Biomedical Engineering Reference
In-Depth Information
Table 5.1 Bilinear cohesive law parameters for different phases in
microstructures (phase volume fractions (V
f
)
SiC
= 0.2 (V
f
)
Si3N4
= 0.7 (V
f
)
GB
= 0.1)
0
(N/m) T
max
(GPa)
(Nm) E (GPa) NP (kg/m
3
)
Component
Φ
Δ
SiC (SC)
19.53
1.02
38.3
449
0.16
3215
Si
3
N
4
(SN)
191.5
2.3
166.5
210
0.22
2770
Grain boundary (G) 238.7
2.38
200.6
200
0.16
4000
SC-G
19.53
1.02
38.3
—
—
—
SC-SN
19.53
1.02
38.3
—
—
—
SN-G
191.5
2.3
166.5 —
—
—
Homogenized (H)
127.8
2.03
125.9
256.8
0.202 2982
H-SC
19.53
1.02
38.3
—
—
—
H-SN
127.8
2.03
125.9 —
—
—
H-GB
127.8
2.03
125.9 —
—
—
partly converted into the surface energy and partly spent on causing damage
in the material adjacent to crack surfaces through microcrack formation
that is not based on a pre-specified criterion. A unique damage parameter
can be defined to phenomenologicaly track the progressive softening of
cohesive surfaces interspersed throughout the composite microstructure.
This parameter D is defined such that:
D
¼
F
d
F
0
½
5
:
2
Note that 0
1, with D=0 indicating fully recoverable interfacial
separation and D=1 signifying complete separation or total fracture. In the
numerical analysis carried out by Tomar and co-workers [46, 47], and in the
presented research, D is used as a state variable quantifying the degree of the
damage, providing a phenomenological measure for failure analysis.
≤
D
≤
5.4.1 Experiment-based calculation of the bilinear cohesive
law parameters
Overall, five parameters are needed to specify the cohesive behavior,
including the maximum tensile strength T
max
, the critical separations
Δ
nc
and
Δ
lc
, characteristic separation
η
0
and
α
. Note that only four of these
parameters are
Δ
lc
. Calibration of these
parameters is an important aspect in the implementation of the CFEM
model. T
max
is commonly assumed to be a fraction of the Young's modulus
(1/100 to 1/1000) [48]. The critical separations
independent
since
α
=
Δ
nc
/
Δ
lc
are usually
obtained by equating the area under the cohesive relation to the formation
energy per unit area of the corresponding fracture surface. In this regard,
experimental efforts have been reported [49, 50]. The value of
Δ
nc
and
α
is typically
