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
half apex angle 70.3°) is given in Fig. 6-4 .
 
 
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