Biomedical Engineering Reference
In-Depth Information
Table 23.2
Material
properties for delamination
test
R
=
8
.
3145 Nmm
/
mmolK
T
=
298 K
10
4
E
=
1
.
4
·
MPa
ν
=
0
.
33
φ
i
=
0
.
2mm
4
/
Ns
0
.
10
K
=
c
ex
10
−
3
mmol
/
mm
3
c
fc
i
10
−
3
mmol
(
eq
)/
mm
3
=
1
.
0
·
=−
1
.
0
·
0
.
2mm
3
/
Ns
K
d
=
k
=
2
G
c
=
0
.
020 N
/
mm
τ
ult
=
1
.
1MPa
10
−
3
l
a
=
7
.
8mm
v
=
1
.
0
·
mm
/
s
influence of local mass balance is considered by decreasing the local permeability
with respect to the standard case or prescribing the chemical potential in the crack.
Considering the chemical potential distribution, Fig.
23.10
, the figures show local-
ization at the crack tip with a negative chemical potential. This low chemical poten-
tial is relaxed by fluid redistribution towards the crack tip. The chemical potential is
largest at the left due to largest opening of the crack.
Figure
23.11
shows the fracture length versus the pull displacement. Crack
growth occurs slightly faster in the case of prestress. With further opening of the
crack, the chemical potential decreases and the tangential flow increases. Numerical
oscillations seem to be present, but the oscillations are actual changes in chemical
potential due to crack growth and redistribution of load. These changes are less in
the case of prestress than when there is no prestress present. In addition in the case
without prestress the growth seems more smoothly. Furthermore, the chemical po-
tential is nonzero from the start in case of prestress. When fluid is not taken into
account, crack growth occurs faster, while the time to damage initiation is almost
the same as in the case with fluid present.
23.5 Discussion
Computations of both mode I and mode II crack propagation in saturated porous
media predict stepwise crack propagation, provided fluid exchange between crack
and formation is accounted for. The time
t
during which the propagation pauses
and the distance
x
over which the crack propagates in one step relates according
to Terzaghi's relationship:
x
2
cK
.
t
=
(23.41)
In mode I, the triaxial tensile stress state at the crack tip results in a strong under-
pressure in the fluid. This pressure (or chemical potential) dip at the crack tip attracts
fluid, particularly from the crack itself, resulting on the one hand into a closing of
the crack a short distance away from the tip, and on the other hand into a progressive
transfer of the triaxial state of tensile stress from the fluid to the effective stress of
the solid. This progressive transfer leads to failure of the solid and further propaga-
tion of the crack. The same scenario repeats itself all over again a little further into
the material.
