Biomedical Engineering Reference
In-Depth Information
microstructural representation shown in Fig. 5.6 are used to characterize the
material behavior. The microstructures have Si
3
N
4
grain size approximately
equal to 1.2
m and SiC particle size approximately equal to 200 nm. The
volume fraction of the SiC phase is fixed at 20%. The average GB width is
approximately 120 nm. Accordingly, the microstructures with GBs have the
approximate GB volume fraction of 10%.
To track complex crack/microcrack patterns, arbitrary crack paths and
crack branching, cohesive surfaces are specified along all finite element
boundaries as an intrinsic part of the finite element model. All cohesive
surfaces serve as potential crack paths in the microstructure; therefore,
fracture inside each microstructural phase and along interphase boundaries
can be explicitly resolved (for more details see [40], [46] and [47]).
Accordingly, the analyses are able to take into account the intergranular
as well as intragranular fracture.
The finite element meshes used have a uniform structure with 'cross-
triangle' elements of equal dimensions arranged in a quadrilateral pattern
(Fig. 5.7). This type of triangulation is used since it gives the maximum
flexibility for resolving crack extensions and arbitrary fracture patterns [40].
Because of the computational limitations and the requirement that stress
wave reflections do not interfere with the analyses results [40], the
microstructures are embedded in a uniform finite element mesh (see the
mesh surrounding the microstructure in Fig. 5.7). The uniform mesh has
elements with higher size increasing the overall size of the sample to delay
the stress wave reflection and minimize its effect on dynamic fracture while
simultaneously reducing the computational load. Since the crack propaga-
tion is limited to the microstructural window whose size had been analyzed
in a previous research [40], the results are unaffected by the presence of the
uniform mesh.
The dimensions for the microstructural region (7.5
μ
μ
6
μ
m) are
limited by the memory sizes of the supercomputers used (a 48 processor
Opteron Linux cluster in this work). These regions are much larger than the
length scales involved in all microstructures. Thus, reasonable representa-
tions of the microstructures are achieved. Material outside the micro-
structure window is assumed to be homogeneous and assigned effective
properties representative of those for the SiC-Si
3
N
4
ceramic composite.
Computations are carried out for side-cracked samples under tensile
loading. The length of the initial crack is a
i
=9.0
m
30
m. Tensile loading is
applied by imposing velocity boundary conditions along the upper and the
lower edges of the specimen in the direction shown in Fig. 5.7. The
boundary velocity V
0
(0.5m/sec and 2 m/sec) is imposed on the bottom and
top edges with a linear ramp from zero to V
0
in the initial phase of loading.
This represents the loading of the pre-crack by a tensile wave with a stress
amplitude of
μ
σ
=
ρ
C
L
V
0
(
ρ
is homogeneous material density and C
L
is the
