Biomedical Engineering Reference
In-Depth Information
(a)
(b)
1.4
7
[001]
[011]
[111]
ε
A
1.2
6
−
[111]
−
1.0
Average
Measured
5
Average
0.8
0.6
4
[011]
3
0.4
Measured
2
σ
S
0.2
0.0
ε
P
1
Rs
[001]
0
−0.2
200
0
200
400
600
800
220
240
260
280
300
320
340
Applied stress (MPa)
Temperature (K)
FIGURE 9.19
(a) Effect of applied stress on transformation strain and permanent strain in a Ti-50.5 at.% Ni film. (b) Trans-
formation strains associated with R-phase as a function of temperature. (From Miyazaki, S., Ishida, A.,
Mater.
Sci. Eng.
, 273-275, 106-133, 1999, with permission from Elsevier.)
ine Ti
3
Ni
4
precipitates, the most preferentially oriented martensite variant can grow eas-
ily under low stresses. The maximum
ε
A
observed in Figure 9.19a is 5.8% under a stress of
470 MPa, at around which macroscopic plastic strain
ε
p
appears.
To calculate the transformation strain
ε
R
, it is necessary to use the lattice constants of the
R-phase. The length of each axis of the R-phase unit cell is almost constant irrespective of
temperature and is the same as that of the B2 phase. Therefore, the transformation strain
ε
R
depends on the temperature. Figure 9.19b shows calculated strains along some specific
orientations and also the average strain as a function of temperature, calculated average
strain is also shown. The strain along each orientation increases with decreasing tem-
perature in the temperature region below
R
s
: the strain along the orientation (111) shows
the maximum and that along the orientation (001) the minimum. The observed strain is
about one-half of the calculated average strain. Because the observed
ε
A
is one-third of the
calculated average strain, the suppressing effect against the growth of the preferentially
oriented variant is less in the R-phase than that in the M-phase. This can be understood
in such a way that the transformation strains associated with the R-phase transformation
is only one-tenth of that associated with the M transformation. Details of the calculation
methods for the strains associated with the M-phase and R-phase transformations are
explained in references (Miyazaki, 1988; Miyazaki and Weyman, 1988).
Superelastic Behavior
Figure 9.20 shows stress-strain curves of a Ti-50.3 at.% Ni film at different temperatures.
Curves (a) and (b) show the stress-strain curves obtained below
A
s
so that the shape
change remains after unloading. The residual strain disappears upon heating to above
A
f
,
revealing the perfect SME. Curve (c) is obtained by deforming the film at a temperature
between
A
s
and
A
f
so that it shows a partial shape recovery upon unloading and further
shape recovery upon heating. Finally, curve (d) shows a perfect SE at a temperature above
A
f
. Because the SE is accompanied by a stress hysteresis, it is necessary to apply a high
enough stress to observe such SE. In this case, the maximum stress applied to the film is
higher than 600 MPa.
