MECHANICS OF INDENTATION - Nanoindentation with Biological Applications - page 123

deformation patterns that are scaled up from indentation tests at small
loads. A disadvantage in the use of spherical and conical tips is that load
is no longer a linear function of displacement, as is the case for a
homogeneous tensile test or a flat-punch indentation test, due to the
changes in tip-sample contact area as the tip is pressed further into the
surface. These load-displacement functional forms for different indenter
tip geometries—and thus the data analysis options for each tip—will be
explored further in Section 3 of this chapter.
2.2. Load functions
The second critical experimental controllable in indentation testing,
as in any sort of mechanical testing, is the input loading function.
Commercial nanoindentation instruments are essentially load-controlled,
in stark contrast to the displacement-control used in servohydraulic
universal test-frames. Because the probe is pressed into the sample and
then retracted, the indentation cycle is most commonly considered as a
load-unload cycle. Standard test profiles ( Fig. 5-2 ) are for ramping at
constant loading and unloading rates, ramping to a peak load and then
holding for a fixed time before unloading, and loading exponentially:
P ( t ) = P 0 exp( rt ) (5-1)
where P 0 is an extremely small tare load at the which the test commences
and r is the effective strain rate. This loading condition ( Eq. 5-1,
Fig. 5-2c ) approximates a constant indentation strain-rate under
geometrically similar indentation with constant material hardness. 7
Some nanoindentation systems are equipped with a feedback-control
mechanism, which allows for displacement-controlled indentation
testing. Again the displacement can be ramped up and down at fixed
rate, and can potentially include a holding period at peak displacement,
resembling Fig. 5-2 (a and b) but with displacement replacing load as the
controlling variable along the y-axis.
In addition to the quasistatic indentation conditions presented in
Fig. 5-2 , a number of indentation loading schemes include dynamic
loading, typically as a sinusoidal variation in the load. The sinusoidal
loading can be of quite small amplitude, and is then superposed on top of