11001259 dissertation
TRANSCRIPT
Design, Modelling and Testing of a synthetic muscle system
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DESIGN, MODELLING AND TESTING OF A SYNTHETIC
MUSCLE SYSTEM AS ACTUATION FOR AN AIRCRAFT CONTROL
SURFACE
BY KUDZAI C.K. MUTASA
STUDENT NUMBER 11001259
MENG (HONS) AERONAUTICAL ENGINEERING
Design, Modelling and Testing of a synthetic muscle system
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I) ABSTRACT
An attempt was made to try and improve the aerodynamic characteristics of modern day low speed
aircraft by using shape changing materials to actuate the control surfaces. Theoretically, a morphing
wing design approach was undertaken with major concentration being on the material for actuation.
Shape memory polymers (SMPs) were chosen over shape memory alloys (SMAs) due to their ease of
manufacture, low cost and highly flexible programming.
The fundamental characteristics of SMPs were presented along with their mechanism and
microstructure. These two factors along with preparation are the main influences into the behavior
of the SMP and this was confirmed through experimental work. Thermomechanical and tensile tests
were undertaken to determine glass transition temperature as well as mechanical strength of the
polymer composite above glass transition temperature and the 5% CB sample was selected to be
incorporated into the design.
The main hindrance towards a successful design in the past has been strength of SMPs as well as
means of actuation therefore an electro active polymer of Polyurethane (PU) incorporating Carbon
Black (CB) as the conductive filler was selected in hope that it would not drastically decrease the
mechanical strength of PU.
A mathematical model was also presented beginning from initial assumptions as well as a relation of
the modelling to a typical shape memory process. This enabled determination of constitutive
modelling parameters such as the frozen volume fraction ( ) , shear moduli of the
frozen and active phases and respectively, and volume ratios in the
frozen and active phases ( ) and ( ) respectively.
Calibration of this model was not possible as the material failed before the required strain was
achieved and reasons for this are given. The composition of PU was found to be directly related to
the modelling as well possible improvements for the material were presented. The material was
determined to have contained not enough hard segment content for adequate shape recovery.
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II) DECLARATION
I declare that this dissertation is my own work and effort and that it has not been submitted
anywhere for any award. If other sources of information have been used, they have been
acknowledged.
Signature: …...........................................................................................
Date: …………………………………………………………………………………………………
This dissertation was submitted in partial fulfillment of MEng (Hons) Aeronautical Engineering at the
University Of South Wales, United Kingdom.
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III) ACKNOWLEDGEMENT
It would not have been possible to write this dissertation without the help and support of kind
people around me, all of which are worth mentioning.
Above all I would like to thank my parents for their undying support and financial dedication towards
my education entirely. I wish to thank my brothers and sister for their emotional support
throughout and laughs provided during tough times.
This dissertation would also not have been possible without the help and support of my supervisor,
Dr. Giuliano Claude Premier, whose advice and support have been invaluable on both an academic
and personal level, for which I am extremely grateful.
I would also like to thank the academic and technical staff at the University of South Wales,
Trefforest Campus, as well as all lecturers who have provided me with engineering knowledge to
reach me to such a stage in my studies. The library and computer facilities have also been second to
none which have enabled access to various publications from great minds all over the world.
For any errors and inadequacies that remain in this work, of course, the responsibility is entirely my
own.
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IV) ABBREVIATIONS
, shape fixity rate
, shape recovery rate TPU, thermoplastic
, glass transition temperature
, isotropic temperature
, crystal melting temperature
, transition temperature
AFM, Atomic force microscopy
BD , 1,4-butanediol
CNFs, carbon nanofibers
CNTs, carbon nanotubes
ED, Ethylenediamine
FT-IR, Fourier transform infrared spectroscopy
LC, liquid crystalline
LCE, liquid crystalline elastomer
LiFeP , Lithium Iron Phospate
MDI, 4,4’-diphenylmethane diisocyanate
MWCNTs, multi-walled carbon nanotubes
Ni, Nickel
OM, Optical microscopy
PB, poly(1,4-butadiene)
PCL, polycaprolactone
PCO, polyoctene
PN, Polynorbornene
Polyurethane
POSS, polyhedral oligomeric silsesquioxane
PPO, poly(propylene oxide
PTMO, poly (tetramethyl oxide) glycol
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PVC, poly(vinyl chloride)
SCPs, shape changing polymers
SEM, Scanning electron microscopy
SMAs, shape–memory alloys
SMEs, shape–memory effects
SMF, shape–memory fiber
SMMs, shape–memory materials
SMPs, shape–memory polymers
SMPUs, shape–memory polyurethanes;
SMPUU, shape–memory polyurethane-urea
SPM, Scanning probe microscopy
STBS , styrene-trans-butadiene-styrene
SWCNTs, single-walled carbon nanotubes
TEM, Transmission electron microscopy
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V) LIST OF FIGURES
Figure 1 aircraft control surfaces ............................................................................................................ 1
Figure 2 aircraft wing internal structure courtesy of nomenclaturo.com .............................................. 2
Figure 3 basic idea behind morphing wings courtesy of Baier and Datashvili (2011) ............................ 2
Figure 4 pneumatic rubber muscle actuator (Peel, Mejia, Narvaez, Thompson and Lingala (2009)) .... 3
Figure 5 various morphing wing mechanisms. Morphing wing skin mechanism(left) and flap activated
by shape memory alloy wire by Kang, Kim, Jeong and Lee (2012) (right) ............................................. 3
Figure 6 different morphing skin concepts a) sandwich concept with elastomer cover and auxetic
material core (Baier and Datashvili (2011)) ............................................................................................ 4
Figure 7 leading and trailing edge mechanisms developed for the f-111 mission adaptive wing
program (Kota, Hetrick, Osborn, Paul, Pendleton, Flick and Tilman (2006)) .......................................... 5
Figure 8 possible solution 1 .................................................................................................................... 5
Figure 9 possible morphing wing design ................................................................................................. 6
Figure 10 the overall architecture of SMPs (Hu and Chen (2010)) ......................................................... 9
Figure 11 strain recovery of a cross-linked, castable shape memory polymer upon rapid exposure to
a water bath at T=80˚C (Liu, Quinn and Mather (2007)) ...................................................................... 12
Figure 12 schematic depiction of shape fixing and recovery mechanisms of semi-crystalline rubbers.
a) cross linked shape at semi-crystalline stage, b) melted sample of stress free stage (high
temperature), c) deformed shape at melt stage (high temperature) and ; crystal frozen deformed
shape (low temperature) (Lu, Chun, Mather, Zhen, Haley and Coughlin (2002)) ................................ 14
Figure 13 PU with micro-phase separation structure (Chun, Cho and Chung (2006)) ......................... 17
Figure 14 four types of shape memory polymers with different shape fixing and shape recovery
mechanisms depicted as a function of their dynamic mechanical behaviour. Tensile storage modulus
versus temperature as measured using a small oscillatory deformation at 1Hz for I) chemically cross
linked glassy thermosets, II) chemically cross linked semi-crystalline rubbers, III) physically cross
linked thermoplastics and IV) physically cross linked block copolymers (Liu, Quinn and Mather
(2007)) ................................................................................................................................................... 18
Figure 15 a) modulus and b) stress at 100% elongation of composites as a function of percentage
MWCNT content (open square : raw, open circle: 90˚C acid treatment, filled circle: 140˚C acid
treatment) (Cho, Kim, Jung and Goo (2005)) ........................................................................................ 19
Figure 16 electro-active shape-recovery behaviour of PU-MWCNT composites at 5% content. The
sample undergoes transition from temporary shape (linear left), to permanent (helix, right) within
10s when a voltage of 40V is applied. (Cho, Kim, Jung and Goo (2005)) .............................................. 20
Figure 17 casting mold and machined sample with imbedded electrodes. Glass tape was used at each
end for securing in tensile testing frame. (Rogers and Khan (2012)) ................................................... 21
Figure 18 results for carbon black filled polymer (Rogers and Khan (2012)) ....................................... 22
Figure 19 (Rogers and Khan (2012)) ...................................................................................................... 23
Figure 20 DSC results of CB at various compositions (Lan, Leng, Liu and Du (2008)) ........................... 23
Figure 21 sequences of shape recovery of CB 10% by passing as electrical current of 30V (Rogers and
Khan (2012)) .......................................................................................................................................... 23
Figure 22 magnetic field curing (Leng, Huang, Lan, Liu and Du (2008)) ............................................... 24
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Figure 23 resistivity vs volume fraction of cb with/without 0.5 vol % ni. red symbol, right after
fabrication; blue symbol, one month later. inset displays how resistance was measured. (Leng,
Huang, Lan, Liu and Du (2008)) ............................................................................................................. 24
Figure 24 evolution of resistivity upon shape memory cycling (Leng, Huang, Lan, Liu and Du (2008))25
Figure 25 storage nodulus versus volume fraction of ni at 0 degrees (Leng, Huang, Lan, Liu, Du, Phee
and Yuan (2008)) ................................................................................................................................... 25
Figure 26 left: values of restistance vs temperature; right: values of restance versus strain for scf-
smp composite (Lu, Yu, Liu and Leng (2010)) ....................................................................................... 26
Figure 27 morphologies of scf-smp composite specim observed by SEM (2% SCF and 5% CB) a)
morphologies of scf fillers and b) morphologies of cb particles (Lu, Yu, Liu and Leng (2010)) ............ 26
Figure 28 stress-strain curves of composites filled with various scf contents in tensile mode (Lu, Yu,
Liu and Leng (2010)) .............................................................................................................................. 27
Figure 29 images showing the macroscopic shape memory effect of 5% cb and 2% scf composite .
the permanent shape is a flat strip and the temporary shape a right angle deformation. (Lu, Yu, Liu
and Leng (2010)) ................................................................................................................................... 27
Figure 30 morphology characterised with different methods. OM and TEM for PC containing 0.688%
vol CNTs. SEM in charge contrast mode shows the distribution of MWNTs in Polypyrrole matrix and
HAADF-STEM pictures show individual carbon black particles and their clusters in polymer
composites: OM and TEM (Deng, Lin, Ji, Zhang, Yang and Fu (2013)) .................................................. 30
Figure 31 some design strategies for SMPs (Meng and Hu (2009)) ...................................................... 32
Figure 32 against CB content (Lan, Leng, Liu and Du (2008)) ......................................................... 32
Figure 33 schematic diagram of the micromechanics foundation of the 3D shape memory polymer
constitutive model with the existence of two extreme polymer states shown. In this diagram the
polymer is in the glass transition state with a predominant active phase. (Liu, Gall, Dunn, Greenberg
and Diani (2006)) ................................................................................................................................... 34
Figure 34 deformation of an SMP in various states during cooling (Chen and Lagoudas (2008)) ........ 39
Figure 35 schematic of SMP thermomechanical cycle showing shape memory effect and constrained
recovery (Atli, Gandhi and Karst (2008)) .............................................................................................. 45
Figure 36 schematic representation of results of cyclic thermo-mechanical investigations (Lendlein
and Kelch (2002)) .................................................................................................................................. 49
Figure 37 material properties of PU (ALchemie.ltd) ............................................................................. 51
Figure 38 experimental set up .............................................................................................................. 52
Figure 39 extension vs temperature for 10% CB .................................................................................. 53
Figure 40 5% CB thermomechanical test .............................................................................................. 54
Figure 41 Thermomechanical testing veil and 5% CB ........................................................................... 54
Figure 42 10% CB stress versus strain ................................................................................................... 55
Figure 43 5% CB stress versus strain ..................................................................................................... 56
Figure 44 5% CB and veil stress versus strain ....................................................................................... 56
Figure 45 5% CB thermal strain ............................................................................................................. 57
Figure 46 5% CB and veil thermal strain ............................................................................................... 57
Figure 47 thermal strain ........................................................................................................................ 59
Figure 48 active phase stress strain graph ............................................................................................ 60
Figure 49 zero stress cooling curve ....................................................................................................... 62
Figure 50 frozen volume fraction .......................................................................................................... 62
Figure 51 fractured test sample displaying crack propagation along regions embedded with wire. .. 67
Figure 52 shape memory behaviour study of a) PTMO250 and b) PTMO650 (Lin and Chen (1998)) .. 69
Figure 53 shape memory behaviour of soft segment investigation (Lin and Chen (1998)) ................. 70
Figure 54 chemical structure of pu block copolymer a) bd type and b) ed type .................................. 71
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Figure 55 mechanical properties of Pu a) maximum stress, b)tensile modulus and c) strain at break
(Chun, Cho and Chung (2006)) .............................................................................................................. 72
Figure 56 shape memory properties vs hard segment content profile of PU chain extended with a)
BD and b) ED after the first test cycle (Chun, Cho and Chung (2006)) ................................................. 72
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VI) LIST OF TABLES
Table 1 possible benefits and setbacks of design 1 ................................................................................ 6
Table 2 (Liu, Quinn and Mather (2007)) ................................................................................................. 8
Table 3 shape memory thermosets (Liu, Quinn and Mather (2007)) ................................................... 13
Table 4 polymer special features (Liu, Quinn and Mather (2007)) ....................................................... 14
Table 5 summary of physically cross linked copolymer blends (Liu, Quinn and Mather (2007)) ......... 16
Table 6 summary of physically cross-linked semi-crystalline copolymer blends (Liu, Quinn and
Mather (2007)) ...................................................................................................................................... 17
Table 7 summary of conductive fillers .................................................................................................. 33
Table 8 ................................................................................................................................................... 48
Table 9 summary of constitutive parameters ....................................................................................... 63
Table 10 percentage extension and corresponding values ............................................................. 66
Table 11 notation and molar compositions of PU when investigation hard segment content. (Lin and
Chen (1998)).......................................................................................................................................... 68
Table 12 molar compositions of pu when studying soft segment (Lin and Chen (1998)) .................... 70
Table 13 composition of PU used (Chun, Cho and Chung (2006)) ........................................................ 71
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VII) LIST OF EQUATIONS
Equation 1 ............................................................................................................................................. 10
Equation 2, Equation 3, Equation 4 ...................................................................................................... 35
Equation 5, Equation 6 .......................................................................................................................... 35
Equation 7 ............................................................................................................................................. 35
Equation 8, Equation 9 .......................................................................................................................... 35
Equation 10 ........................................................................................................................................... 36
Equation 11 ........................................................................................................................................... 36
Equation 12 ........................................................................................................................................... 36
Equation 13 ........................................................................................................................................... 37
Equation 14 ........................................................................................................................................... 37
Equation 15 ........................................................................................................................................... 38
Equation 16 ........................................................................................................................................... 38
Equation 17 ........................................................................................................................................... 38
Equation 18 ........................................................................................................................................... 38
Equation 19 ........................................................................................................................................... 38
Equation 20 ........................................................................................................................................... 38
Equation 21 ........................................................................................................................................... 38
Equation 22 ........................................................................................................................................... 38
Equation 23 ........................................................................................................................................... 39
Equation 24 ........................................................................................................................................... 39
Equation 25 ........................................................................................................................................... 40
Equation 26 ........................................................................................................................................... 40
Equation 27 ........................................................................................................................................... 40
Equation 28 ........................................................................................................................................... 40
Equation 29 ........................................................................................................................................... 40
Equation 30 ........................................................................................................................................... 40
Equation 31 ........................................................................................................................................... 40
Equation 32 ........................................................................................................................................... 41
Equation 33 ........................................................................................................................................... 41
Equation 34 ........................................................................................................................................... 41
Equation 35 ........................................................................................................................................... 42
Equation 36 ........................................................................................................................................... 42
Equation 37 ........................................................................................................................................... 42
Equation 38 ........................................................................................................................................... 42
Equation 39 ........................................................................................................................................... 43
Equation 40 ........................................................................................................................................... 43
Equation 41 ........................................................................................................................................... 43
Equation 42 ........................................................................................................................................... 43
Equation 43 ........................................................................................................................................... 43
Equation 44 ........................................................................................................................................... 43
Equation 45 ........................................................................................................................................... 43
Equation 46 ........................................................................................................................................... 44
Equation 47 ........................................................................................................................................... 44
Equation 48 ........................................................................................................................................... 44
Equation 49 ........................................................................................................................................... 44
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Equation 50 ........................................................................................................................................... 44
Equation 51 ........................................................................................................................................... 44
Equation 52 ........................................................................................................................................... 44
Equation 53 ........................................................................................................................................... 44
Equation 54 ........................................................................................................................................... 45
Equation 55 ........................................................................................................................................... 45
Equation 56 ........................................................................................................................................... 45
Equation 57 ........................................................................................................................................... 45
Equation 58 ........................................................................................................................................... 45
Equation 59, Equation 60 ...................................................................................................................... 46
Equation 61, Equation 62 ...................................................................................................................... 46
Equation 63, Equation 64 ...................................................................................................................... 46
Equation 65, Equation 66 ...................................................................................................................... 46
Equation 67, Equation 68 ...................................................................................................................... 46
Equation 69, Equation 70 ...................................................................................................................... 46
Equation 71 ........................................................................................................................................... 47
Equation 72 ........................................................................................................................................... 47
Equation 73 ........................................................................................................................................... 47
Equation 74 ........................................................................................................................................... 47
Equation 75 ........................................................................................................................................... 47
Equation 76 ........................................................................................................................................... 48
Equation 77 ........................................................................................................................................... 48
Equation 78 ........................................................................................................................................... 48
Equation 79 ........................................................................................................................................... 50
Equation 80 ........................................................................................................................................... 50
Equation 81 ........................................................................................................................................... 50
Equation 82 ........................................................................................................................................... 58
Equation 83 ........................................................................................................................................... 58
Equation 84 ........................................................................................................................................... 58
Equation 85 ........................................................................................................................................... 58
Equation 86 ........................................................................................................................................... 58
Equation 87 ........................................................................................................................................... 58
Equation 88 ........................................................................................................................................... 59
Equation 89 ........................................................................................................................................... 59
Equation 90 ........................................................................................................................................... 59
Equation 91 ........................................................................................................................................... 60
Equation 92 ........................................................................................................................................... 60
Equation 93 ........................................................................................................................................... 61
Equation 94 ........................................................................................................................................... 61
Equation 95 ........................................................................................................................................... 61
Equation 96 ........................................................................................................................................... 61
Equation 97 ........................................................................................................................................... 64
Equation 98 ........................................................................................................................................... 64
Equation 99 ........................................................................................................................................... 64
Equation 100 ......................................................................................................................................... 64
Equation 101 ......................................................................................................................................... 65
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TABLE OF CONTENTS
I) Abstract ........................................................................................................................................... ii
II) Declaration ................................................................................................................................. iii
III) Acknowledgement ..................................................................................................................... iv
IV) Abbreviations .............................................................................................................................. v
V) List of Figures ................................................................................................................................ vii
VI) List of Tables ............................................................................................................................... x
VII) List of Equations ......................................................................................................................... xi
Table of Contents ................................................................................................................................. xiii
Chapter 1 ................................................................................................................................................. 1
1.0 Introduction ................................................................................................................................ 1
1.1 Morphing airfoil approach ...................................................................................................... 2
1.1.1. Morphing wing skins ....................................................................................................... 4
1.2.1 Compliant wing System ................................................................................................... 4
1.2 Possible Wing Designs ............................................................................................................. 5
1.2.1. Possible Solution 1 .......................................................................................................... 5
1.2.2. Possible Solution 2 .......................................................................................................... 6
Chapter 2 ................................................................................................................................................. 7
Literature Survey ..................................................................................................................................... 7
2.1 Fundamentals of Shape memory materials ............................................................................ 7
2.1.1 Shape memory alloys ...................................................................................................... 7
2.1.2 Shape memory polymers ................................................................................................ 8
2.2 General framework of SMPs ................................................................................................... 9
2.2.1. Thermodynamic behaviour ........................................................................................... 10
2.2.2. Entropy elasticity........................................................................................................... 11
2.3. Structure and Mechanism of SMPs ....................................................................................... 11
2.3.1. Covalently cross-linked glassy thermoset networks ..................................................... 11
2.3.2. Covalently cross-linked semi-crystalline networks ....................................................... 13
2.3.3. Physically cross-linked glassy copolymers .................................................................... 15
2.3.4. Physically cross-linked semi-crystalline block copolymers ........................................... 16
2.4 Electro-active polymers ........................................................................................................ 19
2.4.1 SMP filled with carbon nanotubes ................................................................................ 19
2.4.2 SMP filled with Carbon black ........................................................................................ 20
2.4.3 SMP filled with nickel .................................................................................................... 24
2.4.4 SMP filled with hybrid fillers ......................................................................................... 26
2.5. Preparation of Conductive shape memory polymers ........................................................... 28
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2.5.1. Melt compounding ........................................................................................................ 28
2.5.2. In-Situ polymerisation ................................................................................................... 29
2.5.3. Solution mixing.............................................................................................................. 29
2.6 Morphological control of conductive networks in shape memory polymers ....................... 30
2.6.1 Characterisation of conductive network formation ..................................................... 30
2.6.2 Morphological control through polymer blends ........................................................... 31
2.6.3 Influence of filler chemistry on glass transition temperature ...................................... 32
2.7 Material selection and Manufacturing method .................................................................... 33
Chapter 3 ............................................................................................................................................... 34
3.1 Preliminary Modelling for Shape Memory Polymer behaviour ................................................ 34
3.1.1 Preliminary assumptions ................................................................................................... 36
3.1.2 Constitutive Equations ...................................................................................................... 37
3.1.3 Average Scheme ................................................................................................................ 39
3.1.4 The shape memory cycle .................................................................................................. 42
3.1.4.1 Constrained recovery .................................................................................................... 45
3.1.5 Neo-hookean modelling .................................................................................................... 46
3.1.6 Reduction of constitutive model for Uniaxial tension experiment ................................... 47
Chapter 4 ............................................................................................................................................... 49
4.1 Experimental Setup ................................................................................................................... 49
4.1.1 Cyclic characterisation ...................................................................................................... 49
4.1.2 Sample Fabrication............................................................................................................ 51
4.1.3 Determination of Glass transition temperature ............................................................... 52
4.1.4 Extension versus temperature (zero load) ........................................................................ 52
4.1.5 Tensile Testing................................................................................................................... 52
Chapter 5 ............................................................................................................................................... 53
5.1 Results ....................................................................................................................................... 53
5.1.1 Glass transition temperature ............................................................................................ 53
5.1.2 Stress versus Strain ........................................................................................................... 55
5.1.3 Thermal Strain measurement ........................................................................................... 57
Chapter 6 ............................................................................................................................................... 58
6.1 Model calibration ...................................................................................................................... 58
6.1.1 Determination of Constitutive parameters ...................................................................... 58
6.2 Model Implementation ............................................................................................................ 64
6.2.1 Stretch controlled process ................................................................................................ 64
Chapter 7 ............................................................................................................................................... 66
7.1 Validation and Discussion ......................................................................................................... 66
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7.1.1 Influence of modelling on material behaviour ................................................................. 66
7.1.2 Polyurethane analysis ....................................................................................................... 68
7.1.2.1 Material relation to modelling ...................................................................................... 68
7.1.2.2 Chemical structure dependance on perfomance ......................................................... 71
7.1.3 Recommendations ............................................................................................................ 73
Chapter 8 ............................................................................................................................................... 74
8.0 Conclusion ................................................................................................................................. 74
VIII) References ................................................................................................................................ 75
IX) Index .......................................................................................................................................... 79
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CHAPTER 1
1.0 INTRODUCTION
In the modern day of aviation many technological advances have been made in order to increase the
efficiency of aircraft for various flight requirements. One of the factors widely recognized as
influencing the performance of an aircraft are the materials of the mechanisms used for actuation of
aircraft control surfaces. Control surfaces (figure 1) play a vital role as they determine primary and
secondary control of an aircraft and determine most of the aerodynamic characteristics of the
aircraft.
However, hydraulic actuation mechanisms contribute greatly to the weight of an aircraft and this
problem could be improved with the use of a system involving lighter, more responsive materials.
Such materials could lead to a smoother wing and hence more aerodynamically desirable aircraft.
These materials would be of the type which can retain a shape upon temperature modification and
are referred to as shape-memory materials.
FIGURE 1 AIRCRAFT CONTROL SURFACES
The task was then set of designing and testing some sort of synthetic muscle system that may be
applicable to any type of airborne system, beginning with low speed aircraft. Shape memory
material actuation on an airborne system has been attempted before however in this case a
somewhat novel application was proposed. Previous applications have been to actuate the trailing
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edge section of the wing therefore becoming the flap however in this case, a morphing wing design
was attempted.
FIGURE 2 AIRCRAFT WING INTERNAL STRUCTURE COURTESY OF NOMENCLATURO.COM
1.1 MORPHING AIRFOIL APPROACH
FIGURE 3 BASIC IDEA BEHIND MORPHING WINGS COURTESY OF BAIER AND DATASHVILI (2011)
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In order to achieve the morphing airfoil, the shape changing structure would be integrated into the
primary structure of the wing namely ribs and stringers. Figure 2 displays the internal wing structure
for a typical low speed aircraft. Many authors have achieved shape memory actuation of the wing
flap alone. For example, Kang, Kim, Jeong and Lee (2012) achieved a morphing wing mechanism
using an SMA wire actuator and achieved smooth actuation without extension of the wing skin.
Aircraft flap systems consists of discontinuous sections which can possibly cause aerodynamic losses
therefore morphing sections reduce these losses and contribute to aircraft efficiency. It is important
to note that various other setups have been attempted as well.
FIGURE 4 PNEUMATIC RUBBER MUSCLE ACTUATOR (PEEL, MEJIA, NARVAEZ, THOMPSON AND LINGALA
(2009))
Peel, Mejia, Narvaez, Thompson and Lingala (2009) achieved a morphing wing concept by using a
composite skin and pneumatic rubber muscle actuator. James, Menner Bismarck and Iannucci (2009)
proposed a morphing skin as well by using a shape memory polymer as the wing skin. Baier and
Datashvili (2011) provided a cross linking between structures and mechanisms in morphing
aerospace structures in their review paper.
Kang, Kim, Jeong and Lee (2012) are referred to in this last mentioned paper and comment about
how in general, a morphing wing requires a change in length of the wing skin and this requires the
skin to be flexible. At the same time the skin must possess enough stiffness to resist external
aerodynamic pressure. These contradictory characteristics thus prove as a setback in morphing wing
design, which has sparked the need for a novel design. It was also noted that all the previous
research did not include any mechanism of leading edge actuation, this shall also be investigated in
this paper, however as a secondary function.
FIGURE 5 VARIOUS MORPHING WING MECHANISMS. MORPHING WING SKIN MECHANISM(LEFT) AND FLAP
ACTIVATED BY SHAPE MEMORY ALLOY WIRE BY KANG, KIM, JEONG AND LEE (2012) (RIGHT)
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1.1.1. MORPHING WING SKINS
Baier and Datashvili (2011) mention the skins for morphing wings can be a challenging design
element due to the fact that they have to be deformable but at the same time have to take and
transfer high aerodynamic loads. Thill, Etches, Bond, Potter and Weaver (2008) extensively reviewed
concepts of morphing skins such as properly tailored laminates or structural non-isotropy achieved
by corrugation as shown in figure 6. A sandwich morphing skin consists of flexible elastomers as
cover and different types of cores including auxetic materials. This is beneficial in providing relatively
low in-plane stiffness of the skin combined with sufficiently high bending stiffness. It should be
noted that a morphing skin is a mammoth subject on its own and hence it shall be theoretically
assumed that a morphing wing skin is part of the design.
FIGURE 6 DIFFERENT MORPHING SKIN CONCEPTS A) SANDWICH CONCEPT WITH ELASTOMER COVER AND
AUXETIC MATERIAL CORE (BAIER AND DATASHVILI (2011))
1.2.1 COMPLIANT WING SYSTEM
One of the most recent and most successful applications of the morphing wing mechanism has been
achieved by Flexsys.Inc. They have developed the world’s first functional, seamless and hinge-free
wing whose trailing and/or leading edges morph to adapt to different flight conditions. In the
publication by Kota, Hetrick, Osborn, Paul, Pendleton, Flick and Tilman (2006) they refer to the term
a “compliant mechanism’’ which can be defined as a class of mechanism that relies on elastic
deformation of its constituent elements to transmit motion and/or force.
This is a particularly useful mechanism for any morphing wing mechanism as it eliminates the
application of any standard wing internal structure. The primary challenge in a morphing system is to
develop an efficient structure that can distribute local actuation power to the surface of the airfoil to
produce a specified shape change. A compliant mechanism provides a solution to this challenge but
it should be noted that in this case only the leading and trailing edges are able to be modified as
shown by figure 7.
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FIGURE 7 LEADING AND TRAILING EDGE MECHANISMS DEVELOPED FOR THE F-111 MISSION ADAPTIVE WING
PROGRAM (KOTA, HETRICK, OSBORN, PAUL, PENDLETON, FLICK AND TILMAN (2006))
1.2 POSSIBLE WING DESIGNS
It should be noted that the goal was to produce a morphing wing for low altitude, low endurance
and low mach number for application in an unmanned aerial vehicle (UAV).
1.2.1. POSSIBLE SOLUTION 1
FIGURE 8 POSSIBLE SOLUTION 1
A novel design suggested is that shown in the figure below which consists of placing the selected
shape memory material in block fashion around the entirety of the wing rib. The material is thus
lodged between the rib and the wing skin and when the system has been activated, the blocks would
change shape so as to initiate morphing in the material. Another design requirement was to create a
compliant wing to fit within the same space constraints while minimizing the weight and power
requirements.
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Benefits Setbacks
Shape can be changed on any point on the wing circumferential length
Material needs to absorb flight vibrations
Material blocks can be easily replaced Blocks need to be very stable during morphing phase
Limitless design capabilities and application Method of fixing blocks to the internal structure will need to be determined
TABLE 1 POSSIBLE BENEFITS AND SETBACKS OF DESIGN 1
1.2.2. POSSIBLE SOLUTION 2
Another design which incorporates all the requirements is similar to the one has the benefits of a
wing that can be deflected differentially along the span in order vary the deflection and optimize
wing loading. This design has the benefit that the material subparts can be designed to only have
slight differences thus making manufacturing easier. However there is a possibility that the
stabilizing rod could interfere with the mechanical strength of the material.
FIGURE 9 POSSIBLE MORPHING WING DESIGN
Stabilizing rod/spar
SMP
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CHAPTER 2
LITERATURE SURVEY
2.1 FUNDAMENTALS OF SHAPE MEMORY MATERIALS
2.1.1 SHAPE MEMORY ALLOYS
Liu, Quinn and Mather (2007) define a shape memory material as
‘’those materials that have the ability to memorize a macroscopic permanent shape, be manipulated
and fixed to a dormant and temporary shape under specific conditions of temperature or stress, and
then later relax to the original, stress free condition under thermal, electrical or environmental
command.’’
The aforementioned relaxation is associated with an elastic deformation stored within the material
prior to deformation.
The most prominent and widely used shape memory materials are shape memory alloys as Liu,
Quinn and Mather (2007) continue to explain how their shape memory behavior stems from the
existence of two stable crystal structures in the material. SMAs consist of a high temperature
favored austenitic phase and a low temperature favored martensitic phase. Deformations that occur
during the low temperature phase, occurring above a critical stress, are then completely recovered
during the solid-solid transformation to the high temperature austenitic phase.
SMAs come in various combinations but the most common is the Nickel-titanium alloy due to the
combination it possesses of
1. a desirable transition temperature close to body temperature,
2. superelasticity and
3. two way shape memory capability.
Despite these benefits there are also downfalls to SMAs which come in the form of
a) limited recoverable strains of less than 8%,
b) inherently high stiffness,
c) high cost,
d) a comparatively inflexible transition temperature and
e) demanding processing and training conditions.
These limitations encouraged consideration for alternative polymeric shape memory materials. In
general, Liu, Quinn and Mather (2007) state that SMAs achieve pseudo-plastic fixing through
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martensitic de-twinning mechanism, with recovery being triggered by the martenite-austenite phase
transition. This implies that fixing of a temporary shape is accomplished at a single temperature and
recovery occurs upon heating beyond the martensitic transformation temperature.
2.1.2 SHAPE MEMORY POLYMERS
Liu, Quinn and Mather (2007) differentiate these from SMAs in that shape memory polymers
achieve their strain fixing and recovery through a plethora of physical means.
TABLE 2 (LIU, QUINN AND MATHER (2007))
Hu, Zhu, Huang and Lu (2012) refer to how with the rapid development and improvement of SMPs,
the features have become more and more prominent in comparison with SMAs. The advantages of
SMPs are as follows.
1. They can use diverse external stimuli and triggers as compared to SMAs which are only heat
triggered. Diverse stimulation can also result in multi-sensitive materials
2. Highly flexible programming through either single or multi-step processes
3. Broad range of structural designs. Various approaches are possible for designing net points
and switches for the various types of SMPs.
4. They possess tunable properties. SMP properties can be easily and accurately tuned using
composites, blending and synthesis
5. They can be modified to occupy a large space with a small volume in the form of foams. Such
applications have been observed in aerospace configurations and airplane components
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2.2 GENERAL FRAMEWORK OF SMPS
FIGURE 10 THE OVERALL ARCHITECTURE OF SMPS (HU AND CHEN (2010))
Hu and Chen (2010) mention that at the molecular level, shape memory polymers and shape
changing polymers consist of switches and net points as shown by the figure above. Net points
determine the permanent shape of the polymer network and can be of a chemical or physical nature
comprising covalent or non-covalent bonds respectively. The physical cross linking is formed through
the crystals, amorphous hard domains or other forms of entangled chains which will be discussed in
the next section. Switches are the major constituents which are responsible for strain fixation and
partial strain recovery. The switches can either be any of the following
1. the amorphous phase with a low glass transition temperature ( ),
2. semi-crystalline phase with a low melting temperature ( ) or
3. liquid crystalline (LC) phase with a low isotropization temperature ( )
Noted by Hu and Chen (2010), so far the amorphous phase, semi-crystalline phase and
supramolecular entities are used in shape memory polymer (SMP) construction while shape
changing polymers (SCPs) are observed in the liquid crystalline elastomers (LCEs) and cross-linked
polymers with stress-induced crystallization.
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In order for shape memory functionality to be achieved, the polymer network of SMPs must be
temporarily fixed in a deformed state under environmental conditions. Reversible molecular
switches can prevent recoiling of deformed chain segment when the switch is ‘’idle’’ possibly from
re-crystallization of a semi-crystalline soft phase. Under an environmental trigger such as heat or
light, the original shape can be recovered from the deformed shape due to the crystal melting of the
soft phase. However in SCPs the geometry is distinctly mentioned as being governed by the original
three dimensional shape.
For SCPs, the process of deformation and recovery can be repeated several times however shape
geometry change is not possible. This can be explained with the example of LCEs which change their
shape when the temperature is raised above as a result of phase transition from LC phase to
isotropic phase. When the temperature is cooled down the material returns to its original shape by
sampling returning to the LC phase.
In the amorphous state, polymer chains will take up a completely random distribution in the matrix,
with no restriction given by the order of crystallites in semi-crystalline polymers. All possible
conformations of a polymer chain have the same internal energy. Let W represent the probability of
a conformation, which is the state of maximum entropy, represents the most probable state for an
amorphous linear polymer chain according to the Boltzmann equation as follows
EQUATION 1
Where S=entropy, k=Boltzmann constant
2.2.1. THERMODYNAMIC BEHAVIOUR
Lendlein and Kelch (2002) introduce methods for the quantification of shape-memory properties as
well as the corresponding physical quantities based on a description of the macroscopic shape
memory effect. In the glassy state, all movements of the polymer sections are frozen. The transition
from this state to the rubbery elastic state occurs when the thermal activation is increased; meaning
the rotation around the segment bonds becomes increasingly unimpeded. This enables the chains to
take up one of the possible, energetically equivalent conformations without disentangling
significantly.
In the elastic state, a polymer with sufficient molecular weight stretches in the direction of an
applied force and if this tensile stress is applied for a short time interval, entanglements of the
polymer chains with their direct neighbors will prevent a large movement of the chain. If the tensile
stress is applied for an extended period of time, a relaxations process results which is a plastic,
irreversible deformation due to slipping and disentangling of the polymer chains from each other.
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2.2.2. ENTROPY ELASTICITY
The aforementioned slipping or flow of the polymer chains under strains can be stopped almost
completely by cross-linking of the chains as discussed by Lendlein and Kelch (2002). It is described
that the cross-linkage points act as permanent entanglements which prevent the chains from
slipping from each other. The cross links are discussed in more detail in the next section.
Apart from the net points, polymer networks contain amorphous chain segments which are also
flexible components. If the of these segments is below working temperature, the networks will
prove to be elastic, showing entropy elasticity with a loss of entropy. Distance between these
netpoints increases during stretching and they will become oriented thus as soon as the external
force is released, the material returns to its original shape and gains back the previously lost
entropy. Therefore the polymer network maintains mechanical stress in equilibrium.
2.3. STRUCTURE AND MECHANISM OF SMPS
2.3.1. COVALENTLY CROSS-LINKED GLASSY THERMOSET NETWORKS
Liu, Quinn and Mather (2007) refer to this as the simplest type of SMP consisting of a sharp glass
temperature ( ) at the temperature of interest and rubbery elasticity above derived from
covalent crosslinks. Attractive characteristics of this class of materials includes the following
a) Excellent degree of shape recovery due to the rubbery elasticity caused by the occurrence of
permanent cross-linking
b) Tunable work capacity during recovery garnered by a rubbery modulus that can be adjusted
through the extent of covalent cross-linking and
c) An absence of molecular slippage between chains due to the chemical cross linking.
A downside this type of network is that since the primary shape is covalently fixed these materials
are difficult to reshape after casting or molding. An example of this type is chemically cross-linked
vinylidene random copolymer which consists of two vinilydene monomers namely methyl
methacrylate and butyl methacrylate. The homopolymers show two different values of 110˚C and
20˚C which gives the random copolymer a sharp tunable between the two values of the
homopolymers by varying the composition. The work capacity is adjustable by varying the extent of
cross-linking achieved by copolymerization with tetraethylene glycol dimethacrylate. The resultant
performance of the thermoset is complete shape fixing, fast shape recovery at the stress free stage
and is also castable and optically transparent.
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FIGURE 11 STRAIN RECOVERY OF A CROSS-LINKED, CASTABLE SHAPE MEMORY POLYMER UPON RAPID
EXPOSURE TO A WATER BATH AT T=80˚C (LIU, QUINN AND MATHER (2007))
Liu, Quinn and Mather (2007) also include under this category polymers with above room
temperature with ultra-high molecular weight above g/mol due to their lack of flow above
and good shape fixing by vitrification. These polymers are mentioned to possess above 25
entanglements per chain and these entanglements function as physical cross-links on the time scale
of typical deformations which is mentioned to range from 1 to 10 seconds. The physical cross-linking
results in a three dimensional network which gives excellent elasticity above although a downside
is difficult thermal processing which may require solvent-processing. Such characteristics induce
performance results of the just recently discussed polymer type hence their inclusion in this group.
An example is polynorbornene (PN) with and high molecular weight. In this case the
decrease of mobility of PN molecules at temperatures below maintains the secondary shape.
Shape recovery to the original shape is then achieved by heating above the releasing the stored
energy. Performance characteristics were complete shape fixing when vitrified, fast and complete
shape recovery due to the sharp and high entanglement density that forms a three dimensional
network. Disadvantages of such materials were found to be as follows
1. Transition temperature cannot be easily varied
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2. The modulus plateau, responsible for controlling energy stored during deformation, is low
and hard to modify
3. Creep will occur to the polymer under stress at high temperatures due to the finite lifetime
of entanglements
4. Difficulty of processing due to high viscosity associated with high molecular weight polymers
TABLE 3 SHAPE MEMORY THERMOSETS (LIU, QUINN AND MATHER (2007))
2.3.2. COVALENTLY CROSS-LINKED SEMI-CRYSTALLINE NETWORKS
The melting transition of semi-crystalline networks can also be employed to induce a shape recovery
and Liu, Quinn and Mather (2007) mention that it induces a sharper recovery event. In this case the
secondary shape is fixed by crystallization rather than vitrification. The permanent shapes are also in
this case established by chemical cross linking with no reshaping possible after processing.
This class generally proves to be more compliant below the critical temperature and its stiffness is
sensitive to the degree of crystallinity and therefore indirectly to the degree of cross-linking. Shape
recovery speed were also noticed to be faster for the first order transition, usually also with a
sharper transition zone. This class includes the following materials
a) Bulk polymers such as semi-crystalline rubbers and Liquid Crystal Elastomers (LCEs)
b) Hydrogels with phase separated crystalline microdomains
Semi-crystalline rubbers have been considered for shape memory application due to their super
elastic rheological characteristics, fast shape recovery and flexible modulus at the fixed stage. Liu,
Quinn and Mather (2007) successfully developed a chemically cross-linked, semi-crystalline trans-
polyoctenamer (polyoctene, PCO) possessing a trans content of 80%, of -70˚C, of 58˚C and
much better thermal stability for shape memory application. When a strained sample was cooled
below , crystalline domains began to form and ultimately percolated the sample, establishing
strain fixing. When the material was heated above , the crystals melted to an amorphous,
homogenous phase with high mobility, leaving the chemical cross-links to re-establish the primary
shape. PCO has elasticity similar to rubber at temperatures above with easy deformation possible
by an external shape to create a secondary shape. The secondary shape, fixed by crystallization
during the subsequent cooling process, does not change below and as long as the crystals were
not destroyed though was possibly subject to warping.
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TABLE 4 POLYMER SPECIAL FEATURES (LIU, QUINN AND MATHER (2007))
FIGURE 12 SCHEMATIC DEPICTION OF SHAPE FIXING AND RECOVERY MECHANISMS OF SEMI-CRYSTALLINE
RUBBERS. A) CROSS LINKED SHAPE AT SEMI-CRYSTALLINE STAGE, B) MELTED SAMPLE OF STRESS FREE STAGE
(HIGH TEMPERATURE), C) DEFORMED SHAPE AT MELT STAGE (HIGH TEMPERATURE) AND ; CRYSTAL FROZEN
DEFORMED SHAPE (LOW TEMPERATURE) (LU, CHUN, MATHER, ZHEN, HALEY AND COUGHLIN (2002))
Figure 12 displays the discussed shape memory mechanism as it was investigated by Lu, Chun,
Mather, Zhen, Haley and Coughlin (2002). The room temperature stiffness, transition temperatures
and rubbery modulus proved to be able to be tuned independently by blending with rubbery or solid
components which manipulates the tacticity of PCO. Cross linking a semi crystalline material
impedes crystal formation which might cause a lesser degree of crystallinity, broader crystal size
distribution and a lower and broader melting transition temperature span hence slower shape
memory recovery.
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Chernous, Shil’ko and Pleskachevskii (2004) attempted to specifically crosslink the amorphous
fraction but not the crystalline fraction so as to avoid a drop in transition temperature due to cross-
linking. Successful implementation was achieved for a blend composition composed of a semi-
crystalline polymer acting as the reversible phase and a specially functionalized, co-continuous
rubber matrix as the permanent phase. They applied special curing techniques to the rubber matrix
but left the semi-crystalline phase unaffected. Another group applicable are Liquid Crystalline
Elastomers (LCEs) which are discussed later.
2.3.3. PHYSICALLY CROSS-LINKED GLASSY COPOLYMERS
This group is mentioned to solve the issue of ease of processing of shape memory polymers by Liu,
Quinn and Mather (2007) as these polymers display rheological characteristics compliant to
simplistic processing with conventional thermoplastics technology. Here crystalline or rigid
amorphous domains in thermoplastics are able to serve as physical crosslinks affording the super -
elasticity required for shape memory to be developed, which is mainly in the form of phase
separated block copolymers.
It is described that when the temperature exceeds the or of these physical domains,
described as , the material will flow and therefore can be processed and manipulated
physically. Another continuous phase possessing a lower or , which can be represented as
, exists which softens to a rubbery state in the range between the two critical temperatures and
fixes a secondary shape on cooling to a temperature below .
Jeong, Song, Lee and Kim (2001) recognized how for some block copolymers and polyurethanes, the
soft domain displayed a sharp glass-transition which could be tuned for shape memory applications.
Despite this groups’ room temperature stiffness being similar to covalently cross-linked glassy
thermosets, their being only physically cross-linked yields the benefit of being processable above
of the hard domains. An example of this type is one which was investigated by Jeon, Mather
and Haddad (2001) of norbonene copolymerised with a polyhedral oligosilsesquioxane (norbonyl-
POSS) hybrid monomer. This yielded a microphase separated copolymer with fewer repeating units
in the backbone than commercial polynorbonene. The composition improved the thermal
processability and suppressed high temperature yielding of polynorbonene homopolymer, also
enhancing the critical temperature and stored energy during deformation (rubbery modulus). Also
reported results were the broadening of the , which to a certain extent retarded the shape
recovery speed.
Liu, Quinn and Mather (2007) also include in this class some low crystallinity, semi-crystalline
homopolymers, or melt-miscible polymer blends compatible in molten and amorphous states, but
having at least one semi-crystalline component. Liu and Mather (2003) reported that in such a
system, the crystals serve as physical cross-links, or rather hard domains, and the composition
dependent of the amorphous region functions as the transition temperature. For these it was
noted that easy tuning of the glass-transition temperature of the amorphous phase and the work
output during shape recovery was possible by changing the blend composition, akin to the
copolymer thermosets mentioned in the first group discussed.
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Apart from the crystalline and glassy domains, other physical cross-linking techniques include
hydrogen bonding or ionic clusters within the hard domains investigated by Li, Chen, Zhu, Zhang and
Xu (1998) and Kim, Lee, J. S. Lee, Baek, Choi, J. O. Lee and M. Xu (1998) respectively. Existence of
these interactions is said to strengthen the hard domains by decreasing chain slippage during
deformation which therefore increases the extent of shape recovery.
TABLE 5 SUMMARY OF PHYSICALLY CROSS LINKED COPOLYMER BLENDS (LIU, QUINN AND MATHER (2007))
Liu, Quinn and Mather (2007) recognise the diversity in selection of soft domains as examples are
displayed in the table above and conclude that hydrophilic oligomers can be used to create
multiblock copolymers with shape memory properties. These add the benefit of moisture-triggered
shape memory recovery apart from heat stimulation. However slow recovery was reported by
Huang, Yang, An, Li and Chan (2005) due to the relatively slow speed of water diffusion.
2.3.4. PHYSICALLY CROSS-LINKED SEMI-CRYSTALLINE BLOCK COPOLYMERS
It is mentioned by Liu, Quinn and Mather (2007) that for some block copolymers, the soft domain
will crystallize and rather than the , the values will function as shape memory transition
temperatures therefore the secondary shapes are fixed by crystallization of the soft domains. An
example is styrene-trans-butadiene-styrene (STBS) triblock copolymers which feature shape memory
behavior afforded by this mechanism investigated by Ikematsu, Kishimoto and Karaushi (1990).
STBS is referred to as a strongly segregated ABA-type triblock copolymer with a minor component of
polystyrene (PS) segments, ca 10-30 volume percent, serving as A domains at each end of the
macromolecular chains, and a major component of semi-crystalline poly trans-butadiene (TPB)
segments as B-domains in the middle block. As a result of the immiscibility between TPB and PS
blocks, the copolymer phase separates and PS blocks form discontinuous, amorphous micro-
domains having =93˚C. TPB blocks will form a semi-crystalline matrix having a of 68˚C with a
of 90˚C. The rigid PS microdomains are mentioned to remain rigid up to 90˚C which enables them to
serve as physical cross-links whose configuration set the permanent shape when a temperature of
68˚C<T<90˚C was applied, the material became flexible and rubbery due to the melting point of the
TPB crystals but the material will not flow due to the rigid PS microdomains which maintains a
stress-free permanent shape. At his stage the material had a storage modulus similar to rubber
which was dictated by the TPB molecular weight. When cooled below 40˚C, the TPB matrix
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crystallised so that a secondary shape can be fixed by those crystals while energy exerted during
deformation is more or less frozen into the material. Melting of TPB will enable returning to the
original shape via reheating.
Benefits if this polymer are possessing a permanent that can be reprocessed above 100˚C when both
domains flow and is disadvantageous due to the fact that the hard microdomains may creep under
stress when setting the temporary shape near a which limits the extent of recoverable strain.
TABLE 6 SUMMARY OF PHYSICALLY CROSS-LINKED SEMI-CRYSTALLINE COPOLYMER BLENDS (LIU, QUINN AND
MATHER (2007))
Thermoplastic segmented polyurethanes with semi-crystalline flexible segments have also been
investigated as a similar approach. Liu, Quinn and Mather (2007) describe polyurethanes as
conventionally being multiblock copolymers consisting of alternating sequences of hard and soft
segments. Hard segments form the physical cross-links via polar interaction, hydrogen bonding, or
crystallization and these crosslinks are able to resist moderately high temparatures without being
destroyed (≈110˚C). The soft segments capable of crystallization form the thermally reversible phase
with crystallization of the soft segments governing the secondary shape. With regards to the ,
Chun, Cho and Chung (2006) mention that the hard segment generally has much higher than
room temperature while the soft segment has lower than room temperature and endows the
SMP with properties such as high draw ratio, low modulus and high elastic recovery. Polyurethanes
possess the following benefits
1. Easily tunable room temperature stiffness, transition temperature and room temperature
stiffness by manipulating their compositions
2. Biodegradeability for some
3. Can easily be foamed as the foam memory materials CHEM by Sokolowski, Chmielewski,
Hayashi and Yamada (1999)
FIGURE 13 PU WITH MICRO-PHASE SEPARATION STRUCTURE (CHUN, CHO AND CHUNG (2006))
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FIGURE 14 FOUR TYPES OF SHAPE MEMORY POLYMERS WITH DIFFERENT SHAPE FIXING AND SHAPE RECOVERY
MECHANISMS DEPICTED AS A FUNCTION OF THEIR DYNAMIC MECHANICAL BEHAVIOUR. TENSILE STORAGE
MODULUS VERSUS TEMPERATURE AS MEASURED USING A SMALL OSCILLATORY DEFORMATION AT 1HZ FOR I)
CHEMICALLY CROSS LINKED GLASSY THERMOSETS, II) CHEMICALLY CROSS LINKED SEMI-CRYSTALLINE
RUBBERS, III) PHYSICALLY CROSS LINKED THERMOPLASTICS AND IV) PHYSICALLY CROSS LINKED BLOCK
COPOLYMERS (LIU, QUINN AND MATHER (2007))
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2.4 ELECTRO-ACTIVE POLYMERS
For certain applications such as aerospace and automotive, it is not possible to create an external
environment so as to enforce shape memory behavior such as heat, light, pH or water. Liu, Lv, Lan,
Leng and Du (2008) mention how the need to get rid of external heating has led to the application of
electro-conductive fillers in SMPs. This application proves particularly useful with respect to the
desired performance requirements for the morphing wing system
2.4.1 SMP FILLED WITH CARBON NANOTUBES
Cho, Kim, Jung and Goo (2005) investigated shape recovery of Polyurethane (PU) composites by
applying a voltage and not thermal heating. This is a key factor in this study as this would enable the
application of SMPs as smart actuators. In order for electro active shape memory behavior to be
established, multi-walled carbon nanotubes (MWCNTs) were used after being chemically surface
modified in a nitric acid and sulphuric acid mixture. Surface modification was applied in order to
improve the interfacial bonding between polymers and nanotubes as previously investigated.
PU containing 40% hard segments were synthesized by a pre-polymerisation method using
monitored portions of polycaprolactenediol (PCL) as the soft segment and 4-4’-methylene bis
(phenylisocyanate) (MDI) and butane-1,4-diol acting as the hard segments. Composite films were
produced when mixed with the MWCNTs and the electrical conductivity was measured using the
four point probe method, which was in the order of S cm for 5% MWCNT modified content,
which was sufficient to heat the material above 35˚C which is the transition temperature of
polyurethane. In the tensile test, it was noticed that modulus and strength at 100% elongation
increased with increasing surface modified MWCNT content, with elongation at break decreasing as
shown by the figure below.
FIGURE 15 A) MODULUS AND B) STRESS AT 100% ELONGATION OF COMPOSITES AS A FUNCTION OF
PERCENTAGE MWCNT CONTENT (OPEN SQUARE : RAW, OPEN CIRCLE: 90˚C ACID TREATMENT, FILLED CIRCLE:
140˚C ACID TREATMENT) (CHO, KIM, JUNG AND GOO (2005))
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Electrical conductivity was found to increase as the amount of MWCNT content increased, with
surface modification displaying significant results. In the area of surface modification, electrical
conductivity of surface modified MWCNT was lower than that in untreated MWCNT of the same
filler content and Cho, Kim, Jung and Goo (2005) attribute this to the increased defects in the lattice
structure of carbon-carbon bonds formed on the nanotube surface due to the acid treatment. It was
also noticed that severe surface modification lowers mechanical and conductive properties while
modification of nanotubes at optimum conditions could increase the mechanical properties of shape
memory composites. Therefore both mechanical and conducting properties were dependent on the
degree of surface modification of the MWCNTs, with an acid treatment of 90˚C giving desirable
properties for shape memory.
FIGURE 16 ELECTRO-ACTIVE SHAPE-RECOVERY BEHAVIOUR OF PU-MWCNT COMPOSITES AT 5% CONTENT. THE
SAMPLE UNDERGOES TRANSITION FROM TEMPORARY SHAPE (LINEAR LEFT), TO PERMANENT (HELIX, RIGHT)
WITHIN 10S WHEN A VOLTAGE OF 40V IS APPLIED. (CHO, KIM, JUNG AND GOO (2005))
The temperature of the sample was measured using digital multi-meters (M-4660, DM-7241 and
ME-TEX) with a non-contact temperature measuring system. With 60V applied voltage the sample
heated above 35˚C in 8seconds although it was impossible to heat the sample to a temperature
above its transition with less than 40V. Composites with surface modified MWCNTs could show
electro-activated shape memory recovery with an energy efficiency of 10.4% with improved
mechanical properties.
2.4.2 SMP FILLED WITH CARBON BLACK
Rogers and Khan (2012) prepared an electrically conducted SMP through impregnating the resin
conductive carbon black using two dispersion techniques. All filled samples used in this study were
loaded to 10% mass by directly mixing the Carbon Black (CB) into the resin before processing. Higher
mixing percentages were not considered due to increasing difficulty of mixing CB into the resin.
Before curing, copper electrodes were placed in the slurry in order to allow for testing as shown by
the image below. Electrical conductivity tests revealed that high resistivity values of the 2.5% and 5%
systems prevented the attainment of the triggering temperature with the triggering temperature
being easily achieved at 10% content.
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FIGURE 17 CASTING MOLD AND MACHINED SAMPLE WITH IMBEDDED ELECTRODES. GLASS TAPE WAS USED AT
EACH END FOR SECURING IN TENSILE TESTING FRAME. (ROGERS AND KHAN (2012))
The stress-strain temperature curve resulting from a tensile test carried out at room temperature is
shown below. The addition of CB was found to decrease the ultimate tensile strength and
percentage elongation compared to the base resin. Loading curves also indicated little to no changes
in the structure of the polymer when repeated loading was applied. The graphs below also display
the decrease in strength with the temperature just above versus room temperature conditions.
a)
)
b)
)
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FIGURE 18 RESULTS FOR CARBON BLACK FILLED POLYMER (ROGERS AND KHAN (2012))
The use of a filler can adversely affect the properties of the base matrix depending upon factors such
a quality of dispersion, filler-chain interaction and filler surface coatings to mention a few. The figure
above also displays a comparison of the stress-strain behavior of filled and unfilled SMP in which an
increase in flow stress due to the addition of CB is noticeable. Hence a surfactant was also added to
a sample and a comparison of it is displayed below and effect was found to be minimal. There was
little to distinguish the mechanical properties of CB black and surfactant covered CB with higher
electrical resistivity being achieved by the latter.
Deformation based changes in conductivity were linked to reaggregation and/or transformation of
the aggregates. The increase in resistivity of the surfactant covered CB is actually a more
homogenous CB distribution resulting uniform interparticulate and aggregate spacing. The
conductive networks formed in the CB samples provided more efficient pathways for the current. At
small strains, the chain deformation mechanisms such as stretching results in degradation of the
existing pathways thereby increasing resistivity with increasing strain. However, as strain increases,
large segmental motion of the chains results in axial alignment or deformation induced
crystallization. More robust pathways are formed with these effect being more pronounced in
surfactant-covered CB samples where agglomerates are more finer and mobile. It should be noted
however, that in this study, only 30% strain was achievable due to fracture beyond this limit.
a) b)
c)
)
d)
)
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FIGURE 19 (ROGERS AND KHAN (2012))
Lan, Leng, Liu and Du (2008) investigated a similar blend styrene-based resin and analyzed the
thermomechanical properties using differential scanning calorimetry (DSC). DSC results revealed that
decreases slightly with an increase in CB volume fraction, indicating a slight interaction between
the CB powders and SMP. Electrical resistivity tests revealed similar results to the previous case as
well as temperature vs resistivity results. The percolation threshold was found to be 3% which is
lower than many other polymer-based conductive composites.
FIGURE 20 DSC RESULTS OF CB AT VARIOUS COMPOSITIONS (LAN, LENG, LIU AND DU (2008))
Shape recovery was achieved by applying a voltage of 30V. It took a total of 90 seconds for full shape
memory recovery to take place as shown by the image below.
FIGURE 21 SEQUENCES OF SHAPE RECOVERY OF CB 10% BY PASSING AS ELECTRICAL CURRENT OF 30V
(ROGERS AND KHAN (2012))
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2.4.3 SMP FILLED WITH NICKEL
Leng, Huang, Lan, Liu and Du (2008) achieved significant reduction in the electrical resistivity of PU
filled with randomly distributed CB by adding a small amount of randomly distributed Ni
microparticles (0.5 vol. %). Ni chains, formed in a weak magnetic field before curing, served as
conductive channels to bridge CB aggregations so as to significantly reduce the electrical
conductivity. Other properties were reported to remain relatively the same.
FIGURE 22 MAGNETIC FIELD CURING (LENG, HUANG, LAN, LIU AND DU (2008))
Figure 23 displays the relationship of CB versus electrical resistivity of both SMP/CB/Ni chained and
randomly distributed. The resistivity was also measured one month later and is about the same as
before, which shows that the resistivity of the samples was stable. In order to demonstrate shape
recovery, 30V was applied through Joule heating to the samples, all at 10% CB, and samples were
heated to 80 C. Twenty shape recovery cycles at 20% deformation were also done in order to study
evolution of resistivity and it was discovered that the conductive paths in the Ni chain/CB may be
degraded upon thermomechanical cycling.
FIGURE 23 RESISTIVITY VS VOLUME FRACTION OF CB WITH/WITHOUT 0.5 VOL % NI. RED SYMBOL, RIGHT
AFTER FABRICATION; BLUE SYMBOL, ONE MONTH LATER. INSET DISPLAYS HOW RESISTANCE WAS MEASURED.
(LENG, HUANG, LAN, LIU AND DU (2008))
Design, Modelling and Testing of a synthetic muscle system
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FIGURE 24 EVOLUTION OF RESISTIVITY UPON SHAPE MEMORY CYCLING (LENG, HUANG, LAN, LIU AND DU
(2008))
Leng, Huang, Lan, Liu, Du, Phee and Yuan (2008) conducted further experiments on this same setup
using only Ni powder and upon determination of noticed that the it shifted a little bit toward the
low temperature range, which indicated the slight chemical interaction between Ni powders and
SMP. Around 10% volume fraction it was found that the composite was significantly strengthened
and the storage modulus was higher for chained samples.
FIGURE 25 STORAGE NODULUS VERSUS VOLUME FRACTION OF NI AT 0 DEGREES (LENG, HUANG, LAN, LIU,
DU, PHEE AND YUAN (2008))
Design, Modelling and Testing of a synthetic muscle system
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2.4.4 SMP FILLED WITH HYBRID FILLERS
Lu, Yu, Liu and Leng (2010) integrated hybrid fillers in the form of a carbon black and short carbon
fiber combination into a styrene-based SMP with sensing actuating capabilities. The results showed a
decrease in resistance with an increase in fiber fraction. Also the fibrous fillers enhanced the
mechanical properties of the SCF-SMP composites more significantly than the particulate fillers
FIGURE 26 LEFT: VALUES OF RESTISTANCE VS TEMPERATURE; RIGHT: VALUES OF RESTANCE VERSUS STRAIN
FOR SCF-SMP COMPOSITE (LU, YU, LIU AND LENG (2010))
The increase in conductivity was attributed to the numerous interconnections between the SCF
fibers and the CB/SMP composite. As figure 27 shows, the particles distributed uniformly into the
SMP matrix, aggregating as clusters instead of absolutely separating from each other. This way, the
CB fibers will act as nodes among the fibers, with local conductive pathways also formed in the
composite. This improves orientation of the short fibers because of the large amount of conductive
channels formed in the composite, which makes resistivity low and stable.
FIGURE 27 MORPHOLOGIES OF SCF-SMP COMPOSITE SPECIM OBSERVED BY SEM (2% SCF AND 5% CB) A)
MORPHOLOGIES OF SCF FILLERS AND B) MORPHOLOGIES OF CB PARTICLES (LU, YU, LIU AND LENG (2010))
Lu, Yu, Sun, Liu and Leng (2010) also investigated the mechanical properties of the same type of SMP
composite but in different compositions and the results are shown in figure 26. The approach
successfully improved the thermomechanical and conductive properties of SMP materials by the
addition of a hybrid filler into the matrix. The maximum fracture strains of the composites were
found to be dependent on the dispersion of the hybrid filler which could cause cracks propagating
Design, Modelling and Testing of a synthetic muscle system
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along the boundary of the matrix and filler. SMP recovery behavior was also achieved at 5% CB and
2% SCF as shown by figure 28.
FIGURE 28 STRESS-STRAIN CURVES OF COMPOSITES FILLED WITH VARIOUS SCF CONTENTS IN TENSILE MODE
(LU, YU, LIU AND LENG (2010))
FIGURE 29 IMAGES SHOWING THE MACROSCOPIC SHAPE MEMORY EFFECT OF 5% CB AND 2% SCF COMPOSITE
. THE PERMANENT SHAPE IS A FLAT STRIP AND THE TEMPORARY SHAPE A RIGHT ANGLE DEFORMATION. (LU,
YU, LIU AND LENG (2010))
Design, Modelling and Testing of a synthetic muscle system
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2.5. PREPARATION OF CONDUCTIVE SHAPE MEMORY POLYMERS
Deng, Lin, Ji, Zhang, Yang and Fu (2013) elaborate on how the preparation of conductive polymer
composites involves the selection of a suitable mixing method in order to incorporate the filler into
the polymer matrix. Conductive networks must be achieved in order to produce acceptable electrical
conductivity and there are generally three methods for preparation of conductive polymers:
1. Melt compounding
2. In situ polymerisation
3. Melt mixing
2.5.1. MELT COMPOUNDING
Melt compounding is referred to be advantageous by Deng, Lin, Ji, Zhang, Yang and Fu (2013)
because the filler can be directly dispersed into the matrix, no chemical modifications are required
and the fillers are prevented from re-aggregation by the viscous polymer matrix. Apart from this
method fitting seamlessly into industrial practices, a number of studies have displayed successful
application of melt compounding when dispersing conductive fillers into various polymer matrices.
These studies also reveal that processing conditions and filler conditions influence preparation of the
SMPs.
Huang, Ahir and Terentjev (2006) invested the melt compounding of polydimethylsiloxane (PDMS)
with Muilti0walled carbon nanotubes (MWCNTs) with the real part of the composite viscosity being
recorded during the mixture. Viscocity changes were measured as a function of the nanotube-
polymer mixing time and it was observed that every batch with the same concentration tended to
exhibit a similar dispersion level when mixed for a long enough time. Generally the higher the
concentration, the longer the critical time was required to achieve a relatively good dispersion. It
was observed however that in most studies, the same mixing time was used for composites with
different filler contents, which may be too short to achieve good dispersion in some cases.
Villmow, Kretzschmar and Potschke (2010) investigated Carbon nanotube (CNT) and polymer
composites, looking at the effect of different processing parameters on the final properties while
paying particular attention to electrical properties. Results showed that increases in the rotation
speed and the throughput decreased the residence time of the material. It was also observed that
the use of back-conveying elements as well as an extension of the processing lengths produced
opposite results to those just stated. Apart from this, the design of the screw profiles can further
increase filler dispersion.
Another valid factor is the interaction between the filler and the polymer matrix which is crucial
when related to the filler dispersion during melt compounding. Therefore, the chemical polarities of
the polymer matrix and the filler significantly influence the final quality of filler dispersion. An
example is given with the study conducted by Deng, Zhang, Bilotti, Loos and Peijs (2009) which
indicated large aggregates of conductive filler in polypropylene (PP) when melt compounding was
used as the dispersion method. This can be explained by the non-polar nature of the PP polymer
chain. Carbon Nanotubes (CNTs) can be also be easily dispersed in a polyamide 6 (PA6) matrix as a
result of the strong interaction between the PA6 polymer chains and the CNTs as investigated by
Gorrasi, Bredeau, Di Candia, Patimo, De Pasquale and Dubois (2011). These authors also refer to the
Design, Modelling and Testing of a synthetic muscle system
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use of a surfactant to improve the interaction between the filler and the matrix, and, thus, the filler
dispersion in a non-polar matrix .
In general, melt compounding is an effective and efficient method to add a conductive filler to a
polymer matrix however particular attention should be paid to the critical mixing time and the shear
stress inside the mixer. High shear stresses are not recommended as they reduce the filler aspect
ratio during processing.
2.5.2. IN-SITU POLYMERISATION
This being another method of conductive filler dispersion in a polymer matrix, Deng, Lin, Ji, Zhang,
Yang and Fu (2013) mention its advantage is that the polymer chain and fillers can be dispersed and
grafted on the molecular scale. Excellent filler dispersion is given by this method and a potentially
good interfacial strength between the filler and the polymer matrix. Successful investigations have
been reported which will be discussed later and a uniform dispersion of the filler was obtained and
improved both electrical and mechanical properties.
Recently, Liu, Chen, Chen, Wu, Zhang, Chen and Fu (2011) used this method to fabricate conductive
polymer composites (CPCs) containing grapheme, using a relatively high temperature during
polymerisation in order to reduce graphene oxide into graphene in the polymer matrix. This enabled
CPCs to be obtained at the end of the process without further processing. However it should be
noted that this method of in-situ polymerisation is difficult to adapt to the preparation of CPCs in
industry.
Deng, Lin, Ji, Zhang, Yang and Fu (2013) state the importance of in-situ polymerisation as an
essential method for the preparation of thermoset and rubber-based polymers. An example is epoxy
which has been investigated as a polymer matrix for a range of conductive polymers. A better
control of the conductive network structure and electrical properties can be achieved depending on
the special preparation method used. Defining a network before polymerisation is achieved through
a variety of methods including using a vacuum bag or fibre lay-up methods.
2.5.3. SOLUTION MIXING
It is difficult to achieve local homogenous dispersion states without breaking down the entangled
fillers using physical techniques such as those previously discussed, hence other methods such as
solution mixing need to be considered. With regards to the organic solvent mixing method, a
homogenous dispersion can be achieved throughout the solvent and therefore the host matrix.
Solution mixing is generally adding the filler directly into the polymer and this has been described in
the form of section 2.4.2-2.4.4.
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2.6 MORPHOLOGICAL CONTROL OF CONDUCTIVE NETWORKS IN SHAPE
MEMORY POLYMERS
2.6.1 CHARACTERISATION OF CONDUCTIVE NETWORK FORMATION
Deng, Lin, Ji, Zhang, Yang and Fu (2013) emphasize the important influence of the morphology of
conductive networks on the electrical properties of shape memory polymers and how it is crucial to
characterize the morphological details of these networks. A range of microscopic methods can be
used for direct observation of conductive networks in nanocomposites as follows
a) Optical microscopy
b) Scanning electron microscopy
c) Transmission electron microscopy
d) Scanning probe microscopy and
e) Atomic force microscopy.
FIGURE 30 MORPHOLOGY CHARACTERISED WITH DIFFERENT METHODS. OM AND TEM FOR PC CONTAINING
0.688% VOL CNTS. SEM IN CHARGE CONTRAST MODE SHOWS THE DISTRIBUTION OF MWNTS IN POLYPYRROLE
MATRIX AND HAADF-STEM PICTURES SHOW INDIVIDUAL CARBON BLACK PARTICLES AND THEIR CLUSTERS IN
POLYMER COMPOSITES: OM AND TEM (DENG, LIN, JI, ZHANG, YANG AND FU (2013))
These methods are mentioned to have been widely used as general microscopic methods to
characterize the morphology of polymer composites from various aspects or from different scales.
Optical microscopy (OM) is often used to study the morphology of a few microns or above and for
Design, Modelling and Testing of a synthetic muscle system
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anything below this range, all other methods except for scanning probe microscopy are applicable. It
is known that only information near the surface can be captured using conventional scanning
electron microscopy (SEM) due to secondary electrons having only a relatively shallow escape depth
(5-50mm) due to their rather low energy levels. This was reported by Li, Buschhorn, Schulte and
Bauhofer (2011). Although it was later reported that SEM observation of deeply embedded carbon
nanotubes (CNTs) and overall analysis of the CNT dispersion status were possible using voltage
contrast imaging in CNT/polymer based composites. This contrast mechanism was first reported by
Chung, Reisner and Campbell (1983) and has been used by various research groups since then.
Tkalya, Ghislandi, Alekseev, Koning and Loos (2010) utilised conventional SEM in the charge contrast
imaging mode to investigate the morphology of networks of graphene sheets embedded in
polystyrene matrices. They reported that the charge contrast imaging of conductive networks under
high acceleration voltages could provide three-dimensional information on the structure of the
conductive networks.
SEM despite offering valuable information on the morphologies of nanofillers and their conductive
networks, the actual nanofiller size and detailed information on the conductive network are not very
accurate due to local charging of the polymer matrix around the nanofillers. High-angle annular dark
field scanning transmission electron microscopy (HAADF-STEM) has been investigated successfully as
a tool to obtain reliable quantification of images to enhance the characterization of the conductive
network morphology as investigated by Loos, Sourty, Lu, de With and Bavel (2009). When it comes
to polymer materials, STEM is mentioned to possess several advantages over conventional TEM as
follows.
1. Images are easy to interpret due to a lack of phase contrast
2. Signal intensity is linear with thickness variations
3. A high signal to noise ratio is obtained.
These advantages are more pronounced with use of a high-angle annular dark field (HAADF)
detector capable of single-electron counting. Generally, it is believed that HAADF-STEM can be used
as a powerful tool for obtaining high-resolution images of unstrained polymer systems.
2.6.2 MORPHOLOGICAL CONTROL THROUGH POLYMER BLENDS
By constructing a polymer blend with two or more polymers, the advantages of each polymer can be
integrated and thus, balanced and optimized for the properties in the final material. The phase
morphology of the blends also plays a crucial role in the final properties and hence, polymer blends
of various designs and properties can be fabricated by controlling their morphology.
Meng and Hu (2009) mention how Jeong and Song (2001) developed thermoplastic SMPU blended
with poly(vinyl chloride) (PVC) to vary the switch temperature and improve the mechanical strength
of SMPU. The PVC is also miscible with the soft segment of the SMPU thus the switch temperature of
the blends can be varied smoothly with different component compositions. Zhang, Chen and Zhang
(2009) toughened polylactide using a polyamide elastomer from polyamide-12 and
polytetramethyleneoxide. Both polylactide and the polyamide elastomer are bio-degradable and the
mechanical properties of the polylactide were reportedly improved. Some examples of the
numerous design strategies emplored in SMP design are shown below.
Design, Modelling and Testing of a synthetic muscle system
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FIGURE 31 SOME DESIGN STRATEGIES FOR SMPS (MENG AND HU (2009))
2.6.3 INFLUENCE OF FILLER CHEMISTRY ON GLASS TRANSITION TEMPERATURE
Lan, Leng, Liu and Du (2008) during their investigation of the conductivity of SMP filled with CB,
conducted DSC tests on different compositions and it is shown below how the reduces with an
increase in filler content. Despite the fact this was not the primary reason for their study it still gives
adequate insight into the presence of a chemical interaction between the CB and SMP.
FIGURE 32 AGAINST CB CONTENT (LAN, LENG, LIU AND DU (2008))
Design, Modelling and Testing of a synthetic muscle system
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2.7 MATERIAL SELECTION AND MANUFACTURING METHOD
A comparison of all conductive fillers applied in the development of electro-active polymers as well
as some of the results that were obtained. It is clear from the table that the most suitable fillers are
MWCNTs or SCFs followed by CB. Due to the difficulty of processing as well as cost of the MWCNTs
and SCFs, CB remained as the most viable choice and it should be noted that at this stage, this
satisfies the design requirements.
A physically cross-linked semi-crystalline block copolymer in the form of polyurethanes due to their
easily tunable room temperature . The presence of hard and soft segments means that there is
possible benefit of maintaining a significant amount of mechanical strength since only the soft
segment is responsible for crystallization and thus storage of the secondary shape.
As already described, other structures of SMPs would entail heating the sample above the melting
temperature, and in such a case as to embed heating apparatus in the sample, this would mean the
apparatus could possibly deform the test sample. Thus this limits the options to modified
mechanisms.
Filler type Filler content
Storage Modulus at 0 degrees
Tensile strength
conductivity Voltage applied
Glass transition temperature
Shape recovery
Comments
SMP-CB 10% 1 GPa elastic modulus
4 30v 56 85% ( fracture beyond 30% strain…not suitable
SMP-MWCNT
2.5% 145 tensile
10MPa 1
60 80 >90 Energy
conversion of 10.4%.
SMP-SCF 5% 50Mpa 25Mpa
300V 20-60 90% Low shape fixity (30%)
SMP-Ni powder (magnetically aligned)
10% 5GPa low
6V 40 >90 Poor tensile strength due to addition of Ni fibres
SMP-CB-SCF 5%-2% 2.13 GPa 2.13 S/cm
30 V 26 >90
SMP-PPyLE-MWCNT
95-2.5-2.5
100Mpa tensile
9Mpa 0.098 25 40-48 90-95%
PPyLE coated MCWT-CNT
5% 135 tensile
9 5.4 S/cm
25 40-48
SMP-CB-Ni 10%-0.5%
Same as SMP-CB 1 S/cm 30V 80 Same As CB
TABLE 7 SUMMARY OF CONDUCTIVE FILLERS
Design, Modelling and Testing of a synthetic muscle system
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CHAPTER 3
3.1 PRELIMINARY MODELLING FOR SHAPE MEMORY POLYMER
BEHAVIOUR
Chen and Lagoudaz (2007) developed a mathematical model considering large deformations based
on the work of Liu, Gall, Dunn, Greenberg and Diani (2006) who carried out uniaxial experiments and
also developed a constitutive model. This initial model was based on a number of experimental
observations while at the same time considering polymer molecule interactions.
This is because the number of polymer chain segments involved in the cooperative conformational
rotation will increase with a decrease in temperature when T< hence the large scale entropic
changes will be prevented, and only the localized entropic motions occur in the polymer when a
force is applied. The terms ‘’glassy’’ and ‘’rubbery’’ have already been used to refer to the material
states in temperature ranges below and above respectively. Two kinds of idealized C-C bonds
were therefore introduced by Liu, Gall, Dunn, Greenberg and Diani (2006) to specifically quantify the
material state, namely the ‘’frozen bond’’ and the ‘’active bond’’ which coexist in the polymer.
The frozen bond represents the fraction of the C-C bonds that is fully immobilized in regard to
conformational motion and the active bond represents the rest of the C-C bonds that can undergo
localized free conformational motions thus once cooled to the glassy state, frozen bonds are
prevalent.
FIGURE 33 SCHEMATIC DIAGRAM OF THE MICROMECHANICS FOUNDATION OF THE 3D SHAPE MEMORY
POLYMER CONSTITUTIVE MODEL WITH THE EXISTENCE OF TWO EXTREME POLYMER STATES SHOWN. IN THIS
DIAGRAM THE POLYMER IS IN THE GLASS TRANSITION STATE WITH A PREDOMINANT ACTIVE PHASE. (LIU,
GALL, DUNN, GREENBERG AND DIANI (2006))
Design, Modelling and Testing of a synthetic muscle system
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At a capricious temperature during the thermomechanical cycle, the polymer is assumed to be a
mixture of two kinds of extreme phases as already mentioned and displayed in the image above. The
frozen phase, composed of the frozen bonds, implies that the conformational rotation
corresponding to the high temperature entropic deformation is completely locked, while the internal
energic change such as stretching or small rotation of the polymer bonds can occur.
On the other hand the active phase of the model consists of the active bonds, so the free
conformational motion can potentially occur in the polymer exists in the full rubbery state. With a
decrease in the temperature, large-scale conformational motions in the material are gradually
localized in the active phase, which is consistent with the microscopic mechanism underlying the
glass transition. Therefore by changing the ratio of these two phases, the glass transition during the
thermo-mechanical cycle is embodied and the shape memory behavior can be captured.
In the model, the frozen volume fraction of and the active volume fraction can be described as
follows
EQUATION 2, EQUATION 3, EQUATION 4
Where V is the total volume of the polymer, is the volume of the frozen phase and is the
volume of the active phase, with this accounting for the overall volume of the material.
Liu, Gall, Dunn, Greenberg and Diani (2006) considered the macroscopic strain tensor and
temperature T as state variables, with the frozen fraction being defined as a physical internal
state variable which is related to the extent of the glass transition and the state of the polymer.
Theyt also assumed that under the boundary condition of a sufficiently slow strain rate and the
thermal condition of a slow constant heating/cooling rate, and are dependant only on
temperature T.
( ) ( )
EQUATION 5, EQUATION 6
At certain temperatures, it is assumed that certain entropic changes can be frozen and stored
‘’temporarily’’ after unloading; therefore, if the material has been strained at high temperature,
( ) captures the fraction of strain storage as a function of temperature.
Chen and Lagoudas (2008) continue with this same format with the total strain ε being composed of
three parts
EQUATION 7
Where and are elastic and thermal strain given by
( )
( )
EQUATION 8, EQUATION 9
The stored strain is determined by the following evolution equation
Design, Modelling and Testing of a synthetic muscle system
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( )
( )
EQUATION 10
Where θ is the temperature, is the constant strain during cooling in their experiment, and
and are the elastic compliances for the frozen and active phases respectively. Chen and Lagoudas
(2008) identified that shape memory results from a combination of polymer morphology and specific
processing and can be understood as a polymer functionalization and thus particular constitutive
theories are needed.
3.1.1 PRELIMINARY ASSUMPTIONS
Under the philosophy by Chen and Lagoudas (2008), a material is considered to occupy, in the
reference configuration, the domain Ω . A representative material is denoted by XϵΩ with
assumptions that the material is homogenous and in the active phase with constant temperature
in the reference configuration. For this work the physical perspective that defines the glass transition
as a kinetic process in which the glassy phase nucleates at some sites of the material as it cools to a
certain temperature. As the temperature continues to decrease, the regions of glassy phase grow
continuously until the entire material is in the glassy phase. Since stress may change during cooling,
different material particles may enter the glassy phase with different strains. As a result, the
material in the frozen phase is not homogeneous as different material points suffer different local
residue strains.
A frozen region function is introduced whose function ( ) gives the summation of the frozen
region at temperature θ. The boundary of ( ) is composed of the interface between the active
phase and the frozen phase at temperature θ. It is defined how the frozen phase grows during
cooling as follows
( ) ( )
EQUATION 11
With the assumption that the entire material is in the active phase being defined by
( )
EQUATION 12
The frozen region function is assumed to depend on temperature only while the glass transition
process is considered completely reversible in the sense that in the ensuing heating ( ) also gives
the frozen region when temperature increases to θ. This assumption, originally made by Liu, Gall,
Dunn, Greenberg and Diani (2006) leads to simplicity in mathematical analysis, but however has no
justification.
The distribution and orientation of ( ) is assumed to be completely random and statistically
homogenous where only the volume measure of ( ) is needed in the present macroscopic
constitutive theory. The volume faction Φ(θ) of the frozen phase is thus defined by
Design, Modelling and Testing of a synthetic muscle system
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( )
∫ ( )
EQUATION 13
Where V is the volume of Ω. This definition implies that ( ) and that is a non increasing
function of θ.
A deformation in the material is denoted by x(X,t), giving the position vector of the material point X
at time t with the reference configuration being x(X,0)=0 and the deformation gradient being
denoted by F(X,t)= x(X,t). Apart from the deformation, other state variables that were considered
were absolute temperature θ(X,t) and Piola-Kirchoff stress S(X,t).
3.1.2 CONSTITUTIVE EQUATIONS
Chen and Lagoudas (2008) developed the constitutive theory using phenomena of classical nonlinear
thermoelasticity using Gibbs’ free energy function. The constitutive function ( ) which gives the
deformation gradient in terms of Piola-Kirchoff stress and temperature as follows
( ) ( ( ) ( ))
EQUATION 14
Since the material behavior is different in the active and frozen phase, two constitutive functions
representing these two phases are introduced as ( ) and ( ) respectively. Based on
experimental observations, the following assumptions were made
1. The deformation at a material point is stored when it undergoes transition from the active
phase to the frozen phase. As it is assumed that stress and temperature are continuous in
time, then the deformation gradient must also be continuous in time, despite the change of
the constitutive function from to .
2. The stored deformation at a frozen material point is fully recovered when the interface
passes through it again in the process of subsequent heating.
Assumption 2 implies that when a material is in the active phase, its behavior becomes history
independent and hence can replace for the condition is not ϵ ( ( )). On the other hand
in the frozen phase, two material particles frozen at different moments may have different
responses to subsequent changes of stress and temperature. Despite this, the fact that they have
similar molecular composition implies that certain intrinsic mechanical properties are maintained for
these material particles. Two material points are therefore equivalent if there exists a configuration
for each material point so that these two material points have the same constitutive function when
the respective configuration is taken as the reference configuration for each, which in this case is
( ). This phenomena is discussed more in detail by Chen and Hoger (2000).
Consider material point X which, during cooling, freezes at with ( ( )). The
deformation gradient immediately before freezing is given as follows
Design, Modelling and Testing of a synthetic muscle system
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( ) ( ( ) ( ))
EQUATION 15
Immediately after freezing, the deformation gradient from the frozen reference configuration is
given by ( ( ) ( )). With being the deformation gradient from the original reference
configuration Ω to the frozen reference configuration, the deformation gradient at this phase is as
follows
( ) ( ( ) ( ))
EQUATION 16
The continuity requirement leads to the following
( ( ) ( )) ( ( ) ( ))
EQUATION 17
Or
( ( ) ( )) ( ( ) ( ))
EQUATION 18
In consequent cooling, the deformation gradient at a material point is given by the following
( ) ( ( ) ( ))
EQUATION 19
( ) ( ( ) ( ))
( ( ) ( )) ( ( ) ( ))
EQUATION 20
Combining the above analyses
( ) { ( ( ) ( )) ( ( ))
( ( ) ( ))
( ( ) ( )) ( ( ) ( )) ( ( ))
EQUATION 21
Where τ was the last time the material point was being frozen:
⏟
{ ( ( ))}
EQUATION 22
An averaging scheme will now be introduced to derive the overall constitutive equation for the SMP.
Design, Modelling and Testing of a synthetic muscle system
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FIGURE 34 DEFORMATION OF AN SMP IN VARIOUS STATES DURING COOLING (CHEN AND LAGOUDAS (2008))
3.1.3 AVERAGE SCHEME
Chen and Lagoudas (2008) introduce yet another train of thought when they mention how at a
temperature when both active phase and frozen phase coexist, the material can be treated as a
composite. In the literature of composite materials various are mentioned to have been proposed
and the one to be applied in this scenario is based on the assumption that the stress in the entire
representative volume element is constant.
Using this assumption, along with assuming the temperature is spatially uniform, both S and θ are
functions of time only and the constitutive equation reduces to the follows
( ) { ( ( ) ( )) ( ( ))
( ( ) ( ))
( ( ) ( )) ( ( ) ( )) ( ( ))
EQUATION 23
⏟
{ ( ( ))}
EQUATION 24
Chen and Lagoudas (2008) remind us to note that although S and θ are assumed to be independent
of X, the deformation gradient F still depends on X due to the dependence of τ on X as well as the
obvious selection whether X belongs to ( ( )). With the stress being independent of X, the
Design, Modelling and Testing of a synthetic muscle system
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average state variables can be defined by averaging over the entire volume. The average
deformation gradient over Ω can be denote by the following equation
( )
∫ ( ) ( )
EQUATION 25
Integrating equation 14 over Ω and using equation 4, the following expression is obtained
( )
[∫ ( ) ( )
( ( ))
∫ ( ) ( ) ( ( ))
]
EQUATION 26
( )
∫ ( ( ) ( )) ( )
( ( ))
∫ ( ( ) ( ))
( ( ) ( )) ( ( ) ( )) ( ) ( ( ))
EQUATION 27
( ) ( ( )) ( ( ) ( )) ∫ ( ( ) ( ))
( ( ) ( )) ( ( ) ( )) ( ) ( ( ))
EQUATION 28
In order to represent the portion of deformation gradient in the frozen phase in a form that is
convenient for analysis, Chen and Lagoudas (2008) considered the following integral
∫ ( ) ( ) ( ( ))
EQUATION 29
Where f is an intergrable function, and τ, depending on both t and X, is given by equation 15. Using
equations 3 and 4 along with the definition of integral, equation 20 with the temperature being the
integral variable can be integrated as follows
∫ ( ) ( ) ( ( ))
∫ ( ) ( )
( )
EQUATION 30
For the right hand side of the equation, τ now depending on t and θ is given by the following
⏟
{ ( ) }
EQUATION 31
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Equation 28 defines, for a fixed t, a decreasing function τ(θ), which represents the last time the
material experiences the temperature θ. The inverse of this function therefore gives a natural
continuous extension to the interval [0,t], given by the following
( ) ⏟
( )
EQUATION 32
The function ( ) is constant in a region corresponding to a temperature θ at which function τ(θ) is
discontinuous. ( ), in the physical sense, represents a decreasing temperature history obtained by
replacing each cooling/heating portion of the original temperature history θ(τ) with a constant
temperature and was therefore termed ‘’net cooling history.’’ Variables in equation 28 can now be
replaced as follows
∫ ( ) ( ) ( ( ))
∫ ( ) ( ( )) ( )
( )
EQUATION 33
FIGURE 11 NET COOLING HISTORY (CHEN AND LAGOUDAS (2008))
Applying this chain of thought to equation 22 produces the following
( ) ( ( )) ( ( ) ( ))
∫ ( ( ) ( ))
( ( ) ( )) ( ( ) ( )) ( ( )) ( )
EQUATION 34
In this case, the argument of ’ has been safely changed from ( ) to ( ), since ( ) disappears
at a point where ( ) and ( ) differ. The three constitutive functions namely the frozen function
( ) and the deformation gradient functions ( ) and ( ) for the active and frozen phases,
Design, Modelling and Testing of a synthetic muscle system
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respectively, can and will be determined by appropriate experiments. This will enable equation 24 to
be examined in order to discover many aspects of the thermo-mechanical behavior of the SMP for
the temperature/loading path required.
3.1.4 THE SHAPE MEMORY CYCLE
In order to analyse the temperature/loading cycle, it is assumed that the material is subject to
homogenous stress boundary conditions, and that the temperature and stress rates are sufficiently
low so that the inertia and the temperature gradient can be neglected. The aforementioned average
scheme can be described for a typical shape memory cycle as follows.
In the first phase of the cycle in the interval , the material is loaded from zero to stress s1
at initial constant temperature which is above represented as follows
( ) ( ) ( )
EQUATION 35
Using equation 3 and 28, the following expression proceeds
( ) ( )
EQUATION 36
In this region the material is in the active phase and behaves like a nonlinear thermo-elastic
material, with the deformation gradient depending only on the stress and temperature at the
current time.
In the second phase of the cycle when , the material is then cooled to a prescribed
temperature while being held at the constant deformation gradient .
( ) ( ) ( )
EQUATION 37
Since the temperature is monotone decreasing for , it means ( ) ( ) and equation
28 gives the following
[ ( ( ))] ( ( ) ( ))
∫ ( ( ) ( ))
( ( ) ( )) ( ( ) ( )) ( ( )) ( )
EQUATION 38
Chen and Lagoudas (2008) here used the fact that θ’(t)=0 for and for a given cooling
history ( ) equation 38 can be used to determine the corresponding stress S(t) during cooling. Thus
differentiating equation 38 with respect to t yields the following
Design, Modelling and Testing of a synthetic muscle system
~ 43 ~
[ ( ( ))]
( ( ) ( ))
( ( ) ( ))
( ( ) ( )){ [ ( ( ))] ( ( ) ( ))}
EQUATION 39
Eliminating t and treating S as a function of θ, this leads to a first order differential equation for S
( ) {
( ) [
]
( )}
{
( ) [
]
( )}
( ){ ( )] ( )}
EQUATION 40
This equation with the initial condition
|
EQUATION 41
Can be solved to determine S in terms of θ. The stress at the end of cooling is given by the following
|
EQUATION 42
This shows rate independence of the model as the stress does not depend on the cooling rate, but
remember the model is history dependent in the presence of the frozen phase. At t= the stress
may be different from if the material is brought to a deformation gradient and temperature
through a different path. It also follows that
( )] ( ) ∫ ( )
( ( ) ( )) ( ( ) ( )) ( ( )) ( )
EQUATION 43
The third step of the cycle, in the interval , involves unloading to zero stress at constant
temperature
( ) ( ) ( )
EQUATION 44
By equations 28 and 36, and the fact that the temperature is constant in the first and third steps of
the cycle, it is realised that for
( ) ( )] ( ( ) ) ∫ ( ( ) )
( ( ) ( )) ( ( ) ( )) ( ( )) ( )
EQUATION 45
( ) ( )] ( ( ) ) ∫ ( ( ) )
( ( ) ( )) ( ( ) ( )) ( ( )) ( )
Design, Modelling and Testing of a synthetic muscle system
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EQUATION 46
( ) ( )] ( ( ) ) ( ( ) )
( ){ ( )] ( )}
EQUATION 47
The deformation gradient at the end of unloading is given by the following
( ) ( )] ( ) ( )
( ){ ( )] ( )}
EQUATION 48
If temperature is sufficiently low so that the entire material is in the frozen phase where
( ) , equation 48 reduces to the following along with using equation 26
( )
( ) ( )
EQUATION 49
The tensor is the deformation gradient of the temporary shape with respect to the permanent
shape. Upon assuming that the frozen phase is stiffer than the active phase, ( )
( ) is
close to the identity tensor thus the dominant part of is ( ) which is the deformation
gradient before cooling.
The final step of the cycle, when , involves stress free heating to the initial temperature
above which is
( ) ( ) ( )
EQUATION 50
Chen and Lagoudas (2008) let s(t)<t such that ( ( )) ( ) then is constant from s(t) to t. from
equation 28, it is therefore defined that
( ) ( )] ( ( )) ∫ ( ( ))
( ( ) ( )) ( ( ) ( )) ( ( )) ( )
EQUATION 51
( ) ( )] ( ( )) ∫ ( ( ))
( ( ) ( )) ( ( ) ( )) ( ( )) ( ) ( )
EQUATION 52
Since ( ( )) and ( ) , it means that the deformation is completely recovered at the
end of the cycle as follows
( ) ( )
EQUATION 53
The forms of the constitutive functions will now be specified in section 3.1.5.
Design, Modelling and Testing of a synthetic muscle system
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3.1.4.1 CONSTRAINED RECOVERY
FIGURE 35 SCHEMATIC OF SMP THERMOMECHANICAL CYCLE SHOWING SHAPE MEMORY EFFECT AND
CONSTRAINED RECOVERY (ATLI, GANDHI AND KARST (2008))
Atli, Gandhi and Karst (2008) carried out various thermomechanical experiments in order to
investigate the stress strain behavior above . Upon defining the shape memory process, an
alternate cooling process was mentioned which involves heating the SMP to a temperature above
while holding at a strain lower than the initial, which develops a recovery stress. This can be
represented as follows
( ) ( ) ( ) ( )
EQUATION 54
A new stress has been introduced, thus the deformation gradient is different, given as follows
( ) ( )] ( ( ) ) ∫ ( ( ) )
( ( ) ( )) ( ( ) ( )) ( ( )) ( )
EQUATION 55
( ) ( )] ( ( ) ) ∫ ( ( ) )
( ( ) ( )) ( ( ) ( )) ( ( )) ( )
EQUATION 56
( ) ( )] ( ( ) ) ( ( ) )
( ){ ( )] ( )}
EQUATION 57
The deformation gradient at the end of unloading to the lower stress is therefore given by the
following
( ) ( )] ( ) ( )
( ){ ( )] ( )}
EQUATION 58
Design, Modelling and Testing of a synthetic muscle system
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3.1.5 NEO-HOOKEAN MODELLING
In a neo-hookean material, the strain energy function is a linear function of the first principal
invariant only and it is assumed to be incompressible. As Chen and Lagoudas (2008) extended this
model to thermoelasticity, the incompressibility was taken in the sense that all possible
deformations at a constant temperature must correspond to the same deformed volume. This
implies that that both the shear modulus and the volume ratio are functions of temperature which
leads to the following constitutive equations.
( ) ( )
EQUATION 59, EQUATION 60
Where is the hydrostatic pressure required by the incompressibility constraint, ( ) is the shear
modulus, and ( ) is the ratio of the volume at temperature θ and the volume at the initial
temperature. To obtain the model the shear modulus was taken to be constant, with the volume
ratio being taken to be unity. To solve equations 59 and 60, was solved in terms of S and by
observing the polar decompositions of tensors and as follows
EQUATION 61, EQUATION 62
Where and are proper orthogonal tensors, and and symmetric tensors. Substituting these
equations in equations 59 and 60
( ) ( )
EQUATION 63, EQUATION 64
Deducing from these equations,
( )
EQUATION 65, EQUATION 66
Equation 66 implies that and have common eigenvectors such that the spectral
decompositions of these two tensors are as follows
∑
∑
EQUATION 67, EQUATION 68
Substituting equations 67 and 68 into equations 63-66,
( ) ( )
EQUATION 69, EQUATION 70
Eliminating p and solving equations 67 and 68 in terms of in terms of and
Design, Modelling and Testing of a synthetic muscle system
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( )
EQUATION 71
Upon substituting the results into equations 67-68 and 61-62, the constitutive function F(S, ) is
obtained as follows. A constitutive equation for SMPs of the neo-hookean type is then obtained by
using this function in equation 28 with separate ( ) and ( ) for the active and frozen phases.
3.1.6 REDUCTION OF CONSTITUTIVE MODEL FOR UNIAXIAL TENSION
EXPERIMENT
A common experiment undertaken is uniaxial tension for which
EQUATION 72
Where s is the axial tension; the stress profile for the load path being considered. Substituting
equation 72 into equation 71 gives the following
√ ( )
EQUATION 73
Where the axial tension satisfies the following equation
( ) [ ( )
]
EQUATION 74
Thus for a given ( ) and ( ), equation 74 gives a unique function ( ) and without loss of
generality, Chen and Lagoudas (2008) choose Q=R=I which can be represented in component form
as follows
(
( )
√ ( )
( )
√ ( )
( ))
EQUATION 75
A constitutive equation is obtained by now taking both and in the neo-Hookean form with
shear modula ( ) ( ), and volume ratios ( ) and ( ). Subjecting the SMP to uniaxial
tensions , equation 75 when applied to each phase, gives two functions ( ) and ( ).
Design, Modelling and Testing of a synthetic muscle system
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Substituting these into equation 74 gives functions and respectively. If λ(t) is the average axial
stretch at time t, this then follows from equation 33 that
( ) ( ( ))] ( ( ) ( )) ∫ ( ( ) ( )) ( ( ) ( )) ( ( )) ( )
( ( ) ( ))
EQUATION 76
Volk, Lagoudas and Chen (2010) conducted experiments to help model the large deformations and in
further analysis, related the stretch of the material to the extension as follows
( )
EQUATION 77
Where the extension,
, is the change in gauge length divided by the original gauge length.
Assuming the stretches in each phase take the form of equation 72, five functions need to be
calibrated to fully describe the axial stretch of a material undergoing uniaxial tension as shown in
equation 75. The five functions are shown below
Function Description
( ) Frozen volume fraction
( ) Shear modulus of the active phase
( ) Shear modulus of the frozen phase
( ) Volume ratio in the active phase
( ) Volume ratio in the frozen phase TABLE 8
Similarly, the lateral stretch ( ) can be represented as follows
( ) [ ( ( ))]√ ( )
( ( ) ( )) ∫ √
( ) ( ( )) ( ( ) ( ))
( ( ) ( )) ( ( ) ( )) ( ( ))
EQUATION 78
These equations will be used to predict the material behavior but as n consideration of the shape of
the SMP for the desired design it becomes obvious how only one dimension of stretch is required to
calibrate the SMP. One should note that the initial hypothesis was based on small deformations
(<10%) by Chen and Lagoudas (2008) and then a later train of thought was introduced concerning
large deformations.
Design, Modelling and Testing of a synthetic muscle system
~ 49 ~
CHAPTER 4
4.1 EXPERIMENTAL SETUP
4.1.1 CYCLIC CHARACTERISATION
Lendlein and Kelch (2002) discuss how the SME has an ability to be quantified by using cyclic
thermo-mechanical experimentation. The basic requirements for this investigation are a
temperature chamber and a tensile tester, with single cycle including programming the test sample
and then recovering its shape. A typical test protocol consists of the following stages
1) Heating the sample to a temperature above
2) Stretching the sample to a maximum strain
3) Cooling the sample below under constant strain to temperature
4) Heating the sample above thus
5) Recovering the initial shape.
It should be noted that in the case of thermoplasts, it is important not to exceed the melting
temperature of the polymer. The data can be represented in a strain-stress curve as shown by figure
20, with different effects resulting in different changes in the curve.
FIGURE 36 SCHEMATIC REPRESENTATION OF RESULTS OF CYCLIC THERMO-MECHANICAL INVESTIGATIONS
(LENDLEIN AND KELCH (2002))
Lendlein and Kelch (2002) attribute the following effects to play a role in these changes;
differences in the expansion coefficient of the stretched sample above and below as a
result of entropy elasticity
volume changes arising from crystallization in the case of being a melting point
Design, Modelling and Testing of a synthetic muscle system
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Key parameters can be determined from this form of graph such as the elastic modulus E which is
the slope of the measurement range ① in figure 20a). In the case of describing the shape memory
properties of the material at a strain are the strain recovery rate and the strain fixity rate .
( )
( )
EQUATION 79
Where =the programmed strain and =cycle of programming.
defines the ability of a material to memorise its permanent shape. Lendlein and Kelch (2002) also
mention how it is a measure of how far a strain that was applied in the course of the programming
( ) is recovered in the following shape-memory transition. The strain that occurs upon
programming in the Nth cycle ( ) is compared to the change in strain that occurs with
the shape memory effect ( ). ( ) and ( ) represent the strain of the sample in
two successively passed cycles in the stress-free state before yield stress is applied. the total strain
recovery rate is the strain recovery after N passed cycles based on the original shape of the
sample and is shown below.
( )
EQUATION 80
The strain fixity rate describes the ability of the switching segment to fix the mechanical deformation
which has been applied during the programming process. It is given as follows
( )
EQUATION 81
Figure 36 illustrates how a difference can be present within the first cycles, with the curves
becoming more similar with an increasing number of cycles. Lendlein and Kelch (2002) attribute the
initial differences to the history of the sample. During the first cycles a reorganization of the polymer
on the molecular scale takes place which involves deformation in a certain direction. Single polymer
chains will arrange in a more favourable way in regard to the direction of deformation, covalent
bonds being possibly broken during this process.
Design, Modelling and Testing of a synthetic muscle system
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4.1.2 SAMPLE FABRICATION
Based upon the model by Chen and Lagoudas (2008) , as well as the initial experimentation to this
model conducted by Liu, Gall, Dunn, Greenberg and Diani (2006), thermomechanical experiments
were setup in order to investigate electrical, thermal and mechanical properties of SMPs. The SMP
used was thermosetting polyurethane available in two parts purchased from Alchemie. Inc. Carbon
Black was obtained from Norit. Inc.
Based on results by Rogers and Khan (2012), part A polyurethane was mixed with 2.5% wt. CB and
then stirred by hand for 1 minute along with the same being done for polyurethane Part B in a
separate container. The two solutions were then added together so as to aid in better mixing of the
solution, which resulted in a total solution of 5% by weight. The same was done to obtain the 10%
CB sample while carbon veil was simply embedded in the mold over the area to be tested. The
mixture was poured in an open dog-bone shaped mold initially and allowed to settle for 15mins.
However it was observed that a closed mold would be most suitable as it limited the amount of
moisture trapped in the sample. Nickel/chromium heating wire was embedded in the samples
during fabrication so as to provide a means of heating the specimen.
FIGURE 37 MATERIAL PROPERTIES OF PU (ALCHEMIE.LTD)
Design, Modelling and Testing of a synthetic muscle system
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4.1.3 DETERMINATION OF GLASS TRANSITION TEMPERATURE
FIGURE 38 EXPERIMENTAL SET UP
4.1.4 EXTENSION VERSUS TEMPERATURE (ZERO LOAD)
The sample was connected to a power supply operated under voltage control and the sample was
heated and the elongation measured as a function of temperature until the temperature reached
at zero stress. The voltage supply was then switched off and the reduction in length of the
specimen recorded with decrease in temperature. This was carried out in order to determine the
thermal strain of each of the samples of varying composition.
4.1.5 TENSILE TESTING
An instron machine was used to investigate the maximum stress at specified strain the samples
could obtain when heated above . The same was also done at room temperature, a temperature
greatly below in order to investigate the effect of heating on the mechanical strength and storage
characteristics of the sample.
Thermo-mechanical testing was carried out in order to
determine the glass transition temperature of
polyurethane filled with carbon black as well as
polyurethane filled with carbon black and carbon veil. For
each case, the variation in dimensional properties of the
samples was recorded as the sample was heated when
loaded to 5% of the maximum tensile stress of unfilled
polyurethane. This was given in the data sheets. The
sample was clamped at one end with the loaded attached
to the lower end by a clamp and hook system which held
the weights. A dial test indicator was used to measure the
elongation of the specimen with increase in heat. Tests
started at room temperature (273K) and the test was
concluded at 353K. A thermocouple was attached to
surface of the sample so as to record the temperature.
Specimen
Weights
Design, Modelling and Testing of a synthetic muscle system
~ 53 ~
CHAPTER 5
5.1 RESULTS
5.1.1 GLASS TRANSITION TEMPERATURE
For the 10% CB sample, the transition temperature was found to have shifted to be 329K as this was
noticeably the inflection point of the curve hence determining the phase transition from frozen to
active. For the 5% CB sample, there was a noticeable shift in which was found to be 321K. The
figures indicate a transition zone where the shape memory properties dictate the phase transition
from frozen to active and regions outside these zones were concluded to be fixed phases whereas
the transition zone could have shiftable transition temperature parameters. However there was no
prediction of any limits of transition. As for the 5% CB and veil sample, the transition temperature
was very difficult to obtain as it was broadened by the veil. It was however estimated to be 319K.
FIGURE 39 EXTENSION VS TEMPERATURE FOR 10% CB
0
0.5
1
1.5
2
2.5
3
290 300 310 320 330 340 350
Exte
nsi
on
(m
m)
Temperature (Kelvin)
Thermomechanical test 10% CB
Design, Modelling and Testing of a synthetic muscle system
~ 54 ~
FIGURE 40 5% CB THERMOMECHANICAL TEST
FIGURE 41 THERMOMECHANICAL TESTING VEIL AND 5% CB
It was noticed that as filler content increased, the zone of transition became broader, the reason for
this are described later.
0
0.5
1
1.5
2
2.5
3
3.5
4
290 300 310 320 330 340 350
ext
en
sio
n (
mm
)
temperature (degrees)
Thermomechanical Test 5% CB
0
0.2
0.4
0.6
0.8
1
1.2
1.4
290 300 310 320 330 340 350
Exte
nsi
on
(m
m)
Temperature (Kelvin)
Thermomechanical testing veil and 5% CB
Design, Modelling and Testing of a synthetic muscle system
~ 55 ~
5.1.2 STRESS VERSUS STRAIN
Above , the tensile tests indicated less than desirable results however the specimen still showed
an appreciable amount of strength. Critical stress value decreased with an increase in filler content
which shows the trade-off between strength and filler content.
FIGURE 42 10% CB STRESS VERSUS STRAIN
-2
0
2
4
6
8
10
12
14
0 2 4 6 8 10
Str
ess (
MP
a)
Strain %
10% CB
Design, Modelling and Testing of a synthetic muscle system
~ 56 ~
FIGURE 43 5% CB STRESS VERSUS STRAIN
FIGURE 44 5% CB AND VEIL STRESS VERSUS STRAIN
0
1
2
3
4
5
6
7
8
9
0 5 10 15 20 25 30
Str
ess (
MP
a)
Strain %
5% CB
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0 2 4 6 8 10
Str
ess (
MP
a)
Strain (%)
5% CB and veil
Design, Modelling and Testing of a synthetic muscle system
~ 57 ~
5.1.3 THERMAL STRAIN MEASUREMENT
With no force applied, the samples were heated and their extension recorded, as well as their
cooling. These graphs revealed particularly interesting results as gradually increasing curve was
observed for the 5% CB sample whereas for the sample incorporated with veil produced an
unexpected curve. This further added to its reasons for not being incorporated into the final design.
FIGURE 45 5% CB THERMAL STRAIN
FIGURE 46 5% CB AND VEIL THERMAL STRAIN
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
290 300 310 320 330 340 350 360
ext
en
sio
n (
mm
)
temperature (Kelvin)
5% CB Thermal Strain
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
0.28
290 300 310 320 330 340 350
ext
en
sio
n (
mm
)
temperature (degrees)
Thermal strain 5% CB and veil
Design, Modelling and Testing of a synthetic muscle system
~ 58 ~
CHAPTER 6
6.1 MODEL CALIBRATION
6.1.1 DETERMINATION OF CONSTITUTIVE PARAMETERS
With results obtained during thermo-mechanical testing as well as stress-strain measurements, the
determination of material parameters was carried out as follows basing the formulation on work
carried out by Volk, Chen and Lagoudas (2010). Considering the volume ratios first and considering
the material response due to a change in temperature, the volume ratio is proposed to be expressed
as a function of the coefficients of thermal expansion as shown below.
( ) ( )]
EQUATION 82
( ) ( )]
EQUATION 83
Where and are the coefficients of thermal expansion calculated under zero stress in the active
and frozen phases, respectively. For no change in temperature, the volume ratio does not change
and is therefore equal to one and therefore the assumption of incompressibility at a constant
temperature is maintained. Substituting equations 83 and 84 into equation 72 for a zero stress
condition results in the following expressions
( )
EQUATION 84
( )
EQUATION 85
The stretch of the material in each phase is defined as a function of the coefficient of thermal
expansion and the change in temperature. When equations 85 and 86 are substituted into equations
83 and 84, the following expressions are obtained
(
)
( )
EQUATION 86
(
)
( )
EQUATION 87
Design, Modelling and Testing of a synthetic muscle system
~ 59 ~
The stretch of the material can also be related to the extension measured experimentally through
the following equation
( )
EQUATION 88
The coefficients of thermal expansion are going to be determined by using results from the
extension-temperature curve at zero stress. This displays a linear relationship in each of the active
and frozen phases separated by a phase transition region or glass transition temperature zone.
FIGURE 47 THERMAL STRAIN
The shear modulus in each phase can also be related to the tensile modulus and the Poisson’s ratios
through the following equations
( )
EQUATION 89
( )
EQUATION 90
Where and are the tensile moduli in each phase, and and are Poisson’s ratios taken to
be 0.5 with the incompressibility constraint earlier discussed for the active and frozen phases,
-0.005
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
290 300 310 320 330 340 350 360
Stra
in
temperature (Kelvin)
5% CB Thermal Strain
Design, Modelling and Testing of a synthetic muscle system
~ 60 ~
respectively. Values for tensile moduli for each phase will be calculated from the linear region of
loading in the active phase and unloading in the frozen phase presented below.
FIGURE 48 ACTIVE PHASE STRESS STRAIN GRAPH
The frozen volume fraction is determined by assuming it takes a similar shape to that of the shape
recovery profile upon heating at zero load. Support of this assumption comes from reducing
equation 77 and the neo-hookean relationships for the free recovery condition of s (t) =0. If these
equations are reduced, along with the assumption that the thermal stretch is negligible, it can be
shown that
( ) ( )
EQUATION 91
Volk, Lagoudas and Chen (2010) also introduced a hyperbolic tangent function assumed for the
frozen volume fraction of the polymer. This was optimized to fit the profile of the strain recovery
profile used for calibration. The general form of the proposed function is as follows
( ) (
) (
)
(
) (
)
EQUATION 92
Where and are the temperature bounds for which the hyperbolic tangent function is to
be fit, and A and B are the respective shifting and scaling factors for adjusting the shape of the
hyperbolic tangent function. Parameter A represents the inflection point of the hyperbolic tangent
function and represents a measure of . To account for the shift in the recovery temperatures,
Volk, Lagoudas and Chen (2010) assumed A to be proportional to the temperature rate. However in
this case, we shall assume A is equal to the temperature rate due to the fact that the wires were
y = 4.5896x - 0.0624
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.05 0.1 0.15 0.2 0.25
Stre
ss (
MP
a)
strain (mm)
5% CB Loading =4.5896Mpa
Design, Modelling and Testing of a synthetic muscle system
~ 61 ~
embedded in the specimen hence the heat applied to the specimen is directly absorbed into the
specimen, with negligible losses. This is shown as follows
EQUATION 93
Where , in this case and . The parameter B is inversely proportional to the
rate of strain recovery when transforming from the frozen phase to the active phase. The rate of
strain recovery has already been discussed in section 4.1.1 and therefore can be represented as
follows
EQUATION 94
EQUATION 95
The programmable strain to be used in this case is the strain achieved during zero stress heating
during determination of . The constant C was obtained by obtaining the strain recovery ratio at
zero stress heating and cooling.
EQUATION 96
B is mentioned to approach zero in the limit of the phase transition occurring as a step function.
Parameters A and B are adjusted to best match the strain recovery profile from which the model is
being calibrated. Therefore in this case, the desired extension was 20%. However as the results
display, this hyperbolic curve was not achieved by the material and so an attempt of stretching the
graph was undertaken. The strain recovery profile will be set to this requirement to end at a value of
zero and then normalized from zero to one.
Design, Modelling and Testing of a synthetic muscle system
~ 62 ~
FIGURE 49 ZERO STRESS COOLING CURVE
FIGURE 50 FROZEN VOLUME FRACTION
Also, the denominator in equation 87 is to be used to normalize the resulting hyperbolic tangent
function from 0 to 1 to correspond to a material in the frozen and active phase, respectively. A least
squares method on the errors is then used to optimize A and B in equation 87 to the strain recovery
profile. A summary of the calibration requirements is shown below
7
7.5
8
8.5
9
9.5
290300310320330340350
Stra
in %
temperature (Kelvin)
zero stress cooling
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
290300310320330340350
fro
zen
vo
lum
e f
ract
ion
Temperature (Kelvin)
zero stress cooling
Design, Modelling and Testing of a synthetic muscle system
~ 63 ~
Function Description Values
( ) Frozen volume fraction
( ) (
) (
)
(
) (
)
( )
( ) Shear modulus of the active phase
( ) Shear modulus of the frozen phase
( ) Volume ratio in the active phase ( ) ( )]
( ) Volume ratio in the frozen phase ( ) ( )]
Axial stretch in the active phase
Axial stretch in the frozen phase TABLE 9 SUMMARY OF CONSTITUTIVE PARAMETERS
Design, Modelling and Testing of a synthetic muscle system
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6.2 MODEL IMPLEMENTATION
Having determined all the constitutive parameters, equation 77 was to be numerically implemented
in MATLAB and used to simulate various shape memory behaviors. Volk, Chen and Lagoudas (2010)
work focused on a more arbitrary, thermo-mechanical loading path during which the process can
either be stress controlled or stretch controlled and a stretch controlled process shall be discussed in
the next subsection. Due to the inability to program the material, only an analytical approach will be
described below.
6.2.1 STRETCH CONTROLLED PROCESS
To solve for stress, equation 76 is rewritten as follows
( )
( ( ) ( )) ( ( ))]
( ( ) ( ))
( ( ) ( )) ∫
( ( ) ( ))
( ( ) ( ))
( ( )) ( )
EQUATION 97
This is then differentiated with respect to time and the result is shown below
(
( )
( ( ) ( ))) [ ( ( ))]
( ( ( ) ( ))
( ( ) ( )))
EQUATION 98
Manipulating the time derivatives, equation 93 can be rewritten using a backward Euler method as
follows.
(
) [ ( ( ))] [
(
)
(
)]
EQUATION 99
Where the subscripts and ( ) represent the current and previous time steps, respectively and
and are the current values of stretch in the active and frozen phase respectively where the
initial values and in the undeformed state are equal to 1. Volk, Chen and Lagoudas (2010)
point out that equation 94 is homogenous in time therefore can be eliminated. This can be
explained in recollection of the initial assumptions where the model was proposed to be
independent of time. The resulting expression is displayed below.
( ) ( )] [
( )
( )]
EQUATION 100
Design, Modelling and Testing of a synthetic muscle system
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Assuming the same stress is experienced in each phase, the stress-stretch relationships for each
phase are as in equation 72 were combined to eliminate stress and rewritten as follows
( ( )
) (
( )
)
EQUATION 101
Equations 94 and 95 form a non-linear set of equations that were then solved for the axial stretch in
each phase. The equations are linearized until the solution converges, in which case the stress is
then computed from equation 72. Either side of equation 95 can be used to calculate the stress as it
has already been assumed that stress is the same in each phase.
Design, Modelling and Testing of a synthetic muscle system
~ 66 ~
CHAPTER 7
7.1 VALIDATION AND DISCUSSION
7.1.1 INFLUENCE OF MODELLING ON MATERIAL BEHAVIOUR
In order to confirm the predictions of the mathematical model, a test specimen was set to 20%
deformation stored and the thermomechanical characteristics investigated. These results were to be
compared with the MATLAB curve predictions.
Percent extension
TABLE 10 PERCENTAGE EXTENSION AND CORRESPONDING VALUES
It should be noted that a confirmation of the above predictions was not achieved due to the sample
failing at any attempt to store a deformation of 20%. This was primarily attributed to the heating
wires melting the test sample upon heating of the sample. This then proposes the suspicion that the
heating wires somewhat affected the thermo-mechanical testing as well as the zero stress heating
and cooling. An attempt to reduce this effect had already been established by placing the heating
wire in a somewhat sinusoidal fashion so as to eliminate any tensile contribution during the tensile
test. An additional point to this is that the error can be regarded as a constant throughout the entire
experimental stage and is fairly small.
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FIGURE 51 FRACTURED TEST SAMPLE DISPLAYING CRACK PROPAGATION ALONG REGIONS EMBEDDED WITH
WIRE.
Despite the failure to program any deformation, an analytical analysis was still carried out using the
MATLAB programming results with a presentation of the lateral stretch coefficients. This now brings
into consideration the constitutive parameters previously discussed which enables some predictive
curves to be plotted.
It should be noted that the modelling can also be applied to a compliant wing skin as initially
discussed in chapter 1 under the same assumption that the stress in the entire representative
volume element is constant. The morphing set up can be related to this assumption in the sense that
since any point on the wing skin is assumed to be possible of conformational motion to the internally
subjected stress, at some point in the cycle the entire skin experiences a certain amount of stress.
Adding to this the external aerodynamic forces it is subjected to, the net stress can be averaged over
the entire length of the stressed skin.
Let us recall an assumption initially mentioned. The frozen region function is assumed to depend on
temperature only while the glass transition process is considered completely reversible in the sense
that in the ensuing heating ( ) also gives the frozen region when temperature increases to θ.
Another problem we have been faced with is how do we relate the modelling to the fact that the
material is history dependent in the active phase on a practical scale? This can be justified by taking
a closer look at the constitutive parameters with relation to the PU and is discussed in the next
section.
As discussed in section 2.6.2, a confirmation of results obtained by Lan, Leng, Liu and Du (2008) that
decreases with an increase in filler content of carbon black was displayed during the thermo-
mechanical investigations. The use of a filler can adversely affect the properties of the base matrix
depending upon factors such a quality of dispersion, filler-chain interaction and filler surface
coatings. This is shown in the differences in the thermal expansion coefficient of the stretched
sample which is three times greater above than below which, as previously discussed, were
attributed to entropy elasticity.
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The main purpose of this investigation is to expand upon preliminary investigations of the large
deformation SME in carbon black filled PU in order to provide a better understanding of the
complete shape recovery for large values of deformation.
7.1.2 POLYURETHANE ANALYSIS
Let us take a closer look at the material selected for the SMP, Polyurethane. It has already been
discussed how it is a physically cross-linked semi-crystalline block copolymer but an attempted shall
be made to relate its fundamental chemistry to the initial modeling assumptions using already
existing literature.
7.1.2.1 MATERIAL RELATION TO MODELLING
It has been already described polyurethanes as conventionally being multiblock copolymers
consisting of alternating sequences of hard and soft segments. Lin and Chen (1998) synthesized
SMPU with 4,4’-diphenylmethane diisocyanate (MDI), 1,4-butanediol (BD) and poly (tetramethyl
oxide) glycol (PTMO) in order to investigate the influence of the hard segment content on the shape
memory behavior. Using DSC, DMA and TEM it was discovered that hard segment-rich phase would
affect the ratio of recovery, in other words the low content would lead to the recovery of the
deformed specimen being incomplete. Also the greater amount of hard segment (MDI +BDI) used
displayed a higher and a lower modulus ratio of the PU with the modulus ratio being the ratio of
the storage modulus at -20 degrees and storage modulus at degrees
TABLE 11 NOTATION AND MOLAR COMPOSITIONS OF PU WHEN INVESTIGATION HARD SEGMENT CONTENT.
(LIN AND CHEN (1998))
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FIGURE 52 SHAPE MEMORY BEHAVIOUR STUDY OF A) PTMO250 AND B) PTMO650 (LIN AND CHEN (1998))
In the second part of their paper, Lin and Chen (1998) investigated the influence of the soft segment
molecular weight on the shape memory behavior of PU. MDI and BD were synthesized with various
molecular weights of poly (tetramethylene oxide) glycol (PTMO) and the thermal and mechanical
properties observed using DSC and DMA with the morphology analyzed using TEM. The results
indicated that the deformed specimen would recover some deformation at the low temperature
range by using a high molecular weight of PTMO. Deformation of the PUs would completely be
recovered by introducing low molecular weight PTMO and increasing the numbers of the dispersed
phase of the PU.
Using these conclusions we can now refer to some of the initial assumptions namely the presence of
the frozen bonds and active bonds in the polymer and the assumption that they are in the ratio 1:1
as dictated by equation 3.
For PU, a train of thought can be introduced that the active phase, governing storage of the
secondary shape, can be referred to as being ‘soft segment constitutive’ while the frozen phase can
be referred to as being ‘hard segment constitutive.’ This can be justified by the fact that the hard
segments physical cross-links are responsible for the primary shape for the polymer and
crystallization of the soft segments govern the secondary shape. The hard segment discussion
shows how the hard segment content needs to be much greater than 50% by weight for full recovery
to occur. This therefore means that the frozen bond to active bond ratio must be modified and also
that the polyurethane used would not have been ideal for shape memory investigation.
The value of the frozen volume fraction was found to be less than one which, if based upon the just
stated train of thought, means that the soft segment phase is more dominant for this material.
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TABLE 12 MOLAR COMPOSITIONS OF PU WHEN STUDYING SOFT SEGMENT (LIN AND CHEN (1998))
FIGURE 53 SHAPE MEMORY BEHAVIOUR OF SOFT SEGMENT INVESTIGATION (LIN AND CHEN (1998))
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7.1.2.2 CHEMICAL STRUCTURE DEPENDANCE ON PERFOMANCE
FIGURE 54 CHEMICAL STRUCTURE OF PU BLOCK COPOLYMER A) BD TYPE AND B) ED TYPE
Chun, Cho and Chung (2006) mention how an important factor that affects the physical properties of
polyurethane is the chemical structure of each segment such as the type of polyol (ether or ester
type) used for the soft segment and the type of chain extender (diol or diamine) in the hard
segment. The minor difference in the component of each segment is then amplified due to the
repeating nature of the polymer, which results in a drastic change in the phase separation.
Chun, Cho and Chung (2006) investigated the chain extender BD and compared it with
ethylenediamine (ED). increased by 30K from BD to ED which was attributed to the rigid nature of
urea type bonding which made the ED type PU chains hard to rotate and caused them a higher
temperature for phase transition of soft segment.
TABLE 13 COMPOSITION OF PU USED (CHUN, CHO AND CHUNG (2006))
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FIGURE 55 MECHANICAL PROPERTIES OF PU A) MAXIMUM STRESS, B)TENSILE MODULUS AND C) STRAIN AT
BREAK (CHUN, CHO AND CHUNG (2006))
FIGURE 56 SHAPE MEMORY PROPERTIES VS HARD SEGMENT CONTENT PROFILE OF PU CHAIN EXTENDED WITH
A) BD AND B) ED AFTER THE FIRST TEST CYCLE (CHUN, CHO AND CHUNG (2006))
As shown by figure 52, maximum stress
increased with hard segment content for both
types of PU. As shown , ED type PU showed
similar max stress at 20% lower hard segment
than BD type PU and this was attributed to
urea type bonding due to the addition of the
amide linkage. The results therefore show
significant improvement in stress and strain by
changing chain extender. Better shape
memory properties were also acknowledged
for ED type PU then BD type PU. It is reported
that when load was applied, soft segment with
lower than room temperature while the
original shape was restored with the help of
the hard segment that strongly attracted
themselves by hydrogen bonding and dipole-
dipole interaction. The thermodynamic
incompatibility between the hard and soft
segments induces micro-phase separation and
enables the distinct role of each segment in
the shape memory process.
This study explains the low mechanical
strength and shape memory properties
displayed by the 5% CB sample as well as a
recommendation for future studies.
Design, Modelling and Testing of a synthetic muscle system
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7.1.3 RECOMMENDATIONS
Consideration of a design with aero-elastic stimulation in order to predict flutter response can be
undertaken for future application in high speed conditions. Also considerations in the form of three
dimensional models can be developed to study the three dimensional effects of some of the
following phenomena
actuator placement
flap stiffness
fatigue strength, and
dynamic characteristics
Furthermore, an investigation into self-healing properties of the SMP would be desirable to
incorporate into the already developed SMP matrix. Li and John (2008) developed a SMP based
syntactic foam made of polystyrene, glass microballoon and MWCNT. This therefore means that this
idea does not stray far from the already discussed conductive fillers.
An infared video camera can be used to monitor the temperature distribution in the sample and
shape recovery simultaneously as done by Leng, Huang, Lan, Liu and Du (2008). More research into
the various type of SMP blends before consideration of the conductive filler can also be looked into.
Some of the various blends as described by Meng and Hu (2009) can be of the following forms
crystalline/amorphous polymer blend
elastomer/crystalline or amorphous polymer
blending and radiation cross-linking to create novel SMPs
A more intelligent approach in terms of heating of the polymer can be investigated such as
increasing the amount of wire in the test specimen or use of a piezoelectric transducer that could
possibly help in supplying the heating during recovery. Another point is that a laminate structure for
the polymer can be considered as the one achieved by Zhang and Ni (2005) which contributed
towards the mechanical strength of the polymer.
Due to the viscosity problem always making the mixture too thick to release air bubbles, adding a
solution to aid in viscosity can be considered as done by Lu, Yu, Liu and Leng (2010) who added
acetic acid ester to aid the viscosity of a CB and SCF mixture. More elaborate mixing methods can be
added to the process such as high shear mixing and a high energy sonication so as to improve filler
dispersion in the mixture. The mixture can also be treated with a vacuum pump to completely
remove air bubbles.
As discussed in the last section, ED type is more suitable for both its higher mechanical strength as
well as superior shape memory properties compared to BD type PU, along with a greater
composition of hard segment.
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CHAPTER 8
8.0 CONCLUSION
Shape memory polymers allow the benefit of developing shape changing materials at a fraction of
the cost of present day aircraft materials as well as significant weight reduction. The main factor
hindering their application is their structural capability and lack of strength thereof.
The use of a filler evidently adversely affected the properties of the base matrix which can be
attributed primarily to the quality of dispersion during the mixing process as well as the selection of
polyurethane. The inherent chemical properties of the hard and soft segment meant that full
recovery had a possibility of not being achieved. The fact that shape recovery was achieved during
zero load heating doesn’t tell much in terms of storing energy in the polymer apart from calibration
of the frozen volume fraction.
The value of the frozen volume fraction was found to be less than one which implies that the active
phase is more dominant in the material which has been related to the soft segment of PU and thus
the main reason for difficulty in shape recovery.
The maximum fracture strains of the composites were found to be dependent on the dispersion of
the hybrid filler which could cause cracks propagating along the boundary of the matrix and filler.
This would also further influence the wires which began to further weaken the composite. This
highlights the importance of filler dispersion which influences the matrix-filler interaction. Methods
of examination of morphology of polymers are crucial in determining the dispersion of fillers in the
composite matrix.
An attempt was made towards low-cost effective and homogenous thermal activation of an electro-
active SMP while at the same time preserving a maximum amount of mechanical strength. In general
in order to control the hard segment content, one can change either the molecular weight of soft
segment or the mol ratio of hard and soft segments.
The thermodynamic incompatibility between the hard and soft segments induces micro-phase
separation and was therefore responsible the distinct role of each segment in the shape memory
process and therefore the modelling as well
It has undisputedly been shown that shape memory results from a combination of polymer
morphology and specific processing and can be understood as a polymer functionalization and thus
particular constitutive theories are needed to predict this behavior
Polymer physical cross-linking results in a three dimensional network, which enables a shift in
transition temperature when filler content was increased. This also led to broadening of the ,
which to a certain extent can retard the shape recovery speed. A novel approach to morphing wing
systems was attempted and despite an unsuccessful material, a thorough understanding of the
material as well as factors influencing its modelling was determined.
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IX) INDEX
1
1,4-butanediol (BD) · 68
4
4,4’-diphenylmethane diisocyanate · v, 68
4-4’-methylene bis (phenylisocyanate) · 19
A
austenitic · 7
B
butane-1,4-diol · 19
butyl methacrylate · 11
D
deformation · 7
E
ethylenediamine · v, 71
G
graphene oxide · 29
H
High-angle annular dark field scanning transmission
electron microscopy · 31
hydrophilic · 16
M
martensitic · 7
methyl methacrylate · 11
N
nanotube · 28
nanotubes
multi walled · 19
Nickel-titanium
alloy · 7
norbonene · 15
O
oligomers · 16
Optical microscopy · v, 30
P
poly (tetramethyl oxide) glycol (PTMO) · 68
poly(vinyl chloride) (PVC) · 31
polycaprolactenediol · 19
polydimethylsiloxane (PDMS) · 28
polyhedral oligosilsesquioxane · 15
polynorbonene · 15
polyoctene · vi, 13
polystyrene · 16
Polyurethane · 19
S
scanning electron microscopy · 31
Scanning electron microscopy · vi, 30
Scanning probe microscopy · vi, 30
semi-crystalline · 13
styrene-trans-butadiene-styrene · vi, 16
T
thermoset · 11
Transmission electron microscopy · vii, 30
trans-polyoctenamer · 13
V
vinilydene · 11
vitrification · 13
Design, Modelling and Testing of a synthetic muscle system
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