11001259 Dissertation

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


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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 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


~ 8 ~

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


~ 9 ~

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.


~ 10 ~

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.


~ 11 ~

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.


~ 12 ~

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


~ 13 ~

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.


~ 14 ~

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.


~ 15 ~

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.


~ 16 ~

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


~ 17 ~

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))


~ 18 ~

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))


~ 19 ~

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))


~ 20 ~

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.


~ 21 ~

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)

)


~ 22 ~

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)

)


~ 23 ~

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))


~ 24 ~

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))


~ 25 ~

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))


~ 26 ~

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


~ 27 ~

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))


~ 28 ~

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


~ 29 ~

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.


~ 30 ~

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


~ 31 ~

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.


~ 32 ~

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))


~ 33 ~

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


~ 34 ~

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))


~ 35 ~

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

( )

( )


The stored strain is determined by the following evolution equation


~ 36 ~

( )

( )

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


~ 37 ~

( )

∫ ( )

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


~ 38 ~

( ) ( ( ) ( ))

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.


~ 39 ~

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


~ 40 ~

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


~ 41 ~

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,


~ 42 ~

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


~ 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

( ) ( )] ( ( ) ) ∫ ( ( ) )

( ( ) ( )) ( ( ) ( )) ( ( )) ( )


~ 44 ~

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.


~ 45 ~

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


~ 46 ~

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.

( ) ( )


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


Where and are proper orthogonal tensors, and and symmetric tensors. Substituting these

equations in equations 59 and 60

( ) ( )


Deducing from these equations,

( )


Equation 66 implies that and have common eigenvectors such that the spectral

decompositions of these two tensors are as follows

∑

∑


Substituting equations 67 and 68 into equations 63-66,

( ) ( )


Eliminating p and solving equations 67 and 68 in terms of in terms of and


~ 47 ~

( )

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 ( ).


~ 48 ~

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.


~ 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


~ 50 ~

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.


~ 51 ~

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)


~ 52 ~

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


~ 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


~ 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)


Thermomechanical testing veil and 5% CB


~ 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


~ 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


~ 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


~ 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


~ 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


5% CB Thermal Strain


~ 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


~ 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.


~ 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 %


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


zero stress cooling


~ 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


~ 64 ~

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


~ 65 ~

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.


~ 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.


~ 67 ~

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.


~ 68 ~

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))


~ 69 ~

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))


~ 71 ~

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))


~ 72 ~

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.


~ 73 ~

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


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Documents

11001259 Dissertation