieval of the Young ’s modulus from the unloading curve, the
software allows one to set the range of data points to be included in the slope estimate, relative to
the maximum load in the unloading phase (default setting = 60% to 80% of the maximum load on
the unloading curve).
Hertzian contact
The calculation of the effective Young’s modulus by considering the Hertzian contact model, follows
the fit of the loading curve to the following equation:
𝐸
∗
=
𝑃 ∗ 3/4
√𝑅
𝑖
∙ ℎ
𝑒
3/2
Figure 34: Typical load-displacement curve of an indentation (left). The ‘ unloading ’ curve is used to derive
the Young's modulus, by applying the Oliver and Pharr method. Schematic imprint of made by a spherical
indenter after loading and unloading cycle (right).