機電整合研究所 碩士學位論文

機電整合研究所
碩士學位論文
形狀記憶合金螺旋彈簧在雙向形狀記憶
效應下之機械行為
Mechanical Behavior of A SMA Helical
Spring with Two-way Shape Memory Effect
研究生:樂美辰
指導教授:李春穎
中華民國九十九年七月

摘 要
論文名稱:形狀記憶合金螺旋彈簧在雙向形狀記憶效應下之機械行為
校所別:國立台北科技大學 機電整合研究所
i
頁數:54
畢業時間:九十八學年度第二學期 學位:碩士
研究生:樂美辰 指導教授:李春穎 教授
關鍵詞:形狀記憶合金、雙向形狀記憶效應、Brinson 理論模型
本研究為探討形狀記憶合金螺旋彈簧在雙向形狀記憶效應下之機械行為。
當螺旋彈簧經由控制電流給予其焦耳熱進行溫度調變,並在設定之固定長度下,
量測控制電流、溫度與力量間的關係。在單獨記憶合金線材之軸向拉伸負載下,
藉由量測應力及電阻與電流間斜率的改變得知其相變化的發生,並找出相關之材
料模型參數。最後藉由 Brinson 之材料理論模型與螺旋彈簧理論公式的結合,將
記憶合金彈簧在不同變形長度與控制溫度下之理論值與實際量測結果進行比對
及討論。當溫度增加時,彈簧產生的應力在固定的控制長度下會增加,但其是以
非線性的變化達到飽和的沃斯田體相。如果彈簧的控制長度增加時,其在固定溫
度下的負載也會增加,但其負載曲線的斜率並不會維持不變,因此我們推斷其是
受到了應力所引發的麻田散體相變化,因而導致負載曲線的斜率下降。且經由螺
旋彈簧的理論公式的比較下,其量測的結果與理論推導的結果得出了良好的正確
性。

ABSTRACT
Title:Mechanical Behavior of A SMA Helical Spring with Two-way Shape Memory
Effect
School:National Taipei University of Technology
Department:Institute of Mechatronic Engineering
ii
Pages:54
Time:July, 2010 Degree:Master
Researcher:Mei-Chen Yueh Advisor:Chun-Ying Lee
Keywords:SMA, Two-way SME and Brinson model
In this paper, the processes of making SMA (Shape Memory Alloy) helical
springs and training them to be of the two-way SME (Shape Memory Effect) were
presented. The helical spring was activated by controlling the electric current
applied via the Joule heating. The relationship between the applied current and the
resulted temperature was measured. By fixing the SMA spring in certain lengths, the
resulting actuation force of the spring upon different current levels were investigated.
With the variation of the slope in these load-current and load-temperature diagrams,
the rate of phase transformation in the SMA springs could be inferred. The
governing equation of the helical spring in axial loading was also derived by using
Brinson model. The comparison between the measurement and theoretical modeling
was conducted and discussed. When the temperature was raised, the loading on the
spring with controlled fixed length increased. However, the increase of the spring
force was nonlinear and became saturated as the temperature was above the finish
point of the austenite transformation. If the controlled length increased, then the
loading increased at the fixed temperature. The slope of the loading curve, i.e. the
spring constant, was not always constant due to the possible stress induced martensitic
transformation. The transformation tended to lower the slope of the loading curve.

By the theoretical formulation in the helical spring, the comparison between the
measured results and the computational results showed good correlation.
iii

Acknowledgment
Above all, I would like to thank my advisor, Prof. Chun-Ying Lee (李春穎), for
his guidance and encouragement during my research and study at National Taipei
University of Technology. His knowledge and enthusiasm in research had motivated
me and all his advisees. During his working time, he was always thorough and
willing to discuss any problem for his students. Finally, I deeply thank his help in
guidance and suggestion for the modification of this thesis; otherwise, it would not be
achieved.
All my colleagues at Smart Material and Design Laboratory inspired me so
much either in the research or in my daily life; I deeply thank them to accompany me
during these two years no matter what we did. I would like to very thank Jian-Jhang
Chen (陳建彰) for his friendship and help during my research and daily life.
Furthermore, I greatly thank my girlfriend-Sharon Wu who has provided me the
spiritual support for last two years. It is not only in my research, also especially
during my leisure time. I also thank my family, no matter what they always support
me, which include money and soul.
The author gratefully acknowledges the financial support from the Ministry of
Economic Affairs under Project No. 98-EC-17-A-16-S1-127. The DSC analysis of
the SMA wire performed by Dr. F. J. Chen, Department of Materials Science and
Engineering, National Taiwan University is specially acknowledged.
iv

Contents
摘要……………………………………………………………………………………i
ABSTRACT…………………………………………………………………………..ii
Acknowledgment……………………………………………………………………..iv
Contents……………………………………………………………………………......v
List of Tables………………………………………………………….……………vi
List of Figures…………………………………………………………….…………vii
Chapter 1 INTRODUCTION………………………………………………….………1
1.1 Introduction of Shape Memory Alloys…………………………………….1
1.1.1 The Applications of SMA Helical Springs………………………..…2
1.1.2 The History of SMA………………………………………………….3
1.2 Motivation of This Study…………………………………………………..3
1.3 Structure of This Thesis……………………………………………………4
Chapter 2 LITERATURE REVIEW……………………………………...…………..5
2.1 Characteristics of SMA……………………………………………………..6
2.2 Brinson’s Model…………………………………………………………….7
2.3 Training of Shape Memory Alloy…………………………………………...9
Chapter 3 THEORETICAL FORMULATION……………………………………....11
Chapter 4 EXPERIMENTAL……………………………………………...…………17
4.1 DSC Analysis……………………………………………………………17
4.2 Shape Memory Training…………………………………………………..18
4.3 Experimental for Mechanical Property Measurement of SMA Springs…...21
Chapter 5 RESULT AND DISCUSSION…………………………………………….26
5.1 SMA Wire………………………………………………………………….26
5.2 SMA Helical Spring……………………………………………………...30
5.3 The Measurements from the Other ‘Twins’ Spring……………………..39
Chapter 6 CONCLUSIONS……………………………………...…………………..49
6.1 Training and Measuring the SMA Helical Spring………………………….49
6.2 Combination of the Brinson’s Model and the Theoretical Formulation….50
6.3 Future Works…………………………………………………………………50
REFERENCES……………………………………………………………………….51
Writer Introduction…………………………………………………………………...55
v

List of Tables
Table 1 The parameters of the SMA wire used in predicting the mechanical behavior
of the SMA helical spring…………………………………………………22
Table 2 The total parameters of the SMA wire used in predicting the mechanical
behavior of the SMA helical spring…………………………………….....30
Table 3 The updated parameters of the SMA wire used in predicting the mechanical
behavior of the SMA helical spring with the changed Young’s modulus of
the martensite……………………………………………………………...34
Table 4 The updated parameters of the SMA wire used in predicting the mechanical
behavior of the SMA helical spring with the Young’s modulus at austenite
being 30 GPa……………………………………………………………....36
Table 5 The updated parameters of the SMA wire used in predicting the mechanical
behavior of the SMA helical spring with the Young’s modulus at austenite
being 45 GPa………………………………………………………………37
Table 6 The updated parameters of the SMA wire used in predicting the mechanical
behavior of the SMA helical spring with the changed free lengths at phase
of martensite and austenite………………………………………………..39
Table 7 The revised parameters of the SMA wire used in predicting the mechanical
behavior of the SMA helical spring with the changed lengths at phase of
martensite and austenite…………………………………………………47
vi

List of Figures
Figure 1 The transformation from austenite to martensite phase and the shape
memory effect……………………………………………………………..2
Figure 2 Critical stress-temperature phase diagram for SMA transformation.
Critical stresses for conversion of twins and austenite-martensite
transformations are functions of temperature……………………………..9
Figure 3 The schematic diagram of the relactionship between the torque, the axial
force and the radius in the SMA helical spring………………………….12
Figure 4 The schematic diagram of the right and front view in the SMA wire…….13
Figure 5 Result of the DSC analysis for a SMA wire. The lowest and highest heat
fluxes have been measured………………………………………………18
Figure 6 Processes of training one-way SMA helical spring………………………19
Figure 7 Processes of training the two-way SMA helical spring with two-way
SME……………………………………………………………………...20
Figure 8 Result of the DSC analysis for the SMA spring. The lowest and highest
heat fluxes have been measured………………………………………....21
Figure 9 The schematic configuration of our system. The displacement of the sliding
block between the two SMA helical springs was controlled by applying
current to the actuator SMA spring……………………………………23
Figure 10 The schematic diagram of the experimental setup for measuring the
mechanical behavior of the SMA spring in different controlled
temperatures……………………………………………………………..25
Figure 11 The photographs of the experimental setup for measuring the mechanical
behavior of the SMA spring in different controlled temperatures……….25
vii

Figure 12 The temperature-current diagram of the SMA wire in heating or
cooling…………………………………………………………………27
Figure 13 The load-temperature diagram of the SMA wire with heating and
cooling…………………………………………………………………...28
Figure 14 The load-temperature diagram of the SMA wire with heating and cooling
for higher stress….………………………………………………………28
Figure 15 The temperature-current diagram of the SMA helical spring at 55 mm and
60 mm……………………………………………………………………31
Figure 16 The load-temperature diagram of the SMA helical spring at 55 mm and 60
mm………….……………………………………………………………32
Figure 17 The measured and predicted load-temperature results of the SMA helical
spring……….……………………………………………………………33
Figure 18 The stress-strain diagram of the SMA wire under room tepmerature…...34
Figure 19 The updated measured and predicted load-temperature results of the SMA
helical spring.……………………………………………………………35
Figure 20 The updated measured and predicted load-temperature results of the SMA
helical spring with the Young’s modulus at austenite being 30 GPa…….36
Figure 21 The updated measured and predicted load-temperature results of the SMA
helical spring with the Young’s modulus at austenite being 45 GPa…….37
Figure 22 The adjusted measured and predicted load-temperature results of the SMA
helical spring…………………………………………………………….38
Figure 23 The length-temperature diagram of the SMA helical spring at free
deformation………………………………………………………………40
Figure 24 The experimental load-temperature diagram of the SMA helical spring at
55 mm and 60 mm…………………………………………………….…41
Figure 25 The computational load-temperature diagram of the SMA helical spring in
viii

the Young’s modulus at austenite is 30 GPa at 55 mm and 60 mm……...42
Figure 26 The computational load-temperature diagram of the SMA helical spring in
the Young’s modulus at austenite is 45 GPa at 55 mm and 60 mm……...42
Figure 27 The comparison of the measured and predicted load-temperature results
of the SMA helical spring………………………………………………43
Figure 28 The adjusted measured results in comparison with the predicted results of
the SMA helical spring.…………………………………………………44
Figure 29 The computational load-length diagram of the SMA helical spring in the
five certain lengths…………………………………………………….45
Figure 30 The measured load-length diagram of the SMA helical spring in the five
certain lengths………………...………………………………………….46
Figure 31 The revised computational load-length diagram of the SMA helical spring
in the five certain lengths..………………………………………………48
ix

Chapter 1
INTRODUCTION
1.1 Introduction of Shape Memory Alloys
Shape Memory Alloys (SMAs) have been a popular smart material nowadays.
They can be used in many kinds of applications such as medicine [1], biomechanics,
mechanism [2, 3], and structure, etc. Especially, SMAs have been proposed for use
in applications which require large shape changes or large force generation [4]. The
SMA is able to memorize its original shape after it has been deformed, by heating
above the temperature of the phase transformation. With these characteristics, the
SMA wire can be fabricated into helical springs by going through some of the training
steps (it will be talked about in Chapter 4). The SMA helical springs can then be
applied in the situation where the actuation with large force and/or displacement is
required. Figure 1 shows the cycle of the phase transformation from austenite to
martensite after loading, heating, and the return from austenite to twinned martensite
under consequent cooling without loading.
1

Fig. 1 The transformation from austenite to martensite phase and the shape memory
effect [5].
For this reason, the research in this paper will fabricate the SMA helical spring and
measure its properties. Some of the potential applications of the helical spring will
be mentioned in next section.
1.1.1 The Applications of SMA Helical Springs
Lee and coworkers made a micro-robot, which actuates like an earthworm,
using the two-way SMA helical springs to move it by controlling the applied current
[3]. Maeda et al. designed the active endoscope with SMA helical springs to control
its curvy directions [6]. Haga and coworkers also used the SMA helical springs to
2

activate the outer tube of the catheter stiffened by the stainless liner coil where the
connection between the two coils was by electroplating [7]. Zhu and coworkers
proposed the use of SMA springs in the semi-active suspension system for vehicles
[8].
1.1.2 The History of SMA
The first reported discovery of the shape memory effect was in the 1930s.
According to Otsuka and Wayman (1998) [9], Ölander discovered the pseudoelastic
behavior of the Au-Cd alloy in 1932 [10]. Greninger & Mooradian (1938) observed
the formation and disappearance of a martensitic phase by decreasing and increasing
the temperature of a Cu-Zn alloy [11]. The basic phenomenon of the memory effect
governed by the thermoelastic behavior of the martensite phase was widely reported a
decade later by Kurdjumov & Khandros (1949) and also by Chang & Read (1951) [12,
13]. The nickel-titanium alloys were first developed in 1962~63 by the US Naval
Ordnance Laboratory and commercialized under the trade name Nitinol (an acronym
for Nickel Titanium Naval Ordnance Laboratories). Their remarkable properties
were discovered by accident. A sample that was bent out of shape many times was
presented at a laboratory management meeting. One of the associate technical
directors, Dr. David S. Muzzey, decided to see what would happen if the sample was
subjected to heat and held his pipe lighter underneath it. To everyone's amazement
the sample stretched back to its original shape. To date, it is fair to say that
NiTi-based SMAs have the best memory and superelasticity properties of all the
known polycrystalline SMAs [14].
1.2 Motivation of This Study
3

According to the applications mentioned above, the SMA helical spring
could be used in many fields like the micro-robots in mechanism, the active
endoscopes in medicine, the semi-active suspension system in automobile, etc. The
mechanical characteristics of the SMA helical spring upon the activation of thermal
energy were essential in the design of the devices. Therefore, the research in this
study would try to set up a formulation, which combines Brinson’s model (it will be
mentioned in next chapter) with theoretical formulation on the helical spring (Chapter
3). It could be used to simulate the result of the motion control either in the
endoscopes or the micro-robots and others by the input of the basic system parameters.
The formulation derived herein would facilitate the engineers in the design
incorporating the SMA helical spring actuators.
1.3 Structure of This Thesis
The contents of this thesis were separated into six chapters as following:
Chapter 1: Introduce the characteristics and history of SMA, and why the SMA
helical spring would be used in this research.
Chapter 2: Review the previous literatures about the phase transformation of SMA;
and describe the Brinson’s model which determines the volume fraction of
martensite phase in the SMA under the influence of stress and temperature.
Chapter 3: Present the theoretical formulation of the SMA helical spring subjected to
axial loading.
Chapter 4: Describe our experimental setup and how to train the SMA helical spring
to be with one-way and two-way SME.
4

Chapter 5: The experimental results and discussion will be presented in this chapter.
In addition, the measured results and computational results will be
compared with each other.
Chapter 6: The conclusions and future works will be described in this chapter.
5

Chapter 2
LITERATURE REVIEW
This chapter describes the basic characteristics of the NiTi SMA and reviews
the phase transformation formulation in Brinson’s model. The methodology for
training the SMA component from previous literature is also briefly presented.
2.1 Characteristics of SMA
The behavior of SMA is due to a reversible thermoelastic crystalline phase
transformation between a high symmetry parent phase (austenite) and a low symmetry
product phase (martensite); the phase transformation will occur by the activation of
both stress and temperature [4]. For the past few decades, much of the experimental
work on various NiTi alloy systems has been undertaken to understand the
mechanism of their shape memory phenomena. These phenomena include the
thermally induced one-way memory effect, the two-way memory effect (TWME), the
stress-assisted two-way memory effect (SATWME) and pseudoelasticity [15]. The
NiTi family of alloys can withstand large stresses and can recover strains near 8% for
low cycle use or up to about 2.5% strain for high cycle use [14]. In the Brinson’s
model, the martensite volume fraction can be separated into stress-induced and
temperature-induced components (Equation 1). In the stress-free state, a SMA
material can be considered to have four transition temperatures, typically designated
as Mf, Ms, As, Af: Martensite Finish, Martensite Start, Austenite Start, Austenite Finish
[17]. According to the critical stress-temperature phase diagram (Figure 2), if the
stress is higher than the critical stress, the stress-induced martensite (‘detwinned’
6

martensite) will be produced. If the temperature is lower than the Ms, the
temperature-induced martensite (twinned martensite) will be produced. Additionally,
an intermediate phase (R phase) often appears during cooling, having its own start
temperature (Rs) and finish temperature (Rf), before the transformation proceeds to
martensite at lower temperature [14].
2.2 Brinson’s Model
The total volume fraction of martensite phase in the SMA can be written as
where and are the components of martensite due to applied stress and
applied temperature, respectively. These components can be described by four
sections shown below (Figure 1). For the conversion to detwinned martensite, they
are given at the following sections:
1. For and
2. For and
7
(1)
(2)
) (3)
(4)

3. Where, if and
else
For the conversion to austenite, these variables are defined as following:
4. For and
In the above equations, the notations and definitions of all the parameters in the model
followed those presented by Brinson [4, 16 and 17].
8
(5)
(6)
(7)
(8)
(9)
(10)

Fig. 2 Critical stress-temperature phase diagram for SMA transformation. Critical
stresses for conversion of twins and austenite-martensite transformations are functions
of temperature.
2.3 Training of Shape Memory Alloy
Wang et al. [18] had proposed a way for training the SMA helical springs with
two-way SME. According to Wang’s work, the mean diameter of the spring was 4.5
mm, the pitch of the spring was 0.1 mm and the active turns of the spring were 10.
The springs were fastened on the jig and annealing heat-treated. The TiNi alloy
springs were heat-treated at 450 ℃ for 1 hour and TiNiCu alloy springs at 500 ℃
for 1 hour, followed by air-cooling. The spring was dipped into 25 ℃ water to
ensure that the deformation proceeded at the expected state; the spring was extended
until the pitch reached 12 mm at thermomechanical training temperature. The force
was then relaxed and the springs were dipped in 100 ℃ water, which was higher
than the austensite finished temperature (Af). Subsequently, the spring contracted as
a result of reverse martensitic transformation and the length of the spring was
recorded. Finally, the spring was dipped into 25 ℃ water and the length of the
9

spring was also measured.
Wada and Liu [15] used a near equiatomic NiTi wire with diameter = 0.185 mm,
supplied by Nitinol Device and Components, USA. As-received specimens were
annealed at 580 ℃ for 30 minutes in air, followed by air-cooling to room
temperature (approximately 20 ℃). Subsequent to pre-straining, specimen was
reloaded to 200 MPa at which stress was held constant to develop SATWME and later
the TWME via release of constrained stress under stress-free thermal cycling. The
influence of partial reverse transformation on the SATWME and TWME was
characterized by undergoing one and half cycle of constrained thermal cycling (i.e. by
the sequence of heating-cooling-heating) followed by one cycle of stress-free cooling
and heating.
Shaw and coworkers [14] mentioned that the transformation temperature of a
Nitinol alloy can be tailored by the supplier anywhere from cryogenic temperatures to
as high as about 100 ℃ by small changes in chemistry, by aging heat treatment in
the range of 350-500 ℃, and by thermomechanical processing (cold work developed
during wire drawing and/or cyclic loading performed by certain suppliers).
10

Chapter 3
THEORETICAL FORMULATION
This chapter describes some of the basic formulas used for theoretical
formulation on the helical spring, which will be employed for our computational
study presented in the Chapter 5.
For a linear elastic helical spring composed of SMA wire and subjected to an
axial loading, the theoretical formulation of its mechanical behavior is presented as
follows. Some researchers as Lee and his coworkers [19-23] had derived the related
theoretical formulation already. The resultant torque T on the cross-section of the
helical spring due to the axial load F can be written as Eq. (11), which is shown in
free-body diagram of Fig. 3. F is the axial force on the spring and R denotes the
mean radius of the helical spring.
11
(11)

Fig. 3 The schematic diagram of the relactionship between the torque, the axial force
and the radius in the SMA helical spring.
If the deformation of the wire due to the transverse shear and axial reactions is
negligible comparing with the torsion reaction, the relationship between the total axial
deformation on the spring and the angle of twist of the spring wire can be written as
Eq. (12). Herein, represents the extension of the helical spring.
In Eqs. (13) to (15), the following notations are used: L the length of the SMA wire, r
the radius of the spring wire, N the coil numbers, the angle of twist, and the
shearing strain. Among them, the relationship between the angle of twist and the
maximum shear strain of the wire is shown in Fig. 4. Thereby, the wire length
multiplied by the shear strain is equal to the arc length , which is equal to the
radius of the wire multiplied by the angle of twist .
12
(12)

Rearranging the above equation, the shear strain can be written as:
In the above equations, the length of the wire in the helical spring can be calculated
by
L
where p is the axial pitch of the helical spring.
13
(13)
(14)
2 2
N ( 2
R)
p
(15)
Fig. 4 The schematic diagram of the right and front view in the SMA wire.
By using the formulas from Strength of Materials, the angle of twist and shear stress
of circular rod subjected to uniform torsion can be obtained as Eq. (16) and (17). In
these equations, the following nomenclatures are adopted: G the shear modulus of
elasticity, J the polar moment of inertia, T the torque, the radial coordinate from
the center of the spring wire, and the corresponding shearing stress.

Substituting Eqs. (16) and (17) into Eq. (14), we can write the shear strain at radius
inside the wire:
If the influence of the spiral curvature on the spring wire could be neglected such that
the spring wire could be presumed as a straight one, the shearing strain at the outmost
radius could be written as Eq. (19).
Therefore, the shear strain at radius from the center of the SMA wire could be
written as the Eq. (20).
For the SMA materials subjected to simple shear, the constitutive equation proposed
by Brinson can be retrofitted as
14
(16)
(17)
(18)
(19)
(20)

The phase transformation coefficient is a convection constant which is related to
the uni-axial normal loading characteristic on the material. It could be written as the
Eq. (22)
15
(21)
(22)
is the largest allowable permanent strain of the SMA materials, is the elastic
modulus and is the volume fraction of martensite phase. Assume that the material
is all isotropic in nature, and then Eq. (23) could be applied. Wherein is the
Poisson’s ratio.
The phase transformation dynamics of the SMA materials, which is controlled by the
applied temperature and the normal stress, is assumed to follow the Brinson’s model
in this study. The Brinson’s model has been described previously in Eq. (2) to (10).
(23)
For the simple shear, the equivalent normal stress can be found by using
distortion energy criterion .
At applied temperature and stress, the
Brinson’s model is employed to find the volume fraction of the martensite phase. By
denoting and as the shear modulus of the martensite and austenite phase,
respectively, the equivalent shear modulus of the SMA can be obtained by using
rule-of-mixture:

If the total axial deformation and temperature of the spring could be known, the
shearing strain at the radius
is calculated from the Eq. (20). Substituting the
into the Eq. (21) and the Brinson’s model, the shearing stress could be found. As
the resultant torque of the internal shear stress of the SMA wire should be in
equilibrium with the applied loading, the total torque on the cross-section could be
found by the integration of the shearing stress and the moment arm as in Eq. (25).
An analytical form of the above integration cannot be found due to the complicated
phase transformation dynamics. For this reason, a numerical integration using the
Gaussian quadrature was adopted to compute the torque T in this research. With the
computed torque, the corresponding axial force F could be found from Eq. (11).
16
(24)
(25)

Chapter 4
EXPERIMENTAL
This chapter describes the way to train the one-way SMA helical spring further
into the one with two-way SME. The schematic configuration of our system and the
experimental setup for measuring the mechanical behavior of the SMA spring either
in controlled temperatures or controlled lengths will be addressed.
4.1 DSC Analysis
A SMA wire with diameter of 0.8 mm was used in this experiment which was
distributed by King-Yi-Cheng Enterprise Co. Taiwan. The EDS (Energy Dispersive
Spectrometry) analysis showed the compositions of the SMA wire are 40.13 at% in
Nickel and 59.87 at% in Titanium. The DSC (Differential Scanning Calorimetry)
analysis of the SMA wire has been performed before it was used. The controlled
heat and cooling rates were 10℃/min. According to the result of the DSC analysis
(Figure 5), the lowest heat flow occurred at the temperature of 46.4 ℃; it means that
the largest phase transformation was happened at this temperature during heating. In
terms of this, the temperature range from 25 ℃ (As) to 61.2 ℃ (Af) has shown to be
the total phase transformation from martensite to austenite. Then, during the cooling
process two localized highest heat flows were encountered at the temperature of 37.1
℃ and -14.5 ℃. The temperature range from 58.7 ℃ (Rs) to 21.9 ℃ (Rf) is believed
to be the austenite to R-phase transformation and the one from 9.2 ℃ (Ms) to -49.9 ℃
(Mf) should be the further transformation to martensite.
17

Fig. 5 Result of the DSC analysis for a SMA wire. The lowest and highest heat
fluxes have been measured.
4.2 Shape Memory Training
Before training the SMA wire into helical spring, some of the mechanical
properties of this SMA wire have to be measured. The mechanical responses of the
SMA wire under uni-axial tension were measured at different temperatures. These
experiments will be mentioned in the latter result and discussion. With these
mechanical properties, the parameters in the Brinson’s model can be obtained.
Therefore, the theoretical calculation on the performance of the SMA helical spring could
be conducted with the formulation presented in the previous chapter.
The processes of training the helical spring are shown in Fig. 6. At first, the
18

SMA wire was coiled around a screw which served as the mandrel for training the
memorized shape. Next, put the wound mandrel into a heat treatment furnace and
raised the temperature gradually up to 450 ℃ in about two hours. The wound
mandrel was kept at this temperature for 30 to 45 minutes, and then cooled down to
room temperature inside the furnace. Finally, the helical spring was removed from
the mandrel, which possessed one-way shape memory effect. The trained one-way
SMA helical spring had the dimensions of 9-mm outside diameter and 90-mm length
in this study.
Fig. 6 Processes of training one-way SMA helical spring.
For the design in this study, the aforementioned one-way SMA helical springs
could be further trained into two-way shape memory ones. The processes of training
the two-way helical spring are shown in Fig. 7. In the beginning, preparing two
water baths, one was hot (temperature higher than Af) and the other was cold (iced
water). In step 1, we stretched the one-way helical spring to a specific length. In
step 2 and step 3, the helical spring was put into the hot water bath before it was put
19

into the cold water bath for a few seconds. Then in the last step, the length of the
spring was measured to check whether the length became stable with the number of
training cycles. The above steps were repeat for 100 times or more so that the
two-way SMA spring could be obtained. For the two-way SMA helical springs, they
can be controlled to return to a range of lengths which depend on the different cool
bath temperatures.
Fig. 7 Processes of training the two-way SMA helical spring with two-way SME.
With the processes described above, a two-way SMA helical spring had been
made in this study. In order to assure that two identical SMA springs can be
fabricated for the system described in the following section, the trained two-way
spring was cut into two springs with equal length. Therefore, ‘Twins’ was a name
20

we gave them in the following discussion.
The thermal characteristics of the trained SMA spring were measured again by
using DSC. The result of the DSC analysis of the SMA spring was shown in Fig. 8.
It showed the similar result as that in Fig. 4 but with a little change in the
temperatures of the phase transformation. According to the analysis, the lowest heat
flow occurred at the temperature of 57.4 ℃. In terms of this, the phase
transformation temperatures from martensite to austenite during heating were As =
42.1 ℃ and Af = 65 ℃. The other phase transformation temperatures during cooling
were Rs = 51.1 ℃, Rf =34.5 ℃, Ms = 5.3 ℃ and Mf = -35.3 ℃.
Fig. 8 Result of the DSC analysis for the trained SMA spring. The lowest and
highest heat fluxes have been measured.
21

4.3 Experimental for Mechanical Property Measurement of
SMA Springs
Figure 9 presents the schematic diagram for the application of SMA helical
springs in our system. The purpose of the design was to control the linear
displacement of the sliding block between the two SMA helical springs. By
controlling the applied current to each SMA spring, the position of the sliding block
can be manipulated accordingly.
In this study, the wire diameter of the helical springs was 0.8 mm and the outside
diameter was 9 mm. The number of coils was 10 and lengths of the spring were 35.5
mm at room temperature, 33.5 mm at austenite, respectively. Table 1 lists the
parameters used in the computation of the mechanical performance of the SMA
helical springs by the proposed theoretical formulation. dw means the wire diameter,
do the outside diameter, LM the free length at martensite, and LA the free length at
austenite. The computational results will be shown in the latter result and
discussion.
Table 1 The parameters of the SMA wire used in predicting the mechanical behavior
of the SMA helical spring.
dw: 0.8 mm do: 9 mm
Coils: 10
LM: 35.5 mm LA: 33.5 mm
RF: 34.5 ℃ RS: 51.1 ℃
AS: 42.1 ℃ AF: 65 ℃
22

Fig. 9 The schematic configuration of our system. The displacement of the sliding
block between the two SMA helical springs was controlled by applying current to the
actuator SMA spring.
The following nomenclatures were employed in the equations which follow:
d = Length of the sliding block
x0M = Free length of spring in martensite
x0A = Free length of spring in austenite
Δ = The length of extension
L = 2x0M + 2Δ + d
x = Position of the center of the sliding block
23
(26)
(27)
(28)
(29)

The terms on the left-hand side of Eqns (26 to 29) are the different forces of the SMA
helical springs at martensite and austenite phases, respectively.
= Spring force of the left spring in martensitic phase
= Spring force of the right spring in martensitic phase
= Spring force of the left spring in austenitic phase
= Spring force of the right spring in austenitic phase
= Spring constant of the spring in martensitic phase
= Spring constant of the spring in austenitic phase
The schematic diagram and the photographs of the experimental setup for the
testing of the system with one SMA spring are shown in Figs. 10 and 11, respectively.
First of all, the system was fixed at a predetermined overall length. The current
applied to the actuator SMA spring was controlled by the DC power supply. As the
slider block moved to an equilibrium position, the actuating force in the system was
measured by the load cell connected in series with the springs. Herein, the extension
of the spring was adjusted by using micrometer. Between the load cell and the
spring, we used a piece of bakelite to insulate the sensor against the applied current.
Furthermore, beneath the bakelite, a roller on a guide rail was added for holding the
weight of the bakelite and keeping the spring in horizontal alignment with the load
cell. During the measurement, the temperature of the spring had been measured by a
thermocouple.
24

Fig. 10. The schematic diagram of the experimental setup for measuring the
mechanical behavior of the SMA spring at different controlled temperatures.
Fig. 11 The photographs of the experimental setup for measuring the mechanical
behavior of the SMA spring at different controlled temperatures.
25

Chapter 5
RESULT AND DISCUSSION
In this chapter, some of the characteristics from our SMA wire and helical
springs will be presented. The results of the experiment and the computation are
compared and discussed.
5.1 SMA Wire
The measured temperature-current diagram of the SMA wire is shown in Fig.
12. The red points denote the measurements of temperature when the applied
current increased while the blue points the temperature measurements when the
applied current decreased after reaching 3.0 A. The result has shown that the
measured temperature during heating and cooling of the wire were nearly unaffected
whether the applied current was increasing or decreasing. Therefore, whatever it is
heating or cooling, the difference of the wire temperature at the same current could be
ignored.
26

Temperature ( o C)
100
80
60
40
20
heating
cooling
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Current (A)
Fig. 12 The temperature-current diagram of the SMA wire in heating or cooling.
Figures 13 and 14 present the measured relationship between the generated load
and the controlled wire temperature. According to the Brinson’s model, the higher
tensile stress on SMA wire may cause the more martensite volume fraction
(stress-induced martensite) at heating. Therefore, it can be seen in the
load-temperature diagram that the cooling curve shifted to lower temperature
comparing with the heating one at the same loading. Moreover, as the temperature
decreased continuously, the loading on the SMA wire decreased accordingly.
However, there was sharper decrement in the loading near the transformation
temperature range than that at higher or lower temperatures. Figure 14 shows the
similar measurement with Fig. 13 but at higher loading.
27

Stress (Mpa)
340
320
300
280
260
240
220
200
180
160
heating
cooling
140
20 40 60 80 100
Temperature ( o C)
Fig. 13 The load-temperature diagram of the SMA wire with heating and cooling.
Stress (Mpa)
400
350
300
250
200
heating
cooling
150
20 40 60 80 100
Temperature ( o C)
Fig. 14 The load-temperature diagram of the SMA wire with heating and cooling for
higher stress.
28

In terms of these results, when the temperature is higher than the phase
transformation at As (about 25 ℃) along the heating curve, the variation of the slope
is increased. When the temperature is lower than the phase transformation at Rs
(about 58.7 ℃) along the cooling curve, the variation of the slope is also increased.
Thus, the result from the DSC is closely related to the mechanical behavior of the
SMA wire under uni-axial loading. Some of the parameters were adopted from
Brinson’s paper [16], e.g. DM: 26.3 GPa, DA: 67.0 GPa and εL: 0.067. The other
parameters were from the results of this experiment on the SMA wire, like CM: 5.6
MPa/ ℃, CA: 5.3 MPa/ ℃, σS: 86.0 MPa and σF: 167.0 MPa. Table 2 lists the total
parameters including the Brinson’s and ours. DM means the Young’s modulus at
martensite, DA the Young’s modulus at austenite, CM the slope of the austenite to
martensite transformation, CA the slope of the martensite to austenite transformation,
σS the critical stress for the start of transformation, σF the critical stress for the finish
of transformation, and εL the maximum residual strain.
29

Table 2 The total parameters of the SMA wire used in predicting the mechanical
behavior of the SMA helical spring.
dw: 0.8 mm do: 9 mm
Coils: 10
LM: 35.5 mm LA: 33.5 mm
DM : 26.3 GPa DA: 67.0 GPa
CM: 5.6 MPa/ ℃ CA: 5.3 MPa/ ℃
σS :86.0 MPa σF: 167.0 MPa
εL: 0.067
5.2 SMA Helical Spring
RF: 34.5 ℃ RS: 51.1 ℃
AS: 42.1 ℃ AF: 65 ℃
Similar measurements were conducted for the SMA helical spring as for the
SMA wire. The temperature-current diagram of the two-way SMA helical spring is
shown in Fig 15. The helical spring was tested at two fixed total lengths of 55 mm
and 60 mm, respectively. As the results show, when the lengths of the spring
lengthened to the 55 mm and the 60 mm, the relationship between the resulted
temperature and the applied current didn’t have any significant difference. This
result is quite similar to that of Fig. 12. Consequently, comparing the temperature
with the current, the influence due to the lengths of the helical spring could nearly be
ignored.
30

Temperature ( o C)
90
80
70
60
50
40
30
55 mm
60 mm
20
0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
Current (A)
Fig. 15 The temperature-current diagram of the SMA helical spring at 55 mm and 60
mm.
Figure 16 shows the result of the load-temperature diagram of the helical spring.
By observing the variation of the slope in these two curves, the largest slope happened
at the applied current of 1.4 A to 1.6 A for the 60-mm spring; but it occurred at 1.2 A
to 1.4 A for the 55-mm spring. It is noted that the phase transformation from
martensite to austenite occurred at higher applied current, i.e. at higher temperature
according to Fig. 16, which is consistent with the trend in the phase diagram of the
Brinson’s model shown in Fig. 2.
31

Load (N)
5
4
3
2
1
0
55 mm
60 mm
30 40 50 60 70 80
Temperature ( o C)
Fig. 16 The load-temperature diagram of the SMA helical spring at 55 mm and 60
mm.
With the measured results from the SMA helical spring, we can compute the
mechanical behavior by using the theoretical formulation, which has been shown in
Fig. 17. The other parameters of the SMA wire employed in the theoretical
prediction were listed in Table 2. By combining the theoretical formulation with the
Brinson’s model, the yellow and green points are the results of the computation. The
blue and red points are the measured results from the Fig. 16. In these results, the
inaccuracy between the computational results and measured results might be indebted
to the error of resulted temperature when the helical spring was measured.
32

Load (N)
5
4
3
2
1
55 mm
60 mm
55 mm (computation)
60 mm (computation)
30 40 50 60 70 80
Temperature ( o C)
Fig. 17 The measured and predicted load-temperature results of the SMA helical
spring.
After the Young’s modulus of the martensite had been measured from our SMA
wire, which can be found from the stress-strain curve shown in Fig. 18. Then, the
Young’s modulus of the martensite would be changed from 26.3 GPa to 23.1 GPa in
later theoretical predictions. The updated parameters are listed in Table 3.
Accordingly, the updated computational result was reexamined with the measured
result which is shown in Fig. 19. It is seen that the difference between the prediction
and measurement was improved especially at the low temperature region.
33

Stress (Mpa)
200
150
100
50
extention
relaxation
0
0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016
Strain
Fig. 18 The stress-strain diagram of the SMA wire under room tepmerature.
Table 3 The updated parameters of the SMA wire used in predicting the mechanical
behavior of the SMA helical spring with the changed Young’s modulus of the
martensite.
dw: 0.8 mm do: 9 mm
Coils: 10
LM: 35.5 mm LA: 33.5 mm
DM : 23.1 GPa DA: 67.0 GPa
CM: 5.6 MPa/ ℃ CA: 5.3 MPa/ ℃
σS :63.1 MPa σF: 176.0 MPa
εL: 0.067
RF: 34.5 ℃ RS: 51.1 ℃
AS: 42.1 ℃ AF: 65 ℃
34

Load (N)
5
4
3
2
1
55 mm (computation)
60 mm (computation)
55 mm
60 mm
30 40 50 60 70 80
Temperature ( o C)
Fig. 19 The updated measured and predicted load-temperature results of the SMA
helical spring.
Nevertheless, with the tensile test conducted in this study, the Young’s modulus
at austenite in our SMA wire should be smaller than that used in the Brinson’s.
Therefore, the Young’s modulus at austenite in later experiment was changed to 30
GPa and 45 GPa. Tables 4 and 5 show the adjusted parameters of the Young’s
moduli at austenite. Figs. 20 and 21 present the comparison of measured results and
computational results, respectively. According to these results, the computational
result with DA = 45 GPa is closer correlation with the measured one than DA = 30
GPa.
Table 4 The updated parameters of the SMA wire used in predicting the mechanical
behavior of the SMA helical spring with the Young’s modulus at austenite being 30
35

GPa.
Load (N)
5
4
3
2
1
dw: 0.8 mm do: 9 mm
Coils: 10
LM: 35.5 mm LA: 33.5 mm
DM : 23.1 GPa DA: 30 GPa
CM: 5.6 MPa/ ℃ CA: 5.3 MPa/ ℃
σS :63.1 MPa σF: 176.0 MPa
εL: 0.067
RF: 34.5 ℃ RS: 51.1 ℃
AS: 42.1 ℃ AF: 65 ℃
55 mm (computation)
60 mm (computation)
55 mm
60 mm
30 40 50 60 70 80 90
Temperature ( o C)
Fig. 20 The updated measured and predicted load-temperature results of the SMA
helical spring with the Young’s modulus at austenite being 30 GPa.
36

Table 5 The updated parameters of the SMA wire used in predicting the mechanical
behavior of the SMA helical spring with the Young’s modulus at austenite being 45
GPa.
Load (N)
5
4
3
2
1
dw: 0.8 mm do: 9 mm
Coils: 10
LM: 35.5 mm LA: 33.5 mm
DM : 23.1 GPa DA: 45 GPa
CM: 5.6 MPa/ ℃ CA: 5.3 MPa/ ℃
σS :63.1 MPa σF: 176.0 MPa
εL: 0.067
RF: 34.5 ℃ RS: 51.1 ℃
AS: 42.1 ℃ AF: 65 ℃
40 60 80 100
Temperature ( o C)
37
55 mm (computation)
60 mm (computation)
55 mm
60 mm
Fig. 21 The updated measured and predicted load-temperature results of the SMA

helical spring with the Young’s modulus at austenite being 45 GPa.
Since the temperature of the specimen was measured by using thermocouple
which touched the surface of the specimen, the real temperature at the center of the
SMA wire should be higher than the readout of the thermocouple. Although the
difference in temperature might be small due to the thin wire diameter, the effect was
explored. If the temperature of the measured results was adjusted slightly to higher
magnitude, then the difference between the results of prediction and measurement
could be further diminished. The amendatory measured results in comparison
with the computational results are shown in Fig. 22.
Load (N)
5
4
3
2
1
55 mm (computation)
60 mm (computation)
55 mm
60 mm
40 60 80 100
Temperature ( o C)
Fig. 22 The adjusted measured and predicted load-temperature results of the SMA
helical spring.
38

5.3 The Measurements from the Other ‘Twins’ Spring
Next, the characteristics of the other ‘twins’ helical specimen were measured.
The free lengths of the specimen at room temperature and austenite phase were 27
mm and 23.5 mm, respectively. Table 6 lists the parameters of the other SMA
helical spring with different free lengths at phase of martensite and austenite. Fig.
23 presents the measured free lengths of this spring under heating and cooling
situations. When the temperature of the specimen was slightly higher than 50 ℃ at
the heating curve, the spring was nearly at austenite phase. When it was at cooling
curve, the extension of the specimen length minutely lagged that at the heating curve.
Table 6 The updated parameters of the SMA wire used in predicting the mechanical
behavior of the SMA helical spring with the changed free lengths at phase of
martensite and austenite.
dw: 0.8 mm do: 9 mm
Coils: 10
LM: 27 mm LA: 23.5 mm
DM : 23.1 GPa DA: 45 GPa
CM: 5.6 MPa/ ℃ CA: 5.3 MPa/ ℃
σS :63.1 MPa σF: 176.0 MPa
εL: 0.067
RF: 34.5 ℃ RS: 51.1 ℃
AS: 42.1 ℃ AF: 65 ℃
39

Length (mm)
27
26
25
24
23
20 40 60 80 100
Temperature ( o C)
Fig. 23 The length-temperature diagram of the SMA helical spring at free
deformation.
40
heating
cooling
Then, the Young’s moduli of the SMA wire at austenite phase, which have been
adjusted to 30 GPa and 45 GPa as shown in Tables 4 and 5, were employed again in
the theoretical computation. Figure 24 shows the experimental results of the
load-temperature curves at spring lengths of 55 mm and 60 mm. The predictions
under similar loading situations were performed and Figs. 25 and 26 present the
associate results of the load-temperature curves at DA = 30 GPa and 45 GPa,
respectively. The comparison between the measured result and computational result
are shown in Fig. 27. If the measured temperatures were adjusted according to the
argument mentioned previously, then the results of the comparison would be changed
in Fig. 28. Therefore, the real temperature of our experimental results should be
higher than the measured temperature as we thought before.

Load (N)
6
5
4
3
2
1
0
heating (55 mm)
cooling (55 mm)
heating (60 mm)
cooling (60 mm)
30 40 50 60 70 80
Temperature ( o C)
Fig. 24 The experimental load-temperature diagram of the SMA helical spring at 55
mm and 60 mm.
Load (N)
4.0
3.5
3.0
2.5
2.0
1.5
1.0
heating (55 mm)
cooling (55 mm)
heating (60 mm)
cooling (60 mm)
40 60 80 100
Temperature ( o C)
41

Fig. 25 The computational load-temperature diagram of the SMA helical spring in the
Young’s modulus at austenite is 30 GPa at 55 mm and 60 mm.
Load (N)
6
5
4
3
2
1
heating (55 mm)
cooling (55 mm)
heating (60 mm)
cooling (60 mm)
40 60 80 100 120
Temperature ( o C)
Fig. 26 The computational load-temperature diagram of the SMA helical spring in the
Young’s modulus at austenite is 45 GPa at 55 mm and 60 mm.
42

Load (N)
6
5
4
3
2
1
0
40 60 80 100 120
Temperature ( o C)
43
heating (55 mm) (computation)
cooling (55 mm) (computation)
heating (60 mm) (computation)
cooling (60 mm) (computation)
heating (55 mm)
cooling (55 mm)
heating (60 mm)
cooling (60 mm)
Fig. 27 The comparison of the measured and predicted load-temperature results of the
SMA helical spring.

Load (N)
6
5
4
3
2
1
0
40 60 80 100 120
Temperature ( o C)
44
heating (55 mm) (computation)
cooling (55 mm) (computation)
heating (60 mm) (computation)
cooling (60 mm) (computation)
heating (55 mm)
cooling (55 mm)
heating (60 mm)
cooling (60 mm)
Fig. 28 The adjusted measured results in comparison with the predicted results of the
SMA helical spring.
At isothermal temperature, the actuation force of the SMA helical spring
changed with the total length. The reaction force for the selected five spring lengths
at different temperatures were simulated and the results are shown in Fig. 29.
According to this diagram, the phase transformation from martensite to austenite can
be easily observed. At the temperatures of the 20 and 40 ℃, the spring was in
martensite phase (below the austenite start 42.1 ℃, based on the DSC analysis).
Therefore, the load-deformation curve of the helical spring nearly followed the
Hooke's law with constant slope. At the temperature of the 60 ℃, it is between the
austenite start and finish. Because of the stress-induced martensite transformation,
when the length of the spring increases, the martensite volume fraction will also be
increased. The result may show the more ‘martensite’ state on the longer lengths of

the spring. This phenomenon manifests as the slope of the load-deformation curve
decreased at larger spring length. At the temperature of the 80 ℃, it almost reached
the austenite finish (above ‘at least’ 65 ℃). Along with the lengths of the spring
became longer, the phenomenon of the stress-induced martensite transformation also
prevailed. When the temperature was higher than 100 ℃, the helical spring was
totally in ‘austenite’ state. Therefore, it followed closely the Hooke's law again.
Load (N)
7
6
5
4
3
2
1
20 o C
40 o C
60 o C
80 o C
100 o C
120 o C
0
45 50 55 60 65
Length (mm)
Fig. 29 The computational load-length diagram of the SMA helical spring in the five
certain lengths.
Figure 30 shows the measured results of our experiment according to loading
situation depicted in Fig. 29. The curves in this diagram show the correct trend as
those in Fig. 29. However, some of the activation forces were lower than the
computational result. The one possibility of this discrepancy that we suspected was
the ageing of the SMA wire.
45

Load (N)
5
4
3
2
1
60 o C
80 o C
20 o C
40 o C
100 o C
0
45 50 55 60 65
Length (mm)
Fig. 30 The measured load-length diagram of the SMA helical spring in the five
certain lengths.
The re-measured free lengths of the helical spring after the forgoing tests were 29 mm
at room temperature, 27 mm at austenite. Table 7 shows the revised parameters of
the SMA helical spring with the lengths at phase of martensite and austenite. The
drifting of the free length of the spring confirms the ageing effect we suspected.
Hence, with the updated free lengths at these temperatures, the revised result of the
helical spring had been computed and presented in Fig. 31. Comparing the new
result with the original one, when the temperature reached above 60 ℃, it began to
demonstrate the difference between the two results. The revised one would be a
little bit closer to the measured results. It might confirm that the ageing of the SMA
wire under repeated loading cycles deserves attentions in design.
46

Table 7 The revised parameters of the SMA wire used in predicting the mechanical
behavior of the SMA helical spring with the changed lengths at phase of martensite
and austenite.
Load (N)
6
5
4
3
2
1
dw: 0.8 mm do: 9 mm
Coils: 10
LM: 29 mm LA: 27 mm
DM : 23.1 GPa DA: 45 GPa
CM: 5.6 MPa/ ℃ CA: 5.3 MPa/ ℃
σS :63.1 MPa σF: 176.0 MPa
εL: 0.067
RF: 34.5 ℃ RS: 51.1 ℃
AS: 42.1 ℃ AF: 65 ℃
20 o C
40 o C
60 o C
80 o C
100 o C
120 o C
0
45 50 55 60 65
Length (mm)
47

Fig. 31 The revised computational load-length diagram of the SMA helical spring in
the five certain lengths.
48

Chapter 6
CONCLUSIONS
This chapter summarized the entire conclusions about our experiments and
researches, including training the SMA helical spring with two-way SME,
combination of the Brinson’s model and the theoretical formulation, comparison
between the measured results and computational result, some differences between the
results of the prediction and the measurement, and suggestions for future works.
6.1 Training and Measuring the SMA Helical Spring
In this study, a helical spring with two-way shape memory effect was fabricated.
During our research, the two of helical springs called ‘twins’ had been trained and
been measured, individually. Then, the mechanical behaviors of a SMA wire and a
two-way SMA helical spring were measured, respectively. The generated axial load
of the specimen under predetermined length and applied electric current was
investigated. According to the measurement, the result of the characteristic curve
was measured. When the temperature was raised, the loading on the spring with
controlled fixed length increased. However, the increase of the spring force was
nonlinear and became saturated as the temperature was above the finish point of the
austenite transformation. If the controlled length increased, then the loading
increased at the fixed temperature. The slope of the loading curve, i.e. the spring
constant, was not always constant due to the possible stress induced martensitic
transformation. The transformation tended to lower the slope of the loading curve.
49

6.2 Combination of the Brinson’s Model and the Theoretical
Formulation
By the theoretical formulation in the helical spring, the mechanical load at
different temperatures and extension displacements were computed. The program of
the Brinson’s model and the theoretical formulation’s combination was established.
The comparison between the measured results and the computational results showed
good correlation.
6.3 Future Works
However, some differences between the results of the prediction and the
measurement were observed. The reasons could be indebted to:
1. the selected range of the phase transformation in the specific temperatures, or
2. the ageing of the SMA wire under repeated loading cycles,
3. the errors of the measured and selected Young’s modulus or other parameters in
our theoretical formulation.
Therefore, the future works of this research can seek for the improvement on the
difference between the predicted curves and measured curves, and alleviate the ageing
effect for repeated loading cycles in the SMA helical spring. A more elaborate
tensile testing machine on the SMA wire can be built to measure the
loading-extension curve at well controlled temperature environment. This can
determine all the parameters needed in the theoretical formulations.
50

REFERENCES
[1] K. Ikuta, M. Tsukamoto, S. Hirose, “Shape Memory Alloy Servo Actuator
System with Electric Resistance Feedback and Application for Active
Endoscope,” Proceedings IEEE, International Conference on Robotics &
Automation, April 1988, pp. 427-430.
[2] C. B. Churchill, J. A. Shaw, M. A. Iadicola, “Tips and Tricks for Characterizing
Shape Memory Alloy Wire: Part 4 – Thermo-Mechanical Coupling,”
Experimental Characterization of Active Materials Series, 2010, pp. 1-18.
[3] Y. P. Lee, B. Kim, M. G. Lee, and J. O. Park, “Locomotive Mechanism Design
and Fabrication of Biomimetic Micro Robot Using Shape Memory Alloy,”
Proceedings IEEE, International Conference on Robotics & Automation, April
2004, pp. 5007-5012.
[4] L. C. Brinson, M. S. Huang, “Simplifications and Comparisons of Shape
Memory Alloy Constitutive Models,” Journal of Intelligent Material and
Structures, Vol. 7-January 1996, pp.108-114.
[5] J. Ryhänen, “Biocompatibility Evaluation of Nickel-titanium Shape Memory
Metal Alloy,” Ph.D. Departments of Surgery, Anatomy and Pathology, Oulu
University, 2000.
[6] S. Maeda, K. Abe, K. Yamamoto, O. Tohyama, and H. Ito, “Active Endoscope
with SMA (Shape Memory Alloy) Coil Springs,” IEEE, Micro Electro
Mechanical Systems (MEMS), 1996, pp. 290-295.
[7] Y. Haga, M. Esashi, and S. Maeda, “Bending, Torsional and Extending Active
Catheter Assembled Using Electroplating,” 13 th IEEE, International Micro
Electro Mechanical Systems Conference (MEMS), 2000, pp. 181-186.
51

[8] Z. W. Zhu, Z. B. Gou, J. Xu, and H. L. Wang, “Research on Nonlinear Dynamic
Characteristics of Semi-active Suspension System with SMA Spring,” 2008
International Conference on Intelligent Computation Technology and
Automation, pp. 688-692.
[9] K. Otsuka, C. M. Wayman, Shape Memory Materials, Cambridge University
Press, 1998.
[10] A. Ölander, “An Electrochemical Investigation of Solid Cadmium - Gold
Alloys,” Journal of the American Chemical Society, 54, 1932, pp. 3819-3833.
[11] A. B. Greninger and V. G. Mooradian, “Strain Transformation in Metastable
Copper-Zinc and Beta Copper- Tin Alloys,” Transaction of American Institute
of Mining, Metallurgical, and Petroleum Engineers 128, 1938, pp. 337-368.
[12] G. V. Kurdjumov and L. G. Khandros, “First Reports of the Thermoelastic
Behavior of the Martensitic Phase of Au-Cd Alloys,” Doklady Akad. Nauk
S.S.S.R., 56, 1949, pp. 221-213.
[13] L. C. Chang and T. A. Read, “Plastic Deformation and Diffusionless Phase
Changes in Metals. The Gold-Cadmium Beta Phase,” Transaction of American
Institute of Mining, Metallurgical, and Petroleum Engineers 189, 1951, pp.
47-52.
[14] J. A. Shaw, C. B. Churchill, M. A. Iadicola, “Tips and Tricks for
Characterizing Shape Memory Alloy Wire: Part 1 – Differential Scanning
Calorimetry and Basic Phenomena,” Experimental Techniques 32(5), 2008,
pp.55–62.
[15] K. Wada, Y. Liu, “On the Mechanisms of Two-way Memory Effect and
Stress-assisted Two-way Memory Effect in NiTi Shape Memory Alloy,”
Journal of Alloys and Compounds 499, 2008, pp. 125-128.
[16] L. C. Brinson, A. Bekker, and S. Hwang, “Deformation of Shape Memory
52

Alloys Due to Thermo-induced Transformation,” Journal of Intelligent Material
Systems and Structures, Vol. 7-January 1996, pp. 97-107.
[17] H. Prahlad, I. Chopra, “Comparative Evaluation of Shape Memory Alloy
Constitutive Models with Experimental Data,” Journal of Intelligent Material
and Structures, Vol. 12-June 2001, pp. 383-395.
[18] Z. G. Wang, X. T. Zu, J. Y. Dai, P. Fu, X. D. Feng, “Effect of
Thermomechanical Training Temperature on the Two-way Shape Memory
Effect of TiNi and TiNiCu Shape Memory Alloys Springs,” Materials Letters
57, 2003, pp.1501-1507.
[19] C.Y. Lee, C.S. Lin and H.C. Zhao, “Dynamic Characteristics of Platform with
SMA Helical Spring Suspension,” Proceedings of the Thirteenth International
Congress on Sound and Vibration (ICSV13), pp. 2-6 July 2006.
[20] C. Y. Lee, H. C. Zhuo, and C. W. Hsu, “Lateral Vibration of A Composite
Stepped Beam Consisted of SMA Helical Spring Based on Equivalent
Euler–Bernoulli Beam Theory,” Journal of Sound and Vibration, 324, 2009,
pp.179–193.
[21] 許家維,形狀記憶合金螺旋彈簧用於半主動懸吊平台減振之研究,大葉大
學機械工程研究所碩士論文,2008。
[22] 楊子弘,混成形狀記憶螺旋彈簧用於半主動懸吊平台減振之研究,大葉大
學機械與自動化工程學系碩士論文,2009。
[23] F. M. Davidson, C. Liang, “Investigation of Torsional Shape Memory Alloy
Actuators,” SPIE Vol. 2717 1 May 1996, pp. 672-682.
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Name: Mei-Chen Yueh
Birthday: August 6, 1985
Birth place: Miao Li, Taiwan
Education:
Writer Introduction
Bachelor degree: Power Mechanical Engineering, National Formosa University
Master’s degree: Institute of Mechatronic Engineering, National Taipei University
Mobile phone: 0918628500
E-mail: charlieyueh@hotmail.com
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