FORMATION BEHAVIOR OF SHAPE RECOVERY FORCE IN
TINI FIBER REINFORCED SMART COMPOSITE
Keitaro YAMASHITA and Akira SHIMAMOTO
Saitama Institute of Technology
1690 Fusaiji Fukaya Saitama 369-0293 Japan
ABSTRACT
It was examined to monitor the shape recovery force generated by joule heating the smart composite material which buried the
TiNi-SMA(Shape Memory Alloy) fiber under the resin from the electric resistance change of SMA. The main factor on the
formation of the shape recovery force of the SMA single fiber was confirmed first. After the best amount of pre-strain was
confirmed from the characteristic change according to the uniaxial tensile properties of the SMA fiber and the amount of prestrain, an environmental temperature and the energizing current were changed, and the shape recovery force and the electric
resistance were measured, and a linear relation between both was confirmed. It has been understood to be able to monitor the
formation behavior of the shape recovery force from the measurement of the electrical resistance as a result in smart
composite materials. Moreover, it was able to be measured quantitatively that the formation of the shape recovery force shifted
to the side in the straight line for a short time with the rise of an environmental temperature.
Introduction
The shape recovery force is generated by joule heating it to the SMA fiber which pre-strain of several % of the burial in the
resin matrix, and the development of smart composite materials which achieve intellectual effects of the spread obstruction of
the crack and the self-restoration, strengthening etc. is advanced. However, SMA becomes more than reverse-transformation
temperature Af point by Joule heating and because the generated shape recovery force is a thermomechanical phenomenon,
it is influenced by a lot of parameters. Next thermomechanlcal constitutive equation by Tanaka concerning on uniaxial stressstrain-temperature is known well [1].
σ& = Dε& + ΘT& + Ωξ&
(1)
where σ , ε , T , ξ are stress,strain,temperature and volume fraction of the martensite phase. And the first term and second
term are usual thermoelastic elements and the third term shows the strain speed element caused by progressing of phase
transformation. The next expression is used regularly as for the change whenξis reverse-transformation.
ξ = exp[a A ( AS − T ) + bAσ ]
(2)
where As is a reverse-transformation beginning temperature in the stress-free condition, and a A and bA are the material
parameters. By the way, neither equivalent material parameter D, Θ nor the Ω of the alloy which is the mixture of Martensite
phase and Austenite phase are constants in general. Moreover, the dependency ofξis important. It is tried to combine these
expressions and the heat conduction differential equations when joule heating it and to analyze the generated shape recovery
force [2]. Various assumptions are needed from so to the transformation analysis model under thermo mechanical loading of
the composite material which embedded the SMA fiber in the matrix [3,4], and complication caused with the low accuracy.
Then, it has aimed to develop the method of indirectly monitoring the generation behaviour of the shape recovery force by
experimentally measuring the main factor on the shape recovery force generated when joule heating it to SMA fiber reinforced
smart composite materials in this research.
Authors try to measure the displacement of the composite material when Joule heating it, and to evaluate the shape recovery
force from the amount of shrinkage, and have obtained quantitative information on the relations etc. between the structure of
the composite material and the heating condition, etc. [5,6]. However, because many of calories generated from SMA by Joule
heating are spent on the heating of the matrix, the reverse-transformation temperature arrival time of SMA is delayed under
the low temperature environment. Therefore, because the thermal expansion of the matrix is superior, evaluating the formation
behavior of the shape recovery force from the displacement measurement of the composite material becomes difficult. Then, it
was tried to evaluate the behavior of the shape recovery force in the smart composite material which reversely transformed
SMA by Joule heating in this research by measuring the change in the electrical resistance which related closely to phase
transformation of SMA in a wide-ranging operation environment.
Experimental
Material and Specimen.SMA used for this research is TINi type (Ti-50.2%Ni) shape-memory alloy of 0.4mm in the diameter.
The phase transformation temperature by DSC (Differential Scanning Calorimetry) is shown in Table1. The reversetransformation temperature is As: 36.1℃, Af: 55.3℃, has middle R phase transformation (Indicate it with Rs and Rf) at about
40℃, and the exothermic peak is formed before the martensitic transformation during cooling.
Transformation point of SMA used in the experiment (oC)
Table 1.
M → A
Aｓ
Af
36.1
55.3
Rs
48.7
A → M
Rf
Mｓ
Mf
38.5 -3.7 -47.8
Fig.1 is tensile properties at an environmental temperature up to 80℃ transformed from minus 60℃ which is the martensite
phase into the parent phase as for the SMA fiber. The strain rate in the measurement is about 15%/min. Modulus obtained
from the slope of standing up is about 50GPa in T=80℃ (parent phase) and about 17.5GPa in T=20℃ (R phase). The stress
rises gradually without showing a clear yield point in the Martensite phase of T=0℃ or less with the increase of the strain. The
feature the intersection of the stress in the strain of about 6% in 400MPa in the environment of 60℃ or less..
800
T=80℃
700
Stress (MPa)
600
60
500
-60
400
20 -40
300
40
0
200
-20
100
0
0
2
4
6
8
10
Strain (%)
Figure 1. Tensile properties of SMA fiber
Fig.2 shows the temperature change of the electrical resistance of the SMA fiber of stress-free condition. The electrical
resistance is decreased to C point after it increases if it heats it from A point of the low temperature and the maximum value is
indicated with B point, rises again thereafter, and arrives at D point. It decreases with the progress of the martensitic
transformation after it reaches the maximum point with E point by passing C and B point when cooling more than D point and it
returns to former A point. Start point A in usual Joule heating is changed from electric resistance corresponding to the
temperature when the case on not the low temperature like minus 70℃ but the high temperature side is general and starts
toward B point. The area of B, C, and D was reversible compared with the temperature and examined the use of the peak of B
point and the valley of C point as marking for the phase transformation progress confirmation. There are some differences by
the difference of the metrology with the electric resistance change phenomenon though the phase transformation temperature
by DSC is shown in figure.
8.5
Mf
Ms
Electrical resistance （Ω）
8
R f Rs
E
7.5
D
B
7
C
6.5
6
As
A
5.5
-100
-50
0
Af
50
100
Temperature （℃）
150
200
250
Figure 2. Electrical resistance change of evaluated SMA by heat cycle
Fig.3 shows the shape of the smart composite test piece that buries seven SMA fibers of pre-strain by 6% under the
polycarbonate resin by using the hot pressing. It is 70mm because it uses 30mm at both ends for clamping when measuring it
that the effect length of the test piece. Modulus in 25℃ of this test piece is about 2.1GPa. Because the volume fraction of the
SMA fiber is 0.88%, the shape recovery stress generated by Joule heating in the matrix resin can expect only 10MPa or less. It
is difficult to increase the volume fraction of SMA to several % or more in the structure of Fig.3 in an experimental technique.
130
5
20
Figure 3.Dimensions of TiNi fiber reinforced smart composite specimen
Test Procedure. Using the SMA single fiber of 90mm in length, and the influence of an amount of pre-strain, an environmental
temperature, and the energizing current on the shape recovery force and the electrical resistance was examined. It was tried
to monitor the formation behavior of the shape recovery force from the electric resistance change in joule heating to the
composite test piece of Fig.3 by using this result. The SMA fiber and the test piece are set in the thermostatic bath where a
uniform environmental temperature can be maintained and measured.
Results and Discussion
Formation behavior of shape recovery force in SMA single fiber.Fig.4-a shows the influence of pre-strain (PS) which
causes it for the electrical resistance when joule heating it to the SMA fiber under the environment of 0 ℃ by 20 sec in the
current of DC2.5A and the shape recovery force. The residual stress by pre-strain shown in Fig.1 is removed and only the
shape recovery force by Joule heating is indicating. The shape recovery force is not generated in the state of stress-free of
pre-strain 0% according to this data.. After it becomes the maximum after joule heating about 1sec, the shape recovery force
shows the tendency to the decrease for pre-strain. On the other hand, it is understood that the electrical resistance is
decreased corresponding to the peak time of the shape recovery force and corresponds to the point that the phase
transformation into the parent phase progresses.
Fig.4-b shows the relation between the maximum value of the shape recovery force to the amount of pre-strain, the value
after it heats it in 20sec, and an initial value of the electrical resistance and the value after it heats it in 20sec. As for the shape
recovery force, pre-strain showed the maximum by 5-6% and pre-strain made 6% a standard in the examination thereafter.
Electric resistance and pre-strain are in an almost linear relation. There is relation of ⊿ R/R=Kε in a general metallic material
between strain:ε and electric resistance change rate ⊿ R/R. K is called the strain sensitivity and indicates the value of about
2 .The inclination in Fig.5 is strain sensitivity in this SMA, and the value of about 0.9 is indicated in an initial value, and after it
heats it in the joule, the value of about 1.1 is indicated. It decreases to 1.0 or less when heated at the high temperature of 80℃
though these values rise up to about 1.5 with the atmosphere temperature. Moreover, it is low strain sensitivity compared with
the CuNi alloy used for conventional strain-gauge and SMA has the strain sensor sensitivity enough.
(4-b)
T0=0 (℃）
PS 0
400
300
0.55
0.45
σ
PS 6
4
10
8
2
200
100
0
0.35
0.25
0
-100
0.1
1
10
1.3
σmax
σfinal
R-initial
R-final
300
0.65
PS 10
T0=0 (℃）
350
Recovery stress (MPa)
500
Recovery stress (MPa)
0.75
R
Electrical resistance (Ω）
600
250
1.2
1.1
200
1
150
0.9
100
0.8
50
0.7
0.15
0
0.6
0.05
-50
100
Electrical resistance (Ω）
(4-a)
0.5
0
2
4
Time (sec)
6
Prestrain (%)
8
10
12
Figure 4. Change by pre-strain of shape recovery stress and electric resistance
Fig.5-a shows the measurement result of the stress change the cycle of the atmosphere heating, Joule heating, and cooling
was repeated after pre-strain of 6% is given to the SMA fiber at 20℃. When pre-strain 6% is added at 20℃, the stress of about
400MPa is generated as shown by the tensile test result of Fig.3(A point) And, the stress value hardly changes even if it heats
it up to the high temperature 85℃(B point).It decreases to C point when turning it OFF though there is an increase in the stress
of about 200MPa when joule heating it here. Pre-strain stress decreases to D point when cooling to about 0℃ afterwards and
SMA deform plasticity. The state of D point of the singles fiber can be considered to be a state and equal of SMA in smart
composite materials made by burying it under the polycarbonate resin in the hot pressing. A shape recovery stress as strong
as E point is generated if it joule heats it in this low environmental temperature. The shape recovery stress decreases
gradually when joule heating it while raising the atmosphere temperature, the base stress increases to the change, and the
total stress arrives at F point. The change with a similar stress change in cooling from the high temperature is repeated though
there are some differences when heating it.
(5-a)
(5-b)
800
700
σMｓ
σMf
σPS6
σPS3
σTPS6
σTPS3
700
600
E
600
C
400
A
500
Stress (MPa)
Total stress (MPa)
E
F
500
B
300
F
C
400
A
B
300
200
200
100
100
Mf
D
0
0
20
40
60
Temperature (℃）
80
100
0
-80
-60
-40
Ms
D
As
-20
0
20
40
Temperature (℃）
Af
60
80
Figure 5. Stress change in 6% pre-strain SMA fiber by atmosphere heating and Joule heating
100
The temperature change of base line stress (A,B,C,D) for pre-strain 6% and total stresses (E,F) is shown in Fig.5-b with data
for pre-strain 3%.Moreover, the phase transformation regions of the phase of the re-arrange of the stress induced martensite
from the data such as the tensile properties and DSC and the martensite phase, the heat induced martensite phase, and the
parent phases, etc. were shown in the dotted line in figure. It can be understood for the shape recovery force generated by
Joule heating to be influenced greatly according to an environmental temperature, and to disappear almost in the reversetransformation region to the parent phase from this figure. That is, the shape recovery stress generated by Joule heating for
pre-strain 6% is shown by CD-EF in an environmental each temperature.
Fig.6 shows the influence of an environmental temperature when joule heating it on the shape recovery stress and the electric
resistance change. The energizing current is DC2.5A constant. The formation time of the shape recovery stress is delayed
become low environmental temperature. The change in the electrical resistance almost corresponds to the change in the
shape recovery stress, and the minimum value arrival time of the electrical resistance and the maximum value arrival time of
the shape recovery stress are almost corresponding. The peak of the electrical resistance becoming a low temperature
environment related to R phase transformation appears remarkably. (Refer to B point in Fig.2. )
0.75
1000
900
0.7
800
700
T=23℃
0.65
3.0
-25
600
-55
500
0.6
400
300
23
0.55
3.0
200
σ
-25
Recovery stress (MPa)
Electrical resistance （Ω）
R
100
-55
0.5
0
0.1
1
10
Time (sec)
Figure 6. Enviromental temperature influence on shape recovery stress and electric resistance.
Fig.7-a is a shape recovery force when the energizing current is changed from 1 to 3A at an environmental temperature of 2℃,
a change in the electrical resistance, and the phenomenon has shifted to the side for a short time with an increase in the
current. The maximum point arrival time of the shape recovery stress and the minimum value arrival time of the electric
resistance correspond well. Fig.7-b shows the relation between the electrical resistance and the shape recovery stress. The
electrical resistance decreases with the progress of Joule heating, and the shape recovery force rises straight. The generation
behavior of the shape recovery force can be monitored from the measurement of the electric resistance with the value at the
energizing time zone from an initial value to a minimum value of the electric resistance and the shape recovery force because
it is in an excellent, straight correlation. 2.5A is assumed to be a standard current in the examination thereafter in 2.5A and 3A
though the shape recovery force has some after the maximum point reaches and has the tendency to decrease.
(7-a)
(7-b)
T 0 =2 (℃）
0.75
T0 =2 (℃）
1000
400
900
350
I=1.0A
0.7
2.5A
800
1.5
300
3.0A
600
0.65
3.0
500
400
0.6
3.0
Recovery stress (MPa)
700
Rercovery stress :σ(MPa)
Electrical resistance:R (Ω）
2.0
2.5
250
200
Progress of Joule heating
σ = 2276-3157R
150
300
2.5
100
2.0
200
0.55
1.5
50
1.0
0.5
0.1
1
10
Time (sec)
100
0
100
0
0.6
0.62
0.64
0.66
0.68
0.7
0.72
Electrical resistance (Ω）
Figure 7. Influence of current value on shape recovery stress and electric resistance
0.74
Formation behavior of shape recovery force in smart composite materials. The measurement of the generation behavior
of the shape recovery force in smart composite materials which buried SMA under the resin matrix by Joule heating was tried
by using the evaluation result of the above-mentioned SMA single fiber. The volume fraction of SMA is Vf=0.88% as shown by
the test piece of Fig.3, and the shape recovery stress generated in the matrix resin by Joule heating is average 2-3MPa level,
a little value, and it is difficult to measure the shape recovery stress directly. Therefore, the shape recovery force influence
factor has been indirectly evaluated dynamically measuring the amount of displacement of the test piece generated by Joule
heating before this research. [5,6]. The electrical resistance was measured with the amount of displacement in Joule heating in
this research and the formation behavior of the shape recovery force was examined. Fig.8-a is a measurement result of the
amount of displacement of the test piece and the electrical resistance of SMA when the smart composite materials test piece is
joule heated in 60sec and it was air-cooled afterwards. Displacement at 20 and 60℃ in environmental temperature is seen
shrinkage by the shape recovery force in a few seconds of the heating beginning, and shifts to a big thermal expansion by the
heating of the matrix resin afterwards. The shape recovery force generated while energizing is opened when Joule heating is
turned off with 60sec and the displacement of the thermal expansion decreases with cooling after generating a momentary
expansion of tens of microns. Shrinkage is not generated because many of calories generated from SMA by Joule heating are
spent on the heating of the matrix resin in the low temperature environment minus like 20 and 60℃, the thermal expansion of
the matrix it advancing before SMA is heated up to the reverse-transformation temperature. Therefore, obtaining information
on the shape recovery force from the amount of shrinkage becomes impossible
On the other hand, the change in the electrical resistance can confirm a minimum in each environmental temperature value
and it is understood the reverse-transformation of SMA is completed between Joule heating of 60sec and the shape recovery
force is generated in the low temperature environment.. Moreover, it is understood that Joule heating OFF has changed during
the following cooling along (D,C,B,E,A) of the electric resistance change curve of SMA single fiber of Fig.2. Fig.8-b shows the
relation between 3 characteristics of expansion (δ2) generated with maximum shrinkage (δ) formed with Joule heating,
maximum expansion (D.max), and Joule heating OFF and environmental temperatures. The amount of shrinkage becomes
the maximum in the reverse-transformation temperature region of this SMA and is about 30 microns. Shrinkage is not
generated at 0℃ or less. Oppositely, the total heat expansion increases when it becomes a high temperature environment
after it decreases from the low temperature environment to the reverse-transformation temperature region. The expansion at
current OFF decreases by becoming the maximum at minus 20℃ and becoming the high temperature. The analysis of
displacement is very complex because of the thermal expansion though amount (δ) of shrinkage and amount (δ2) of the
expansion are greatly related to the shape recovery force. Then, a dynamic change in the electric resistance in Joule heating
was measured and the relation to the generation behavior of the shape recovery force was evaluated.
(8-a)
(8-b)
I=2.5A
δ（μm)
11.5
δ2
Shurinkage (μm)
400
11
Dmax
10.5
300
60 (℃）
10
35
30
25
20
15
10
5
0
-5
-100
-50
9.5
-60
20
9
8.5
100
On
0
Off
8
7.5
δ
20 (℃）
7
60
6.5
0
Temperature (℃）
50
100
50
100
50
100
Dmax(μm)
D.max (μm)
Displacement (μｍ）
200
Electrical resistance (Ω）
-20
700
600
500
400
300
200
100
0
-100
-50
0
Temperature (℃）
-20
-60
6
-200
0.1
1
10
Time (sec)
100
5.5
1000
δ2(μm)
δ2（μm)
-100
30
25
20
15
10
5
0
-100
-50
0
Temperature (℃）
Figure 8. Environmental temperature that causes it for displacement and electric resistance of test piece in Joule heating
Fig.9-a is an electric resistance change of SMA in the composite material when joule heating it in an environmental
temperature from minus 60℃ to 80℃. The peak related to R phase transformation is clearly generated in the low temperature
region of 0℃ or less, and the formation time (t1) shifts to the side for a long time with the decrease in an environmental
temperature. It is arrival time of valley (t2) of a gradual electrical resistance that the maximum shape recovery force is formed.
(9-a)
(9-b)
I=2.5A
I=2.5A
7
50
45
t1
20 (℃）
40
( ⊿t = t 2 - t1 = 1 3 .6 - 0 .0 8 5 8 T )
35
60
Time : t (sec)
Electrical resistance (Ω）
00
6.5
Time fo r max r e c o ve ry st r e ss
t 2 = 1 9 .1 - 0 .4 5 2 5 T
40
-20
t2
-40
-60
30
25
P e ak t ime o f e le c t ric al r e sist an c e
t1 = 5 .5 - 0 .3 6 6 7 T
20
80
6
15
10
5
0
-100
5.5
0.1
1
10
100
-50
0
50
100
Ambient temperature ： T (℃）
Time(sec)
Figure 9. Environmental temperature influence in Joule heating on electric resistance and reverse-transformation progress
Fig.9-b shows the relation between t1 and t2 and an environmental temperature. Joule heating of 45sec or more is necessary
at minus 60℃ though the formation time of the maximum shape recovery force is a few seconds in the reverse-transformation
temperature region. If t1 and t2 can approximate the straight line to the temperature, and measure t1 that confirms clear arrival
time in the low temperature environment easily excluding a part of the high temperature side, maximum shape recovery force
formation time t2 can be obtained from the following empirical formula according to environmental temperature T.
t 2 = t1 + 13.6 − 0,0858T
(3)
Comparison between SMA single fiber and smart composite materials, There is a big difference in the heat transfer
characteristic in air and the polycarbonate resin and it influences Joule heating and the cooling behavior. The maximum shape
recovery force formation time from the SMA single fiber of Fig.6 and the data of the composite material of Fig.9: The result of
reading t2 is shown in table2. The condition of arranging it in air compared with the condition of burying it under the
polycarbonate resin is about 10-15 times as fast at time that the SMA fiber forms the shape recovery force with Joule heating.
Fig.10 is a comparison of the temperature characteristics of the electrical resistance of an initial value of the electrical
resistance of the composite material before it joule heating and the stress-free SMA single fiber.. E area in Fig.2 is shown, and
it is understood that the phase transformation temperature of SMA shifts to about 25℃ high temperature side by pre-strain of
6% in this graph.
Table 2. Comparison of t2 of SMA fiber and composite materials
Ambient temperature (℃)
-55
- 25
3
23
t2 of SMA single fiber (sec)
a
4.3
2.3
1.5
0.8
t2 of Composite specimen (sec) b
44.0
30.4
17.7
8.7
Ratio
10.2
13.2
11.8
14.8
b/a
9
25
Electrical resistance (Ω）
8.5
8
Single fiber
7.5
7
6.5
6
Composite
5.5
5
-80
-60
-40
-20
0
20
40
60
80
100
Temperature (℃）
Figure 10. Influence of pre-strain that causes it for temperature characteristic of electric resistance
Conclusions
The relation between the electric resistance change characteristic and the shape recovery force of the SMA single fiber was
measured in detail. The cases of the electric resistance change in smart composite materials which buried this SMA fiber
under the resin matrix and SMA single fiber were compared. As a result, it has been understood to be able to monitor dynamic
behavior of the shape recovery force generated by Joule heating by measuring the electrical resistance of smart composite
materials.
The summary of this research is following.
1. Pre-strain about 6% makes the shape recovery force the maximum.
2. The electric resistance change of SMA is proportional to the amount of pre-strain.
3. SMA in the composite material test piece in the room temperature environment is in the state of the plastic deformation.
4. The shape recovery force decreases with the rise of the atmosphere temperature, and the base level stress increases
oppositely.
5. The electric resistance change of SMA is in a straight line relation with the shape recovery force.
6. The formation time of the maximum shape recovery force and the minimum value formation time of the electric resistance
change correspond.
7. The speed of Joule heating in air is about 10-15 times as fast compared with the polycarbonate resin.
Acknowledgments
This work was supported by“ High-Tech Research Center of Saitama Institute of Technology” Project for Private Universities:
matching fund subsidy from MEXT(Ministry of Science and Technology),1999-2003,2004-2008.
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