Biomedical Engineering Reference
In-Depth Information
expressed by the Selsing formula (Selsing, 1961):
DaD
T
s
T
¼
½
4
:
15
ð
1
þ n
m
Þ=
2E
m
þð
1
2
n
p
Þ=
E
p
where
Δα
=
α
p
α
m
is the difference in thermal expansion coefficient,
Δ
T
room
,
n
is Poisson's ratio, E is Young's modulus, and the
subscripts m and p represent matrix and particle respectively.
The tangential,
T=T
pl
.
σ
Tt
, and radial,
σ
Tr
, stress distributions in the matrix
around the particle are:
3
s
T
2
r
x
s
Tt
¼
½
4
:
16
and
3
r
x
s
Tr
¼ s
T
½
4
:
17
where r denotes the radius of the particle and x is the radial distance from
the particle surface.
In Al
2
O
3
with SiC nanoparticles, the compressive stresses inside the SiC
nanoparticles may reach several gigapascals, while the tensile stresses
around them are of the order of hundreds of megapascals. These
calculations have been experimentally confirmed by similar values of
average residual stresses in Al
2
O
3
-SiC nanocomposites. The described
residual stresses mean that, during propagation, the crack in Al
2
O
3
deflects
towards the nearest SiC particle because of the tangential tension around it.
With an increase in applied stress, the crack leaves the particle and starts to
propagate to the nearest SiC particle.
Fracture morphology
Figures 4.16 and 4.17 compare the crack propagation mechanism in
monolithic alumina (Al
2
O
3
), where it is intergranular, and in nanocompo-
sites where, due to residual stresses, it becomes transgranular. This change
in the crack path is a specific feature that differentiates the fracture
mechanisms of monolithic alumina and nanocomposites. In alumina, the
crack path changes from transgranular to intergranular as the grain size
decreases (Vekinis et al., 1990) but remains transgranular in the
nanocomposites, even where the grain sizes are very small. Figure 4.18
compares the detailed representative fracture surfaces of nanocomposites
containing 5% and 10% SiC. It should be noted, however, that
intergranular crack propagation in alumina usually leads to energy
dissipation in the wake of the crack by grain bridging/interlocking, and to
