Biomedical Engineering Reference
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obtained from the strain energy,
U
, per unit cross section according to beam theory under
plane strain conditions:
=
∂
∂
U
a
G
(4.6)
where
a
is the propagated crack length.
G
ss
during crack propagation can be expressed in
the nondimensional form (Charalambides et al. 1989; Murakami 1992):
(
)
2
2
M
1
2
−
ν
1
λ
2
G
=
−
(4.7)
ss
E
I
I
2
2
c
where
E
is Young's modulus,
I
is the inertia moment,
v
is Poisson's ratio, and
M
=
Pl
/2
b
(4.8)
2
2
=
E
(
1
−
)
/
E
(
1
−
)
(4.9)
λ
ν
ν
2
1
1
2
3
3
2
I
=
h
/
12
+
h
/
12
+
h h h
(
+
h
)
/
4
(
h
+
h
)
(4.10)
λ
λ
λ
c
1
2
1 2
1
2
1
2
3
I
=
/
h
12
(4.11)
2
2
In order to determine
G
ss
, both the applied load and the displacement of the loading points
were continuously monitored and recorded. The specimen was loaded until both cracks
had propagated out to the internal loading points. Stable crack advance should ideally
occur at a constant load, whereas a crack burst causes a sharp drop in load between two
values having a mean of
P
c
(Howard et al. 1993).
Critical strain energy release rate value of ~1.1 kJ m
−2
was revealed for the nanostruc-
tured coatings and no significant difference was revealed among the coatings with dif-
ferent nanostructural features (Figure 4.26) (Li et al. 2007a). While the different
G
ss
values
can be well explained by the nanostructures of the coatings, in order to reveal the effect of
coating microstructure on the
G
ss
, failure mechanism was discussed through observing
the worn morphology after bending by SEM (Li et al. 2007a). It was noted that the crack
induced by bending stress did not grow along the coating/substrate interface. HA coatings
remained on the substrate with varied thickness from several microns to approximately
25 μm depending on the locations. The thickness is roughly equal to that of one splat or
two. The crack growth mechanism has already disclosed that the crack always propagates
along the direction with minimum strain energy. According to Sih (1991), once a crack is
initiated the fracture path follows the trajectory of points of minimum strain energy den-
sity remarkably well. Concerning the complex residual stresses and the applied stresses
from bending moment at the crack front, the crack propagation into the coating side can
be explained by the possible flaws such as micropores and microcracks within the coating.
Observation of the microstructure from the cross sections of the coatings gives insight
into the flaws inside the coating. There is clear evidence of micro-/nanosized pores and
unbonded area between the HA splats. The sizes of the pores in the nanostructured HA
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