CHANGE OF YOUNG’S MODULUS BY CONSTRICTION EFFECT
OF REINFORCED SMART TiNi-FIBER COMPOSITE
T. Aoki*, A. Shimamoto**
*Department of Computer & Control Engineering
Oita National College of Technology
Oita, JAPAN 870-0152
**Advanced Science Laboratory
Saitama Institute of Technology
Saitama, JAPAN 369-0293
ABSTRACT
SMA(TiNi) fiber was embedded into the matrix of epoxy resin And the fiber was instantaneously is applied by electric current,
which causes reverse transformation on austenite side and produces compressed stress. It is already reported that the
structure recovers and reinforces itself by the compressed stress. Thus, structure-members are supposed to be able to
decrease the excessive member stress caused by sudden attacks from earthquakes or accidents. And as specimen models of
the structure-members, TiNi-fiber-reinforced /epoxy-resin composite materials are manufactured. The specimen models made
of epoxy-resin matrix with pre-strained fiber were embedded, by making the volume fraction change. During hardening of
epoxy resin in the process of manufacturing, the temperature of TiNi fiber often exceeds the austenitic finish (Af), so that TiNi
fiber of matrix contracts before the experiment. To prevent that phenomenon, both ends of the fibers were firmly fixed with jigs.
And, keeping the pre-strained volume, the epoxy resins were embedded and hardened. In the experiment, as the specimen, the
central beam was supposed. And the central part vibration experiments were conducted with TiNi fiber heated by electric
current. The change of Young's modulus by heating TiNi fiber was considered and discussed. The results have shown that
Young's modulus can be controlled by changing the volume fraction of TiNi fibers, pre-strain volume and applied current
volume.
Introduction
Recently, Shape Memory Alloy (SMA) has been researched and developed as one of the most valuable and feasible materials
because of its high performance comparable to those of living organisms in such points as perception, judgment and respond
and so on. Previously, the present authors proposed a design concept of composite materials imbedded by SMA fiber, which
can restore itself and strengthen on the high temperature side by generating compressive stress inside the matrix by using
shape recovery or restoration effects caused by reverse transformation on the high temperature side(cf. Fig.1). Figure 2 shows
the smart structural system with reinforced shape memory alloys and an AE sensor. The system can analyze and evaluate with
a computer by using frequency characteristics and strength signal sensed by the AE sensor. When this system judges the
signal above critical level set beforehand, the SMA is instantly heated by electric current and the structure contracts and is
strengthened. In this research, TiNi-fiber-reinforced /epoxy-resin composite materials were made, based on the above design
concept. Using specimen models, and assuming structure-members can decrease the excessive member stress caused by
attacks from earthquakes or sudden accidents, the central part of the specimen was experimentally vibrated. The variations of
Young’s modulus of TiNi-fiber accompanied by contraction under electric heating, fiber volume-fraction and pre-strain volume
were measured and evaluated.
Specimen and Experiment
Specimen
The specimens used in this experiment are TiNi-fiber-reinforced /epoxy-resin composite materials. The dimension of a
specimen is shown in Fig. 3. The table 1 shows the mechanical properties of the TiNi fiber and the epoxy resin. The
transformation temperatures of the TiNi fiber were determined as martensitic start Ms=31℃, martensitic finish Mf=15℃,
austenitic start As=57 C ℃ and austenitic fnish Af=63℃. TiNi fibers had been previously given four kinds of tensile pre-strain
volume(from now on, it is called as pre-strain volume)εpt＝0,1,3 and 5％ and next the TiNi fibers were heat treated and
embedded with the same interval into the matrix. In making the specimen, the temperature often rises higher than austenitic
finish (Af) during epoxy resin hardening and the TiNi fibers in the matrix often contract before the experiments. To prevent this
happening, the both ends of the fibers were fixed firmly with jigs. And the fibers were hardened by epoxy-resins being cast with
keeping their pre-strain volume.
Fig.1 Basic design concept of intelligent composite material
Fig.2 Schematic of the basic functional factors associated with smart material systems
170
15
6
15
3
4 4
2
2 22 2 2
Number
of fibers
Fig.3 Specimen for center beam
Table 1 Mechanical property of constituents
Material
Young’s
Modulus(GPa)
Poisson’s
Ratio
Tensile
Strength(MPa)
TiNi fiber
30(M)
82(A)
3
0.43
1200∼1300(M)
1700(A)
50
Epoxy resin
0.39
M: Martensite
A: Austenite
Accelerometer
Sensor
DC Power
Supply
Current
Specimen
Jig
Fibers
Impedance
Head
Power
Amplifier
Personal Computer
Fig.4 Experiment system for measuring vibration amplitude of beam
Experimental Method
Unexpected happenings such as earthquakes and the like often cause various kinds of load stress to the member of the
structure. Therefore, in the case of both ends free and center vibration (central vibration type) , the inland earthquakes are taken
consideration, the experiments were conducted under the environmental conditions as similar to the natural conditions as
possible. It was made free the both ends of the specimen and vibrated the center of the specimen. It performed experiment
under the environmental condition which is close to the naturally. The Experimental system used for measuring vibration
amplitude of beams is shown in Figure 4. By using the regulated DC power supply device, five levels of current, 0, 1, 2, 3 and
3.5, were applied directly from both ends to the TiNi fiber in parallel. In the experiment, attention was paid for the both ends not
to be constrained. The relationship between the applied current values and temperature of TiNi fiber is investigated as shown in
Figure 5. Figure 5 shows that the temperature of the fiber rises according to the applied current value increases in all cases of
the experiment, which confirms that the relationship is very good. And the vibration frequencies of the specimen were measured
with the contact type accelerometer sensor installed on the impedance head and the contact-less type beam sensor, and the
resonance frequencies and loss factors were calculated. .The variations of Young’s modulus of the specimen was investigated
by applying heating current to TiNi fibers.
RESULTS AND DISCUSSION
YOUNG’S MODULUS OF TiNi-FIBER REINFORCED COMPOSITE MATERIAL
The variations of Young’s modulus of TiNi-fiber by contraction under applied electric current, fiber volume-fraction and
pre-strain volume were measured and evaluated. The central part of the specimen was vibrated in the experiments. From the
experimental results by application of electric current to TNi fibers embedded into the matrix, the resonance frequency was
measured and the Young’s modulus E was obtained by using the following equation.
Ei n
2
i
2 l2
2
2
i
A
LL (i 1,2,3, L)
Ig
(1)
Where
ni
l
A
I
g
i
=
resonance frequency of i-th-order
=
=
=
length of the specimen
weight volume ratio
cross section area of the specimen
=
=
cross section of the geometrical moment of inertia
gravitational acceleration
value obtained by numerical analysis method from
characteristic equation of vibration
=
Each Young’s modulus was calculated by the resonance frequencies of the first, second and third order, respectively, and the
average value was set to be Young’s modulus E. The results are shown in Fig.6(a),(b) and (c). Figure 6(a) shows the
relationship between the pre-strain value and Young’s modulus, Figure 6(b) shows the relationship between the volume fraction
of fiber and Young’s modulus. Figure 6(c) shows the relationship between applied current and Young’s modulus. As is seen
from Figure 6(a),(b) and (c), the Young’s modulus of center beam increases in accordance with the increase of pre-strain
volume, fiber volume fraction, and constriction of SMA. However, from Figure 6(c), the following can be observed: in the case of
pre-strain volume 0%, the Young’s modulus is constant, despite the increase of the applied current: in the case of pre-strain 5%
and volume fraction 2.51%, the Young’s modulus lies 4.8∼4.6 between 0.17A ∼0.83 of applied current values: and in the case
of volume fraction 1.26%, the values are found to be slightly lowered to 4.6∼4.3. Generally speaking, it has already reported
11)
that the Young’s modulus of composite matrix decreases in accordance with the rise of temperature.
The Young’s modulus
E of SMA can be described as follows.
E Vm E m
Vf Ef
Where
Vm
=
Volume fraction of Matrix
Em
=
Young’s Modulus of Matrix
Vf
=
Volume fraction of SMA-fiber
Ef
=
Young’s modulus of SMA-fiber
(2)
Temperature[℃]
100
80
60
40
20
0
0
0.2
0.4
0.6
0.8
1
Current[A]
Young's modulus[GPa]
Fig.5 Relationship between current and temperature
5
4.5
○
△
□
◇
＊
●
▲
■
×
Current Volume
of a fiber
fraction
of fiber
0.17A 2.51%
0.33A 2.51%
0.5A
2.51%
0.58A 2.51%
0.0A
2.51%
0.33A 1.26%
0.67A 1.26%
1.0A
1.26%
0.0A
1.26%
□
△
○
＊
Current Pre-strain
0.33A
5%
0.5A
5%
0.58A
5%
0.0A
0%
4
0
1
2
3
4
5
6
Pre-strain[%]
Young's modulus[GPa]
(a) Relationship between pre-strain and Young’s modulus
5
4.5
4
0
0.5
1
1.5
2
2.5
3
Volumu fraction of fiber[%]
Volume
(b) Relationship between volume fraction of fiber and Young’s modulus
Young's modulus[GPa]
5
Volume fraction
2.51%
1.26%
Pre-starin
4.5
○
△
□
◇
5%
3%
1%
0%
●
▲
■
◆
5%
3%
1%
0%
4
0
0.2
0.4
0.6
0.8
1
1.2
Current[A]
(c) Relationship between current and Young’s modulus
Fig.6 Relationship between fiber volume, pre-strain, current and Young’s modulus
As equation (2) shows, the Young’s modulus of SMA can be obtained by the Young’s modulus of the matrix and the Young’s
modulus of embedded fiber into the matrix and by the volume fraction of the matrix and of the fiber embedded into the matrix.
But, in the case of pre-strain of TiNi fiber 0%, the Young’s modulus lowers despite the increase of the applied current volume,
which can be considered by the effect of Vm and Em of the matrix. This agrees to the result by Shimamoto and et al. well. From
the results, it can be confirmed that the application of heating to TiNi changes the Young’s Modulus of TiNi fiber reinforced
composite materials and that the change of the Young’s Modulus can prevent the destruction by external vibrations.
Conclusion
Taking material function characteristics such as SMA with self-reinforcement of upper temperature austenite phase and the
shrinkage force due to SMA into consideration, the variations of the Young’s Modulus were studied on the center vibration of
smart matrix composite (TiNi-fiber reinforced /epoxy-resin composite materials). And the possibility of prevention of destruction
by controlling Young’s modulus was researched. As a result, it was found that Young's modulus of material can be controlled by
changing the volume fraction, applied current volume and pre-strain volume of TiNi-fibers.
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