Biomedical Engineering Reference
In-Depth Information
not all of the varying rich information during loading were taken. Cao
and Lu 67 have applied the idea of representative strain to normalize the
loading Ph
curves of spherical indentation, and took measurements at
two very shallow indentation depths. However, for spherical indentation,
the loading curvature
varies continuously with h during both
loading and unloading processes. The self-similarity of the P curves
is not well-preserved and the apparent dependence of n cannot be
completely removed with the incorporation of the representative strain. 70
Moreover, the conventional shallow spherical indentation cannot
distinguish the mystical materials, as remarked earlier.
Let the radius of spherical indenter to be R . Chen et al . 83 have
speculated that in terms of indentation work and contact area, there exists
an analogy between the geometrical factor h / R of spherical indentation
and α in conical impression. In essence, during the penetration of a
spherical indenter, C decreases continuously as if the sharp indenter
angle α is keep decreasing. Thus, a deep spherical indentation test can
yield the similar effect of using very distinct sharp indenters, mimic the
effect of a very sharp indenter (without the disadvantage of actually
using a very sharp indenter), which may also circumvent the mystical
material problem and lead to unique solution of the reverse analysis.
Zhao et al . proposed that by utilizing the contact stiffness, along with
the normalized indentation loads obtained at two moderate indentation
depths during loading, it is possible to measure the material elastoplastic
properties ( E ,
2
CPh
=
/
from one spherical indentation. 70
During penetration, the normalized loading curvatures are taken from
h / r = 0.13 and 0.3, (the first one roughly corresponds to the sharp
Berkovich indenter 83 ); the contact stiffness is measured at unloading
where h m / R = 0.3. Within such framework, the normalized loading
curvature and contact stiffness become
,
n ) (with
0.3)
σ
ν =
y
C
P
E
1
1
=
f
,
n
,
(6-15)
1
σ
(1)
h
2
σ
(1)
σ
(1)
R
1
R
R
C
P
E
2
2
,
,
(6-16)
=
f
n
2
σ
(2)
h
2
σ
(2)
σ
(2)
R
2
R
R
 
 
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