Smart materials and structures

Smart structures or smart materials systems are those which incorporate actuators and sors that highly integrate into the structures and have structural functionality, as well ashighly i

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SMART MATERIALS AND STRUCTURES

Lecture at Swiss Federal Institute of Technology Z¨urich (ETH)

Copyright c⃝2015 by Bohua Sun All rights reserved.

Published by Cape Peninsula Univerisity of Technology

Cape Town, South Afica.

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Smart Materials and Structures / Bohua Sun [et al.].

Printed in South Africa.

To My Dear Father, Mother

and Family

[I hope that I may succeed in deserving and obtaining your confidence But in the first place, I can

ask nothing of you but to bring with you, above all, a trust in science and a trust in yourselves The love of truth, faith in the power of mind, is the first condition in Philosophy Man, because

he is Mind, should and must deem himself worthy of the highest; he cannot think too highly of the greatness and the power of his mind, and, with this belief, nothing will be so difficult and hard that it will not reveal itself to him ]

—Georg Wilhelm Friedrich Hegel, Oct 28, 1816 at Heidelberg University

Smart structures or smart materials systems are those which incorporate actuators and sors that highly integrate into the structures and have structural functionality, as well ashighly integrated control logic, signal conditioning, and signal power amplification elec-tronics Such actuating, sensing and controlling are incorporated into a structure for thepurpose of influencing its states or characteristics, be they mechanical, thermal, optical,chemical, electrical, or magnetic For example, a mechanically smart structure is capable

sen-of altering both its mechanical states (its position or velocity) or its mechanical teristics (its stiffness or damping) Optically smart structures could, for example, changecolor to match its background

charac-In the following decades, it is expected that there will be widespread application ofthe technology under development, in its current and evolutionary forms The breath ofapplication of this technology is expected not only towards high-tech but also towardscivilian fields

This lecture notes is specially prepared for the Seminar at Institute of Structural neering at ETH I would like to take this opportunity to address important issues of smartmaterials and structures and to introduce some work from my research group

Engi-I would like to express my deep gratitude to Prof Dr Eleni Chatzi1 for his warmhospitality and to the South African National Research Foundation for financial support

1 Prof Dr Eleni Chatzi is the Chair of Structural Mechanics at ETH

v

2.6.2 Characteristics, Advantages and Capabilities of Fibre Optic

CONTENTS ix

6.2.4 The Mechanical Performance Analysis of the Rectangular

6.3 The Electrical Field Distribution in the Part-circular Shape DPA 58

LIST OF FIGURES

1.2 Active material devices used as actuator (top) and sensor (bottom) 5

2.3 Representation of domain rotation and switching during poling of a

2.9 Illustration of the Shape Memory Effect: Original single crystal lattice

structure in (a); upon cooling down to the martensite finish temperature(Mf) self-accomodated martensite forms without significant change

in external dimensions (b); upon mechanical defomation (c and d)

system minizes energy through twinning (lattice invariant shear)

while maintaining atomic bonds; heating above the austenite finish

temperature reverts variants to the parent phase in the original

xi

xii LIST OF FIGURES

2.10 Stress-strain curves of SMA at phase of austenitic and martensite 17

3.1 Schematic representation of a discrete actuator a) and a distributed

actuator b) Distributed actuator systems are often based on multipleindividual strain actuators (modularity); note that the actual contact

area is very thin and can be typically a mechanical connection in a) and

5.1 Laminated beam with integrated piezoelectric sensor and actuator 48

5.4 Effect of negative velocity feedback gain on the tip transient response

LIST OF FIGURES xiii

6.1 The principal type of DPA element with interdigital electrode (IDE) 56

6.4 The strain result comparison between the analytical model and the FEM 60

7.3 Results for Displacement for substrate/PZT thickness ratios (for 1mm

7.4 Results for the force for substrate/PZT thickness ratios (for 1mm PZT

8.2 Comparison of experimental and theoretical prediction for optical

power through a fibre subjected to elongation due to an axial force 69

LIST OF TABLES

5.1 The material properties of the main structure and piezoelectric 526.1 The constants in the charge density with different h/a and b/a 58

xv

CHAPTER 1

INTRODUCTION

[study hard, improve every day.]

The demand for new generations of industrial, military, commercial, medical, automotiveand aerospace products has fuelled research and development activities focused on ad-vanced materials and smart structures This situation has been further stimulated by theintellectual curiosity of humankind in synthesising new classes of bio-mimetic materials.And, of course, global competition among the principal industrial nations has also been

a parameter in the equation governing the rate of technological progress A fundamentalaxiom of this field of advanced materials is that the ultimate materials are the biologicalmaterials which replicate such characteristics and properties in synthetic materials, andwhich can be employed in diverse scientific and technological applications

Thus, by integrating the knowledge bases associated with the mega-technologies ofadvanced materials, information technology and biotechnology, the creation of a new gen-eration of biomimetic materials and structures can be facilitated, with inherent brains, n-ervous systems and actuation systems –this is at present a mere skeleton compared withthe anatomy perceived in the not-too-distant future This quantum jump in materials tech-nology will revolutionise the future in ways far more dramatic than the way the electronic

Smart Materials and Structures.

2 INTRODUCTION

Figure 1.1 Approach for classification of active materials

chip has impacted on our lifestyles These new materials are termed Smart Materials orIntelligent Materials and they will typically feature fibrous polymeric composite materials,embedded with powerful computer chips of gallium arsenic which will be interfaced withboth embedded sensors and embedded actuators by networks of embedded optical-fibrewave-guides, through which large volumes of data will be transmitted at high speeds.Today’s material revolution is the cornerstone of the triumvirate of mega-technologies,which comprise the essential integrates of this embryonic field These technologies willhave a mutually symbiotic relationship and will significantly impact on one another re-sulting in synergistic technological advances which cannot be foreseen today However, anatural consequence of advancing on these technological disciplines will be the impendingrevolution in smart materials and structures

The classes of smart materials and intelligent structures are diverse and the applications

of them are largely unknown However, what is known is that this new generation ofmaterials will certainly revolutionise our quality of life as dramatically as the state-of-artmaterials did in the past, with stone implements triggering the Stone Age, alloys of copperand tin triggering the Bronze Age, and the smelting of iron ore triggering the Iron Age.The time-line of humankind is located at the dawn of a new age, The Smart Materials Age

Human civilisation has been so profoundly influenced by materials technologies that torians have defined time periods by the materials that dominated during these eras Thus,

his-as humankind embarked upon the continual quest for superior products and weaponry ricated from superior materials, terms such as the Stone Age, the Bronze Age, and the IronAge have entered the vocabulary The current Synthetic Materials Age featuring plasticsand fibrous composites is providing a viable precursor to the dawn of a new era, the Smart

fab-SMART STRUCTURES AND DEVELOPMENT BACKGROUND 3

materials Age, which will capitalise on these synthetic materials in order to exploit

sever-al eclectic emerging technologies for the synthesis of smart materisever-als exhibiting nervoussystems, brains, and muscular capabilities The degree of sophistication displayed by thisnew generation of materials will depend mostly on the individual applications; however,

it is anticipated that various innovations in diverse fields of science will emerge, such asnanotechnology, biomimetics, neural networking, artificial intelligence, materials science,and molecular electronics, for example

This new generation of smart materials will significantly impact on civilisation Forexample, some classes of materials will be able to select and execute specific function-

s autonomously in response to changing environmental stimuli; others will only featureembedded sensory capabilities in order that a structural member is manufactured to com-ply with the quality control specifications Self-repair, self-diagnosis, self-multiplicationand self-degradation are also some of the characteristics anticipated to be a feature of thesupreme classes of smart, or intelligent, materials in an engineering context that all as-pects of civilisation will be influenced by these new generations of innovative materials asdesigners capitalise on their unique capabilities in industries as diverse as aerospace, man-ufacturing, automotive, sporting goods, medicine, semi-conductive technology and civilengineering

Smart structures or smart materials systems are those which incorporate actuators and sors that highly integrate into the structures and have structural functionality, as well ashighly integrated control logic, signal conditioning, and signal power amplification elec-tronics Such actuating, sensing and controlling are incorporated into a structure for thepurpose of influencing its states or characteristics, be they mechanical, thermal, optical,chemical, electrical, or magnetic For example, a mechanically smart structures is capable

sen-of altering both its mechanical states (its position or velocity) or its mechanical teristics (its stiffness or damping) Optically smart structures, for example, could changecolour to match its background

charac-Three historical trends have combined to establish the potential feasibility of smartstructures The first is a transition to laminated materials In the past, structures weremanufactured from large pieces of monolithic materials which were machined, forged, orformed to a final structural shape, making it difficult to imagine the incorporation of activeelements However, in the past 30 years, a transition to laminated materials technologyhas occurred Laminated materials, which are built up from smaller constitutive elements,allow for the easy incorporation of active elements within the structural from One cannow envision the incorporation of a smart ply carrying actuators, sensors, processors, andinter-connections within the laminated materials

The second trend has been the exploitation of the off-diagonal terms in the material stitutive relations, which currently enables smart structures The full constitutive relations

con-of materials include characterisation con-of its mechanical, optical, electromagnetic, cal, physical, and thermal properties For the most part, researchers have focused only onblock diagonal terms Those interested in exploiting a material for its structural benefitshave focused only on the mechanical characterisation However, much can be gained byexploiting the off-diagonal terms in the constitutive relations, which, for example, couplethe mechanical and electrical properties The characterisation and exploitation of these

of smart structures is the development of information processing, artificial intelligence, andcontrol disciplines.

The sum of these three evolving technologies (the transition to laminated materials, theexploitation of the off-diagonal terms in material constitutive relations and the advance

in microelectronics) has created the enabling infrastructure in which smart structures candevelop

The technological field of “smart materials”is not transparent or clearly structured It hasevolved over the past decades with increasing pace during the 1990s to become what it istoday, at the transition to the next millennium Generally speaking these materials respondwith a change in shape upon application of externally applied driving forces Typically thisshape change is reflected in an elongation of the sample, thus allowing the use as e.g asmall linear motor

The term ”smart materials” sometimes also called intelligent materials or active als describes a group of material systems with unique properties At this stage, followingmaterials are the active ones:

Consequently, the term “smart materials”is not very well defined and frequently used

to describe different systems and systems’behaviors Although there have been

approach-es to quantify and classify different levels of smartnapproach-ess or intelligence in systems, from apractical standpoint it is most important to understand that none of the classifications isestablished and used as a standard in the academic, scientific, or industrial community.Furthermore one should note that the terms：

Smart materials

Intelligent Materials

Active Materials

SMART STRUCTURES 5

Adaptive Materials

and to some extent “actuators”and “sensors”

are almost always used interchangeably This can sometimes lead to confusion as differentterms can really describe the same effect or property of a material

To add to the confusion the terms “smart devices”, “smart systems”or “smartstructure”are often carelessly used Here one should note that in general the system com-plexity increases from the unit “material”to “device”to “systems”to “structures”.Any permutation of the adjective (smart, active) with the subject (material, device,…) ismore or less meaningful and seems to have been used already in one way or the other inpublished reports and papers Much more important than the actual word definition is thegeneral understanding of the field

Figure 1.2 Active material devices used as actuator (top) and sensor (bottom)

The term ”smart structure” is more commonly applied to a super-system where sically adaptive materials are employed Smart structures are the structures made of smartmaterials, in other words, are those which incorporate actuators and sensors that are inte-grated into the structure and have structural functionality, as well as integrated control log-

intrin-ic, signal conditioning and power amplification electronics Such actuating, sensing andsignal processing elements are incorporated into a structure for the purpose of influencingits states or characteristics, be they mechanical, thermal, optical, chemical, electrical ormagnetic For example, a mechanically intelligent structure is capable of altering both me-chanical states, i.e its position or velocity, or its mechanical characteristic, i.e its stiffness

or damping An optically intelligent structure could, for example, change colour to match

6 INTRODUCTION

its background The truly intelligent structural system learns and adapts its behaviour inresponse to the external stimulation provided by the environment in which it operates.However there is a wide variety of less sophisticated smart materials and structures whichexploit the basic sub-disciplines, which defines three classes of smart materials Theseinclude materials with only sensing capabilities, those with only actuation capabilities andthose with both sensing and actuation capabilities, at primitive level relative to notions ofintelligence

In the context of intelligent materials there is considerable focus on sensors and actuatorsand control capabilities The current generation of smart materials and structures incorpo-rate one or more of the following features:

Sensors: which are either embedded within a structural materials or else bonded tothe surface of that material Alternatively, the sensing function can be performed by afunctional material, which, for example, measures the intensity of the stimulus associatedwith a stress, strain, and electrical, thermal, radioactive, or chemical phenomenon Thisfunctional material may, in some circumstance, also serve as a structural material.Actuators: which are embedded within a structural material or else, bonded to the sur-face of the material These actuators are typically excited by an external stimulus; such aselectricity in order to either changes their geometrical configuration or else change theirstiffness and energy-dissipation properties in a controlled manner Alternatively, the ac-tuator function can be performed directly by a hybrid material, which serves as both astructural material, and also as a functional material

Control capabilities: which permit the behaviour of the material to respond to an nal stimulus according to a prescribed functional relationship or control algorithm Thesecapabilities typically involve one or more microprocessors and data transmission links,which are based upon the utilisation of an automatic control theory

exter-To get a better understanding of the active materials field it is appropriate to introduce

an approach to classify different smart materials Ideally the classification should be lectively exhaustive and mutually exclusive The most common way of structuring is bylooking at the input and the output of a material system as illustrated in Figure 1.1.The input or stimulus can be for example a change in temperature or in magnetic field.The material then intrinsically responds with an output, which in turn can be for example

col-a chcol-ange in length of the mcol-atericol-al, chcol-ange in viscosity or chcol-ange in electriccol-al conductivity.Active materials can be divided into two groups One group comprises the classicalactive materials as viewed by the academic community and is characterized by the type ofresponse these materials generate Upon application of a stimulus the materials respondwith a change in shape and/or in length of the material(Figure 1.2)

Thus input is always transformed into strain, which can be used to introduce motion

or dynamics into a system These materials are the most widely used group for design ofsmart structures, where active materials are integrated into a mechanical host structure (forexample a building or a helicopter rotor blade) with the goal to change the geometricaldimensions of the structures

The desired change in geometrical dimensions is mostly time dependant and often thesteady state of the structure is a dynamic system where integrated active materials or de-vices are constantly agitated to change in real time the characteristics of the host Devices

SMART MATERIALS AND MEMS 7

based on materials that respond with a change in length are often referred to as actuators

or solid state actuators to be more specific

Conversely active materials can be also used as sensors where a strain applied on thematerial is transformed into a signal that allows computation of the strain levels in the sys-tem The figure below illustrates the basic principles of an actuator/sensor smart materialsystem Depending on the stimulus-response-direction an active materials device can beused as both actuator and sensor

The second group consists of materials that respond to stimuli with a change in a keymaterial property, for example electrical conductivity or viscosity While they are equallyimportant from a scientific point of view, they are less frequently integrated into mechanicalstructures but rather used to design complex modules, for example clutches, fasteners,valves or various switches Frequently these materials are used as sensors

Although materials in this group do not produce strain upon application of an externalstimulus they are sometimes also referred to as actuator systems Examples include theelectro- and magnetorheological fluids, which respond with an increase in viscosity uponapplication of an external electrical or magnetic field

Ultra-small machines are everywhere these days Tiny mechanical devices, so minute that

a hundred thousand could sit on a pencil eraser, are responsible for triggering your airbagsduring an accident, spitting colors out in precise detail on your inkjet printer and projectinglight in the newest digital theaters

MEMS123: Micromachining methods, based on techniques utilized in the manufacture

of microelectronic devices, are being used to produce a growing array of micromechanicalstructures, including membranes, beams, valves, gears, etc The marriage of electrical andmechanical functions on a single chip has led to the development of ”microelectromechan-ical systems” (MEMS), which have over the last decade become well embedded in thehigh-tech landscape The MEMS is a small machine at a very small scale, but not a smallcircuit

NEMS: Now engineers and physicists are taking the next step in machine tion, building mechanical devices on the nanometer scale (a billionth of a meter) If theresearchers succeed, their work could lead to ultra sensitive sensors that can detect even themost subtle genetic alterations responsible for a disease, or to ultra strong artificial musclesthat might replace damaged human tissue or power tiny robots

miniaturiza-This next frontier in mechanization is called nano-electromechanical systems (or S) With MEMS, you could make a mirror and it was still a mirror, just smaller But withNEMS, the whole interaction of matter with light is different You get completely newphysical properties, and that’s a big opportunity for new devices

NEM-1 Bohua Sun, MEMS Technology, CPUT, Cape Town, 2010

2 Bohua Sun and Bo Zhang, Analysis of MOEMES gyroscope, Journal of Astronautics, Vol30, No.5, 2009, 1925-1928.

3 Bohua Sun and Lin Wang, A novel MEMS single mass 3-axis accelerator and single mass 3-axis gyro, Journal

of Mechanics and MEMS, 3(1) 2011 pp.11-23.

CHAPTER 2

SMART MATERIALS AND STRUCTURES

There are several material systems that exhibit an electromechanical coupling that

result-s in a diresult-splacement of the material upon application of an electric field The two mainclasses are piezoelectric materials (PZT) Both are typically ceramics with the exception

of some polymers (like PVDF) that exhibit piezoelectric behavior The conceptual ference between piezoceramics and electrostrictors is their response upon reversing of theelectric field Piezoceramics can be elongated and compressed, while electrostrictors onlyexhibit an elongation, independent of the direction of the applied electric field Differen-

dif-t underlying physical principles musdif-t dif-thus govern dif-these behaviors The general idea ofelectromechanical coupling in a piezoceramic is illustrated Figure 2.1

Piezoelectricity, discovered in on Rochelle salt 1880 by the brothers Jaques and PierreCurie is defined as a change in electric (not to be confused with electronic) polarization;with change in applied stress , which is usually referred to as the direct piezoelectric effect.The converse piezoelectric effect is in analogy the change in strain for a free crystal (orstress for a clamped system) with change in applied field Thus the converse piezoelectriceffect is typically used when a material system is to be used an an actuator: Input is avoltage gradient, output a strain For low fields, there is a linear relationship betweenstrain and electrical field Reversing the field also reverses the direction of the strain

Smart Materials and Structures.

10 SMART MATERIALS AND STRUCTURES

Figure 2.1 Piezoelectric materials

Historically, Rochelle salt and quartz are the most frequently used piezoelectric rials However only relatively new materials system like PZT offer properties that enablethe development of active structural devices

mate-The microscopic origin of the piezoelectric effect is the displacement of ionic chargeswithin a crystal structure In the absence of external strain, the charge distribution withinthe crystal is symmetric and the net electric dipole moment is zero However, when anexternal stress is applied, the charges are displaced and the charge distribution is no longersymmetric

Figure 2.2 Perovskite structure

A net polarization develops and results in an internal electric field A material can beonly piezoelectric if the unit cell has no center of inversion Virtually all piezoelectricmaterials crystallize in the perovskite structure

PIEZOELECTRIC MATERIALS 11

A representation of eight perovskite unit cells, on which most commercially availablepiezoceramics are based on The generic formula is ABO3 Oxygen sits in the octahedralsites (red dots), an A++ material (e.g Pb) in the cube corners (green dots) and a smallB++++ cation (e.g Zr, Ti) in the center (small black dots) The unit cell is electricallyneutral

Figure 2.3 Representation of domain rotation and switching during poling of a polycrystallineceramic

It should be furthermore noted that of course all piezoceramics (like all materials) arealso electrostrictive However, the piezoeffect usually dominates and the electrostrictivecontribution is virtually always ignored in piezoceramics

Each unit cell within a material has a net polarization vector A region of equally ented polarization vectors within a material is called a domain (in analogy to magneticdomains in ferromagnetic materials Piezoelectrics are always ferroelectric which in turnowes much of its terminology to magnetism Ferroelectrics have for example also a Curiepoint, above which a material looses both its ferroelectric and piezoelectric material Typ-ical Curie temperatures for piezoceramics are between 200C and 300C)

ori-Ideally polarization vectors of all unit cells would add up and results in the total larization, forming one large domain within the crystal However commercially availablepiezoceramics are always polycrystalline The sum of all polarization vectors of all unitcells (and of all polarization vectors of all domains) results in an electrically neutral sample

po-as vectors cancel each other out due to a random statistical distribution of directions.Thetrick is then to pole the ceramic at high electric fields to force the domains to rotate andswitch into the desired direction This is represented in Figure 2.3 and 2.4

12 SMART MATERIALS AND STRUCTURES

Figure 2.4 Polarization and electrostrictive

The result is never a full orientation off all domains, nevertheless the polycrystalline ramic exhibits significant net polarization that can be used for actuation or sensing purpos-

ce-es The simple reason that singly crystal piezoceramics are not used is that so far nobodywas able to grow crystals of sufficient size at reasonable costs (Single crystal piezoce-ramics as well as lead-free systems - for environmental reasons - are currently an area ofsignificant research activities)

After poling linear constitutive relationships describe material behaviour:

)

,

(

D ε

elec-Single sheets can be energized to produce motion in the thickness, length, and widthdirections They may be stretched or compressed to generate electrical output

Thin 2-layer elements are the most versatile configuration of all They may be used likesingle sheets (made up of 2 layers), they can be used to bend, or they can be used to extend

”Benders” achieve large deflections relative to other piezo transducers

Multilayered piezo stacks can deliver and support high force loads with minimal pliance, but they deliver small motions

Given today’s remarkable array of applications for piezoelectrics, it is hard to imagine anarea in which these products cannot make a positive difference in design and function

PIEZOELECTRIC MATERIALS 13

Figure 2.5 Piezo transducers (a)

Our ceramic elements can be manufactured to your specifications — to be both technicallyadvantageous and economically efficient Many companies offer a wide range of leadzirconate titanate (PZT) and lead metabolite ceramic elements, generally produced in ring,disc or plate form

14 SMART MATERIALS AND STRUCTURES

Figure 2.6 Piezo transducers (b)

We offer custom cutting, dicing, grinding, lapping, and polishing, along with preciserounding and core drilling When considering applications for our piezo products, take alook at the many ways others have used piezoceramics to great advantage

Piezoelectric actuators have been used for active shape, vibration and acoustic control ofstructures because of their adaptability and light weight Their ability to be easily integrat-

PIEZOELECTRIC MATERIALS 15

ed into structures makes them very attractive in structural control since all the moving partsencountered with conventional actuators are eliminated Structural control is achieved bysimply embedding PZT actuators in the structure or bonding them on the surface of thestructure(Figure 2.5 and 2.6)

Active Fiber Composites (AFCs) (Figure 2.7))developed by MIT are an innovative bination of active and passive materials to create a new hybrid material capable of meet-ing the increasingly high demands of current and upcoming applications in the aerospaceindustry Its potential Applications: Vibration Suppression - Rotorcraft and Airplanesincreased structure life, increased passenger comfort, improved flight performance (bet-ter fuel efficiency, higher payloads, increased cruising speeds) Acoustic Control- He-licopter/Aircraft Fuselages and Submarines decreased cabin noise minimizing acousticsignatures in aircraft, submarines and torpedos, Sensors, Others airplane wing de-icingmicro-air vehicles

com-Figure 2.7 Active Fibre Composite (Piezoelectric fibre) from MIT

Another proposed application for piezoelectrics is in flow-induced vibrations reduction

An application for the vibration control of a cantilever plate by using the digital PID Theplate composed of two PVDF (Polyvinylidene Fluoride) piezoelectric films and a plasticbase plate has been placed parallel to the flow in a low turbulent wind tunnel

An integrated distributed actuator design methodology based upon the converse electric effect and aimed at actively controlling the in-vacuo flapping and lagging eigen-vibration characteristics of rotating blades carrying a tip mass is presented The helicopter

piezo-16 SMART MATERIALS AND STRUCTURES

blade is modeled as a thin/thick walled closed cross-section untwisted cantilevered beamrotating with constant angular velocity

The state-of-the-art research in the application of PZT materials indicates that ous issues remain unanswered about the application of piezoelectrics and their limitations.Research on modeling is needed to predict the behavior On the materials engineering sideinvestigation for enhancing mechanical properties of piezoelectrics is needed Previousresearch performed on PZT-actuated beam and plate structures has led to models describ-ing their response However, much less research has been performed on structures withcurvatures and further research in this area is needed

The most common group of materials that respond to a temperature change with a shapechange or elongation are Shape Memory Alloys (SMAs)(Figure 2.8)

These alloys, for commercial use mostly Titanium-Nickel alloys, undergo a phase formation upon temperature change This austenitic to martensite transformation can di-rectly lead to a volume and change shape of the sample Furthermore, if properly designed,the material (e.g in wire or spring form) can be trained to transform fully reversibly in anexactly reproducible way, thus representing a micro-motor that can be driven by tempera-ture increase and decrease

trans-Shape Memory Alloys can be operated in a one-way mechanism, e.g upon heatingabove a critical temperature (the austenite finish temperature) the shape memory systemadapts to the desired shape it had originally

However it also possible to ”train” the material to operate fully reversible which isknown as the two-way shape memory effect Here the twinning (see ”c” and ”d” in Figure2.9) during each cycle takes place in exactly the same manner resulting in a nearly identicalmicrostructure after each deformation Generally the one-way shape memory effect leads

to higher strains than the two-way effect

Many metals exhibit a phase change as they are heated and cooled We can illustratethis using a crude ‘stick and ball’model of the metallic lattice

SHAPE MEMORY MATERIALS 17

Figure 2.9 Illustration of the Shape Memory Effect: Original single crystal lattice structure in(a); upon cooling down to the martensite finish temperature (Mf) self-accomodated martensite formswithout significant change in external dimensions (b); upon mechanical defomation (c and d) systemminizes energy through twinning (lattice invariant shear) while maintaining atomic bonds; heatingabove the austenite finish temperature reverts variants to the parent phase in the original orientation(e)

Figure 2.10 Stress-strain curves of SMA at phase of austenitic and martensite

The higher temperature austenitic structure has the characteristic stress-strain curve ofmost metals The lower temperature martensitic structure has a stress-strain curve morelike that of an elastomer in which there is a ‘plateau’stress All the deformation up

to about 8/100 is ’elastic’or in other words it can be recovered –but not by simply

relaxing the stress whilst in the martensitic condition (Figure 2.10))

There are numerous alloys which exhibit this memory The most useful for fluid ting applications is the Titanium-Nickel family known by the Raychem Corporation Tinel?

fit-18 SMART MATERIALS AND STRUCTURES

name and particularly the Titanium-Nickel-Iron Alloy A and higher strength A-HS whichexert very high forces on recovery and have transformation temperatures in the region -100oC to -150oC

Ferromagnetic Shape Memory Alloys (FSMA) (Figure 2.11))are a recently discoveredclass of actuator material, whose salient features are magnetically driven actuation (fieldintensity varies, about 3KG and larger) and large strains (around 6/100) FSMA are still

in the development phase; so far only alloys in the Ni-Mn-Ga ternary have been proven toshow satisfactory performance, but other systems have interesting potential

As the name suggests FSMAs are ferromagnetic alloys which also support the shapememory effect This means that they undergo the characteristic martensitic transformationupon cooling, and show all features of conventional shape memory alloys However, theactuation mechanism in these materials is radically different to ordinary shape memoryalloys Rather than being heat driven, they are magnetically driven This difference allowsfor increased frequency response (fast actuation)

FSMA operate solely in the martensitic phase, the martensitic phase transformationbeing immaterial for anything other than setting an upper operation temperature (if thetemperature rises above the austenite start temperature As, then the material transforms toaustenite (the high temperature phase) and cannot be magnetically driven.) The deforma-tion mechanism relies on two facts:

that the martensitic phase of an FSMA has twinning as its preferential deformationmechanism, and,that the martensitic phase has a high magneto-crystalline anisotropy, that

is, that the magnetization is strongly pinned to specific crystallographic orientations Inother words, there are axes in the crystal where the material is easily magnetized (easydirections), and increasingly higher field-intensities are required to align the magnetizationwith the field on directions away from these easy axes

SHAPE MEMORY MATERIALS 19

Unlike slip (dislocations) twinning is a planar defect The twinning process is a pureshear of the crystal which transforms its crystallographic structure into a new one Forthe materials of interest, the twinned structure is mirror symmetric to the original one(type I twins, mixed type twins) The structures related by a twinning shear are calledtwin variants Because each is a sheared version of the other, twin variants have differentmagnetic easy axes

In a situation where two twin variants exist in a single crystal, a magnetic field will tend

to align the magnetic moments But because of the high magneto-crystalline anisotropythe magnetic moments will not readily sway away from their easy axes Instead, it ispossible that one crystal twin shears into the other variant so that there the magnetic easyaxes is better aligned with the field This is magnetically driven twin boundary motion, themechanism of operation of FSMA

The coupling of using Shape memory alloys has been the best application for single rials so far (Figure 2.12, and 2.13)

mate-Couplings are machined from Tinel bar-stock to a size such that their inside diameter

is slightly smaller than the outside diameter of the tubes they are intended to join Thecouplings are then immersed in liquid nitrogen so that the metal becomes martensitic.They are then mechanically expanded by driving a tapered steel mandrel through thebore using a hydraulic press So long as they are kept cold they maintain this expandedshape in which the bore is now large enough to accommodate the tube outside diameter

It is in this condition that they are delivered to the user If they are allowed to warm upthey will undergo ’free recovery’, that is they will shrink back to the as-machined size andagain will be too small to slip over the tube

Constrained recovery on the other hand is what happens when we place something inthe way of the recovery back to the original austenitic shape

In the case of the couplings, it is the tube which prevents complete recovery

20 SMART MATERIALS AND STRUCTURES

The Tinel alloy from which the couplings are machined recovers with tremendous forceand if a tube is interposed it will be swaged as the coupling tries to get back to its originalshape

The tubing resists this force and the two come into equilibrium with about 2/100 strainremaining in the coupling, but this is a dynamic equilibrium, if the tube grows or shrinksthe coupling follows; it is always trying to get back to its as-machined dimensions

Unlike mechanically swaged couplings whose pressure on the tube relaxes as soon theswage head is removed, this constrained recovery or ‘live crimp’provides a dramaticbenefit in terms of the reliability of the coupling Even in high vibration conditions or withthe coupling slipped or rotated about the tube the seal is still good

of cubic laves phase iron alloys containing the rare earth elements Dysprosium, Dy, orTerbium, Tb; DyFe2, and TbFe2 However, these materials have tremendous magneticanisotropy which necessitates a very large magnetic field to drive the magnetostriction.Noting that these materials have anisotropies in opposite directions, Clark and his co-workers at NSWC-Carderock, prepared alloys containing Fe, Dy, and Tb These alloysare generally stochiometric, of the form TbxDy1−xFe2and have been coined Terfenol-D.

MAGNETOSTRICTIVE MATERIALS 21

Figure 2.14 Strain versus magnetic field

Terfenol-D, operated under a mechanical-bias, strains to about 2000 microstrain at roomtemperatures For typical transducer and actuator applications, Terfenol-D is the mostcommonly used engineering magnetostrictive material

The mechanism of magnetostriction at an atomic level is relatively complex subjectmatter but on a macroscopic level may be segregated into two distinct processes The firstprocess is dominated by the migration of domain walls within the material in response toexternal magnetic fields Second, is the rotation of the domains These two mechanismsallow the material to change the domain orientation which in turn causes a dimensionalchange Since the deformation is isochoric there is an opposite dimensional change in theorthogonal direction Although there may be many mechanism to the reorientation of thedomains, the basic idea, represented in the figure, remains that the rotation and movement

of magnetic domains causes a physical length change in the material

Magnetostrictive materials (MS) are typically mechanically biased in normal operation

A compressive load is applied to the material, which, due to the magneto-elastic coupling,forces the domain structure to orient perpendicular to the applied force Then, as a magnet-

ic field is introduced, the domain structure rotates producing the maximum possible strain

in the material A tensile preload should orient the domain structure parallel to the appliedforce though this has not yet been observed due to the brittleness of the material in tension.The very first positive identification of a magnetostrictive effect was in 1842 whenJames Joule observed that a sample of nickel changed in length when it was magnetised.Subsequently cobalt, iron and alloys of these materials were found to show a significantmagnetostrictive effect with strains of about 50ppm The reciprocal effect, in which ap-plying a stress to a body is known as the Villari effect An additional phenomenon known

as the Wiedemann effect is a twisting in a material when a helical magnetic field is plied The inverse of this, called the Matteuci effect is the creation of a helical field when

ap-a map-agnetostrictive map-ateriap-al is subject to ap-a torque

22 SMART MATERIALS AND STRUCTURES

One of the first practical applications of magnetostriction was its use in SONAR vices in echo location during the second world war Another early application includedtorque sensing and these applications are as important today as they were then The nickelbased materials used in these devices had saturation magnetostriction values of 50 partsper million (ppm) These strains are quite low and so have limited applications

de-In the 1960s the rare-earth elements terbium (Tb) and dysprosium (Dy) were found tohave between 100 and 10,000 times the magnetostrictive strains found in nickel alloys.However because this property only occurs at low temperatures, applications operating atambient temperature and above were not possible

What researchers were looking for was a material which would operate at high atures, have a large magnetostrictive strain but would only require a low magnetic field.They found that the addition of iron to Tb and Dy to form the compounds TbFe2 andDyFe2 brought the magnetostrictive properties to room temperature These materials re-quired very large magnetic fields to generate large strains By alloying the two compounds

temper-it was found that the magnetic field required to produce saturated strains were considerablyreduced The resulting alloy Tb.27Dy.73Fe1.95 (commercially known as Terfenol-D) is atpresent the most widely used magnetostrictive material Terfenol is capable of strains ashigh as 1500ppm and, since the 1980’s, has been a commercially available material forapplication in a great many fields

In ferromagnetic materials, the existence of local magnetic moments is inextricably related

to the electronic configurations The wave functions of the electrons in a multi-atom systemare related to the interatomic distance in self-consistent manner They differ significantlyfrom atomic orbital for short interatomic distances, such as are found in solids

Figure 2.15 Thermal expansion of a magnetic material

Compared to the atomic orbitals that electrons would occupy, the energy of the tronic states when there is a local magnetic moment is higher (lower) This results in anincreased (diminished) interatomic distance compared to non magnetic species, an effectthat can generally be described as a strain This strain is termed magnetostriction

elec-MAGNETOSTRICTIVE MATERIALS 23

Magnetostriction is further affected by long-range magnetic ordering, such as takesplace below the Curie temperature TC in ferromagnetic materials In as much as the mag-netic ordering can be modified by applied magnetic fields, the latter will also influence theobserved magnetostriction

A better picture of the different types of magnetostriction can be gained from the ious contributions to the thermal expansion of a magnetic material, which are depicted inFigure2.15 The dotted line (marked ”no local moment”) indicates normal linear thermalexpansion for a solid The dot-dashed line labeled ”Local moment” is displaced from thefirst to indicate the volume expansion that accompanies the formation of a local magneticmoment

var-Because the local magnetic moment does not vanish immediately above TC but merelyloses its long-range ordering, the internal pressure associated with it does not vanish com-pletely above TC (Figure2.15, solid line) The solid lines show the form of the thermalexpansion for a ferromagnet above and below TC Below TC, additional magneto-volumeeffects due to long-range magnetic ordering are turned on; they may add to, or subtractfrom the volume expansion due to the presence of a local moment

The slope of these solid lines (the thermal expansion coefficient, alpha) can be of eithersign just below the Curie temperature (a property that is used in invar alloys, such asFe70Ni30) All of these effects are isotropic, involving the bulk modulus These isotropiceffects are called volume magnetostriction or, when the magnetic ordering is produced by

an applied field, they are called forced magnetostriction

Figure2.15, schematic of the thermal expansion of a magnetic material as a function

of temperature illustrating the increased volume due to the presence of a local

magnet-ic moment and the onset of magnetmagnet-ic anomalies below the Curie temperature A smallanisotropic strain, depending on the direction of magnetization (circled inset), is also ob-served below TC The latter is usually referred to as anisotropic magnetostriction

On a smaller scale, the volume expansion can show an anisotropy for T ¡ TC , i.e., thelinear strain is different in different directions relative to the direction of magnetization(Figure2.15, circled inset) That is, the magnetization vector has associated with it a stressdirected along M which causes a uniaxial mechanical deformation

Magnetosrtictive devices may be incorporated in multifunctional composites for tailoring

of mechanical deformations as well as for the sensing of these deformations/forces Whendistributed as microscale devices in a host, magnetostrictives can act as distributed sen-sors in multifunctional composites Alternative applications include distributed actuationfor composites capable of vibration suppression, micropositioning, damage mitigation andshape control

Preliminary results show that simple analog control systems consisting of Terfenol-Dactuators can significantly reduce flexural vibrations in a rotating shaft with application inmachine tools Passive damping and velocity sensing using magnetostrictive transductionhas been discussed

A prototype magnetostrictive actuator is shown in Figure 2.16

An integrated model to analyze the embedded magnetostrictive mini actuators (MMA)and the vibration suppression capability of a cantilever beam embedded with MMA is de-veloped The simulation results has indicated that by embedding MMA in the host struc-ture, the vibration suppression of host structure can be achieved by using the magneto-thermoelastic