Biomedical Engineering Reference
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where
m
can be derived from the classic solution of indentation on
elastic materials,
71
and it agrees well with FEM calculations
7
:
2tan
γ
α
(6-10)
m
=
π
When
(rigid plastic),
approaches a constant:
E
/
σ
→∞
C
/
σ
R
R
C
=
m
as
E
/
σ
→∞
.
(6-11)
p
R
σ
R
where
m
is the rigid plastic limit of conical indentation into a material
that obeys the Mises yield criterion. Theoretical solutions of the plastic
limits are available for either conical indentation on a specimen that
obeys the Tresca yield criterion, or for wedge indentation with either
Tresca or Mises yield criterion.
7
Although the errors of the existing
solutions of the rigid plastic limits are not very large, in order to ensure
maximum accuracy, the variation of
m
with respect to the indenter
angle can be fitted from FEM simulations of conical indentations with
the Mises yield criterion
72
:
2
(6-12)
m
=
13.2 tan
α
+
6.18 tan
α
−
8.54
p
for
50
.
m
is equal to 112.1 for the Berkovich indenter. In
vie
w
of the importance of these two limits, a very simple form of
(
°≤
α
≤
80
°
)
can be proposed to incorporate both limits
7,72
:
Π
E
/
σ
R
−
1
C
1
1
Π=
=
+
,
(6-13)
σ
E
m
R
m
⋅
p
e
σ
R
from whic
h
the representative stress can be obtained as
m
CE
mmEC
without iteration.
Equation 6-13
not only incorporates
σ
=
e
(
)
R
−
p
e
the elastic and plastic limits (thus having physical meaning and wider
range of application), but it is also involves no fitting parameter if
m
could be solved analytically. The example for Berkovich indenter (with
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