Biomedical Engineering Reference
In-Depth Information
120000
S
(N/m)
100000
80000
PMMA, Berkovich indenter,
CSM mode,
f
=
75 Hz
60000
40000
20000
h
(nm)
0
0
1000
2000
3000
4000
FIGURE 17.2
Harmonic contact stiffness
S
as a function of indenter penetration
h
into
polymethyl-methacrylate.
17.2.3
Work of Indentation and Other Information from
P-h
Curves
The load-unload
P
-
h
curves in depth-sensing tests also bear information about energies involved in
the process, such as the total work of indentation
W
tot
(area under the curve OABO in
Figure 17.1
),
the elastic work
W
el
, released during unloading (area CABC), and the plastic work
W
pl
(area OACO),
giving the energy dissipated during indentation. The energy components can be used for the charac-
terization of plastic properties of the material. As the work depends on the indenter load, nondimen-
sional quantities are useful (e.g.,
plasticity index
)
[11,12]
,
(17.9)
W
/
This index changes from 0 for purely elastic response to 1 if all energy is dissipated. For a
homogeneous material and pointed indenter, the load-unload curves for different nominal loads are
self-similar, so that the plasticity index does not depend on the load, and can be used as material
characteristic. He and Swain
[6,13]
used the plasticity index for the study of irreversible processes in
enamel.
The
P
-
h
curves are not always as smooth as in
Figure 17.1
. Discontinuities, small jumps, or
change of slope indicates irreversible changes in the specimen, e.g., nucleation of cracks or plastic
flow. Analysis of the pertinent parts of a
P-h
diagram enables one to measure the work spent in the
individual processes, such as formation and propagation of cracks or delamination, and to use it for
the determination of specific energies. If the energy is divided by the imprint volume, energy density
is obtained, which can also serve as a material characteristic.
ω
pl
pl
tot
17.2.4
Indenter Calibration
The basic indenter shapes, described in Section 16.3.3, are simple (a pyramid or a sphere). Pointed
indenters (
Figure 17.3A
), such as Berkovich or Vickers, create self-similar stress field, where the
