Biomedical Engineering Reference
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obtained from the ratio between the tangential and normal energy release
rates [54].
In this study, the approach for parameter selection as described by Xu
and Needleman [48] is used. The value of characteristic separation
η
0
is
taken as 0.001 [50]. GBs in the nanocomposites have a glassy structure
consisting of densification aids such as Y
2
O
3
and other rare earth oxides
such as samarium, gadolinium, dysprosium, erbium, and ytterbium (verified
using the TEM observations on the Si
3
N
4
phase [52]). Experimental data on
the fracture properties and strength of GBs are not available. The GBs'
chemical composition is a complex and uncharacterized combination of
different compounds such as Y
2
O
3
, MgO, etc. with glassy structure.
Accordingly, the fracture properties for GBs cannot be specified based on
chemical composition. However, experiments for polycrystalline Si
3
N
4
have
shown that the presence of GBs results in lowering of mechanical strength
owing to GB sliding (attributed to glassy structure) and an increase in
fracture strength owing to the crack-deflection effect (roughly of the order
of 5%) [53]. Accordingly, the GBs are arbitrarily assigned 5% higher
fracture strength than that of the Si
3
N
4
matrix. An increase in fracture
strength for structural and glassy materials is often accompanied with a
reduction in elastic modulus. Accordingly, while arbitrary assigning 5%
higher fracture toughness to GBs than Si
3
N
4
phase, the elastic modulus is
made smaller than that of the Si
3
N
4
phase by 5%. The immediate effect is
that the simulations are qualitative in nature. With the availability of
experimental measurements on GB properties, more realistic properties of
GBs can be incorporated to increase the accuracy of
the simulation
predictions.
Because the GBs have finite widths, there are three phases (GBs, SiC, and
Si3N4) in the microstructures analyzed. The cohesive parameters are
calculated using experimental information on the elastic moduli and
Ф
0
[1,
41-44, 54-57]. Homogenized properties are calculated using volume
weighted averaging. The values for
Ф
0
are obtained based on surface
energy release rate measurements during fracture experiments on bulk SiC
and Si
3
N
4
reported in the literature. An interface between any two of the
three phases is assigned the cohesive properties corresponding to the weaker
phase. Table 5.1 shows the material properties for analyzing microstructures
shown in Fig. 5.6.
5.4.2 CFEM problem setup
Microstructures analyzed using CFEM are shown in Fig. 5.6. Since a given
unique set of phase morphology defining parameters (such as the location of
SiC particles in the current research) corresponds to multiple sets of phase
morphologies,
three different random samples corresponding to each
