Encyclopedia of Smart Materials (Vols 1 and 2) - M. Schwartz (2002) Episode 11 pptx

Typical SMA behavior in tensile tests and bending applications: a stress-strain curve of shape memory martensite material, b schematic of a shape memory application, c stress– strain cur

AppliedHeating

InitialPosition

InitialPosition

Superelastic Effect Shape Memory Effect

Figure 1 Typical SMA behavior in tensile tests and bending applications: (a) stress-strain curve

of shape memory (martensite) material, (b) schematic of a shape memory application, (c) stress–

strain curve of superelastic (austenite) in tension, (d) superelastic behavior in a bending application.

Shape-memory alloys may also be trained to exhibit

a two-way shape memory effect Similar to the thermal

shape-memory effect, two-way shape memory (TWSM)

requires special thermomechanical processing to impart

shape memory in both martensitic and austenitic phases

A trained shape in the austenitic phase reverts to a

sec-ond trained shape upon cooling, allowing the material to

cycle between two different shapes This TWSM is

theoret-ically ideal for many shape-memory applications; however,

practical uses are limited due to behavior instability and

complex processing requirements

Superelastic Effect This effect, known also as

pseudoe-lastic, describes material strains that are recovered

isothermally to yield mechanical shape-memory behavior

The phenomenon is essentially the same as the thermal

shape-memory effect, although the phase transformation

to austenite (Af) occurs at temperatures below the expected

operating temperature If the austenitic phase is strained

by an applied load, a martensitic phase is induced by

stress, and the twinning process occurs as if the material

had been cooled to its martensitic temperature When the

applied load is removed, the material inherently prefers

the austenitic phase at the operating temperature, and

its strain is instantly recovered A typical stress–strain

curve is depicted in Fig 1c, and a schematic example of asuperelastic application is shown in Fig 1d The stress–strain curve indicates a difference in stress levels dur-ing loading and unloading, that is known as superelasticstress–strain hysteresis

Alloys

Several alloys have been developed that display ing degrees and types of shape-memory behavior Themost commercially successful have been Ni–Ti, Ni–Ti-Xand Cu-based alloys, although Ni–Ti and ternary Ni–Ti–Xalloys are used in more than 90% of new SMA applications(6) Ni–Ti alloys are more expensive to melt and producethan copper alloys, but they are preferred for their duc-tility, stability in cyclic applications, corrosion resistance,biocompatibility, and higher electrical resistivity for resis-tive heating in actuator applications (6)

vary-The most common Cu-based alloys, Cu–Al–Ni and Cu–Zn–Al, are used for their narrow thermal hysteresis andadaptability to two-way memory training Ni–Ti ternaryalloys are used to enhance other parameters Examplesinclude Ni–Ti–Nb for wide thermal hysteresis, Ni–Ti–Fefor extremely low TTR, Ni–Ti–Cr for TTR stability duringthermomechanical processing, and Ni–Ti–Cu for narrowthermal hysteresis and cyclic stability (7)

Material Forms

SMAs are manufactured in many of the conventional forms

expected of metal alloys: drawn round wire, flat wire,

tubing, rolled sheet, and sputtered thin films Additional

forms include shaped components, centerless ground

ta-pered wires and tubing, alternate core wire (Ni–Ti filled

with a conductive or radiopaque material), PTFE coated

wire, stranded wire, and embedded composites At present,

Ni–Ti–X alloys are the most readily available in all of these

forms

The processing of SMA material is critical for

optimiz-ing shape-memory behavior Many adjustments can be

made to optimize the properties of a material form for a

particular application; however, most efforts are made to

optimize a balance of strain recovery, ductility, and

ten-sile strength SMAs such as Ni–Ti are melted using

ex-treme purity and composition control, hot worked to bars

or plates, cold worked to their final form, and subjected to

specialized thermomechanical treatments to enhance their

shape-memory properties

DESIGNING WITH SHAPE MEMORY ALLOYS

Shape-memory alloys have intrigued engineers and

inven-tors for more than 30 years One might conclude from the

large number of SMA patents that have been issued and

the knowledge that relatively few of the ideas have been

commercially successful that the majority of these designs

have not fully accounted for the unique behaviors,

limita-tions, and constraints of SMAs The focus of this section is

to highlight the properties best used in SMA applications

and to discuss SMA design considerations

Functional Properties

SMA applications are often categorized in terms of the

spe-cific material property used The majority of these

pro-perties are either thermal shape memory or mechanical

shape memory (superelastic), but some unique properties

are only indirectly related to these shape-memory effects

General categories of applications are classified according

to these properties

Shape Memory The thermally activated ability of a

shape memory material to change shape yields several

types of applications that can be summarized in three

dis-tinct categories: applications that use the shape change to

display motion, those that actuate, and those that harness

stresses produced from constraining the recovery of the

shape-memory material

Displayed motion, also referred to as free recovery,

de-scribes applications that exploit the pure motion of thermal

shape memory (8) An example of this application, a moving

butterfly, is displayed in Fig 2 These butterflies, produced

by Dynalloy, Inc., use a specially processed form of Ni–Ti

wire to move wings back and forth for thousands of cycles

without significant signs of fatigue This processed wire,

known as FlexinolTM, changes shape via cyclic heating by

electric current The small mass of the butterfly body is

sufficient to extend the Ni–Ti wire when cooled, but the

Ni–Ti wire can contract and close the wings when heated

to its stronger austenitic shape

Actuation applications are designed to perform work

A simplified example is a mass suspended from a memory tension spring When cooled, the weaker marten-sitic phase deforms, and the spring is extended by the mass.When heated to austenite, the spring recovers its shapewith forces sufficient to lift the weight, resulting in actua-tion that performs work

shape-Constrained recovery applications use the change inmaterial strength from martensite to austenite to pro-duce a stress that can be harnessed as a clamping force

A popular example of a constrained recovery application

is a shape-memory coupling which is expanded at lowtemperatures, then heated to shrink and clamp to join twopipes

Superelasticity Unlike thermal shape-memory

applica-tions, which can be categorized into several types, cations that exploit this mechanical shape memory aredefined as those that require high strain recovery at

appli-Figure 2 Photograph of a FlexinolTM actuated butterfly tesy of Dynalloy, Inc.).

(cour-Figure 3 Suture retrieval loops designed to recover their shape once deployed from a 6 fr cannula

(courtesy of Shape Memory Applications, Inc.).

operating temperatures Many examples of applications

that use superelasticity are found in the medical

indus-try (Fig 3), but one of the most well known is found in

consumer eyeglass frames marketed as Flexon® by

Mar-chon Eyewear, Inc (Fig 4)

Energy Absorption for Vibrational Damping An energy

absorbing ability found in both the martensitic and

austenitic phases of SMAs is indirectly related to their

shape-memory behavior The energy absorption of SMA

materials has demonstrated excellent vibrational

damp-ing characteristics, which can be harnessed for use in

various damping applications The types of devices that

exploit this property are classified in three categories of

damping : martensitic, martensitic transformation, and

superelastic

Martensitic damping devices operate by using only the

martensitic phase of SMAs Energy is absorbed by the

martensite during its twin reorientation process, and

acco-mmodates large strains for high-amplitude, low-frequency

loading They offer the best damping characteristics ofthe three categories, and although they cannot recoverlarge strains without subsequent heating, they provideexcellent damping properties across a broad temperaturerange

Martensitic transformation damping elements are signed to operate near martensitic transition temperaturesfor peak performance in vibrational attenuation Thispeak is due to a sharp increase in internal friction dur-ing the martensitic phase transformation These dampingelements offer ideal properties for low-amplitude, high-frequency vibrations within a small operating temperaturerange (9) This type of device could be used in ski materi-als to damp vibrations when the ski is in contact with snow(6)

de-Superelastic damping devices use the plateau sis portion of the stress–strain curve for properties similar

hystere-to those of a rubber band Superelastic SMA materials arepretensioned to reach this stress–strain plateau, and anyadditional strains are accommodated easily by changes in

Figure 4 Deformation resistant eyeglass frames (courtesy of

Marchon Eyewear, Inc.).

the applied load This property optimizes a combination of

damping capacity, shape recovery, and temperature range

of operation (9) Unlike martensitic damping elements,

superelastic devices recover their original shape when

vi-brational loading is removed Suggested superelastic

ten-sioning devices are presented in a U.S patent regarding

hysteretic damping (10); one example is shown in Fig 5 (9)

These SMA tension elements cycle through a

superelas-tic stress–strain hysteresis to dissipate energy and serve

as a damping mechanism Vibrations due to

environmen-tal impacts such as violent winds and earthquakes deform

the tensioned elements, and when the vibrational impact

is lessened, the elements recover their shapes

Cavitation-Erosion Resistance Cavitation erosion is a

phenomenon that affects equipment and machinery in

many industries Small bubbles explode with large

Figure 5 Schematic of a superelastic damping device, using

loops of SMA wire in tension Reprinted with permission from D.E.

Hodgson and R.C Krumme, Damping in Structural Applications,

SMST Proceedings, 1994.

impacts, causing pitting and erosion in metallic surfacesand reducing the service life of expensive equipment Boththe martensitic and austenitic phases of SMAs have dis-played cavitation-erosion resistance; they recover from im-pact and minimize material loss when exposed to vibratorycavitation Studies that explored the performance of Ni–Ti

on stainless steels have indicated that both martensiticand austenitic Ni-Ti have significant potential for coveringand protecting equipment that suffers wear from cavita-tion erosion Ni–Ti cladding could be used in applicationssuch as machinery, hydraulics, large hydroelectric genera-tor turbines, and ship propellers (11)

Low Elastic Modulus The martensitic phase of SMA

ma-terials is soft and pliable, in contrast to the stiff, springycharacteristics of the austenitic phase This softness, orlow effective (nonlinear) elastic modulus, is often used

in applications that require deformability and excellentfatigue characteristics This property is exploited alone

or in conjunction with a shape-memory effect in resistant applications

fatigue-An example of a low elastic modulus application isshown in Fig 6: a martensitic tool developed by St JudeMedical, Inc., is used by surgeons during open heartsurgery to orient a tissue-restraining device During thisprocedure, surgeons must make adjustments to optimizethe tool geometry for each patient, and the use of SMAsallow surgeons to bend the martensitic handle to an ap-propriate angle Upon completing the operation, the tool issterilized in an autoclave where it is exposed to elevatedtemperatures and reverts to its trained, austenitic shape.Due to its ability to recover large strains repeatedly, thesetools are marketed for both fatigue resistance and shape-memory properties

Design Constraints and Considerations

When assessing a potential design challenge, designers areoften anxious to develop a solution that uses the uniqueand exciting properties of SMAs It is critical, however, fordesigners to understand the complexity of SMA behavior

As a general rule, if conventional materials and designscan be applied to yield an acceptable and desirable result,the use of SMAs to provide an alternative solution willincrease complexity and cost SMAs are best used whentheir unique properties are necessary for design success—when conventional materials cannot meet the demands ofthe application

The design of SMA applications requires more than ditional design techniques and textbook methods Due tothe many unique properties of SMA materials, several con-siderations specific to SMA design must be addressed andaccounted for This section discusses the majority of issuesthat should be addressed before designing an applicationusing SMAs

tra-General Guidelines

Recoverable Strain The expected recoverable strain of

SMA material must be within the limitations of the alloy

Figure 6 Medical tools and devices Left to right: Flexible martensitic, Ni–Ti handle developed by

St Jude Medical for open heart surgery procedures; superelastic, tapered guidewire core; shaped Ni–Ti tubing component; retractable, superelastic component within a small diameter cannula (courtesy of Shape Memory Applications, Inc.).

chosen For example, Ni–Ti may recover 8% strain for a

single cycle application, but less than 4% for higher cycle

applications Recommended strain limits are 6% for Ni–Ti

and 2% for Cu–Zn–Al for lower cycle applications and 2%

and 0.5% for higher cycle applications, respectively (3) A

maximum strain recovery of about 2% is expected for

ap-plications that require two-way shape memory (12)

High Temperature Stability Alloy stability must be

con-sidered when an application requires or will be subject to

high operating temperatures Ni–Ti alloys tend to be the

most stable of all SMAs at elevated temperatures and can

withstand exposure to temperatures up to approximately

250◦C before previously memorized shaping is deleted For

Cu–Zn–Al, this maximum temperature is around 90◦C

Fatigue SMA fatigue can be defined as degradation of

any or all of its functional properties SMAs affected by

application cycle quantity, frequency, temperature range,

stress, and strain may fatigue by fracture, decreasing

recoverable strain, shifting transformation temperatures,

or decreasing recovery stress

Manufacturability SMA materials are infamously

dif-ficult to machine Tool wear is rapid for conventional

machining methods such as turning, milling, drilling, andtapping (2) Currently, the most successful machining tech-niques include surface grinding, abrasive cutting, EDM,and laser cutting Component shaping must be considered

as well; the memories of SMA shapes are trained at hightemperatures, typically around 500◦C (932◦F) Unlike mostconventional materials that may be cold formed, SMAsmust be rigidly clamped in a desired shape and exposed

to these elevated temperatures

Designing for assembly is also an important turing consideration Fastening SMAs to other materials

manufac-by bonding and joining presents additional challenges cause SMAs are designed to exhibit strains up to 8% andother materials have a strain limit of less than 1%, whenthe two are rigidly joined, the conventional material maybreak during operation This often causes problems in us-ing plated or painted SMA materials because the coating

Be-on the SMA will often crack and flake during the strains

of operation

Cost Most SMAs are inherently more expensive than

conventional materials due to the higher cost of both rawmaterial components and processing methods The com-positional control necessary for the raw forms of SMA

Figure 7 Finite element analysis model of a self-expandable Ni–Ti stent: displays a quantified

mapping of stress and strain amplitudes in both expanded and compressed positions (courtesy of Pacific Consultants, LLC).

material requires special furnaces and processes, the

se-quence of cold working and annealing to ensure

opti-mal SMA properties is extensive, and the special tooling

and fixturing required for producing the many forms and

shapes of the materials increase the cost of using SMAs

Computer Modeling Capability Finite element analysis

(FEA), often used in conventional material design, has also

been used to model the behavior of SMAs The analysis is

difficult, however, and should not depend on standard

ma-terial templates and subroutines because the functional

properties of SMAs rely on nonstandard factors, such as

composition and processing history Highly specific and

complex modeling techniques must account for the state

of the SMA material once formed in its trained shape, and

then must incorporate the nonlinearity of the stress–strain

curve, the property dependence on temperature, and the

difference between loading and unloading stress behavior

Figure 7 is an illustration of a FEA model of a superelastic

coronary stent that was achieved by using custom

model-ing subroutines to predict mechanical properties

Shape Memory Applications

Temperature Cycling Thermally activated SMA

applica-tions require temperature control to optimize the effect

of shape memory To harness the unique properties

ob-tained from martensitic transformations, temperatures

usually cycle between the extremes of the SMA

temper-ature hysteresis Depending on the alloy selected, this

hysteresis might be smaller than 1◦C (1.8◦F) or larger than

100◦C (180◦F) Applications must incorporate a method

of heating and cooling SMA components through their

hystereses; the rate of cycling for a shape-memory vice is limited by the rate of temperature cycling Thebutterfly example of Fig 2 has a hysteresis of about

de-30 to 50◦C The FlexinolTM actuator wire is heated to atemperature above 90◦C to contract, but must be cooled

to approximately 40◦C to transform to martensite Thisapplication uses ambient air for cooling—only a fewseconds are required for the wire to cool and stretch withthe mass of the butterfly body A few alloys have beendeveloped to reduce or to increase this temperature hys-teresis, as mentioned earlier In addition, a secondarymartensitic phase transformation found in many SMAs,called an R-phase transformation, can be exploited for itshysteresis of less than 2◦C Although recoverable strainsare limited to about 0.5% by this transformation, it may beideal for certain applications (13)

Power SMAs require thermal energy for memory

acti-vation that is most often delivered as direct heat or appliedcurrent for resistive heating Applications that use ther-mal shape memory must account for the power require-ments of the material, the connection of the power source

to the SMA, space requirements to house the source, andany safety mechanisms necessary to prevent overheating

Force Requirements SMA applications typically exploit

the strength differential between the martensitic andaustenitic phases of the material In many actuating de-vices, an SMA element is paired with a conventionalmaterial element to serve as a biasing mechanism Theconventional element, such as a steel coil spring, displacesthe SMA element when martensitic, but yields to the SMA

when heated to its stronger austenitic phase This enables

a one-way shape memory element to behave as a

two-way shape-memory device The forces delivered at each

of the temperature extremes must be considered in SMA

design

Superelastic Applications

Operating Temperature Range The temperature range of

operation for a superelastic application must be above the

Af temperature for optimal superelasticity, but must also

be below its Md temperature (the temperature at which

martensite can no longer be stress induced) This range is

typically 50 to 80◦C above the Af(14)

Force Requirements As operating temperatures

in-crease above the SMA Af temperature, loading and

un-loading stresses increase as a function of the Clausius–

Clapeyron equation (14) Due to variations in the latent

heat of transformation among alloy types, the increase in

stress, as temperature changes, ranges from 2.5 MPa /◦C to

more than 15 MPa /◦C (15)

SMA APPLICATIONS

Applications that use each of the unique properties of

SMAs have been designed, prototyped, and marketed

throughout the world This section provides examples of

these applications and includes some discussion of design

choices, material limitations, and SMA behavior These

examples are categorized by industry to demonstrate the

varied and widespread use of SMA applications

Aeronautics/Aerospace

Many of the initial product ideas and applications that

incorporate SMAs were pioneered in the fields of

aero-nautics and aerospace SMA materials are used in these

industries to take advantage of properties such as high

power-to-mass ratios and ideal actuating behavior in

zero-gravity conditions Designs that use these

prop-erties replace heavier, more complex conventional

de-vices because of reduced weight, design simplicity, and

reliability

Cryofit® Hydraulic Pipe Couplings SMA couplings

were the first successful commercial application of

shape-memory alloys (Fig 8) In 1969, Raychem

Corpora-tion introduced shrink-to-fit hydraulic pipe couplings for

F-14 jet fighters that were built by Grumman Aerospace

Corporation This coupling is fabricated from a Ni–Ti–Fe

alloy whose martensitic transformation temperature is

be-low −120◦C It is machined at room temperature to an

inner diameter approximately 4% smaller than the outer

diameter of the piping it is designed to join When cooled

below−120◦C by liquid nitrogen, the coupling is forced to a

diameter 4% greater than the pipe diameter for an overall

internal strain of about 8% When warmed above its TTR,the coupling diameter decreases to form a tight seal be-tween the pipes (16)

This shape-memory application of constrained recoverycontinues to be a commercial and financial success Despitethe difficulties of cooling the couplings to liquid nitrogentemperatures for expansion and storage, the aerospace in-dustry has welcomed their many advantages over tradi-tional pipe-joining techniques such as welding or brazing.Installation is simple, less costly, and does not rely on highlevels of operator skill The replacement of couplings andhydraulic lines is straightforward, and the possibility ofannealing and damaging the hydraulic lines as in welding

or brazing is eliminated (2)

Frangibolt® Release Bolts Shape-memory bolts were

developed by the TiNi Alloy Company to replace tional exploding bolt devices in aerospace release mech-anisms The bolts are used to attach spacecraft acces-sories during launch and to release them after launch byusing an activated heating element (17) A martensitic,shape-memory cylinder is compressed and assembled to

conven-a notched bolt When conven-activconven-ated by conven-an electricconven-al heconven-ater, thecylinder increases in length and delivers a force greaterthan 22 kN (5000 lbs) to fracture the bolt at its notch(18) These release bolts were used successfully aboardthe spacecraft Clementine in 1994, and have improvedupon designs for conventional explosive mechanisms byeliminating the risks of off-gassing, accidental activationduring shipment, and potential spacecraft damage duringexplosions

Mars Sojourner Rover Actuator An SMA wire was used

to actuate a glass plate above a small solar cell on theRover unit during the recent Pathfinder/Sojourner mission

to Mars A material adhesion experiment performed ing the mission used the actuator to replace large, heavymotors and solenoids A small, simple length of Ni–Ti wireheated and contracted when the Rover applied power andpulled a glass plate away from the solar cell to allow com-parison of sunlight intensity with and without the plate.The rate of dust collection was then determined, and theresulting data will be used to design cleaning methods forfuture missions to Mars (19)

dur-Self-Erectable Antenna A prototype space antenna was

constructed by Goodyear Aerospace Corporation Designed

to fold compactly at room temperature, the device wouldunfold into a large, extended antenna shape when heated

by solar energy (2) Although this did not become a mercial success, the concept is feasible, and the prototypehas served as a model for similar designs pursued withinthe aerospace industry

com-Smart Airplane Wings Composite structures that have

SMA wires embedded can be used to change the shape of

an airplane wing The embedded wires may be activated

Figure 8 Shape memory devices Clockwise from top left: memory card ejector mechanism for

laptop computers; Cryofit® hydraulic pipe couplings; Cryocon® electrical connector; fire safety lid release for public garbage receptacles (courtesy of Shape Memory Applications, Inc.).

to constrict and improve the vibrational characteristics of

the wing, heated to change their effective modulus to

re-duce vibration, or activated to alter the shape of the wing

for optimal aerodynamics All of these properties can be

used to produce an adaptive airplane wing that alters as

environmental conditions change to improve efficiency and

reduce noise

Space System Vibrational Damper Vibrational dampers

comprised of composite materials using pre-strained,

embedded SMA wire or ribbons can reduce unwanted

mo-tion in various space systems A sensor detects vibramo-tion

in the system and sends a signal to activate the embedded

composite, which then alters the structural dynamics to

damp or cancel the existing vibration (1)

Consumer Products

SMA devices and components have been used in

high-volume consumer products for more than 20 years

Al-though many consumers who use these products are

un-aware of their SMA components, there is a growing public

awareness of SMAs due to recently marketed items thatadvertise their merits

Flexon® Optical Frames Superelastic eyeglass frames

marketed by Marchon Eyewear, Inc., are one of themost widely known uses for SMAs They are frequentlyadvertised in television commercials and can be found atmost optical frame retailers The components of eyeglassframes that are most susceptible to bending, the bridgeand temples, are wire forms of Ni-Ti, the remainder of theframe is comprised of conventional materials for adjustingpurposes and cost savings Due to the high strain recoverycapability of Ni-Ti, these frames are highly deformation-and kink-resistant (Fig 4) Marchon is aware of the highstrain and high cycle fatigue limitations of Ni-Ti materi-als, as demonstrated by the marketing brochures that ap-propriately suggest bending and twisting limits that arewithin the design guidelines for the material

Portable Phone Antennae The growing demand for

portable phones has resulted in a high-volume tion for superelastic Ni-Ti material because most cell

applica-phone antennae produced today are Ni–Ti wires coated

with polyurethane The superelasticity resists permanent

kinking and withstands the abuses of user handling during

the lifetime of portable phones

Greenhouse Window Opener An SMA that has a small

temperature hysteresis is used as an actuator to open and

close greenhouse windows at predetermined temperatures

for automatic temperature control The opener is a

spring-loaded hinge that has a Cu–Zn–Al shape-memory spring

and a conventional metal biasing spring The SMA spring

is compressed by the biasing spring at temperatures

be-low 18◦C, and the window is closed The SMA spring

acti-vates around 25◦C, overcomes the force of the bias spring,

and opens the window (21) This actuator design relies on

reduced thermal hysteresis using a biasing force As the

SMA spring cools to 18◦C, although not sufficiently cool

to completely transform to its softer martensitic phase, it

is transformed enough to accommodate deformation via

stress-induced martensite

Recorder Pen Mechanism A shape-memory pen driver

was designed by The Foxboro Company in the early 1970s

to replace conventional pen-drive mechanisms, which used

a galvanometer to actuate a pen arm The replacement

used Ni–Ti wires pretensioned in a driver unit and

actu-ated by heat from an induction coil in response to input

signals The new design reduced the number of moving

parts, improved reliability, and decreased costs The new

recorder pen units were first introduced in 1972; by 1980

more than 500,000 units were produced (16,21)

Nicklaus Golf Clubs Superelastic SMA golf club inserts

were developed by Memry Corporation for a line of Jack

Nicklaus golf clubs The damping properties of the inserts

hold the golf ball on the club face longer and provide more

spin and greater control for golfers (22)

Brassiere Underwires Superelastic Ni–Ti shapes that

conform to the user’s body are ideal for underwire

applica-tions, because they are unaffected by the temperatures and

external forces from repeated washings Wires are shaped

in predetermined configurations, using either round wire

or flat ribbon The product is a commercial success in Asia,

but the increased cost compared to that of conventional

underwires has prevented the product from entering

mar-kets in North America and Europe

Residential Thermostatic Radiator Valve SMA actuators

have been used to regulate the temperature of

residen-tial radiators An actuator expands when the room

tem-perature increases, overcomes a biasing spring force, and

closes a radiator hot water valve Assisted by the biasing

spring, the SMA temperature hysteresis can be as low as

1.2◦C (21) The thermostatic valve can be adjusted via a

knob that alters the compression of the biasing spring—

the more compression it exerts, the higher the

tempera-ture required for the SMA actuator coil to activate and

close the hot water valve (16)

Rice Cooker Valve SMA valve mechanisms have been

successfully employed to improve the performance of ricecookers The mechanism, comprised of an SMA spring and

a bias spring, is inserted into the top lid of a rice cooker Thevalve is open while rice cooks and steam is generated, butwhen the rice is finished cooking, the SMA spring cools andthe bias spring closes the valve to keep the rice warm ANi–Ti–Cu alloy is used for the SMA spring because of itslow strain, high cycle fatigue properties Although its re-covery force decreases due to repeated cycling, this applica-tion has demonstrated repeatability for more than 30,000cycles, which corresponds to several daily operations for 10years (23)

Robotic Doll SMA actuator wires were designed to

move the arms and legs of a doll to display humancharacteristics The application is technically feasible, andprototypes were successful; however, the power required

to activate the wires was too great The battery changesrequired were sufficiently frequent to limit market accep-tance of the product

Miscellaneous Products Furukawa Electric Co Ltd of

Japan produced SMA-actuating air-conditioning louvers todeflect air up or down, depending on temperature Theyalso manufactured coffee makers that use temperature-control valves to initiate the brewing process when waterstarts to boil (24) Other products include superelastic fish-ing lures, superelastic SONY EggoTM headphones for theminidisk Walkman®, and novelty items, such as a magicteaspoon that has a memory The teaspoon is given to some-one to stir a hot drink, and when the spoon is exposed to thehot liquid, it is immediately transformed to a bent position

Commercial/Industrial Safety

Many safety devices for temperature sensing and tion have been successfully used in actual operation Thefollowing examples have all been sold in consumer orindustrial markets

actua-Antiscald MemrySafe® Valve An SMA valve was

de-signed to shut off a faucet’s hot water source when ter temperatures become too high (above 50◦C) The valvereopens when the water cools to safer temperatures andprotects the user from scalding water ShowerGard®,BathGard®, and Flow-Gard®are similar products, and allhave been marketed in retail hardware stores

wa-Firechek®Valve A safety device that employs an SMA

actuator is often used in industrial process lines to shutoff a gas supply in the event of fire Exposure to hightemperatures activates a valve and cuts off the pneumaticpressure that controls flammable gas cylinders and processline valves (25)

Circuit Breakers SMAs have been used in circuit

break-ers to replace conventional bimetals Due to the highforces required in large circuit breakers, a series of leversmust be employed to amplify the forces available from bi-metals Cu–Al–Ni alloys have been used in this application

for their high temperature activation and low hysteresis.

Simple cantilever beam designs increase force and stroke

and eliminate the need for levers

Proteus®Safety Link Device A chain link has been

fab-ricated from Cu–Zn–Al to change shape at high

tempe-ratures and act as a release mechanism The release may

activate sprinkler systems or trigger fire doors to close,

de-pending on the application (26)

Telecommunication Line Fuses Cu–Zn–Al shunts are

coupled with high-sensitivity fuses throughout Europe to

protect communication systems from lightning strikes

During normal operation, the fuse heats up more rapidly

than the SMA, and the shunt remains inactive Under

heavy usage, however, the shunt increases in temperature

and activates to bypass the fuse and protect it from a

criti-cal burnout temperature (26)

Safety Trash Lid Mechanism An SMA device has been

de-signed to smother accidental fires in public trash

recepta-cles The device holds a trash lid in the open position at

nor-mal operating (ambient) temperatures, but when heated

by a fire within the trash can, the shape-memory

compo-nent releases a latch and the lid drops to extinguish the

fire (Fig 8)

Medical

The medical industry is rapidly accepting the use of SMAs

in a wide variety of applications From simple pointed

need-les to complex components implanted in the bloodstream,

Ni-Ti has been adopted by the industry for its ability to

of-fer unique and ideal solutions to traditional medical

chal-lenges Well known for its excellent biocompatibility and

corrosion resistance, Ni–Ti has been used in many

succes-sful medical devices and is now widely accepted throughout

the medical industry

The majority of SMA medical applications use the

su-perelastic property of Ni–Ti, and many of them are in the

expanding field of minimally invasive surgery Due to the

high strain recovery of Ni-Ti, components can withstand

extreme shape changes for minimal profiles during

deliv-ery and then expand to larger devices within the body

Many of these SMA devices have eliminated the need for

open heart surgery and thereby reduce patient risk and

decrease hospital recovery periods

Orthodontic Dental Arch Wires Dental arch wires, one

of the first medical applications that used SMAs, were first

introduced in 1977 to replace stainless steel arch wires for

straightening teeth The wires were initially used in the

martensitic condition, cold worked, and deformed around

the teeth They exhibited sufficient springback properties

for this application, although later superelastic (austenitic)

forms of Ni–Ti wire were introduced to improve product

performance The superelastic arch wire is now designed

to exploit the plateau region of SMA’s stress–strain curve,

which provides nearly-constant stress on the teeth as the

wire recovers its shape and straightens the teeth

Mitek Homer Mammalok® Mitek Surgical Products,

Inc., introduced a superelastic needle wire localizer in 1985which is used to locate and mark breast tumors to makesurgical removal less invasive The needle is used as aprobe to pinpoint the location of a breast tumor first identi-fied by mammography Surgeons find it difficult to discernthe tumor from surrounding tissue, so the probe highlightsthe correct location for the surgical procedure (27)

Mitek Suture Anchors Mitek anchors, fabricated from a

titanium or NiTi body that has two or more arcs of elastic NiTi wire, are secure, stable suture holders used

super-to reattach tendons, ligaments, and soft tissues super-to bone.The anchors are placed in a hole drilled into a patient’sbone and are locked in place by Ni–Ti arcs In 1989, MitekSurgical Products, Inc., introduced these anchors for use

in shoulder surgery to fasten sutures to bone Since then,the firm has expanded its product line for use in manyother orthopedic applications, such as ligament anchorsused for reattaching the anterior cruciate ligament (ACL)

of the knee (28)

Guidewire Cores Ni–Ti wires are snaked through the

tortuous pathways of the human body to guide and liver other tools and devices for interventional procedures.These superelastic guidewires are optimal for use in min-imally invasive surgery where procedures are performedthrough a small portal in a major artery, and offer supe-rior flexibility, kink resistance, and torquability for optimalsteering and ease of operation (29)

de-Stents SMA stents are becoming increasingly popular

in the medical industry These structural, cylindrical ponents, designed to prop open and support human bloodvessel walls, ducts, and other human passageways, areimplanted to prevent collapse or blockage and to patchlesions Ni–Ti materials are used in place of more conven-tional metals for coronary artery stenting but are most of-ten used in a peripheral location such as the carotid artery,esophagus, or bile duct Several shapes and forms of Ni–Tistents are displayed in Fig 9

com-Stents currently on the market and in development usevarious functional properties of SMAs: the superelastic-ity of austenite, the thermal shape memory, and the loweffective modulus of martensite Many of these SMA stentsuse a combination of superelastic and shape-memory prop-erties For example, a stent may be chilled in ice water fortransformation to martensite, compressed in the marten-sitic state, covered with a protective sheath for a minimalprofile, and then delivered into the body through a smallportal When in place, the sheath is retracted, and thestent warms to body temperature to recover its originalshape Once recovered, or transformed to austenite, thesuperelastic properties of the stent result in gentle andconstant radial forces on the vessel wall Stents that aremartensitic at room and body temperature must be com-pressed on a delivery balloon for expansion once deliveredinto the body The Paragon Coronary Stent developed byVascular Therapies is an example of a martensitic stentthat is marketed for its even, symmetrical expansion andits flexibility during delivery

Figure 9 Nitinol stents Left to right: Superelastic stent (5 mm OD× 40 mm long), laser-cut from Ni–Ti tubing; Ni–Ti ribbon set in a coil configuration; Ultraflex TM esophageal knitted stent with fabric covering (courtesy of Shape Memory Applications, Inc.).

Simon Nitinol Filter® An SMA vena cava blood clot

fil-ter was invented by Dr Morris Simon of Nitinol

Medi-cal Technologies, Inc The design is a Ni–Ti wire form

shaped like an umbrella frame or wire basket For

de-livery in the body, the filter is chilled below its

trans-formation temperature and collapsed into a small

inser-tion tube The filter is cooled by a flow of cold saline

solution while inserted into the patient and then

ex-pands when exposed to body temperature Its recovered,

umbrella-shaped form is designed to catch blood clots in the

patient’s bloodstream to prevent a pulmonary embolism

(30)

AMPLATZER®Septal Occluder Occlusion devices are

de-signed to serve as Band-Aids to cover and heal holes

in the heart without requiring open heart surgery and

are typically fabricated from traditional materials The

AMPLATZER Occluder is an SMA device, comprised of

a Ni–Ti wire frame that is woven and shaped into two

flat caps connected by a short tubular section The

de-vice is deployed through a portal in the femoral artery

of a patient and placed at the center of the hole to be

patched A sheath is then retracted, and the two flat

caps spring to shape and clamp on either side of the

hole, thus closing the hole and providing a tight seal(31)

Orthopedic Devices SMA materials are used for their

superelasticity and shape-memory properties in a variety

of orthopedic devices designed to accelerate bone and tilage formation under constant compressive stresses Pre-strained SMA plates are used to treat bone fractures; whenattached on both sides of a fracture and screwed together,they provide a compressive force to heal the fracture area.Staples are used to heal fractures as well A Ni–Ti staple

car-in the martensitic state is positioned so that its legs can

be driven into bone sections across the fractured area to

be closed When heated, the legs of the staple bend inwardand pull the bone sections together, creating a compressiveforce (32) Ni–Ti spacers are also used to assist spinal re-inforcement in surgical procedures In this procedure, aspacer is inserted as a compressed ring and then is heated

to expand and force open a gap in the vertebrae Bone chipsare placed in the gap and fusion occurs over time to createsolid bone SMAs in solid rod form have been used to treatspinal curvature Martensitic rods are pre-deformed to con-form to a patient’s original spinal curvature, wired to thespine, and then gradually recovered to move the spine toits corrected position (1)

Miscellaneous Instruments and Devices Thousands of

other medical devices have been developed to exploit the

unique behavior of SMAs A few additional, typical SMA

products include catheters, endodontic files, aneurysm

clips, retrieval baskets, surgical needles, and retractable

grippers

Automotive

SMA applications for the automotive industry are

chal-lenging for two primary reasons: the extreme range of

op-erating temperatures expected during use and the market

demand for low-cost components Most automotive devices

are expected to perform during exposure to the

tempera-ture extremes of climates throughout the world The

suc-cess of SMA automotive devices has been limited due to

the deterioration of shape-memory properties over time

caused by exposure to high temperatures (21) The

success-ful SMA devices have exploited the benefits of lightweight,

simple solutions For example, SMA actuators are used

as replacements for thermostatic bimetals and wax

ac-tuators and provide single metal components in place of

complex systems The simple SMA solutions further

im-prove design performance by activating more quickly

be-cause they can be completely immersed in a gas or liquid

flow (24)

Pressure Control Governor Valve A shape-memory

gov-ernor valve developed by Raychem Corporation and

Mercedes-Benz AG was introduced in 1989 Mercedes cars

to improve the rough cold weather shifting of automatic

transmissions The valves employ Ni–Ti coil springs to

counteract the effects of increased oil viscosity A Ni–Ti

coil is immersed in the transmission fluid At low

temper-atures, it is martensitic and is forced by a steel bias spring

to move a piston This activates a mechanism to reduce

pressure and ease shifting At higher temperatures, the

NiTi spring is much stronger and pushes the bias spring

in the opposite direction to optimize shifting pressure at

the warmer temperatures (24)

Due to the ideal performance parameters of the

applica-tion this governor valve design is one of the few technical

and economic successes in the automotive industry

Ope-rating temperatures are within the limits of the material,

required force output is low, and expected life is less than

20,000 cycles These conditions reduce the possibility of

fatigue and degradation of SMA properties during the life

of the product (33)

Toyota Shape-Memory Washer Ni–Ti Belleville-type

washers were developed by Toyota Motor Corporation and

were used in Sprinter/Carib cars to reduce vibration and

rattling noise at elevated temperatures Automotive

as-semblies such as gearboxes are often combinations of many

dissimilar metals During the temperature increase in

standard operation, a difference in the thermal expansion

rates of the metals causes assemblies to loosen and rattle

The washers were designed to change shape at high peratures using forces up to 1,000 N (225 lb), which is suf-ficient to tighten the assembly and reduce the undesiredrattling noise (24)

tem-Shock Absorber Washer This component, an application

similar to the governor valve, is also designed to teract the high viscosity of oil at colder temperatures.SMA washers are placed in shock absorber valves to altertheir performance effectively in cold and hot temperatures(24)

coun-Automotive Clutch Fan An SMA device, developed as a

selective switching mechanism for air cooled engines, quires the activation of a Cu-based SMA coil to control theoperation of a clutch fan The coil is activated at a tempera-ture close to 50◦C and engages a clutch to power the enginefan The fan speeds up to cool the engine until the temper-ature is reduced, at which point the SMA coil is forced todisengage the clutch via a set of four steel leaf springs thatserve as a biasing force The device is designed to reduceengine noise and fuel consumption when the car is idle(21)

re-Industrial/Civil Engineering

Many SMA solutions have been designed and implemented

to satisfy some of the rigorous, large-scale demands of civilengineering projects and miscellaneous industrial appli-cations Although the constraints of SMA properties of-ten restrict use in industrial applications (the limited ac-ceptable temperature range of operation, for example),many creative SMA solutions and design alternatives havesuccessfully improved or replaced traditional industrialdesigns and devices

Pipe Couplings Cryogenic couplings developed by

Raychem Corporation for the aerospace industry have beenadapted for use in deep sea operations and are also used inthe chemical and petroleum industries The advancement

of a Ni–Ti–Nb alloy for its wide hysteresis has helped toexpand the use of these shape-memory couplings Whenthe components are machined at room temperature andthen chilled in liquid nitrogen for expansion, they will notrecover their shape until temperatures reach approxi-mately 150◦C This allows storing and transporting ex-panded couplings without using liquid nitrogen Once ap-plied to the piping and heated to transform to austenite,they maintain their strength at temperatures colder than

−20◦C (33)

Structural Elements Superelastic SMA materials can be

used to increase strength and energy dissipation in abuilding A project is currently underway to reinforce theBasilica of St Francis in Assisi, Italy, after severe damage

during earthquakes in 1997 SMA wires will be placed in

series with horizontal conventional steel ties to connect

the walls to the Basilica’s roof The superelastic behavior

of the wires will allow ductile, high strain motion to occur

without breakage during an earthquake and will recover

the strain by using a gentler, lower force stroke (exploiting

the lower plateau of the stress–strain curve) It has been

estimated that the SMA structural design will withstand

an earthquake at least 50% stronger than if the Basilica

were reinforced with conventional steel bars (34)

Rock Breakers SMAs are used to replace explosives in

demolition, which is similar in function to the Frangibolt®

release mechanisms used in the aerospace industry A

pre-strained SMA cylinder is placed within a crevice of a

struc-ture, electrically heated to expand, and the recovery forces

produced are sufficient to destroy rocks and cement

struc-tures This concept has been employed in Russia to yield

demolition forces greater than 100 tons of force (1) Rock

breakers comprised of Ni–Ti rods are also used in Japan

Nishimatsu Construction Co., Ltd uses rods 29 mm long

and 15 mm in diameter, which are compressed and

in-serted into boreholes in rock using an assembly of

wedge-shaped platens The NiTi rods are heated by attached

elec-tric heaters, causing them to expand and break the rock

apart Tests have demonstrated forces as high as 14 tons

when they are heated to 120◦C (23)

Power Line Sag Control SMA materials are often used

to prevent a sag or droop in overhead power lines Using

thermal shape-memory alloys, sag control in power lines

has been successfully tested in Canada, the Ukraine, and

Russia (35) When temperatures increase because of

am-bient temperatures or high load along the power lines, the

lines tend to sag Nitinol wires are attached to the lines

and deform at the colder, high tension state, but contract

when warm and remove the slack from the lines

Steam Pipe Sag Control Similar to the power line

appli-cation, pipe hangers made from Ni–Ti are used to reduce

the sagging of large steam pipes heated by the steam This

reduces the load variation in the system, rather than

coun-teracting the shifts in geometry, as in power lines (35)

Transformer Core Compression SMAs assist in

com-pressing transformer cores, a critical aspect of transformer

design Ni–Ti bolts are prestrained axially to couple core

sheets in large transformers, then heated to contract and

provide high compressive forces on the sheets This SMA

solution improves on traditional techniques of tightening

with nuts and bolts, where core sheets are placed in a

vac-uum to withdraw air from between sheets, then removed

from the vacuum to install the bolts Although technically a

design improvement, the Ni–Ti solution requires 2–3 inch

diameter bolts, which is larger than ideal for SMA

prod-ucts (35) The cost to process and machine the bolts may

offset the benefits gained in the assembly process

Multiwire Tension Device SMA devices are used to

in-crease piping integrity They prevent crack initiation and

propagation by compressing areas of a pipe using the

concept of multiwire tension (MWT) developed by the ABBNuclear Division in Sweden A split-sleeve coupling iswrapped with pretensioned SMA wire, the wire ends arefixed, and the coupling is placed over a weld point on apipe Then, the assembly is heated so that the wire con-tracts and the coupling then clamps to a tight fit MWTtechniques are used to improve stress in welded areas,preventing stress corrosion cracking and connecting theends of the pipe should the weld point fail and break (35)

Indicator Tags SMAs can be used to indicate high

tem-perature points in a system Wires used as tags are bentmanually at typical operating temperatures, and the tagsstraighten when temperatures reach a critical level (thematerial’s Aftemperature) Operators note the site of thehigh-temperature source and can fix the problem (35)

Sentinel® Temperature Monitoring System SMAs are

used on the low-voltage side of step-down transformers

to indicate maximum temperatures and to close a switch

at critical temperatures This SMA mechanism is used toprovide information for monitoring, so that operators canprevent overheating (35)

Injection Molding Mandrels Centerless ground Ni–Ti

round bar and wire are often used to replace conventional,deformation-prone mandrels Plastics are molded in theshape of a superelastic Ni–Ti mandrel, and during roughhandling as the mandrel is withdrawn from the cured poly-mer, the superelastic material recovers its original shape

Heat Engines SMA elements are used in heat engine

de-signs to convert thermal energy to mechanical energy viathermal shape-memory behavior Thermodynamic analy-ses of ideal, theoretical SMA heat engines have resulted in

a wide range of calculated efficiencies, although the mostthorough calculations yield maximum thermal efficiencies

of only 2–4% (36) A great number of prototype engines hasbeen constructed using SMA elements that change shapewhen they pass between hot and cold reservoirs However,due to loss factors, such as friction, hysteretic effects inher-ent in the material, and energy input required to maintain

a reservoir temperature differential, the practical cies of these heat engines are much too low to serve aslow-cost, high-volume energy converters

efficien-The pursuit of a revolutionary SMA heat engine fies a common occurrence in SMA application design In-trigued by the potential of SMAs to provide unique anddramatic design solutions, inventors often pursue creativesolutions before completing cost /benefit analyses Al-though suitable for small-scale demonstrations, manySMA applications (as in heat engines) do not provide thenecessary efficiencies—cost or energy—to warrant replac-ing conventional designs

typi-Electronics

The electronics industry has adopted SMA materials marily for connection mechanisms Applications in nearlyall industries use the electronic activation capability ofSMA materials to exploit thermal shape-memory behavior

pri-Flexible Circuitry Spring Steel/BECU Nickel Titanium SMA Contact “Window”

PCB

PART A: OPEN

PART B: CLOSED

Heater (Build into Flex Circuit)

FLEXSTRIP CONNECTOR (DOUBLE) WITH HEATER IN FLEXSTRIP

Conductor (Top) Conductor(Bottom) Flexstrip (2x)

Flexstrip Heater Element

Flexstrip (Bottom)

Stainless (.015 thk) Nitinol (.020 thk)

Exposed Contacts Lock

Flexstrip (Bottom)

Window (Both Sides) Exposed Contacts Kapton Covered Flexstrip (Top)

Figure 10 Schematic diagram of a zero insertion force connector Reprinted with permission

from J.F Krumme, Electrically Actuated ZIF Connectors Use Shape Memory Alloys, Connection

Technology Copyright 1987, Lake Publishing Corporation

(including robotics); however, a few examples are highly

specific and unique to the electronics industry

Cryocon®Electrical Connector An SMA connector has

been designed to attach the braid sheathing of an electrical

cable to a terminal plug The connector is a shape-memory

ring sheath on a split-walled, collet-shaped tube whose

dia-meter expands when chilled due to the radial forces of the

tube When warmed to room temperature, the ring recovers

its smaller diameter shape and clamps the tubing collet

prongs together to form a tight electrical connection (3,37)

ZIF Connector A Zero insertion force electrical

connec-tor was designed by Beta Phase, Inc., to simplify the

instal-lation and increase the quality of circuit board connections

(Fig 10) A U-shaped strip of Ni–Ti is martensitic at

oper-ating temperatures and is forced to grip the boards via the

bias force of a conventional closing spring When heated

by electrical current, the Ni–Ti strip overcomes the force

of the closing spring and opens the radius of its U shape,

allowing insertion or removal of the boards without force

This combines installation simplicity and maintains

op-timal, high force electrical contact between mother and

daughter circuit boards (38)

Microactuators

SMAs have been successfully processed as thin film

ac-tuators for microactuating devices such as tiny valves,

switches, and microelectromechanical systems (MEMS)

(39) Ni–Ti films are sputter deposited on silicon

sub-strates, and actuators are fabricated by chemical milling

and lithographic processes Devices one millimeter in

diameter and three microns thick have been fabricated, sulting in tiny actuators such as microvalves for fluid andpneumatic control The Ni–Ti film actuators can provide

re-up to 3% strain recovery (40)

FUTURE TRENDS

SMA applications continue to gain acceptance in a variety

of industries throughout the world SMAs are introduced to

an increasing number of students who study engineeringand metallurgy and to the general public via the growingnumber of SMA products available to consumers Althoughproperty values and design techniques for SMAs are not asreadily available or as thoroughly standardized as those

of conventional materials, current trends indicate a steadycourse toward complete characterization of SMA materials.The medical industry has already prompted the standardi-zation of material production, testing, and mechanical be-havior; current efforts include the formation of an ASTMstandard for using Ni–Ti in medical devices Spearheaded

by supplier representatives of both the medical device andSMA material supply industries, the standard is scheduled

to be completed and approved before this article is lished This new standard represents a significant mile-stone in the continual effort to demystify shape-memoryalloys and augment their use in engineering and design

pub-BIBLIOGRAPHY

1 L McD Schetky, Proc: Shape Memory Alloys Power Syst Palo

Alto, CA, 1994, pp 4.1–4.11.

2 C.M Jackson, H.J Wagner, and R.J Wasilewski, NASA Report

SP-5110, Washington, DC, 1972, pp 74, 78, 79.

3 H Funakubo, ed., Shape Memory Alloys Gordon and Breach,

NY, 1987, pp 201, 206.

4 T.W Duerig, K.N Melton, D Stoeckel, and C.M Wayman,

Engineering Aspects of Shape Memory Alloys

Butterworth-Heinemann, London, 1990.

5 D.E Hodgson, M.H Wu, and R.J Biermann, Shape Memory

Alloys, Vol 2 10, (1990), pp 897–902.

6 J.V Humbeeck, Manside Project Workshop Proc Rome, Italy,

1999, pp II-1, II-2, II-22 II-28.

7 M.H Wu, Proc Shape Memory Alloys Power Syst Palo Alto,

CA, 1994, pp 2.1–2.2.

8 T.W Duerig and K.N Melton, MRS Int Meet Adv Mater.,

Tokyo, Japan, 1988, Vol 9, p 583.

9 D.E Hodgson and R.C Krumme, Proc 1st Int Conf Shape

Memory Superelastic Technol Pacific Grove, CA, 1994,

pp 371–376.

10 Hysteretic Damping Apparatus and Methods, US Pat 5, 842,

312, Dec 1, 1998, R.C Krumme and D.E Hodgson.

11 R.H Richman, C.A Zimmerly, O.T Inal, D.E Hodgson, and

A.S Rao, Proc 1st Int Conf Shape Memory Superelastic

Tech-nol., Pacific Grove, CA, 1994, pp 175–180.

12 J Perkins and D Hodgson, in Engineering Aspects of

Shape Memory Alloys, Butterworth-Heinemann, London,

1990, p 204.

13 K Otsuka, in Engineering Aspects of Shape Memory Alloys,

Butterworth-Heinemann, London, 1990, pp 36–45.

14 C.M Wayman and T.W Duerig in Engineering Aspects

of Shape Memory Alloys, Butterworth-Heinemann, London,

1990, pp 3–20.

15 K.N Melton, in Engineering Aspects of Shape Memory

Alloys, Butterworth-Heinemann, London, 1990, pp 21–

35.

16 L.McD Schetky, Sci Am 241(5): 79, 81 (1979).

17 http://www.sma-mems.com /aero.htm.

18 J.D Busch, Proc 1st Int Conf Shape Memory Superelastic

Technol pp 259–264, Pacific Grove, CA, 1994.

19 http://www.robotstore.com /mwmars.html.

20 Marchon Company Brochure, 1998.

21 C.M Wayman, J Met pp 129–137 (June, 1980).

26 W.V Moorleghem, Proc.: Shape Memory Alloys Power Syst.

Palo Alto, CA, 1994, pp 9–1, 9–3.

27 J.P O’Leary, J.E Nicholson, and R.F Gatturna, in Engineering

Aspects of Shape Memory Alloys, Butterworth-Heinemann,

London, 1990, p 477.

28 Mitek Surgical Products, Inc Company Brochure, 1995.

29 J Stice, in Engineering Aspects of Shape Memory Alloys,

Butterworth-Heinemann, London, 1990, p 483.

30 http://www.nitinolmed.com /products /

31 http://www.agamedical.com /patients /index.html

32 J Haasters, in Engineering Aspects of Shape Memory

Alloys, Butterworth-Heinemann, London, 1990, pp 426–

37 E Cydzik, in Engineering Aspects of Shape Memory Alloys,

Butterworth-Heinemann, London, 1990, pp 149–157.

38 J.F Krumme, Connection Technol Lake, 1987.

39 http://www.sma-mems.com/t film.htm

40 A.D Johnson and J.D Busch, Proc 1st Int Conf Shape

Mem-ory Superelastic Technol Pacific Grove, CA, 1994, pp 299–

304.

41 D Stoeckel, Shape-Memory Alloys, Adv Mater Process pp 35,

38 (Oct, 1990).

ADDITIONAL READING

A Pelton, D Hodgson, S Russell, and T Duerig, Proc 2nd Int.

Conf Shape Memory Superelastic Technol (SMST-97), Pacific

Grove, CA, 1997.

Jan Van Humbeeck, Non-Medical Applications of Shape Memory

Alloys, Mater Sci Eng A273–275: 134–148 (1999).

T Duerig, A Pelton, and D Stoeckel, An Overview of Nitinol

Medical Applications, Mater Sci Eng A273–275: 149–160

265 K in the martensitic phase of a Ni2MnGa singlecrystal The crystal contracts in the direction of the appliedfield The strain components conserve volume and are ofeven symmetry in the field There is some hysteresis in thestrain with change in sweep direction of the field, and there

is some unrecovered strain after the first field cycle By way

of comparison, piezoelectrics show strains of order 0.1%(5) and the leading magnetostrictive material, Terfenol-D(Tb0.33Dy0.67Fe2), shows a field-induced strain of about0.24% (6,7)

The strain-versus-temperature (ε-T) curves of

thermo-elastic martensite, Fig 1(a), bear little resemblance tothe ε-H curves of Fig 1(b) The former typically show a

2 C.M Jackson, H.J Wagner, and R.J Wasilewski, NASA Report

SP-5110, Washington, DC, 1972, pp 74, 78, 79.

3 H Funakubo, ed., Shape Memory Alloys Gordon and Breach,

NY, 1987, pp 201, 206.

4 T.W Duerig, K.N Melton, D Stoeckel, and C.M Wayman,

Engineering Aspects of Shape Memory Alloys

Butterworth-Heinemann, London, 1990.

5 D.E Hodgson, M.H Wu, and R.J Biermann, Shape Memory

Alloys, Vol 2 10, (1990), pp 897–902.

6 J.V Humbeeck, Manside Project Workshop Proc Rome, Italy,

1999, pp II-1, II-2, II-22 II-28.

7 M.H Wu, Proc Shape Memory Alloys Power Syst Palo Alto,

CA, 1994, pp 2.1–2.2.

8 T.W Duerig and K.N Melton, MRS Int Meet Adv Mater.,

Tokyo, Japan, 1988, Vol 9, p 583.

9 D.E Hodgson and R.C Krumme, Proc 1st Int Conf Shape

Memory Superelastic Technol Pacific Grove, CA, 1994,

pp 371–376.

10 Hysteretic Damping Apparatus and Methods, US Pat 5, 842,

312, Dec 1, 1998, R.C Krumme and D.E Hodgson.

11 R.H Richman, C.A Zimmerly, O.T Inal, D.E Hodgson, and

A.S Rao, Proc 1st Int Conf Shape Memory Superelastic

Tech-nol., Pacific Grove, CA, 1994, pp 175–180.

12 J Perkins and D Hodgson, in Engineering Aspects of

Shape Memory Alloys, Butterworth-Heinemann, London,

1990, p 204.

13 K Otsuka, in Engineering Aspects of Shape Memory Alloys,

Butterworth-Heinemann, London, 1990, pp 36–45.

14 C.M Wayman and T.W Duerig in Engineering Aspects

of Shape Memory Alloys, Butterworth-Heinemann, London,

1990, pp 3–20.

15 K.N Melton, in Engineering Aspects of Shape Memory

Alloys, Butterworth-Heinemann, London, 1990, pp 21–

35.

16 L.McD Schetky, Sci Am 241(5): 79, 81 (1979).

17 http://www.sma-mems.com /aero.htm.

18 J.D Busch, Proc 1st Int Conf Shape Memory Superelastic

Technol pp 259–264, Pacific Grove, CA, 1994.

19 http://www.robotstore.com /mwmars.html.

20 Marchon Company Brochure, 1998.

21 C.M Wayman, J Met pp 129–137 (June, 1980).

26 W.V Moorleghem, Proc.: Shape Memory Alloys Power Syst.

Palo Alto, CA, 1994, pp 9–1, 9–3.

27 J.P O’Leary, J.E Nicholson, and R.F Gatturna, in Engineering

Aspects of Shape Memory Alloys, Butterworth-Heinemann,

London, 1990, p 477.

28 Mitek Surgical Products, Inc Company Brochure, 1995.

29 J Stice, in Engineering Aspects of Shape Memory Alloys,

Butterworth-Heinemann, London, 1990, p 483.

30 http://www.nitinolmed.com /products /

31 http://www.agamedical.com /patients /index.html

32 J Haasters, in Engineering Aspects of Shape Memory

Alloys, Butterworth-Heinemann, London, 1990, pp 426–

37 E Cydzik, in Engineering Aspects of Shape Memory Alloys,

Butterworth-Heinemann, London, 1990, pp 149–157.

38 J.F Krumme, Connection Technol Lake, 1987.

39 http://www.sma-mems.com/t film.htm

40 A.D Johnson and J.D Busch, Proc 1st Int Conf Shape

Mem-ory Superelastic Technol Pacific Grove, CA, 1994, pp 299–

304.

41 D Stoeckel, Shape-Memory Alloys, Adv Mater Process pp 35,

38 (Oct, 1990).

ADDITIONAL READING

A Pelton, D Hodgson, S Russell, and T Duerig, Proc 2nd Int.

Conf Shape Memory Superelastic Technol (SMST-97), Pacific

Grove, CA, 1997.

Jan Van Humbeeck, Non-Medical Applications of Shape Memory

Alloys, Mater Sci Eng A273–275: 134–148 (1999).

T Duerig, A Pelton, and D Stoeckel, An Overview of Nitinol

Medical Applications, Mater Sci Eng A273–275: 149–160

265 K in the martensitic phase of a Ni2MnGa singlecrystal The crystal contracts in the direction of the appliedfield The strain components conserve volume and are ofeven symmetry in the field There is some hysteresis in thestrain with change in sweep direction of the field, and there

is some unrecovered strain after the first field cycle By way

of comparison, piezoelectrics show strains of order 0.1%(5) and the leading magnetostrictive material, Terfenol-D(Tb0.33Dy0.67Fe2), shows a field-induced strain of about0.24% (6,7)

The strain-versus-temperature (ε-T) curves of

thermo-elastic martensite, Fig 1(a), bear little resemblance tothe ε-H curves of Fig 1(b) The former typically show a

− 15

− 10

− 5 0 5

− 15

− 10

− 5 0 5

Figure 1 Contrast between (a) the thermally induced strain in

the shape memory alloy, NiTi and (b) the magnetic-field-induced

strain in a ferromagnetic shape memory alloy Here, strain versus

applied field is measured at 265 K in the martensitic phase of

Ni 2 MnGa Inset: Relative orientation of sample, strain gauge, and

applied field (4).

large thermal hysteresis, with martensite and austenitestart and finish temperatures defined by the sharplycurved points of theε-T curves; the change in sample strain

through the thermoelastic hysteresis can be several cent Theε-H curves of Fig 1(b) bear some resemblance to

per-those of a negative magnetostriction material: the strain

is of even symmetry in the applied magnetic field and

increases superlinearly in H before saturating However,

the FSMA strain effect differs in many ways from netostriction as will be shown in detail later The strainshown in Fig 1(b) represents only a small fraction of the6% or 7% transformation strain expected to be accessible

mag-by field-induced twin selection in Ni–Mn–Ga FSMAs Infact, FSMAs have recently exhibited the full field-inducedstrain associated with their crystallographic distortion byapplication of a field of 320 kA/m (4 kOe) to a single-variantsample of an off-stoichiometry crystal of Ni–Mn–Ga (8).The mode of actuation shown in Fig 1(b), namely field-induced strain within the fully martensitic state, is to

be contrasted with application of a magnetic field to theaustenitic (A) phase of an FSMA to induce the transforma-tion to the single-variant martensitic (M) phase, Fig 2(a)

Here the A-M phase boundary is shown as a surface in H- σ

-T space As is the case with most martensites, a shear stress

applied to the A phase at a temperature just above theM-start temperature can initiate the A→ M transforma-tion; see vertical pathε–σ in Fig 2(a) (1,9,10) The A → M

transformation is accompanied by the release of a

heat of transformation measured to be Q= 40 MJ/m3

(288 cal/mole) (11) and Q= 98 MJ/m3(706 cal/mole) (12)

Kanomata et al (13) find that hydrostatic pressure bilizes the A phase (the transformation temperature de-

sta-creases with increasing hydrostatic pressure) This

oc-curs despite the smaller volume of the martensitic phase:

aA= 0.582 nm, aM= 0.592 nm, and cM= 0.557 nm In

con-trast, a shear stress stabilizes the M phase (14) The Mphase should also be stabilized by application of a mag-netic field to an FSMA; see the horizontalε-H path in Fig.

2 (a) (15) However, the Clausius-Clapeyron equation dicates that a magnetic field of order 107A/m (B= 12 T)would be needed to induce the transformation in a sam-ple held about 1◦C above the martensite start temperature(14) Experiments on Ni2.19Mn0.81Ga bear this out (16) Thefield required for transformation could be reduced by si-multaneous application of an appropriate stress Such afield-induced phase transformation would release the fulltransformation strain accompanied by a stress compara-ble to the yield stress of the detwinned martensite Stress-assisted, field-induced transformations have been inves-tigated by Vasil’ev et al (17) On transforming back to A,the heat of transformation is absorbed by the material (11).Such field-induced and stress-induced transformations canshow significant hysteresis because phase boundary mo-tion is involved

in-The present article focuses on the application of a netic field to a twinned M phase that is ferromagnetic,Fig 2(b) It is necessary that the magnetic anisotropy ofthe M phase be large compared to the energy required fortwin boundary motion and, further, that the preferred di-rection of magnetization changes across the twin bound-ary When this is the case, application of a magnetic fieldresults in a difference in Zeeman energy, (µ Ms ·H),

mag-(a) Magnetic field-induced

Figure 2 (a) Magnetic field-induced transformation of an austenitic sample to a single-variant

martensitic structure The A-M phase boundary is shown below in field-stress-temperature space;

the arrow indicates how an increasing field can induce the transformation (horizontalε-H path).

This process may be assisted by application of a suitable stress (vertical pathε–σ path) (b) A field

may be able to move twin boundaries in a twinned martensitic FSMA, changing the state of strain

of the martensite Compare the strain-versus-temperature hysteresis loop in lower panel with Fig.

1(a) The added field axis shows how application of a field in the martensitic state (bold line on ε-T

loop) can alter the state of strain of the sample.

across the twin boundary This energy difference exerts a

pressure on the twin boundary so as to grow the twin

vari-ants having the more favorably oriented magnetization

The resulting field-induced twin-boundary motion

pro-duces a large strain, fully within the martensitic state of an

FSMA

This article describes the crystallography and

magnetism of Ni–Mn–Ga in order to explain the very

large strains produced by field-induced twin-boundary

motion in martensite Examples of field-induced strain

by twin boundary motion in Ni–Mn–Ga FSMA samples

having different twin structures are given Martensitic

Fe70Pd30 has also shown field-induced strains of 0.5%

(18), and efforts are under way to develop other iron-base

FSMAs (19–21) These other materials will not be covered

in depth The state of theoretical modeling of strain

and magnetization in FSMAs is reviewed FSMA

field-induced strains are compared and contrasted with the

thermoelastic shape-memory effect and magnetostriction

FIELD-INDUCED STRAIN IN FSMAs

Crystallography and Mechanical Properties

The chemically ordered austenitic phase of Ni2MnGa has

the L21 Heulser structure (Fm¯ 3 m) with room

tempera-ture lattice constant a = 0.582 nm (22) Figure 3(a) shows

the chemical ordering favored below 800◦C, and the{101}

slip planes are shaded in The eight Ni atoms are located

at the center of each of the eight cubic sub-units; Ni ders to these sites in the high-temperature cubic phasenear or above the melting temperature The Mn and

or-Ga atoms order on the remaining sites (as shown bythe two sizes of spheres in Fig 3a) below 800◦C (23)

In the martensitic state, this structure is tetragonally

distorted with a = b = 0.592 nm, c = 0.557 nm The c axis

contraction is c /a = 0.94 The appropriate unit cell of the

tetragonal martensite (I4/mmm, having c = c and a =

b = a/2) is shown in Fig 3(b) The twin plane identified

in the structure at left as (101) has Miller indexes (112)

when referred to the tetragonal unit cell axes The c /a ratio in the unit cell has the magnitude√

2· c/a ≈ 1.33.

In this article, discussions are referenced to the ture at left ({101} twin planes) rather than the true body-centered unit cell, in order to bring out the fact that themartensitic phase of Ni2MnGa is contracted along its pre-ferred direction of magnetization, relative to the austeniticphase

struc-The off-stoichiometry phases of Ni–Mn–Ga generallyused in engineering studies may have more complex struc-tures The most useful phase is a five-layerd, tetragonalmartensite (22) Slight variations in composition near sto-ichiometry can result in different tetragonal structures

having very different magnetic anisotropy, c /a ratios

and responses to applied magnetic fields For example,Sozinov et al (24) report that while Ni49.2Mn29.6Ga21.2 is

an easy axis (M  c-axis), tetragonal five-layered site with c /a = 0.94, and field-induced strains of several

marten-Figure 3 (a) Model of the cubic Heusler, L21, structure of austenitic Ni2MnGa In the martensitic

state this structure contracts along its c-axis (c /a < 1), and it may twin along {101} planes (b) The I4/mmm, body-centered tetragonal (c’/a’ > 1) martensitic unit cell is shown with the same twinning

planes, now identified as {112}.

percent, Ni52.1Mn27.3Ga20.6 is an easy plane (M ⊥ c-axis),

tetragonal martensite with c /a = 1.2, and negligible

field-induced strain Some Ni–Mn–Ga samples (both

polycrys-talline) show orthorhombic structures (16,25) While

orthorhombic structures have more possible twin-plane

orientations than tetragonal structure, the models

described below for the field-induced strain still seem to

apply

The mechanical properties of FSMAs in the martensitic

phase are similar to those of conventional SMAs (Fig 4)

With increasing stress, the material first shows a

modu-lus, C0, characteristic of the single-variant state Above a

critical stress,σ0, at which deformation by twin-boundary

motion initiates, the modulus decreases to Ctband the

ma-terial may strain to its full transformation strain,ε0, after

which it is mechanically detwinned The transformation

Figure 4 Schematic of the stress–strain behavior of martensite.

Above a critical stress,σ0, the modulus drops to Ctb as the mode

of deformation becomes twin-boundary motion Depending on the

twin-variant structure atσ0 the material may deform as much as

ε0 , the transformation strain, before it is detwinned and reverts

to the stiffness of the single-variant state, C.

strain is the crystallographic distortion in a martensitictransformation:ε0= 1 − c/a referred to the austenitic unit

cell For still larger stresses, the modulus reverts to itssingle-variant value

Values of the parameters in Fig 4 measured for

Ni2MnGa crystals are typically of orderσ0= 1 − 10 MPa,

C0= 2 GPa, ε0= 0.06, and Ctb= 18 − 30 MPa (26,27) The

small value for C0 relative to the stiffness of the parentphase, which is of order 70 GPa, probably reflects a smalldegree of twin-boundary motion in the martensite beforethe initiation of abundant twin-boundary motion at σ0.Hence 70 GPa should be regarded as more typical of themartensitic stiffness at constant strain

Magnetization

Ni2MnGa shows a saturation magnetization at 265 K (in

the martensitic phase) of M s= 484 kA/m (484 emu/cm3)(4) Given its mass density of 8.3 g/cm3, this translates to

a saturation flux density of B s = 0.6 T (4π Ms= 6 kG) TheCurie temperature is about 350 K This is greater thanthe martensite transformation temperature, which variesstrongly with composition and stress and is typically about

273 K (1,11,27) The strength of the uniaxial anisotropy

of tetragonal Ni2MnGa has been measured from crystal magnetization curves and found to be about 1.2

single-× 105 J/m3 at −8◦C, favoring magnetization parallel to

the c axis (4) Tickle and James (29) made measurements

on single crystals of a Ni51.3Mn24.0Ga24.7 constrained to

be in the single-variant state during magnetization They

find Ku= 2.45 × 105 J/m3 at−17◦C The samples cited

in this article, close in composition to Ni50Mn28Ga22, show

a magnetic anisotropy in the single-variant constrained

M phase at room temperature that ranges from 1.6 to

Figure 5. µ0M-H measured on a sample of Ni49.8Mn28.5Ga21.7

constrained to by in the single-variant state The two curves are

measured with the field parallel (square loop) and perpendicular

(linear M-H process) to the c-axis of the variant (27).

1.9 × 105 J/m3(27) Figure 5 shows M-H loops taken on a

small crystal constrained to be in a single-variant state at

room temperature Loops are shown for field-applied

par-allel () and perpendicular (⊥) to the c-axis of the variant

(shape effects have been removed from both M-H loops).

The coercivity of the H|| loop suggests that the parallel

magnetization process takes place by magnetic

domain-wall motion The zero-coercivity, linear H⊥loop indicates

magnetization by a rotation of the moment from the c axis

to the field direction The area between the H|| and H⊥

curves, 1.6× 105 J/m3, is the strength of the uniaxial

mag-netocrystalline anisotropy, Ku A key factor that allows

FSMAs to be deformed by application of a magnetic field is

the relatively large field required to rotate the

magnetiza-tion from the c-axis.

Field-Induced Twin Rearrangement

The magnetic driving force behind field-induced twin

boundary motion is well illustrated by considering a

NiMnGa sample showing large twins Figure 6 shows an

off-stoichiometry single-crystal sample, Ni49.4Mn29.7Ga20.9,

in the single-variant state and with a sharp kink (bend)

at the position of a twin boundary introduced by

appli-cation of a field at room temperature (30) The kink at

the twin boundary spanning the cross section of the

ma-terial can be moved along the sample length by varying

the field strength and direction In this mode of operation,

the material always expresses its full transformation shear

strain,γ o, across a twin boundary The shear strain across

the twin boundary is given byγ0= (a/2c)(1 − c2/a2) Thus,

for c /a = 0.93, 0.94, and 0.95, γ0= 7.3%, 6.2%, and 5.1%,

respectively

When a single-variant sample, cut as that in Fig 6(a),

is placed in a magnetic field, the long sample axis does

not align with the field as magnetostatic considerations

alone would dictate Instead, it aligns at about 45◦ to the

field and is stable for only one orientation about its shape

Figure 6 a) Photo of single-variant sample of

Ni 49.4Mn29.7Ga20.9 at room temperature in zero external field.

b) The same sample with a 6 ◦kink at a twin boundary introduced

by application of a field of 320 kA/m (4 kOe) This kink defines a 5% shear strain relative to the unchanged variant at the left end

of the sample (30).

axis The same orientation is stable if the field is reversed.This indicates that this sample is characterized by auniaxial magnetic anisotropy with the easy axis of magne-tization oriented at about 45◦to the sample length X-raydiffraction shows this magnetic easy axis to lie along the

crystallographic c-axis.

Given this orientation of the crystal structure, Fig 7illustrates how the crystal shown in Fig 6 can be cut tooptimize axial strain The orientation of the twin boundaryobserved in Fig 6 and sketched in Fig 7(b), coincides with

a{101} plane (a {112} plane in the unit cell of Fig 3b) Note

that the orientation of the c axis changes across the twin

boundary

Because the c-axis changes direction across the twin

boundary, the preferred direction of magnetization alsochanges The directions of magnetization shown in Fig.7(b) have been confirmed by scanning the four long sam-ple surfaces with a small Hall probe (30) The field normal

to the sample surface, arising from the component of itsmagnetization perpendicular to the surface, was found tomap very closely with the twin structure, changing signacross the twin boundary and from the front to the back

H = 0 H = 4 kOe

c axis

c axis, M c axis, MM

TwinboundaryM

Figure 7 At the top are shown schematic views of the sample in

Fig 6 with the directions of magnetization shown for each variant.

Below is sketched the orientation of the martensitic crystal

struc-ture, left, and the twinned martensite, right The atomic

displace-ments increase further to the right of the twin boundary shown,

maintaining a constant shear angle.

of the sample This change in the preferred direction of

magnetization provides the mechanism for field-induced

motion of the atoms that constitutes twin-boundary

motion

Application of a field orthogonal to the magnetization of

a single-variant sample may cause a new variant to

nucle-ate (perhaps at a surface defect) and grow The twin

bound-ary in Fig 6(b) can be moved along the sample length by

sliding the sample over the edge of a suitably oriented

per-manent magnet (30) The field at the corner of the magnet

is approximately 320 kA/m (4 kOe) The magnetic field

ex-erts a pressure on the twin boundary largely by virtue of

the difference in Zeeman energy,µ0M s ·H, between the

two variants For this pressure to exist, it is necessary that

the anisotropy energy density, Ku= 1.8 ×105J/m3, be

com-parable to or greater than the Zeeman energy density

dif-ference, Ku> µ0MsH (If, on the other hand, the Zeeman

energy is much greater than the anisotropy energy, the

magnetization vectors in the two variants align with the

field, and the Zeeman energy difference vanishes.) If the

magnetic pressure on the twin boundary is greater than

the energy density utbassociated with twin-boundary

mo-tion,µ0MsH > utb, then field-induced twin-boundary

mo-tion may result The energy utbcan be estimated from the

stress-strain data such as that depicted in Fig 4 A critical

mechanical stressσ0 is needed to initiate twin-boundary

motion in martensite (30,31) Martynov and Kokorin (26)

show thatσ0can be as small as a few MPa Usingε0≈ 0.06

at this critical strain, utb≈ ε0σ0is of order 105J/m3 The

de-tailed interplay of these comparable energy densities, Ku,

µ0MsH, and utb, as well as the magnetostatic energy (which

is a strong function of sample shape and is of order 104to

105J/m3for Ni2MnGa) is best understood using

quantita-tive models These are described in the next section

Because the strain across a twin boundary is a pure

shear strain, samples having the active twin planes at 45◦

to the sample end faces can show extensional strain under

twin boundary motion (as observed in Fig 1) When the

active twin planes are at 45◦ to the sample surfaces, theFSMA behaves more like a magnetostrictive material such

as Terfenol-D, [(Tb0.3Dy0.7)Fe2] or a piezoelectric; it extends

or contracts in the field direction and conserves volume tofirst order

QUANTITATIVE MODELS

OF TWIN-BOUNDARY MOTION

Three of the models describing the field-induced motion

of twin boundaries in FSMAs are reviewed They are thenumerical micromagnetic model (2,18), and the analytic,thermodynamic models of O’Handley (32) and Likhachevand Ullakko (31,33,34) Thermodynamic models developed

by Vasil’ev et al (17) to describe the composition

depen-dence of TCand Tmand by L’vov et al (35) to describe themagnetization versus temperature behavior through themartensitic transformation are not described A thermo-dynamic model of the relative stability of limiting states in

a twinned FSMA (36) will be discussed later

These models generally include the Zeeman energy,magnetic anisotropy energy, and an external stress Theymay also include a magnetostatic energy (which tends to

restore M to zero when the field vanishes), an internal

elas-tic energy (which tends to restore the field-induced strain

to zero when the field is removed), and energies associatedwith the parametersσ0and Ctbshown in Fig 4 The action

of the external stress depends on its orientation relative tothe field-induced deformation Here, the stress is assumed

to be oriented to oppose the field-induced strain When theanisotropy is very large, the models generally predict astress-strain product that increases linearly with appliedfield times the saturation magnetization (If the externalstress is increased, less strain-per-unit-field results.) Whenthe anisotropy is not sufficiently strong to keep the mag-netization along the crystallographic easy axis in the un-

favorably oriented twins (i.e., those variants in which M is perpendicular to H), the Zeeman energy difference across

the twin boundary is decreased by application of a field andthe achievable strain is limited

Micromagnetics

James and Wuttig (2) adapted for FSMAs a numerical cromagnetic theory originally developed to describe themagnetostriction of Terfenol-D (37) Their model includesZeeman energy, external stress, and magnetostatic energy

mi-in a twmi-inned sample at the micromagnetic level:

g ( ε, H ) = −µ o H o M − σ o ε +  µ o

2



MDM (1)

The strain ε (x) and magnetization M(x) are position

de-pendent, and the energy density is calculated from theiraverage values in each twin variant or domain, respec-tively The external magnetic field and stress are given by

H0andσ0, respectively D is the demagnetization tensor of

the twin or domain This energy is minimized subject to theconstraint that the strains be determined by the allowedtwin systems in the martensite In addition to predict-ing linearε-H0characteristics (18), detailed magnetization

2000 Oe

5000 Oe

8000 Oe

Figure 8 Crystallography and variant magnetization directions

calculated for martensitic Ni 2 MnGa from Eq (1) Increasing

applied field (vertical in this figure) stabilizes variants having

smaller lattice constant in the magnetization direction (38).

distributions in the twins can be plotted Figure 8 shows

the results of numerical minimization of Eq (1) with the

field applied orthogonal to the initial single-variant

mag-netization direction The variant magmag-netization prefers to

lie along the tetragonal c-axis Increasing the field strength

results in stabilization of new twin variants having

magne-tization more closely aligned with the field direction Note

the mirror symmetry in the crystal structure across the

twin boundaries In addition to a net contraction of the

material in the direction of the applied field, the surfaces

become ridged at the twin boundaries

When µ0MsH ≈ Ku, the external field can cause the

moment in unfavorably oriented variants (M nearly

hori-zontal in Fig 8) to rotate away from the local c-axis As

the magnetization vectors in two adjacent variants become

parallel to each other, the Zeeman energy difference across

the twin boundary decreases and the field-induced twin

boundary motion is diminished When magnetocrystalline

anisotropy is included in the micromagnetic model (39),

the rotation of the domain magnetization by the external

field can be mapped from variant to variant as an applied

field alters the variant distribution Plots similar to those

Figure 9 Two-dimensional representation of field-induced twin-boundary motion The

parame-ters fi(i = 1, 2) are the volume fractions of variants 1 and 2 and δ f = f1 − 1 describes the placement of the twin boundary fromε = 0 as shown at the far right.

dis-in Fig 8 have been used to dis-interpret the rich twdis-in/domadis-inimages observed by magnetic force microscopy in NiMnGasamples (40)

These numerical micromagnetic models can include cromagnetic effects not tractable in analytic models How-ever, numerical models do not offer some of the insightsafforded by analytic models

mi-Analytic models

O’Handley (32) wrote a free energy expression for anFSMA comprised of two twin variants separated by asingle mobile twin boundary Zeeman energy, µ0M s ·H,

magnetic anisotropy energy, Kusin2θ, and an internal

restoring elastic energy, Ceffε2

o /2, were included initially;

an external stress-induced energy, σ . e, was added later

(8,41):

gi= −µ o M i · H + K usin2θ i+

12



Ceffe2+ ¨σ · ¨ε. (2)

The subscript i corresponds to variant 1 or 2 and the tions of the c axis and the local magnetic moment define the

direc-angleθias in Fig 9 The elastic energy density expresses

energy stored in unresponsive variants; Ceffis the stiffness

of the martensite in the presence of mobile twin boundaries(Fig 4) The two-dimensional representation is justifiedbecause the deformation and magnetization changes occur

only in the plane defined by the c-axes of adjacent variants.

It applies to multivariant samples having more than two

c-axis directions only with modifications (33).

The field-dependent strain is expressed purely as a

func-tion of the volume fracfunc-tion, fi, of each variant: ε(H) =

ε o δ f (H), where ε o is the transformation strain andδ f =

f1−1

2 is defined in Fig 9 The equivariant state, f1=

f2= 1

2, is defined here asε = 0 In contrast, the

expres-sion for magnetization includes contributions from bothtwin-boundary motion and magnetization rotation withinthe twin variants (32)

In the strong anisotropy limit, the sample is magnetizedonly by twin-boundary motion rather than magnetization

rotation The external stress is applied in a direction that

opposes the action of the field; for Ni2MnGa, that would be

a compressive stress parallel to the c-axis of the twin

vari-ant that is unfavorably oriented with respect to the field

The total energy density in Eq (1) can be minimized with

respect to the twin-boundary displacement,δ f , as well as

with respect to the anglesθ i In the special case H || M1,

θ1= 0 and only the θ2minimization need be done The

lat-ter minimization gives h = sin θ2, where h = µ0MsH/(2Ku),

and the two minimizations combine to give

For large Ku (small h), Eq (3) indicates that ε(H) =

(µ o M s H − σε o)/Ceffε o That is, the low-field strain response

of the system is governed by the balance between the

Zeeman energy and the external stress This equation

de-scribing strain by twin variant rearrangement as

posi-tive linear in H is to be compared with the quadratic

form for conventional magnetostrictive strain in an

elasti-cally isotropic, magnetielasti-cally uniaxial material,ε = (3/2) λs

(x2− 1/3) where x = cos θ = M/Ms= H/Hafor a hard-axis

magnetization process (42) The field-induced strain in

Eq (3) can be shifted rigidly toward negative values by

an external compressive stress Further, the strain scales

inversely with the internal elastic restorative stress, Ceffε o,

due to the noncompliant parts of the sample If this

restora-tive stress is small (i.e., the twin boundaries move easily),

a twinned sample strains easily (d ε/dH approaches

infin-ity), and even for large Ku, it magnetizes easily (dM/dH

intermediate anisotropy case, h ≈ 1 for µ o M S = 1.25 T (M S=

1000 emu/cm 3 ) The twin geometry and field orientation are chosen to be as shown in Fig 9 Curves are plotted for six combinations of magnetic anisotropy and internal elastic en- ergy densities given by the bold ticks on the outer coordinate axes Note that in all cases the remanence is 0.5 because of the geometry chosen A nonzero applied stress would simply

shift the strain values negative, including the value at H =

0 (32).

approaches infinity) once the critical field for boundary motion is exceeded

twin-On approaching rotational magnetic saturation (h = 1),

ε(H) scales with (Ku− σ ε o)/Ceffε o and is no longer linear

in H That is, the maximum field-induced strain is

lim-ited by the balance between the anisotropy and the nal stress The FSMA can show positive or negative straindepending on the relative magnitudes of anisotropy andapplied stress

exter-These conclusions are plotted numerically in Fig 10for six different combinations of anisotropy-energy densityand internal strain energy (32) At the upper left, for large

anisotropy (Ku= 3 × 106J/m3) and small internal

stress-induced energy (0.5Ceffε o2= 2 × 105J/m3), the sample can

be magnetized only by twin-boundary motion, not by

mag-netization rotation Thus, the reduced magmag-netization, m,

and the reduced strain, εy, increase together, linearly inapplied field They reach their saturation values in rela-tively small fields Moving across the top row of panels,the anisotropy remains strong, but the internal restoring

stress increases The field dependence of m and ε remain

correlated and close to linear even up to µ o H= 1 T butthe magnetic and strain response achieved in these fieldsare reduced because twin-boundary motion faces greaterinternal elastic opposition The lower row of panels be-gins with both weak anisotropy and weak internal restor-ing force The weak anisotropy allows the field to rotatethe magnetization in the unfavorably oriented variant, in-

creasing m However, the rotation of the magnetization

re-duces the Zeeman pressure on the twin boundary As aresult, the magnetization can increase (by rotation intothe field direction) while the strain lags behind because

it depends only on twin-boundary motion Further, the

field-induced strain gained by twin-boundary motion at

weak fields may be reclaimed by the material (depending

on the irreversibility of the twin-boundary motion) as the

Zeeman pressure on the twin boundaries decreases with

in-creasing field, allowing the internal stored stress to relax

These effects become even more pronounced on moving to

stronger internal stress as shown in the bottom row of

in-set figures The magnetization curves calculated here differ

from the hard-axis, magnetization-rotation process shown

in Fig 5 because these are the result of twin boundary

motion as well as magnetization rotation; that in Fig 5 is

for magnetization rotation only as the sample there is

con-strained to the single-variant state It should be noted that

when M2 rotates toward H in the weak anisotropy limit,

the Zeeman energy difference decreases like sinθ2and the

anisotropy energy difference increases like sin2θ2 The net

magnetic pressure reaches a maximum value of Ku when

h= 1

This model also indicates that the field component

re-sponsible for driving twin-boundary motion is that parallel

to the twin plane The data of Fig 1(b), as well as M(H) for

that sample, are well described by this model withσ = 0,

Ku= 2.2 × 105J/m3, and Ceffε o = 2.6 MPa (32).

The consequences of the parametersσ0and Ctb(Fig 4)

are to increase the irreversibility of the strain-versus-field

loops The twin boundary yield stress,σ0, adds a term to

the applied field in Eq (3) with a sign that always opposes

the applied field: H −> H ± σ0ε0/µ0Ms This addition to the

applied field is a twin-boundary coercivity, the field needed

to initiate twin-boundary motion If one were to take

account of the threshold field needed to initiate

twin-boundary motion, the curves in Fig 10 would be shifted on

the field axis to show hysteresis with the increasing-field

(decreasing-field) curves displaced to the right (left) by Hc

Likhachev and Ullakko (31,33,34) have taken a more

general analytic approach to the problem in three

dimen-sions They integrate the Maxwell relation

They assumed that from the equivariant state, one-third of

the material is easily magnetized (the variant fraction that

has its c-axis parallel to the field); H||is the anisotropy field

for such axial variants H||should be the shape anisotropy

of the sample; about 0.1 MA /m in Fig 5) Also, two-thirds

of the material (those variants with c perpendicular to H )

will have to be magnetized in their hard direction with a

transverse anisotropy field, H⊥> H|| (compare Fig 5) As

the equivariant state is upset by twin-boundary motion

under the application of a field, the magnetization and

strain can be expressed as functions of x, the volume

frac-tion of axial variants, which plays a role similar toδ f in the

2-D model (Fig 9) The parameter x is eliminated between

the expressions forεFSMA(H , x) and M(H, x), giving

area between the two M(H) curves in Fig 5) that must

be overcome by the applied field in order to saturate the

material Experimental M(H) and σ(ε) data are used as

input to Eq (6) to allow prediction of ε (H, σ ) (31) At

saturation Eq (6) reduces to

εFSMA Sal = 13



ε o

dσ o dε

−1

ε=0

(H 1 − H a)µ o M s≈ µ o M s H

3C o ε o (7)The term µ0MsH( H/H) expresses succinctly and ele-

gantly the dual importance of both the Zeeman energy,

µ0MsH, and the anisotropy, H/H, which make up the

energy difference across a twin boundary This interplay

of both Zeeman and anisotropy energy is represented

by the first two terms in the numerator of Eq (3) Themodel of Likhachev and Ullakko suggests that the field-induced strain is limited by the internal stress,σ o = Ctbε o,needed to nucleate and move mobile twin boundaries inthe martensitic phase This term has a different meaning

than Ceffε oin Eq (3) although the magnitude of both terms

is similar In both models, a value forσ oof order a few MPaprovides a good fit to data in Fig 1

The analytic models suggest that large values of the

dif-ference H⊥− H||(or large Ku), large saturation tion, and low-threshold stress,σ0, are critical parametersfor achieving large field-induced strain by twin-boundarymotion

magnetiza-Finally, it is important to be able to extend the results

of these single-crystal models to polycrystalline materialsthat may be used in some applications Bhattacharya and

Kohn (43) have given a Taylor (lower) bound to the strain

that can be achieved in a random polycrystalline shapememory material They find that for cubic-to-tetragonalmartensites, the lower bound to the strain is zero However,for lower symmetries, some fraction of the transformationstrain can be induced by stress because in lower symmetrystructures there are more planes along which the systemcan twin to accommodate an external stress

Marioni et al (44) have taken FSMA twin variants, scribed in a model similar to that in O’Handley (32), and as-sembled them with various textures to simulate noninter-acting grains in a polycrystalline sample This model gives

de-an upper bound for the maximum field-induced strain

be-cause grain-to-grain elastic interactions are treated only in

a mean-field way by the parameter Ceffε o They find that fortetragonal FSMAs, a random polycrystalline sample couldgive a field-induced strain up to 20% ofε0 For a texture

in which twin plane normals are distributed about thefield direction at a common angle (a texture which may beachieved by uniaxial compression), the field-induced straincan be as much as 34% ofε0 In addition, this model pre-dicts a threshold field below which there is little strain

(a) (b) (c)

Figure 11 Above left: Orientation of M, H, and σ relative to the twinned sample High-speed

video frames (a), (b), and (c) show the sample in the initial vertically compressed (σ ≈ 1 MPa)

state (H = 0), in an intermediate state, and in the final magnetically saturated (and fully strained

vertically by 6%) state, respectively Below: Selected field-induced strain curves at various external opposing stresses at room temperature for a Ni 49.7Mn28.5Ga21.7single crystal (8).

response because the component of the applied field

paral-lel to the twin planes of a given orientation is less than the

twin-motion coercivity For fields above this threshold, the

strain increases rapidly toward the linear value predicted

by the thermodynamic models The physical origin of this

threshold field in polycrystalline samples is different from

that associated withσ0and the initiation of twin-boundary

motion

FIELD-INDUCED STRAIN UNDER LOAD

With the background developed so far, it is now possible to

describe and analyze in more detail the measurements of

field-induced strain under load that form the basis for use

of FSMAs as actuator materials

dc Actuation under Static Stress

Figure 11 shows the results of field-induced strain

mea-surements in a Ni49.8Mn28.5Ga21.7 single crystal at room

temperature for various axial external stresses that oppose

the field-induced strain The sketch at the upper left shows

the orientation of the magnetization, magnetic field, andexternal stress relative to the twinned sample The threephotographs are frames from a high-speed (1200 frames/s)video taken on the sample close to the initially stressed

state (approximately 1 MPa) at H= 0 (frame a), at about

15 ms into the actuation (frame b), and at saturation afterabout 23 ms (frame c) The structure in frame (a) is domi-

nated by the dark twin bands (M parallel to stress) In frame (b) the lighter twin bands (M parallel to H) fill more

than half the area on the front surface In frame (c) thesample is essentially filled by the light-colored twin bands(except for the thin twin band that apparently remainspinned)

The graph in Fig 11 shows the ε-H loops with fairly

abrupt strain changes of several percent, occurring over anarrow field range On returning the field to zero, signifi-cant hysteresis is evident With increasing external stress,the threshold field for strain actuation increases and thestrain at saturation decreases At low external stress, thefield-induced stain does not reset to ε = 0 upon removal

of the field This suggests that Ceff is small in this case

At strain levels in excess of 0.7 MPa, the sample resets

Table 1 Mechanical and Magnetic Parameters measured

for Single-Crystal Ni–Mn–Ga and Used in Eq 3 in the

Model Results of Fig 12

Parameter Range of Measured Values Values used in Fig 12

to condition a) when H= 0 The hysteresis appears

non-monotonic in applied stress Nearly the full

transforma-tion strain is achieved in this sample for stresses less than

0.5 MPa Some samples have shown strains of 6.1% at

sat-uration (8,45)

The data of Fig 11 can be modeled with Eq 3

us-ing the measured Ni–Mn–Ga parameters (see Table 1)

The hysteresis is accounted for in an ad-hoc manner by

adding to the applied field a coercive (offset) field H c=

±σ o ε o/(µ o Ms)= 93.3 kA/m (1.17 kOe) The model results

displayed in Fig 12(a) and (b) show that these parameters

give a reasonable reproduction of the major trends in the

experimental data, namely the shape ofε(H), as well as the

increase in threshold field and decrease in strain with

in-creasing external stress The model does not account for the

observed change in coercivity with external stress The

pre-dicted decrease in saturation strain with increasing stress,

Fig 12 (b), is consistent with observations

The limitations of the model in fitting the data may be

the result of neglecting magnetostatic effects in the model

It is not the result of a stress-induced anisotropy (3σ λ/2)

adding to Ku as external stress is increased Based on

the measured magnetostriction of the martensitic phase,

λs= −145 × 10−6 (28), the magnetoelastic anisotropy at

σ = 2 MPa is more than two orders of magnitude smaller

than Ku

Alternating-Field Actuation under Dynamic Load

The quasi-static, field-induced strain measurements

shown in Fig 11 have also been carried out at actuation

frequencies up to 330 Hz To perform these measurements,

the static load was replaced with a spring against which

the sample extends under a transverse field (Fig 13)

Figure 14 shows a set of field-induced strain curves

taken at 1 Hz drive, 2 Hz actuation in the system shown

in Fig 13 (46) The sample is a single crystal of Ni–Mn–Ga

measuring 1× 5 × 7 mm, with the field applied normal to

the 1× 7 mm face and the strain measured along the 7 mm

direction The saturation strain at any given stress level

increases with increasing stress, reaching a maximum

value near 1.4 MPa Note the much smaller hysteresis

in this case compared to the quasi-static situation shown

in Fig 11 For larger stresses, the saturation strain

decreases, and the hysteresis as well as the threshold field

for actuation increase

When the sample is driven to higher frequencies than

in Fig 14, the saturation strain is unchanged up to an

Field (MA/m)

σ =1.8 MPa

Field (kOe)0

024

0.250.7

(a)

0

246

Stress (MPa)

(b)

Figure 12 a) Calculated strain versus applied field curves from

Eq (3) b) Calculated strain at peak field versus stress with laid experimental points from the full set of data depicted in Fig 11 (8).

over-actuation frequency of about 100 Hz Beyond that value,the peak output strain drops off sharply However, it isclear from the data in Fig 15 that the drop-off in res-ponse is due to the reduction in the applied field Above

a drive frequency of about 50 Hz, the inductive reactance

of the field coils becomes sufficiently large that the powersupply can no longer deliver the current needed to gen-erate a field sufficient to saturate the strain Power sup-plies must be designed to match the impedance of theload over the operating bandwidth Pulsed-magnetic-fieldmeasurements with a drive-field rise time of 1 ms indi-cate that single-crystal samples of Ni–Mn–Ga can strain

at a rate that keeps up with the rise time of the pulse(47) This implies a bandwidth of at least 1 kHz for thesematerials

Photograph of dynamicFSMA tester.

H Micrometer

advance

Schematic of dynamicFSMA tester

Spring for

bias stress

H

Figure 13 Test system, schematic (left) and photograph (right)

The FSMA sample is subjected to a bias stress along one axis and

an ac magnetic field along an orthogonal axis A micrometer

ad-vances the sample into the spring to establish the desired bias

stress level The sample elongation under applied field is

sured with an eddy-current proximity sensor The apparatus

mea-sures approximately 12 × 15 × 30 cm (46).

DISCUSSION

Engineering Parameters

James and Wuttig (18) have observed the rearrangement

of twin boundaries in martensitic Fe70Pd30accompanying

a field-induced 0.5% extensional strain Similarly, Ni–Mn–

Ga crystals show extensional strains under quasistatic

ex-citation ofε > 4% at room temperature (8,45) AC strains

in excess of 3% in Ni–Mn–Ga crystals at room temperature

have been reported (46) The response of active magnetic

materials is generally described by the magnetostrictivity

defined as dij= ∂ε1/∂ Hj, where the subscripts refer to

di-rections in Cartesian coordinates Magnetostrictive

ma-terials such as Terfenol-D are often operated under field

bias In the case of the FSMA data shown in Fig 14,

application of a bias field of about 2 kOe and an ac field

of ± 1kOe about that bias, would result in actuation at

the drive frequency with an output strain of about 2%

peak-to-peak The value of d31 under such actuation is

about 1% per kOe or 12.5 × 10−8m/A This value compares

1.9

1.6

1.41.1

0.5

0.3

2.10.9

Field (kOe)

Strain(%)

Figure 14 Field-induced strain data for several values of

ap-plied stress at an actuation frequency of 2 Hz The sample

elon-gates against the spring for both positive and negative field cycles,

giving an actuation frequency twice the drive frequency.

5.0

4.0Field (kG)

Figure 15 Frequency dependence of peak field generated in the

system shown in Fig 13 (upper curve) and the strain at peak field The decrease in actuation strain above a drive frequency of 50 Hz has been identified as due to the decrease in field applied to the sample (46).

favorably with the value of d33for Terfenol-D in Table 2

Table 2 compares the magnetostrictivities, dij, for twoactive FSMAs and the leading magnetostrictive material,Terfenol-D, Fe2(Tb0.3Dy0.7)

The negative (positive) sign of d33 (d31) for Ni–Mn–Gareflects the fact that it contracts along the axis in which themagnetization increases and expands along the original

axis of M The magnetomechanical coupling coefficient, k,

is defined for a magnetically driven actuator by the ratio

of the output mechanical energy to the total input energy(magnetic plus mechanical) For purposes of determiningthe coupling coefficient, the following relations based onclamped and free permeabilities or free and clamped elasticmoduli, can be derived:µ ε = (1 − k2)µ σ or C H = (1 − k2)C M

(6) From Fig 4 and the data in Table 1, the latter relation

suggests that k approaches unity for these materials, that

is, they couple magnetic energy to a mechanical load with

near-perfect efficiency (48) (The free modulus, CHis taken

as Ctbin Table 1 and the clamped modulus, CMis given by

C0in Table 1.)

Stress Dependence of ε(H )

The introduction of an external stress in the

thermo-dynamic model when Ceff= 0 predicts a strain that creases linearly with applied stress, Eq (3), and Fig 16(a)

de-Table 2 Comparison of Currently Achieved Field-Induced Strain and Magnetoelastic Coupling Coefficients d 33 and d 31 in FePd and Ni–Mn–Ga FSMAs with the Magnetostrictive Material, Terfenol-D

Active Magnetic ε H-field d33 d31 Material (%) (kA/m) (10 −8m/A) (10−8m/A) k

Figure 16 (a) Field-induced strain versus stress predicted by single-variant thermodynamic

model (32) (b) Field-induced strain versus stress observed in Ni2MnGa at −15 ◦C (38) (c) induced strain versus stress calculated with no restoring force (30) (d) Field-induced strain versus stress observed in Ni–Mn–Ga at room temperature (36).

Field-Figure 16(b) shows one set of strain versus stress data

for Ni2MnGa at−15◦C and H=12 T (29) The saturation

strain achieved here is less thanε0, suggesting that many

of the twin variants are not responding to the applied

magnetic field These unresponsive twins may present

an elastic resistance (Ceff= 0) to the deformation caused

by motion of the active twin boundaries The observed

blocking stress of 9.2 MPa (σ at which ε = 0) is

calcu-lated from Eq (3) to be 5 MPa (using Ku= 2.45 × 105J/m3

andε o = 0.05) In contrast, Murray et al (36) have noted

that different Ni–Mn–Ga crystals may respond to an

ap-plied field with little or no restoring force, namely Ceff≈ 0

When the stored elastic energy is omitted from Eq (2), the

free energy cannot be minimized for|δf | < 0.5 Instead, an

instability arises in which the twin boundary moves

com-pletely (δf = ±0.5) in the direction favored by the field if

µ0MsH > σε oand in the opposite direction ifµ0MsH < σ ε o

There is no internal elastic opposition to this motion when

there are no unfavorably oriented twin planes In such

situations, the strain under load does not decrease linearly

with stress but rather maintains a constant value until a

critical stress is reached,σc= µ o MsH/ ε o, at which point

the strain vanishes abruptly as in Fig 16(c) Recent data

on Ni–Mn–Ga at room temperature, Fig 16(d), support

this instability model (36) In addition, the field-induced

strain in these FSMAs is more bistable (like a Barkhausen

jump), whereas the FSMAs whose response is shown in

Fig 16 (b) show smoother, more reversibleε (H) as

de-picted in Fig 1 (36) Likhachev et al (49) have recently

shown data for the strain dependence of Ni48Mn30Ga22that

fall between these two limits and are well described bytheir model

It thus appears that a range of e(H, σ ) responses may

be able to be achieved with FSMAs Smaller output strainwith larger blocking stress may be achieved in some crys-tals, Fig 16 (b), or larger output strain with smaller block-ing stress may be observed in other crystals, Fig 16 (d).The reasons behind these different types of response arenot yet well understood In the present case, the differenttemperatures and compositions (and hence different mag-netic anisotropies, magnetizations, and mechanical pro-perties) may be factors Another difference between thetwo samples contrasted in Fig 16 is that the one in panel(b) shows a much finer twin structure (measured in tens ofmicrons) with multiple twin systems present The samplerepresented in panel (d) shows a much coarser twin struc-ture (twin spacing of order 0.5 – 1 mm), and only one family

of twin boundaries is present It may be possible that some

of the variously oriented twin systems in the former ple may not respond to the applied field and hence provide

sam-a mechsam-anism for storing energy elsam-asticsam-ally (0.5Ceffε0 ) asthe active twins respond to the field

Comparison with Shape-Memory Effects

Here, we compare the field-induced strain observed inFSMAs with (1) the thermoelastic shape memory effect(pseudoplasticity) and (2) stress-assisted martensitictransformations (superelasticity)

First, in the thermoelastic shape memory effect, a

twinned, martensitic material is macroscopically deformed

in a manner that appears to be plastic In fact, the

de-formation is not the result of dislocation de-formation and

motion, but rather twin-variant rearrangement

(twin-boundary motion) Upon heating to the austenitic phase,

the macroscopic deformation is erased by the structural

transformation of the martensite to austenite This is the

one-way shape memory effect if cooling back to the

marten-sitic state does not restore the macroscopic deformation

In some cases, cooling back to the martensitic state can

restore the macroscopic deformation This is called the

“two-way shape-memory effect.”

This thermoelastic shape-memory effect achieves a

shape change by structural transformation of the

mate-rial between a twinned phase and a different untwinned

phase By contrast, the shape changes so far observed

in FSMAs are induced by a magnetic field fully within

the martensitic state It involves the field-induced motion

of twin boundaries Thus, the effect in FSMAs may be

faster and more efficient compared to the thermoelastic

shape-memory effect where the need for heat transfer

lim-its the kinetics

Second, when a material showing the shape-memory

effect is subjected to a stress at a temperature just above

the martensite start temperature, the stress can facilitate

the transformation to the martensitic phase Once twinned

martensite is formed, the stress can result in a large

(sev-eral percent) macroscopic deformation of the material

(su-perelasticity) Upon removal of the stress, the material

re-transforms to the austenitic phase and the large

defor-mation is erased This effect can be much faster than

ther-mally induced shape changes associated with the

marten-sitic transformation

FSMAs have been shown to exhibit stress-induced

martensite that then responds to a magnetic field with an

additional strain (19) When the external stress is removed,

the material reverts to the austenitic phase and the large

field-induced strain decreases to the smaller value typical

of the austenitic phase

Comparison with Magnetostriction

The field-induced strain observed in FSMAs is similar in

some ways to the magnetostriction generally observed in

ferromagnetic materials

1 In both cases, the strains conserve volume to first

order Thus, the strain measured from the tized or equi-twin-variant state in a direction per-pendicular to the field will beε⊥≈ −ε/2, where ε

demagne-is the field-induced strain parallel to the field uniform initial distributions of domain magnetiza-tions or twin variants can upset this relation (as

Non-in field-biased or pre-stressed samples such as thatshown in Fig 11 whereε⊥≈ −ε)

2 The bending effect across the twin boundary (which

is also a 90◦ domain wall), shown in Fig 6 forNi–Mn–Ga, would also occur in an appropriatelycut ferromagnetic crystal such as Fe (<100> at 45◦

to bar axis) if a single 90◦ domain wall could be

isolated (Because the magnetostriction coefficient of

Fe in the [100] direction,λ100, is positive, the domainmagnetization would be orthogonal to those pictured

in Fig 6 or the bending would be in the otherdirection.) However, in Fe the bend angle across the

90◦domain wall would be only 0.002◦corresponding

to a shear strain of 2× 10−5.The differences in field-induced-strain between FSMAsand magnetostrictive materials are more important thanthe similarities

1 Field-induced strain in FSMAs is due to boundary motion, which brings with it a change inthe direction of magnetization The FSMA strain

twin-is tied to the crystallography, not to the direction

of M That is, it is possible to rotate M with no

FSMA strain, only conventional magnetostriction, inFSMAs that are characterized by relatively weakanisotropy In magnetostrictive materials, on theother hand, field-induced strain is a result of magne-tization rotation relative to the crystallography; the

strain is tied to M, and not to the crystallographic

orientation

2 In the ferromagnetic martensitic phase, the creased magnetocrystalline anisotropy relative toaustenite means that saturation of the magnetiza-tion requires stronger magnetic fields than in austen-

in-ite If TC> Tmart, there is no large FSMA field-induced

strain between Tmart and TC because the material is

in the austenitic phase and twins are not present.The FSMA strain shows a peak on heating through

Tmart (28,49) If TC< Tmart, there is a static strain in

each variant of the martensitic phase above T C, but

it cannot be controlled by a field because M = 0

It can be controlled by an applied stress

Magne-tostrictive strain becomes possible below TC with a

second-order magnetic transformation; it has a

tem-perature dependence governed by [M(T) /M(0)] l(l +1)/2 (51) (Here, l defines the symmetry of the lowest-order crystal field term: l = 2 is uniaxial and l = 4 is cubic.)

The crystal strain in an FSMA, on the other hand,

ap-pears in the martensitic phase by a first-order

struc-tural transformation below Tmart[James and Wuttig(2)]

3 Field-induced strains in FSMAs decrease as thestrength of the magnetocrystalline anisotropy of themartensitic phase decreases belowµ0MsH For weak

anisotropy martensite, the field may rotate M

with-out moving the twin boundaries, and there is nochange in macroscopic strain The field-dependence

of strain in FSMAs—that do not show discontinuous

ε(H) versus σ behavior in Fig 16(b) and (d)—is

pre-dicted to be linear in H below saturation in the strong

anisotropy limit (18,32) Reduced anisotropy can troduce strong nonlinearities inε(H) (18,31–34) On

in-the oin-ther hand, in-the magnetostrictive strain

accessi-ble in a given field H < H awill be greater, the smallerthe anisotropy The field dependence of magnetostric-tive strains in a hard-axis magnetization process is

quadratic in H or M below saturation (42).

Ferromagnetic shape-memory alloys have shown

field-induced strains at room temperature greater than those of

any magnetostrictive, piezoelectric, or electrostrictive

ma-terial This strain is due to the motion of twin boundaries

in the martensitic phase A variety ofε(H, σ)

characteris-tics appears to be possible in FSMAs Some samples tend

to show abrupt twin-boundary motion as the sign of the

quantity 2Kuh(1 − h/2) − σε0changes In the other limit of

FSMA behavior, twin-boundary motion appears to be

op-posed by an internal elastic restoring energy, possibly

as-sociated with unfavorably oriented twin boundaries In the

latter case, the field-induced strain is smaller and more

lin-ear in the applied field for h < 1, and the blocking stresses

can be greater

Micromagnetic and analytic thermodynamic models are

able to describe the main features of the magnetization

pat-terns in the twinned FSMAs and the forms ofε (H, σ), and

M(H) in single-crystal FSMAs, respectively Field-induced

strains in FSMAs show some incidental similarities to

magnetostrictive strains but are essentially different,

aris-ing from the field-induced motion of twin boundaries in a

martensitic phase that is strongly distorted by a first-order

transformation not connected to T C The field-induced

strains occur at smaller fields as the stress required to

nucleate twin boundary motion,σ o, decreases Decreased

magnetocrystalline anisotropy or increased external stress

limits the magnitude of the field-induced strains Unlike

the thermoelastic shape-memory effect, large

magnetic-field-induced strain in FSMAs so far is observed fully

within the martensitic state

ACKNOWLEDGMENTS

The authors acknowledge fruitful discussions with R.D

James and M Wuttig The work at MIT described in this

review was carried out largely by S.J Murray, M Marioni,

and C.P Henry It has been supported by the Finnish

Min-istry of Science and Technology (TEKES) with a consortium

of Finnish companies, by a subcontract from Boeing

Cor-poration on a DARPA contract, by grants from the Lord

Corporation, Mid´e Technologies, and the Office of Naval

Research, as well as by contracts from DARPA, ACX

Cor-poration, and Mid´e Technologies The crystals used in our

study were grown by Dr V.V Kokorin, Institute of

Met-allurgy, Kiev (Fig 1) and by Dr Tom Lograsso of Ames

Laboratory, Department of Energy (Figs 6, 11, and 14)

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SHAPE MEMORY ALLOYS, TYPES

SHAPE-MEMORY ALLOY SYSTEMS

Many systems exhibit martensitic transformation

Gen-erally, they are subdivided into ferrous and nonferrous

martensites A classification of the nonferrous martensites

was first given by Delaey et al (1) (Table 1), and ferrous

al-loys that exhibit a shape-memory effect were first reviewed

by Maki and Tamura (2) (Table 2)

Table 1 Classification of Nonferrous Martensitesa

1 Terminal solid solutions 1 Cobalt and its alloys based on an element 2 Rare-earth metals and their alloys that has allotropic phases 3 Titanium, zirconium, and their alloys

4 Alkali metals and their alloys and thallium

5 Others such as Pu, Ur, Hg, and alloys

2 Intermetallic solid 1.β-Hume–Rothery phases of Cu-, Ag-, and Au-based alloys

solutions that have a 2.β-Ni–Al alloys

bcc-parent phase 3 Ni–Ti–X alloys

3 Alloys that show cubic 1 Indium-based alloys

to tetragonal trans 2 Manganese-based alloys (paramagn ↔ antiferromagn.) (incl Quasi-martensite) 3 A15 compounds

4 Others: Ru–Ta, Ru–Nb, Y–Cu, LaCd, LaAg x –In 1 −x

a

Of the systems mentioned in both tables, only one tem became industrially successful: Ni-Ti(X,Y) in whichX,Y are elements that replace Ni or Ti Besides the Ni-Tisystem, a lot of attention had been given in earlier times

sys-to Cu-based alloys (3) and sys-to Fe–Mn–Si alloys (4) more, in recent years, special attention has been given tohigh-temperature shape-memory alloys (HTSMA) (5).The aim of this article is mainly an introduction to in-dustrially applicable shape-memory alloys; the followingalloy systems will be reviewed:

The austenite (fcc-γ phase) in ferrous alloys can be

trans-formed to these three kinds of martensites, depending oncomposition or stress:γ -α (bcc),γ → ε (hcp) and γ → fct

martensite

Although a shape-memory effect has been observed inall three types of transformation, most attention in de-veloping a commercial alloy has been given to the alloysthat have aγ → ε transformation These alloys have a low

stacking fault energy in austenite (Fe–Cr–Ni, Fe–high Mnalloys) The austenite toε-martensite transformation pro-

ceeds by the a/6 [112] Schockley partial dislocations that

trail a stacking fault ribbon on every{111} austenite planeand change the crystal structure to martensite The shape-memory effect, which is of the one-way type, results mainlyfrom reverse motion of the Schockley partial dislocationsduring heating

A complete shape-memory effect has been reached inboth single-crystal (7,8) and polycrystalline Fe–Mn–Si al-loys (9,10) that contain suitable amounts of Mn and Si

A 9% shape-memory strain in single crystals (8) and 5%

in polycrystals (9) have been reported

Any factors that impede the reversibility of the motion

of partial dislocations lead to incomplete recovery and inturn a poor shape-memory effect

Table 2 Ferrous Alloys That Exhibit a Complete or Nearly Complete Shape-Memory Effecta

Crystal Structure Nature of Alloy Composition of Martensite Transformationb

Fe–Ni–Co–Ti 23%Ni–10%Co–4%Ti bct (α ) —

33%Ni–10%Co–4%Ti bct (α ) T.E.

28 ∼33%Mn–4∼6%Si hcp (ε) Non-T.E.

aRef 2.

bT.E.: Thermoelastic martensite, non-T.E.: Nonthermoelastic martensite.

The internal factors that hamper recovery include alloy

composition, N´eel temperature, transformation

tempera-ture, and lattice defects External factors are applied stress

and strain, deformation, recovery annealing temperature,

and thermomechanical treatment

For example, Murakami et al (11) showed that Fe–Mn–

Si alloys that contained 28–33% Mn and 4–6% Si exhibit a

nearly perfect shape-memory effect But alloys whose Mn

content is less than 20% have also been developed

success-fully Cr (less than 20%) and Ni are added to improve the

corrosion resistance of commercial Fe-based alloys

So far, Fe-based alloys are not successful SMA They

ex-hibit only a (limited) one-way shape-memory effect after

a labor-intensive thermomechanical treatment No

signif-icant two-way effect or pseudoelastic properties have been

reported, whereas only moderate damping capacity might

have some interest Therefore the only reported successful

applications of these Fe-based alloys are couplings This

type of application is based on the one-way effect The

re-covery stresses are moderate but sufficient (12)

Cu-Based Alloys [(1,3,13–16)]

Copper-based shape-memory alloys are derived from

Cu–Zn, Cu–Al, and Cu–Sn systems The composition

range of these alloys corresponds to that of the well-known

β-Hume–Rothery phase In most shape-memory alloys,

this phase has a disordered bcc structure at high

tem-peratures but orders to a B2, D03, or L21 form at lower

temperatures The shear elastic constant of theβ phase

ex-hibits anomalous behavior as temperature decreases, that

is, it is lowered till the lattice instability with respect to

{110} <1¯10> shears at some temperature and transforms

β to martensite The temperature of the transformation

to martensite, Ms, varies with the alloy composition The

elastic anisotropy of theβ phase is much higher compared

to normal metals and alloys and increases further as the

martensitic transformation is approached

Cu–Zn and Cu–Al martensites are of three typesα ,β

orγ : the subscript 1, 2, or 3 is added to indicate the

order-ing schemes inβ, namely, B2 (2) or D03(1) or L21(3) Some

conversion from one martensitic structure to another, for

example β → γ , may also take place The net result is a

coalescence of plates within a self-accommodating group

and even coalescence of groups Heating this deformed

martensitic microstructure transforms it to theβ phase,

and the shape-memory effect accompanies the structuralchange

Copper-based shape-memory alloys presently used arederived from Cu–Zn and Cu–Al systems, and elementsare added for various metallurgical reasons The workingmartensite in these alloys is only or predominantly the

β

1, 2 or 3, type whereγ martensite is the minor constituent

in the latter case Alloys that haveα martensites have sofar not been used Therefore, alloys of β

1, 2 or 3 martensiteare the subject in this part

Two criteria should be taken into account when lecting an alloy composition to obtain a complete β mi-

se-crostructure that transforms to martensite: (1) Theβ phase

must be stable across as wide a temperature range aspossible The less wide this temperature range, the fasterthe cooling rate required to retain the β phase without

diffusional decomposition (2) Transformation tures must fall within a range that satisfies the require-ment for the shape-memory application (−150 to 200◦C).The three alloy systems in Table 3 satisfy these criteria.They are used nowadays, but in limited amounts Apartfrom composition, transformation temperatures are alsostrongly influenced by other factors

tempera-The Influence of Chemical Factors on the Transformation Temperature

The Influence of Composition Several authors have

at-tempted to quantify the Ms–composition relationship forseveral Cu-based alloys An overview is given in (3) Dif-ferent authors weight the same element differently Themain reason for this discrepancy might be that the sam-ples measured have different thermomechanical histories,that is, one has probably not measured “identical samples.”Indeed, composition is not the only chemical factor that af-

fects the Mstemperature The type and degree of order oftheβ and the martensite lattice also affect the Ms Thermaltreatments can, therefore, influence the transformation, asdiscussed in the following sections

Quenching and the Order State of the β Phase The

trans-formation temperatures of Cu-based alloys are very sitive to minute changes of the degree of order in the

sen-β phase Such changes are easily brought about by

quenching from intermediate and high temperatures in theform of dilute disorder in an otherwise well-ordered mate-rial The effect is noticeable in both Cu–Zn–Al (17,18) and

Table 3 Industrial Cu-based Alloys

Other Alloying Current Grain Refining Elements in Elements Producing Remarks on the Base Base Alloy Composition (wt%) M s ( ◦C) Hyst (◦C) Solution (%) Precipitates Alloy

Cu–Zn–Al 5–30 Zn −190 to +100 10 (β ) Ni (5%) Co (CoAl); B (AlB

2 ); Good ductibility and

prone to martensitic stabilization;

poorβ stability

(T > 200◦C)Cu–Al–Ni 11–14.5 Al −140 to +200 10 (β ) Mn (5%) Ti [(Cu, Ni)2TiAl]; Low ductility;

stabilization;

goodβ-stability

Cu–Al–Be 9–12 Al −80 to +80 6 (β ) Ni (5%) B (AlB2or AlB12) Poor reproducibility;

(T > 200◦C)

Cu–Al–Ni (19,20) alloys and manifests as a suppression of

the transformation temperatures thereby stabilizing theβ

phase relative to the martensitic The suppression is

tem-porary, but it is easily recoverable in Cu–Zn–Al alloys by

aging in theβ condition at as low a temperature as room

temperature However, the recovery of Cu–Al–Ni alloys

tends to be more sluggish and requires higher aging

tem-peratures For example, Cu–Al–Ni alloys aged at 300◦C for

1 hour can have transformation temperatures up to 60◦C

higher than the as-quenched alloys

Aging and the Order State of Martensite Aging a Cu–Zn–

Al alloy in the martensitic condition can appreciably shift

the reverse transformation temperatures of the martensite

to theβ phase (21) This shift to higher temperatures

stabi-lizes the martensitic relative to theβ phase This

stabiliza-tion is brought about by a thermally activated diffusional

process and, is it presumed, alters the ordered state

inher-ited by the martensite from theβ to a relatively disordered

state (21,22) The effect is more pronounced in the

pres-ence of excess vacancies retained after a prior quench from

higher temperatures A quench to a temperature above

the Ms followed by a hold at the same temperature (step

quenching) to rid the alloy of excess vacancies reduces the

problem considerably (21) But even then, stabilization of

martensite can recur during subsequent aging, and the

effect is worse, the higher the aging temperature in the

martensitic condition

Manganese or nickel addition to Cu–Zn–Al, it has been

shown, too lessens the problem of stabilization This

hap-pens possibly through a slowing of diffusion in the

marten-site in the presence of the added elements More

interest-ingly, the effects it has been shown are inhibited, even in

the absence of these elements, by dislocations introduced

into theβ phase during hot rolling (23) or through

trans-formation cycling (24) Further understanding of the role

of these dislocations in such inhibition might provide the

information needed to improve the stability of these alloys

for use at higher temperatures Stabilization of Cu–Al–Ni

martensite is much slower compared to Cu–Zn–Al (19,25)

The former alloys thus are more thermally stable than Cu–

Zn–Al and are more suited for use at higher temperatures

Influence of Other Factors on the Transformation Temperature Besides the chemical factors such as com-

position and order; certain nonchemical factors may also

influence the Mstemperature Among the latter are butions from defects such as vacancies, dislocations, grainboundaries, and precipitates

contri-Influence of Nonequilibrium Precipitates Precipitates

like theγ phase can be formed in Cu–Zn–Al by flash

heat-ing to an intermediate temperature after prior dissolutionfollowed by quenching (17) These precipitates may shiftthe transformation temperatures with respect to theirnominal values and also may produce variations in thetransformation temperature range and the hysteresis thataccompanies the transformation The exact changes de-pend on the coherency, size, and distribution of the precip-itates The variations are brought about by an alteration

in the chemical, stored, elastic, and frictional energies ofthe transformation because of the presence of the addi-tional phase Stored elastic energy plays a dominant rolewhen the precipitates are small and coherent and whentheir presence does not appreciably change the composi-tion of the matrix This usually leads to a suppression of the

Msand to minor changes in the hysteresis, providing theprecipitates are deformed in the transformation Largersemi- or incoherent precipitates that substantially alterthe composition of the matrix and impede the growth ofmartensitic plates lead to changes in the Msthat depend onthe partitioning of the elements and an enlarged hysteresis(26)

Precipitation and concomitant changes in tion temperatures can be disadvantageous if they are pro-duced inadvertently during service, but they can be incor-porated in the heat treatment schedule to fine-tune thetransformation temperatures or when wider hysteresis isrequired

transforma-The Influence of Grain-Refining Elements that Form Precipitates Copper-based shape-memory alloys exhibit

rapid grain growth at higher dissolution temperatures.When grain sizes are of the order of millimeters andthe elastic anisotropy in theβ phase is high, they suffer

intergranular cracking and plastic deformation during

quenching The problem has been solved by adding grain

refining elements to the two shape-memory alloys Zr (0.4–

1.2 wt%), Co (0.4–0.8%), Ti (0.5–1.0 wt%), and B (0.4–

0.2 wt%), have been added to Cu–Zn–Al alloys to reduce

the grain size to the 100-µm level Titanium is also

effec-tive in refining the grain size in Cu–Al–Ni alloys to the

50–100 µm range (27,28).

Refining is brought about by the formation of

insolu-ble particles that aid nucleation of the grains or retard

their growth These grain refining elements have four

di-rect or indidi-rect effects on transformation temperatures:

(1) By forming intermetallics, they deplete the original

β lattice of alloying elements that change the

transforma-tion temperatures (2) Part of these elements remain in

solution within theβ matrix Depending on the atom size,

this can give rise to solid-solution hardening that decreases

the Msand eventually the other transformation

tempera-tures (29) (3) They can also have a chemical contribution,

which means that the global composition determines the

transformation temperatures on a purely thermodynamic

basis (4) The precipitates limit grain growth during

an-nealing, which influences the transformation

tempera-tures, as discussed in the next section

The Influence of Grain Size Several authors have shown

that small grain size results in stabilizing the parent phase

and depressing the transformation temperatures up to

40◦C (30,31) This effect is observed in alloys with and

with-out the special addition of grain-refining elements, which

indicates the restraining effect of grain size itself on the

transformation Lowering of transformation temperatures

is attributed to the increasing grain restraint as grain size

decreases This is the conclusion of most authors (32,33)

and is also consistent with Hornbogen’s argument that the

increase in yield stressσyis proportional to the stress

re-quired to start the transformation (20) Hornbogen’s

impor-tant assumption is that matrix strengthening increases the

undercoolingT(= T0− Ms) but does not influence

neces-sarily the T0temperatures T0is the temperature at which

the free energy of theβ phase is equal to the free energy of

the martensitic phase

Adnyana (30) and Jianxin (33) found a linear

relation-ship between the Mstemperature and the yield stress

de-rived via the classic Hall–Petch relationship for Cu–Zn–Al

alloys The restraining effect of grain size is, however, also

influenced by the grain size (gs) to thickness (t) ratio At

high gs/t ratios, the contribution of the free surface becomes

important and Ms no longer changes linearly with gs, as

observed by Wood (34) This is consistent with the

conclu-sion of Mukunthan and Brown (35) who showed that the

flow stress in all specimens decreases as specimen

thick-ness decreases when the value of t/d becomes smaller than

a critical value These authors showed further that this

critical value of t/d increases as both grain size and

stack-ing fault energy decrease These elements that contribute

to high stacking fault energy have an effect similar to a

small grain size

Influence of Defects Often it is not only the effect

of the grain size or the grain size thickness ratio that

accounts for changes in transformation temperatures nealing a sample at higher temperatures can give rise tograin growth but will also reduce the amount of defects andthus the nucleation sites In Cu-based alloys, the situation

An-is again complicated by the quenched-in vacancies and thesize of the antiphase domains, which can also be regarded

as strengthening the matrix An increase in the energy

of theβ phase due to a higher defect concentration such

as foreign elements in solid solution, precipitates, internalstrain fields (e.g., coherency strains) causes a lowering of

Ms (32) Moreover, if the defect density is proportional tothat of the nucleation sites, a higher defect density givesrise to much smaller martensitic plates A Hall–Petch typerelationship is also found between martensitic plate thick-ness and fracture stress (36)

Specific defect configurations can be introduced by mal cycling and also by two-way memory training The in-fluence of such defects, notably dislocations, has been dis-cussed in some recent literature It has been suggested thatthe changing character of the same dislocation in theβ and

ther-martensitic phases alters the relative phase stability of thetwo phases

Ni–Ti Alloys

Ni50–Ti50 and near equiatomic Ni–Ti alloys are the bestexplored system of all shape-memory alloys and occupy al-most the whole SMA market Ni50–Ti50is an intermetallicphase that has some solubility at higher temperature.The science and technology of Ni–Ti is overwhelminglydocumented The influence of composition and thermome-chanical processing on functional properties is well under-stood and described in the literature Therefore, we refer

to some very interesting and relevant publications such as(37–41)

The basic concept of processing Ni–Ti alloys is that themartensitic andβ phases have to be strengthened to avoid

plastic deformation during shape-memory or pseudoelasticloading This occurs by classic methods: strain hardeningand during cold deformation, solution hardening, and pre-cipitation hardening Ni–Ti alloys have the significant ad-vantage that these techniques can be easily applied due toexcellent ductility and a very interesting but complicatedprecipitation process (42)

The compositions of Ni–Ti SMA are approximately tween 48 and 52 at% Ni and the transformation tempera-tures of the B2 structure to the martensitic phase that has

be-a monoclinic B19 structure are very sensitive to the nickelcontent (a decrease of about 150◦C for an increase of 1 at%Ni) Transformation temperatures can be chosen between

−40 and +100◦C

Ni–Ti alloys have the best shape-memory behavior ofall SMA Even in the polycrystalline state, 8% shape re-covery is possible, 8% pseudoelastic strain is completelyreversible above Af, and the recovery stress is of the order of

800 MPa

In some cases, the martensitic transformation is ceded by the so-called R-phase transition The R transi-tion is a B2↔ rhombohedral transformation that also hassecond-order characteristics (43)

pre-The most specific characteristics of this R-phase sition are that it shows clear one- and two-way memory

tran-effects of the order of 1% recoverable strain and that the

hysteresis of the transformation is very small, only a few

degrees which creates possibilities for accurately

regulat-ing devices

Note that further cooling transforms the R phase into

B19 martensite During heating, generally only the

re-verse martensitic transformation is observed It has been

shown that the appearance of the R phase depends on

com-position, alloying elements, and thermomechanical

pro-cessing (39) The major common point is that all effects

that depress the martensitic forward transformation

be-low room temperature favor the appearance of the R-phase

transition that is quite stable near 30◦C

Ternary Ni–Ti Alloy Systems

Adding third elements opens even more possibilities for

adapting binary Ni–Ti alloys to more specific needs of

applications Adding a third element implies a relative

replacement of Ni and/or Ti Therefore, it must be always

very well indicated which metal, Ni or Ti or both, is

re-placed by the third element

Alloying third elements influences the transformation

temperatures and also affects hysteresis, strength,

ductil-ity, shape-memory characteristics, and the B2→(R)→B19

sequence The influence of several elements has been

de-scribed in (44–48)

Although more application oriented, one can distinguish

four purposes to add third elements:

1 to decrease (Cu) or increase (Nb) hysteresis,

2 to lower transformation temperatures (Fe, Cr, Co, Al),

3 to increase transformation temperatures (Hf, Zr, Pd,

Pt, Au), and

4 to strengthen the matrix (Mo, W, O, C)

Some ternary alloys have been developed for large-scale

applications We will summarize only the two most well

developed: Ni–Ti–Cu and Ni–Ti–Nb

Ti–Ni–Cu Ternary Ti–Ni–Cu alloys in which mainly Ni

is substituted by Cu are certainly as important as

bi-nary Ti–Ni Increasing the Cu content decreases the

formation stress in the martensitic state and also

de-creases the pseudoelastic hysteresis without affecting the

Ms temperature significantly (49) However, addition of

more than 10% Cu embrittles the alloys and hampers

formability

It should also be remembered that Ti–Ni transforms

from a B2 into a monoclinic phase, but Ti–Ni–Cu that

con-tains more than 15 at% Cu transforms from a B2 into an

orthorhombic phase Ti-Ni-Cu that has less than 15 at%

Cu transforms in two stages (37)

A disadvantage of most Ti–Ni–Cu alloys is that the

transformation temperatures do not decrease below room

temperature Cr or Fe can be alloyed to obtain

pseudo-elastic alloys at room temperature that have small

hys-tereses An Ni39.8–Ti49.8Cu10Cr0.4alloy was developed that

has small hysteresis (130 Mpa), one-fourth compared with

Ni50-Ti50, and an Msbelow room temperature (50)

Ti–Ni–Nb (51,52) The inherent transformation

hystere-sis of Ni–Ti–Nb is larger than that of binary Ni–Ti alloys

By using a large dispersed volume fraction of deformable

β-Nb particles, the hysteresis can be further widened by

an overdeformation of stress-induced martensite,

gener-ally between Msand Md Originally, Ni–Ti–Nb (more cifically Ni47–Ti94–Nb9) was developed by Raychem Corp.for clamping devices The large shift of reverse transforma-tion temperatures from below to above room temperature

spe-by deformation, allows room temperature of storage opencouplings

Recently, pseudoelastic Ni–Ti–Nb alloys have also beendeveloped that have three significant differences from bi-nary alloys (52):

1 Stress rate is much lower

2 σP −Mstresses are much higher

3 The superelastic window is much larger

High-Temperature Shape-Memory Alloys (5)

Actual shape memory alloys (SMA) are limited to imal Af temperatures of 120◦C: Ms is generally below

max-100◦C However, because market demands for SMA haveexpanded greatly, the need for SMA that transform athigher temperatures than presently available is increas-ing The main application areas of interest are actua-tors in the automobile and oil industries and in safetydevices

There is also an interest in robotics because memory alloys that have high transformation tempera-tures allow faster cooling, which would significantly in-crease the bandwidth in which the robot can operate.Although many alloy systems have high transforma-tion temperatures, no large-scale applications have beendeveloped A major breakthrough has not been reportedyet mainly due to the following problems: (much) lowerperformance than the successful Ni–Ti alloys, stabilization

shape-of martensite, decomposition shape-of the martensitic or parentphase, and brittleness due to high elastic anisotropy or due

to the presence of brittle phases or precipitates

Another condition for a good shape-memory effect is thatthe stress to induce martensite or the stress to reorientmartensite is (much) lower than the critical stress for nor-mal slip Because the critical stress for slip generally de-creases as temperature increases, this condition is quitedifficult to fulfil, especially at high temperatures Thus, aHTSMA should be designed at such a composition and/orthermomechanical treatment that strengthening mecha-nisms are incorporated to increase the critical stress forslip

Table 4 summarizes the systems under investigation.For references to this table, see (5)

OTHER TYPES OF SHAPE MEMORY ALLOYS

β-Ti Alloys

In spite of the good biocompatibility of NiTi-alloys, doubtsremain on the long-term stability or on the danger ofbad surface treatment leading to Ni leaching Since Ni is

Table 4 High-Temperature Shape-Memory Alloysa

Other Alloying Elements

Fe–Mn–Si Nonthermoelasticγ ⇔ ε Co, Ni, Cr To improve corrosion resistance 150–200 ◦CCu–Al–Ni Thermoelastic Mn, Ti, B, Zn To improve machinability, control of 100–200 ◦C

Grain refinement to improve ductility.

(Ni–X)–Ti Thermoelastic X = Pt, Pd, Au, Rh Based on B2-Ti–X intermetallic 150–500 ◦C

transformation at very high temperatures

B To reduce the grain size and

improve the strength Ni–(Ti–X) Thermoelastic X = Hf, Zr Based on Ni–X intermetallic 120–350 ◦C

pseudobinary with Ni–Ti.

B 2 ⇔ 3R (7R) (L1 o structure) temperatures

Fe, Co, Mn, B To improve ductility Ni–Mn Thermoelastic (?) Al, Ti, Cu for Ni To decrease Ms and to improve 500–750 ◦C

B2⇔ θ (L1 o structure) shape-memory characteristics

Mg, Al, Si, Ti, V, Sn, To increase Ms and to improve

Cr, Co, Fe, Mo for Mn shape-memory characteristics

intermetallics Cu–Zr Nonthermoelastic

Zr2–Cu–Ni Nonthermoelastic

Zr2–Cu–Co Thermoelastic

aRef 5.

known for his high allergic reaction, Ni-less shape

mem-ory alloys could be attractive Such alloys might be

de-veloped based on the allotropic transformation in Ti, a

highly biocompatible material Pure titanium shows an

allotropic transformation from β (bcc) to α (hexagonal)

phase at 1155 K Transition elements (TM) stabilise the

β-phase Thus the temperature of the (α + β)/β

transi-tion decreases with increasing concentratransi-tion of the alloying

element

β-phase Ti alloys can be martensitically transformed if

they are quenched from the stableβ-phase Two types of

martensite, respectivelyα andα can be formed,

depend-ing on the composition and the solution treatment

condi-tions (53)

The α -martensite is hexagonal, while α has an

or-thorhombic structure (54) It is the α -martensite that

shows the shape memory effect The shape memory effect

was first studied in detail by Baker in a Ti-35 wt% Nb

alloy (127) Since then several observations of SME

especially in Ti-Mo base alloys have been reported (57,58,

59,60,61) A systematic work on the influence of

differ-ent alloying elemdiffer-ents on the shape memory effect can be

found in (62), a patent deposited J Albrecht, T Duerig and

D Richter

The authors come to the conclusion thatα -martensite

can be obtained when the following condition is fulfilled:

−1100 ≤ εAiXi+ BiXi2

≤ −700where Xiis the atomic percentage for each element, Aiand

Biare constants given in the patent for each element (V, Al,

Fe, Ni, Co, Mn, Cr, Mo, Zr, Nb, Sn, Cu) Ta was not claimedalthough it also offers its contribution to SME as described

in (61)

Generally, a shape recovery in the order of 3% can beobtained based on strain-induced martensite and recoverystresses up to 170 MPa have been reported (60) The dis-advantage is that those alloys are very prone to stabilisa-tion and decomposition due to the fact that theβ-phase is

retained after quenching in its metastable state and petes withω-phase during quenching Also spinodal de-

com-composition ofα -martensite in Ti-Mo and Ti-Nb has beenobserved (53) The sensitivity to decomposition at moder-ate temperatures is less, if not, important at room tem-perature Therefor pseudoelasticβ-Ti alloys could offer an

interesting alternative to Ni-Ti alloys for example for thodontic wires Such an alloy has recently been developed

or-by Lei et al (63) Ti–11Mo–3Al–2V–4Nb was selected foroptimization Good pseudoelasticity of the order of 3% wasobtained after cold working and heat treatment

Magnetic-Field-Induced Martensitic Transformation

T Kakeshita et al (64) defined a magnetoelastic sitic transformation: when a magnetic field is applied(above Af) to an alloy that exhibits a thermoelastic marten-sitic transformation, martensite variants may be inducedwhile a magnetic field is applied and revert to the parentphase when the magnetic field is removed This has beenobserved in Fe31.9–Ni9.8–Co4.1–Ti (at%) (64,65) Apart from

marten-Fe-based alloys, Ni–Mn–Ga near the Ni2MnGa compound,

which is a ferromagnetic Heusler ordered alloy, is one of

the candidates (66,67)

Besides their very interesting fundamental properties,

these alloys might act much faster than classic SMA-based

actuators that are thermally driven The bandwidth of

the latter is limited to a few hertz (for very thin wires)

due to cooling restrictions In magnetoelastic martensitic

transformations, bandwidths of some orders larger can be

obtained

FUNCTIONAL PROPERTIES OF SHAPE-MEMORY ALLOYS

Shape-memory alloys have different shape-memory effects

and can be used in different ways These effects and ways

of use are described in general terms here As explained

be-fore, binary and ternary Ni–Ti alloys are probably used for

more than 90% of new SMA applications Therefore,

quan-titative data refer to Ni–Ti alloys, unless otherwise stated

One-Way Shape-Memory Effect

A shape memory element can be deformed in its

marten-sitic state to almost any “cold shape.” The basic

restric-tion is that the deformarestric-tions may not exceed a certain

limit, typically 8% These apparent plastic deformations

can be recovered completely during heating when the

re-verse transformation occurs and results in the original “hot

shape.” This strain and shape recovery during heating is

called the one-way shape-memory effect because only the

hot shape is memorized (Fig 1)

The physical basis for this one-way effect is a

re-verse martensitic transformation from a preferentially

ori-ented martensitic phase and shape to the original

high-temperature phase and shape, as explained more in detail

earlier and in many review papers on shape-memory

al-loys The preferential orientation of the martensitic

vari-ants originates from the application of stress either below

Mfthat causes martensitic reorientation, or during the

for-ward transformation that causes preferentially oriented

formation of martensite Thus, the apparent plastic strain

is caused by the preferential orientation of martensite

Figure 1 The one-way memory effect The sample is deformed

(A→B) and unloaded (B→C) at a temperature below Mf The

ap-parent plastic deformation is restored during heating to a

temper-ature above Af(C →D) Length change, load, and temperature are

indicated, respectively, by L, F, and T [from (69)].

(A) (B) (C)

T>Af T<Mf T>Af

F T

Figure 2 The two-way memory effect A spontaneous shape

change occurs during cooling to a temperature below Mf (A →B) This shape change is recovered during subsequent heating to a temperature above Af(B →C) [from (69)].

Therefore, the reverse transformation to the parent phaseduring heating is accompanied by a strain and shape re-covery The one-way shape-memory effect is thus a prop-

erty inherent in the reversible, thermoelastic martensitic

transformation

Thermoelasticity was observed as early as 1938 byGreninger and Mooradian (70) Since then, thermoelas-ticity and the one-way memory effect have been found inmany different alloy systems (71) In 1962, the one-wayshape-memory effect was also found in Ni–Ti (72)

Two-Way Shape-Memory Effect and Training

The two-way memory effect involves memorization of twoshapes Figure 2 shows that a cold shape is obtained spon-taneously during cooling Different from the one-way mem-ory effect, no external forces are required to obtain the

“memorized” cold shape During subsequent heating, theoriginal hot shape is restored The maximum strains are

in general substantially smaller than those of the way memory effect A strain limit of about 2% has beenmentioned (73), although higher TWME strains have beenfound in specific cases

one-In 1972, Tas et al proposed the term “two-way memoryeffect” (abbreviated to TWME) to refer to this spontaneous,reversible shape change between a “hot” shape linked tothe parent phase and an acquired “cold” shape linked tothe martensitic phase (74) This spontaneous shape changewas observed only after particular thermomechanical pro-cedures Since that time, many papers have been published

on the TWME, the thermomechanical procedures and themechanisms of the TWME, especially for Cu-based SMAs(73,75–83) There have not been many systematic studies

of Ni–Ti shape-memory alloys, however, to investigate theTWME and the effects of the thermomechanical procedures(77,78)

The essential difference from the one-way effect is themacro stress-free shape change during the forward trans-formation or, in physical terms, the spontaneous formation

of preferentially oriented martensitic variants Thus, theTWME requires some sort of asymmetry in the microstruc-ture of the parent phase, such as retained martensite ordislocation structures (76,82) The microstructural asym-metry and the resulting TWME are not inherent charac-teristics of shape memory alloys, as is the one-way effect,and can be induced only after particular thermomechani-cal procedures These thermomechanical procedures are in

general based on the repetition of thermomechanical cycles

through the transformation region (73,76,79), that consists

of transformation cycles from the parent phase to

prefer-entially oriented martensite The goal of these repetitive

procedures is to acquire the cold shape; therefore, these

procedures are referred to as “training.” Some examples

of such training procedures are temperature cycling at a

constant strain or at a constant stress and superelastic

cy-cling It can be easily understood that many combinations

and variants of these procedures can also be applied As a

result, new procedures have been regularly reported in the

literature In most of these publications, the new aspects

of the procedures are emphasized, but almost no attention

is paid to the points of similarity to previously described

procedures (81)

It is important to note that the training results in

con-comitant effects, such as changes of the transformation

temperatures and heats and residual deformations of the

austenitic shape (75,76,81,84) In general, these

charac-teristics become insensitive to cycling as the number of

training cycles increases So, the repetitive procedures to

induce the TWME can also be used merely to stabilize the

shape-memory behavior The term training is also

gener-ally used to indicate such stabilization treatments, though

the TWME can be negligible and should in this case be

con-sidered a side effect of the stabilization treatment It is

gen-erally agreed that cyclic training procedures generate some

kind of microstructural asymmetry in the parent phase, so

that preferential martensitic variants are formed in

sub-sequent thermal cycles, thus causing the TWME (76,82)

Basically, three mechanisms for the TWME have been

pro-posed in the literature It has been observed that training

cycling results in generating complex dislocation arrays

(76,79,80) Based on this observation, the TWME has been

attributed to the residual stress fields of these dislocation

arrays (75,76) It was proposed that these residual stress

fields favor the nucleation and the beginning of the growth

of some preferentially oriented variants, and at the same

time, the residual stresses are relaxed by the

accompany-ing shape change Duraccompany-ing further coolaccompany-ing, these

preferen-tial variants grow without any assistance and result in the

TWME

A second proposed mechanism is based on local

stabi-lization of remnants of preferential martensitic variants

that are retained above the original Aftemperature

Dur-ing coolDur-ing, these small martensitic plates would grow

and influence the subsequent positioning of other

vari-ants, thus causing the TWME (76,79) However, specific

experimental observations obtained on Cu-based alloys

in-validate these two proposed TWME mechanisms (82) A

third mechanism became widely accepted in the past years

Based on a thermodynamic analysis of specific

experimen-tal results, it was shown that the defect energy of the

com-plex dislocation arrays generated during training is

min-imal in the trained variants, that is, in the preferentially

oriented variants that have been repeatedly induced

dur-ing traindur-ing cycldur-ing (82,85) From thermodynamic

consid-erations, it follows that the growth of these trained

vari-ants are also favored during subsequent thermal cycling,

which explains the TWME This thermodynamic

analy-sis has also allowed us to explain many other phenomena

related to the TWME (83,86) Because the TWME is closelyrelated to the “trained” dislocation arrays, the TWME can

be removed by annealing at moderate temperatures (75).Next to the cyclic training procedures, the following one-time procedures to induce the TWME have been reported.Remnants of preferentially oriented variants can be stabi-lized by holding a constrained or stressed sample at tem-peratures above the nominal Affor a sufficiently long time.The TWME obtained by this procedure is attributed to thegrowth of those remnants (76) Aging of a sample at suf-ficiently high temperatures and stresses can also result

in a reversible shape effect (73,76,87,88) Precipitates areformed during the aging The observed reversible effect isattributed to the residual stress field generated by theseprecipitates and to the interaction between martensiticformation and the preferentially oriented precipitates ATWME of small magnitude can also be obtained by a sin-gle, sufficiently high plastic deformation of the martensiticphase (73) However, the disadvantages of these one-timeprocedures are numerous, including large deformations ofthe hot shape; large shifts of the transformation tempera-tures; and strong dependence on the stabilization or agingtemperatures, stresses, and times (76)

Superelasticity

The shape-memory effects described before require perature changes In contrast, the superelastic effect, alsocalled the pseudoelastic effect, is isothermal (89,90) Thetwo-dimensional graph of Fig 3 shows that a superelasticspecimen exhibits normal elastic behavior until a criticalstress is reached Under further stressing, the specimenelongates substantially, as if it were plastically deformed.However when the stress is removed, the specimen con-tracts to its original dimensions, and the apparent plasticstrain is recovered

tem-Superelasticity can be considered the mechanical log of the thermal shape-memory effect Isothermal load-ing at a temperature above Afresults in a stress-inducedmartensitic transformation that starts at a critical stress

6Strain (%)

321

Unloading Hysteresis Loading

Figure 3 Superelastic behavior at constant temperature due to

stress-induced transformation and retransformation.

σMs Further straining occurs at a nearly constant stress

level until the transformation finishes at σMf Thus, the

apparent plastic strain is caused by the shape strain that

accompanies the stress-induced formation of preferentially

oriented martensite During subsequent unloading, the

re-verse transformation occurs at a lower stress level between

σA sandσAf, and the apparent plastic strains are recovered

Large reversible deformations up to 10% can be obtained,

compared to 0.2–0.5% elastic strain in most other metallic

alloys Further straining at stress levels aboveσMf results

in elastic straining of the stress-induced martensite,

fol-lowed atσyby plastic yielding of the martensite

The stress-induced transformation exhibits stress

hys-teresis that is revealed by the different stress levels for

the forward and reverse transformations This hysteresis

is typically 150–300 MPa in Ni–Ti and results in

dissi-pating of energy during superelastic cycling The energy

dissipated per cycle is given by the area enclosed between

the upper and lower curves in Fig 3 Superelasticity also

involves the storage of potential energy, given by the area

under the unloading curve in Fig 3 The capacity of this

elastic energy storage can be as high as 10 J/g All of

the previously mentioned superelastic characteristics are

strongly affected by processing and composition (91,92)

The critical transformation stresses (σM s,σMf,σA s, and

σAf) increase, in a first approximation, linearly as

tem-perature changes starting from zero at the corresponding

transformation temperature, as described by the Clausius–

Clapeyron equation It follows that at a temperature,

de-noted as Md, the stress for plastic yielding becomes equal to

the stress for martensitic formation Thus, superelasticity

occurs only across a relatively narrow temperature window

between the temperatures Af and Md This temperature

range of typically 50–100 K is too small for applications in

most industrial and consumer fields The strong

tempera-ture dependence of mechanical behavior, described by the

Clausius–Clapeyron equation, is a further impediment to

the general use of superelasticity (93)

The temperature dependence and small temperature

range are no barrier to use in mammalian bodies, where

temperature is constant Moreover, the superelastic effect

Figure 4 The generation of recovery stresses is shown in three two-dimensional figures:

(a) stress–strain, (b) strain–temperature, and (c) stress–temperature A deformation is imposed

at a temperature Tdin the martensitic state Shape recovery is impeded at a contact strain ec From

the corresponding contact temperature Tc , recovery stressσrare generated at a stress rate d σr/dT

to temperature-activated shape-memory effects (94) cordingly, the largest commercial successes of SMAs in re-cent years are linked to using superelasticity in biomedicalapplications (93–95) Other advantages related to super-elasticity and relevant for medical applications have beendescribed in detail by Duerig et al (93)

Ac-It must be mentioned also that Ni–Ti alloys in theiras-cold worked state can exhibit nearly linear elastic be-havior across an extremely broad strain range This linearbehavior that has a low elastic modulus of typically 30 GPa

is called linear superelasticity (96,97) Reversible mations as high as 4% can be induced that have a verysmall hysteresis between the loading and unloading curve.Clearly different from the superelastic effect described be-fore, stress-induced martensitic transformation is not thecontrolling mechanism of linear superelasticity As a re-sult, temperature and composition have only a minor effect

defor-on this behavior

Generation of Recovery Stresses

If an external constraint prevents an SMA element fromreturning to its hot shape when heated, high recoverystresses are gradually generated during heating, as illus-trated in Fig 4 Stresses upto 800 MPa can be obtained(99)

Four parameters have to be introduced to describe this

shape-memory property (100): the contact strain ec, the

contact temperature Tc, the recovery stress σr, and the

stress rate d σr/dT Similar to the one-way and two-way

memory effects, the generation of recovery stresses startsfrom a macroscopic deformation in the martensitic state.During subsequent heating, free recovery occurs until a

com-composition of< i>α -martensite in Ti-Mo and Ti-Nb has beenobserved (53) The sensitivity to decomposition at moder-ate temperatures is less, if not, important at room tem-perature...

transformations, bandwidths of some orders larger can be

obtained

FUNCTIONAL PROPERTIES OF SHAPE-MEMORY ALLOYS

Shape-memory alloys have different shape-memory effects

and