Biomedical Engineering Reference
In-Depth Information
(A)
(B)
(C)
(D)
Cono-spherical
Flat-end
Berkovich
90
°
Cube corner
Side view
2R
2R
Face angle
=
65.3
°
Face angle
=
35.3
°
60
°
60
°
2R
<
2R
Indent geometry
Ideal area function
Area
=
24.5
h
c
2
Area
=
2.598
h
c
2
Area
=
−π
h
c
2
+
2
π
R
Area
=
π
R
2
FIGURE 16.2
Schematic representation of common indenter tips with their indent geometries and ideal area
function. (A) Berkovich tip, (B) cube corner tip, (C) cono-spherical tip, and (D) flat-end tip.
at a preset rate. The load-displacement data obtained in this quasi-static test mode are most fre-
quently analyzed with the Oliver and Pharr method
[8]
that is included in the ISO14577 standard
“Metallic Materials—Instrumented Indentation Test for Hardness and Materials Parameters.” The
contact stiffness,
S
, maximum load,
P
max
, and the maximum penetration depth,
h
max
, are obtained
from the load-displacement data at the onset of unloading as seen in
Figure 16.1B
and are used for
calculating the contact depth
h
c
P
S
max
(16.1)
h
h
ε
c
max
e
h
c
is then used to find the total tip-sample contact area,
A
c
, through an area function of the tip.
Figure 16.2
shows the ideal area functions of different tip geometries, but for accurate measure-
ments, it is important to calibrate the actual area function of a given tip since deviation from the
ideal geometry may occur as a result of bluntness at the very end of the tip.
A
c
can then be used for
calculating hardness according to
P
A
max
(16.2)
H
c
and
E
r
can be calculated as
π
2
S
A
E
(16.3)
r
c
The Young's modulus
E
of the sample can be obtained using the relation
2
2
1
1
v
1
v
+
E
E
E
r
(16.4)
sample
indenter
