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5.2
The m
easurement and calculation of the Young’s modulus
The determination of the Young’s modulus relies of the measurement of
load-indentation curves,
which subsequently can be analysed by different material models. For elastoplastic materials, the
unloading part of the curve can be fitted by software with the so-called
Oliver&Pharr model
1
,
2
,
which
excludes any plasticity bias from the results. However, a more direct
Hertzian contact model
can be
used for purely (visco-) elastic materials.
Oliver and Pharr
This method derives the Young's modulus from the slope of the unloading part of the stress-strain
curve, indenter tip radius and final indentation depth using the following formula:
𝐸
∗
=
𝑆
2
⁄
√𝑅
𝑖
∙ √ℎ
𝑚𝑎𝑥
+ ℎ
𝑟
1
W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and elastic modulus using load
and displacement sensing indentation J.Mater. Res. Vol. 7 No. 6 1564 (1992)
2
W.C. Oliver, G.M. Pharr, Measurement of hardness and elastic modulus by instrumented indentation:
Advances in understanding and refinements to methodology J.Mater. Res. Vol. 19 No. 1 3 (2004)
Figure 33: Schematic picture of probe (left) and picture of probe mounted in the Piuma Nanoindenter.
Summary of Contents for CHIARO NANOINDENTER
Page 1: ...PIUMA NANOINDENTER USER MANUAL ...
Page 63: ...63 Flowchart Calibration ...
Page 65: ......