Biomedical Engineering Reference
In-Depth Information
GBs significantly increases the strength of these nanocomposites. While
some nanocomposite morphologies have sharply defined SiC-Si
3
N
4
inter-
faces [e.g. 23], other nanocomposite morphologies have diffusion of C, N, or
Si atoms at the interfaces [e.g. 24].
Classical MD replaces a comprehensive quantum mechanical treatment of
interatomic forces with a phenomenological description in the form of an
interatomic potential. MD has been used recently to achieve nm/cycle
fatigue crack extension rate similar to that observed in experiments [e.g. 25].
The MD simulation results of deformation twinning in two-dimensional
nanocrystalline Al with grain sizes from 30 nm to 90 nm by Yamakov and
co-workers [26] have been found to be in close agreement with experimental
observations reported by Liao et al. [27]. MD simulations have proven to
provide phenomenological trends on deformation mechanisms of nanocrys-
talline materials in agreement with experiments [e.g. 28, 29]. Atomistic
analyses of the nanocomposite mechanical strength as a function of phase
morphology are relatively new and have focused on a very limited set of
issues [e.g. 30-34]. Both SiC and Si
3
N
4
have been individually analyzed in
atomistic simulations for different mechanical strength related issues [e.g.
35-38]. However, SiC-Si
3
N
4
nanocomposite morphologies are analyzed in
this work for the first time.
5.4
The cohesive finite element method (CFEM)
Molecular dynamics (MD) simulations are performed using a well-
established nanocomposite molecular dynamics simulation framework [32,
39]. The CFEM analyses are performed using the analyses criterion
developed and reported in [40]. The CFEM is based on continuum
mechanical foundations. In the CFEM meshes, each phase is modeled
with hyperelastic constitutive behavior based on available experimental
evidence [41-44]. In the absence of experimental information, the distribu-
tion of the crystalline orientation of the Si
3
N
4
and SiC phases is neglected.
In the MD morphologies, crystalline orientations are explicitly considered.
The complete CFEM framework has been described earlier [21, 22], so it
is only briefly described here. A Lagrangian finite deformation formulation
is used to account for the finite strains and rotations in crack tip regions.
The CFEM simulations are carried out under plane strain assumption.
Although the discussion in the presented research focuses on tensile loading,
compression and contact can also be dealt with within this framework [48].
An irreversible bilinear cohesive law is used [21, 22]. Fracture energy per
unit cohesive surface area is the same as the fracture energy of the material,
Ф
0
(Table 5.1). The damage in cohesive surfaces is tracked through a
parameter
Ф
d
, which is a function of the extent of the separation of cohesive
surfaces.
Ф
d
=
Ф
0
when surfaces have separated to cause fracture.
Ф
d
is
