Biomedical Engineering Reference
In-Depth Information
plastic deformation
H
—not the contact hardness,
H
c
—and a viscous time
constant τ
Q
). For constant loading-rate indentation testing where
P
(
t
) =
kt
,
k
= constant,
1
1
2
t
()
1/2
ht =
()
+
+
t
(5-44)
load
(
)
1/2
(
)
1/2
(
)
1/2
α
H
α
E
3
Q
τ
α
E
1
2
2
where the α
i
values are dimensionless constants related to the indenter
included angle.
36
For a load reversal at
t
=
t
R
(i.e. the second phase of a
1
1
2
t
(
)
1/2
h=
+
+
R
kt
unload
(
)
1/2
(
)
1/2
(
)
1/2
R
α
H
α
E
3
τ
α
E
2
1
Q
2
1
(
)
1/2
(
)
1/2
+
2
kt
−
kt
−
kt
(5-45)
(
)
1/2
R
R
α
E
2
2
(
)
3/2
(
)
3/2
−
2
kt
−
kt
−
kt
(
)
R
R
1/2
3
k
τα
E
Q
2
This approach has also been expanded to incorporate the effects of a
polymer film on a stiff and time-independent elastic substrate.
37
6.1.4.
Dynamic contact measurements
In the case of dynamic sinusoidal loading for frequency-based
measurements, the input is an oscillation at force amplitude
P
0
, where the
value
P
0
is a small perturbation on the primary peak force
P
max
such that
P
0
<<
P
max
and
P
(
t
) =
P
max
+
P
0
sin(
t
) for frequency
. The response is a
displacement of amplitude
h
0
and a phase shift
φ
such that the response
to the load perturbation has an
h
(
t
) =
h
0
sin(
) dependence. The real,
or storage (
E
S
) and imaginary, or loss (
E
L
) parts of the elastic modulus
are then calculated where the complex modulus is
E
* =
E
S
+
i
E
L
and
t
−
φ
E
S
S
π
(5-46)
)
=
2
(1
− ν
2
A
C
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