Biomedical Engineering Reference
In-Depth Information
a)
b)
Figure 8.4
(a)
ε
-
σ
diagram of the strain-
controlled programming and stress-free
recovery of the shape-memory effect: (1)
deformation of the sample to a maximum
deformation
ε
m
at
T
high
; (2) cooling to
T
low
while
σ
m
is kept constant; (3) unloading to
zero stress; (4) clamp distance is driven back
to original starting distance, heating up to
T
high
while keeping
σ
=
0 MPa; (5) start of
second cycle; (b)
ε
-
T
-
σ
diagram of the
strain-controlled programming and stress-free
recovery of the shape-memory effect: (1)
stretching to
ε
m
at
T
high
; (2) cooling to
T
low
with constant cooling rate while
σ
m
is kept
constant; (3) clamp distance is reduced until
the stress-free state
σ
=
0 MPa is reached; (4)
heating to
T
high
with a constant heating rate;
and (5) start of the second cycle [4]. Taken
from [4]. Copyright Wiley-VCH Verlag GmbH
& Co. KGaA. Reproduced with permission.
strain-controlled
stress-controlled
Shape fixity ratio (
R
f
)
ε
(
N
)
ε
(
N
)
R
(
N
)
=
u
(8.1)
R
(
N
)
=
u
(8.3)
f
f
ε
ε
(
N
)
m
l
Shape recovery ratio (
R
r
)
ε
−
ε
(
N
)
ε
(
N
)
−
ε
(
N
)
m
p
l
p
R
(
N
)
=
(8.2)
R
(
N
)
=
(8.4)
r
r
ε
−
ε
(
N
−
1
ε
(
N
)
−
ε
(
N
−
1
m
p
l
p
Figure 8.5
Equations for the determination of
R
f
and
R
r
from cyclic, thermomechanical
measurements.
change of the expansion coeffi cient in the vitrifi ed or viscoelastic state or changes
in volume of the sample due to crystallization effects for
T
trans
=
T
m
[4] . After
cooling, the stress is released (
σ
=
0 MPa) leading to the elongation
ε
u
(3). Finally,
the sample is heated again to
T
high
and the permanent shape
p
is recovered (4).
From these cyclic, thermomechanical tests, the values of
R
r
and
R
f
at a given
strain
ε
m
can be determined according to the four equations in Figure 8.5.
In a strain-controlled protocol,
R
f
is given by the ratio of the strain in the stress-
free state after the retraction of the tensile stress in the
N
th cycle
ε
ε
u
(
N
) and the
maximum strain
ε
m
(Eq. (8.1), Figure 8.5).
R
f
describes the ability to fi x the
