1

Introduction to Shape Memory Alloys

P. K. Kumar and D. C. Lagoudas

Shape Memory Alloys (SMAs) have been on the forefront of research for thelast several decades. They have been used for a wide variety of applications invarious fields. This chapter introduces the unique behavior that is observed inSMAs. Their characteristic properties and associated microstructural behaviorwill be discussed in detail. The different types of SMAs and some commonapplications will also be reviewed.

1.1 Introduction: Overview of Active Materials

For centuries, metals have played an important role as structural materials.Techniques of alloying, smelting, and forging have been evolving since thebronze and iron ages. With advancements in science and technology, and adeeper understanding of the effects of microstructure and processing tech-niques on the material behavior, the field of material science has radicallyimproved through the past decades. The capability to engineer different mate-rial properties (mechanical, thermal, electrical, etc.) for a variety of applica-tions has enabled the development of new alloys and composites. The demandfor lighter, stronger materials with tailored properties that address both strin-gent structural requirements and provide additional engineering functionality(e.g., sensing, actuation, electromagnetic shielding) has spawned a new branchof materials called multifunctional materials. A specialized subgroup of mul-tifunctional materials exhibiting sensing and actuation capabilities is knownas active materials.

In sensing, a mechanical signal is converted into a non-mechanical output(e.g., voltage), while an actuator converts a non-mechanical input (e.g., elec-trical power) into a mechanical output. Active materials in general exhibit amechanical response when subjected to a non-mechanical field (thermal, elec-trical, magnetic, optical, etc.). The mechanical response of these materials istypically one or more orders of magnitude greater than the response result-ing from conventional material behavior such as thermal expansion. Someexamples of active materials include piezoelectrics and electrostrictives (cou-pling of mechanical with electric fields), piezomagnetics and magnetostrictives(coupling of mechanical with magnetic fields), and shape memory materials

D.C. Lagoudas (ed.), Shape Memory Alloys, DOI: 10.1007/978-0-387-47685-8 1,© Springer Science+Business Media, LLC 2008

2 1 Introduction to Shape Memory Alloys

(coupling of thermal with mechanical fields). Active materials can be fur-ther subdivided into materials that exhibit direct or indirect coupling. Piezo-ceramics, piezoelectric polymers, magnetostrictive ceramics, shape memoryalloys and magnetic shape memory alloys are examples of active materialsthat exhibit a direct coupling. This implies that either the mechanical orthe non-mechanical field can serve as an input while the other as the out-put. In contrast, for active materials such as electro-rheological fluids (ERF)and magneto-rheological fluids (MRF), a change in the electric field or themagnetic field can indirectly couple with the mechanical behavior through achange in the viscosity of the fluid. This indirect, or one-way, coupling usuallylacks the reciprocity of the two-way coupling exhibited by active materialsthat directly couple two fields.

The suitability of an active material with direct coupling for actuationapplications depends on many factors. Two key design drivers are the actu-ation energy density (available work output per unit volume) and the actu-ation frequency of the material. An ideal active material would have botha high actuation energy density and a high actuation frequency. Figures 1.1and 1.2 compare the actuation energy densities and the actuation frequencies,respectively, of some common active materials. The actuation energy densityis denoted in Fig. 1.1 by the dotted lines and is defined as the product ofthe actuation strain (related to the stroke of an actuator) with the actuationstress, assuming here that the active material is operating under constantstress. The specific actuation energy density (work output per unit mass)

0.01

0.1

1

10

100

1000

0.01 0.1 1 10 100

Actuation Strain (%)

Act

uatio

n S

tres

s (M

Pa)

Shape Memory Alloys (SMAs)

Piezoelectricpolymers

MagneticSMAs (MSMAs)

Shape Memory Polymers (SMPs)

Ionic electroactivepolymers

Electrostrictiveceramics

Magnetostrictiveceramics

Piezoelectric ceramics

10 J/m 3

100 J/m 3

1 kJ/m 3

10 kJ/m 3

100 kJ/m 3

10 MJ/m 3

100 MJ/m 3

0.01

0.1

1

10

100

1000

0.01 0.1 1 10 100

Actuation Strain (%)

Act

uatio

n S

tres

s (M

Pa)

Shape Memory Alloys (SMAs)

Piezoelectricpolymers

MagneticSMAs (MSMAs)

Shape Memory Polymers (SMPs)

Ionic electroactivepolymers

Electrostrictiveceramics

Magnetostrictiveceramics

Piezoelectric ceramics

10 J/m 3

100 J/m 3

1 kJ/m 3

10 kJ/m 3

100 kJ/m 3

10 MJ/m 3

100 MJ/m 3

Fig. 1.1. Actuation energy density diagram indicating typical ranges of actuationstress, actuation strain, and the actuation energy densities of different active mate-rials that exhibit direct coupling.

1.1 Introduction: Overview of Active Materials 3

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07

Actuation Frequency (Hz)

Sp

ecif

ic A

ctu

atio

n E

ner

gy

Den

sity

(J/

kg)

Shape Memory Alloys (SMAs)

Shape Memory Polymers (SMPs)

Piezoelectric polymers

Electrostrictive ceramicsMagnetostrictive ceramics

Piezoelectric ceramicsIonic electroactivepolymers

10-1 100 101 102 103 104 105 106 107

103

102

101

100

10-1

104

Magnetic SMAs (MSMAs)

Fig. 1.2. Actuation frequency diagram comparing the actuation frequency rangesof different active materials that exhibit direct coupling.

for a specific active material can be calculated from Fig. 1.1 by dividing theactuation energy density by the mass density.

Shape Memory Alloys (SMAs) are a unique class of shape memory materi-als with the ability to recover their shape when the temperature is increased.An increase in temperature can result in shape recovery even under highapplied loads therefore resulting in high actuation energy densities as shownin Fig. 1.1. In addition, under specific conditions, SMAs can absorb and dis-sipate mechanical energy by undergoing a reversible hysteretic shape changewhen subjected to applied mechanical cyclic loading. These unique charac-teristics of SMAs have made them popular for sensing and actuation, impactabsorption and vibration damping applications. SMAs do, however, exhibitlow frequency response, as shown in Fig. 1.2. Higher actuation frequencies areachievable for a class of SMAs called magnetic shape memory alloys, whichhave recently been investigated.

The application of SMAs spans a wide variety of industrial sectors suchas aerospace, automotive, biomedical, and oil exploration. Over the past fewdecades, several key works have explored the microstructural mechanisms,engineering effects, and applications of shape memory alloys, including theexperimental work of Jackson and coworkers [1], the application considera-tions of Duerig and others [2], and the comprehensive summaries of Perkins,Funakubo, and Otsuka and Wayman [3–5]. In the context of the currenttextbook, this chapter will provide insights into the history of SMAs, theirproperties, their microstructural behavior, and their varied industrialapplications.

4 1 Introduction to Shape Memory Alloys

1.2 Shape Memory Alloys - A Brief History

The discovery of martensite in steels in the 1890s by Adolf Martens wasa major step toward the eventual discovery of shape memory alloys. Themartensitic transformation was perhaps the most widely studied metallur-gical phenomenon during the early 1900s. The martensitic transformation,as observed in the Fe-C system, was established as an irreversible process.The concept of thermoelastic martensitic transformation, which explained thereversible transformation of martensite, was introduced in 1949 by Kurdju-mov and Khandros [6], based on experimental observations of the thermallyreversible martensitic structure in CuZn and CuAl alloys. By 1953, the occu-rance of thermoelastic martensitic transformation was demonstrated in otheralloys such as InTl and CuZn.

The reversible martensitic transformation and the alloys that exhibitedthem remained unutilized until 1963. The breakthrough for engineering appli-cations occurred with the discovery of NiTi by Buehler and coworkers whileinvestigating materials useful for heat shielding [7]. It was noticed that inaddition to its good mechanical properties, comparable to some common engi-neering metals, the material also possessed a shape recovery capability. Fol-lowing this observation, the term “NiTiNOL” was coined for this NiTi mate-rial in honor of its discovery at the Naval Ordnance Laboratory (NOL). Theterm Shape Memory Effect (SME) was given to the associated shape recoverybehavior. The discovery of Nitinol spearheaded active research interest intoSMAs. The effects of heat treatment, composition and microstructure werewidely investigated and began to be understood during this period [1].

In 1965, studies [8] showed that the addition of a third alloying elementsuch as Co or Fe to the existing NiTi system caused a dramatic decrease inthe SMA transformation temperatures. The new alloys inspired the first com-mercial SMA application, known as Cryofit, where SMA material was usedfor pipe couplings in F-14 fighter aircraft [9, 10]. The transformation temper-atures for Cryofit were so low that, to prevent actuation from occurring beforethe assembly, the pipe couplings were transported in liquid nitrogen. Contin-ued research to address this issue led to the development of the NiTiNb systemin 1989, which was easier to handle due to its larger temperature hysteresis,and found widespread applications in battle damage repairs and in repairsfor nuclear reactors [11]. High Temperature SMAs (HTSMAs), such as TiPd,TiPt and TiAu (with transformation temperatures greater than 100 C), werealso developed as early as 1970 [12]. Meanwhile, Melton and Mercier [13],while studying the fatigue properties of NiTi in 1978, showed that alloyingthe material with Cu did not change the transformation temperatures con-siderably, but narrowed the stress hysteresis. Later in 1999, Miyazaki showedimproved fatigue life for NiTiCu alloys [14]. The improved fatigue life andthe low cost associated with this material system made it suitable for a widevariety of engineering applications.

1.3 Phenomenology of Phase Transformation in Shape Memory Alloys 5

Since the initial discovery of Nitinol in 1963, many commercial applica-tions have been developed. During the 1970s, several uses of NiTi in biomedi-cal applications appeared, but it wasn’t until the 1990s that NiTi stents madetheir commercial breakthrough. By this time, SMAs had found additionalapplications in air conditioning vents, electronic cable connectors, valves anda variety of other products. In addition, over the last decade the demandfor actuation under high temperature operating conditions, driven by theaerospace and oil industries, has revived a great deal of interest in the devel-opment of HTSMAs. Finally, alloys that exhibit shape change characteristicssimilar to SMAs but under the influence of a magnetic field have recentlybeen under investigation [15, 16]. The high actuation frequencies and the largestrains generated in Magnetic SMAs (MSMAs) have made these materials astrong candidate for high frequency actuation devices.

1.3 Phenomenology of Phase Transformation in ShapeMemory Alloys

A metallurgical phase diagram for a metallic alloy is a schematic represen-tation of the equilibrium conditions between distinct phases. Phase diagramsconsist of equilibrium lines or phase boundaries that separate different phasesfrom each other. For an alloy consisting of at least two elements, the concen-tration becomes an important variable and is generally represented along theabscissa axis. The other variable commonly used is the temperature, repre-sented along the ordinate axis. A phase diagram can have different controlvariables (stress, temperature, concentration, electric field etc.) within thebounds of which the equilibrium phases can be represented. For an alloy at afixed composition (i.e. any vertical line parallel to the ordinate axis), the for-mation and disassociation of phases with the change in temperature is shown.Similarly, within the typical operating temperature range, SMAs have twophases, each with a different crystal structure and therefore different proper-ties. One is the high temperature phase called austenite (A) and the other isthe low temperature phase called martensite (M). Austenite (generally cubic)has a different crystal structure from martensite (tetragonal, orthorhombicor monoclinic). The transformation from one structure to the other does notoccur by diffusion of atoms, but rather by shear lattice distortion. Such atransformation is known as martensitic transformation. Each martensitic crys-tal formed can have a different orientation direction, called a variant. Theassembly of martensitic variants can exist in two forms: twinned martensite(M t), which is formed by a combination of “self-accommodated” martensiticvariants, and detwinned or reoriented martensite in which a specific variant isdominant (Md). The reversible phase transformation from austenite (parentphase) to martensite (product phase) and vice versa forms the basis for theunique behavior of SMAs.

6 1 Introduction to Shape Memory Alloys

Upon cooling in the absence of an applied load, the crystal structurechanges from austenite to martensite. The phase transition from austenite tomartensite is termed the forward transformation. The transformation resultsin the formation of several martensitic variants, up to 24 for NiTi. The arrange-ment of variants occurs such that the average macroscopic shape change isnegligible, resulting in twinned martensite. When the material is heated fromthe martensitic phase, the crystal structure transforms back to austenite, andthis transition is called reverse transformation, during which there is no asso-ciated shape change.

A schematic of the crystal structures of twinned martensite and austenitefor an SMA and the transformation between them is shown in Fig. 1.3. Thereare four characteristic temperatures associated with the phase transforma-tion. During the forward transformation, austenite, under zero load, beginsto transform to twinned martensite at the martensitic start temperature (Ms)and completes transformation to martensite at the martensitic finish temper-ature (Mf ). At this stage, the transformation is complete and the material isfully in the twinned martensitic phase. Similarly, during heating, the reversetransformation initiates at the austenitic start temperature (As) and the trans-formation is completed at the austenitic finish temperature (Af ).

If a mechanical load is applied to the material in the twinned marten-sitic phase (at low temperature), it is possible to detwin the martensite byreorienting a certain number of variants (see Fig. 1.4). The detwinning pro-cess results in a macroscopic shape change, where the deformed configurationis retained when the load is released. A subsequent heating of the SMA to

TwinnedMartensite

Austenites fA A

TwinnedMartensite

Austenitef sM M

TwinnedMartensite

Austenites fA A

TwinnedMartensite

Austenitef sM M

TwinnedMartensite

Austenites fA ATwinnedMartensite

Austenites fA A

TwinnedMartensite

Austenitef sM MTwinnedMartensite

Austenitef sM M

Fig. 1.3. Temperature-induced phase transformation of an SMA without mechani-cal loading.

1.3 Phenomenology of Phase Transformation in Shape Memory Alloys 7

Detwinned Martensite

Twinned Martensite

Str

ess,

σ

Temperature, Tf s s fM M A A

sσfσ

Detwinned Martensite

Twinned Martensite

Str

ess,

σ

Temperature, Tf s s fM M A A

sσfσ

Fig. 1.4. Schematic of the shape memory effect of an SMA showing the detwinningof the material with an applied stress.

a temperature above Af will result in a reverse phase transformation (fromdetwinned martensite to austenite) and will lead to complete shape recovery(see Fig. 1.5). Cooling back to a temperature below Mf (forward transforma-tion) leads to the formation of twinned martensite again with no associated

Detwinned Martensite

Austenite

Str

ess,

σ

Temperature, Tf s s fM M A A

sσfσ

Detwinned Martensite

Austenite

Str

ess,

σ

Temperature, Tf s s fM M A A

sσfσ

Fig. 1.5. Schematic of the shape memory effect of an SMA showing the unloadingand subsequent heating to austenite under no load condition.

8 1 Introduction to Shape Memory Alloys

shape change observed. The process described above is referred to as the ShapeMemory Effect (SME). The load applied must be sufficiently large to start thedetwinning process. The minimum stress required for detwinning initiation istermed the detwinning start stress (σs). Sufficiently high load levels will resultin complete detwinning of martensite where the corresponding stress level iscalled the detwinning finish stress (σf ).

When the material is cooled with a mechanical load greater than σs appliedin the austenitic phase, the phase transformation will result in the directformation of detwinned martensite, producing a shape change. Reheatingthe material will result in shape recovery while the load is still applied. Aschematic of the above-described loading path is shown in Fig. 1.6. Recog-nizing that the forward and reverse transformations occur over a range oftemperatures (Ms to Mf , As to Af ) for a given SMA composition, we canconstruct transformation regions in the stress-temperature space. The trans-formation temperatures strongly depend on the magnitude of the applied load,with higher values of applied load leading to higher transformation tempera-tures. As a consequence, the transformation regions representing the A→Md

and Md→A transformations have a positive slope in stress-temperature space.Irrespective of the nature of applied load (tension or compression), the trans-formation temperatures increase with an increase in the magnitude of theload. Under an applied uniaxial tensile load with a corresponding stress, σ, thenew transformation temperatures are represented as Mσ

f , Mσs , Aσ

s and Aσf for

martensitic finish, martensitic start, austenitic start and the austenitic finishtemperatures, respectively. It should be noted that σ refers to the magnitude

Detwinned Martensite

Austenite

Str

ess,

σ

Temperature, Tf s s fM M A A

f sM Mσ σ

s fA Aσ σ

sσfσ

Detwinned Martensite

Austenite

Str

ess,

σ

Temperature, Tf s s fM M A A

f sM Mσ σ

s fA Aσ σ

sσfσ

Fig. 1.6. Temperature-induced phase transformation in the presence of appliedload.

1.3 Phenomenology of Phase Transformation in Shape Memory Alloys 9

of a uniaxial stress state or an appropriate scalar measure for a multiaxialstress state, as will be explained in Chapter 3.

In addition to thermally induced phase transformation, transformation canalso be induced by applying a sufficiently high mechanical load to the materialin the austenitic phase. The result of this load is fully detwinned martensitecreated from austenite. If the temperature of the material is above Af , a com-plete shape recovery is observed upon unloading to austenite. This materialbehavior is called the pseudoelastic effect. A loading path demonstrating thepseudoelastic effect is shown schematically in Fig. 1.7, while the associatedmacroscopic shape change due to the applied load is captured in the resultingstress-strain diagram, as shown schematically in Fig. 1.8. The stress levelsat which the martensite transformation initiates and completes are denotedby σMs and σMf , respectively. Similarly, as the SMA is unloaded, the stresslevels at which the material initiates and completes its reverse transforma-tion to austenite are denoted by σAs and σAf , respectively. If the material inthe austenitic phase is tested above the Ms temperature, but below the Af

temperature, only partial shape recovery is observed.Figure 1.9 shows a schematic representation of the different phases of

the SMA, which include the austenitic phase and both the twinned (self-accommodated) and detwinned martensite, along with the transition zones,in a stress-temperature diagram. Such a diagram, illustrating the differentphases in a stress-temperature space for a given SMA with fixed composition,is called the phase diagram. Note that the phase diagram of Fig. 1.9 is a specialcase of the metallurgical phase diagram introduced in the beginning of Sec-tion 1.3, which involves composition as another variable. Construction of the

Temperature, T

Austenite

Str

ess,

σ

f s s fM M A A

Detwinned Martensite

sσfσ

Mfσ

Msσ

Afσ

Asσ

Temperature, T

Austenite

Str

ess,

σ

f s s fM M A A

Detwinned Martensite

sσfσ

Mfσ

Msσ

Afσ

Asσ

Fig. 1.7. A pseudoelastic loading path.

10 1 Introduction to Shape Memory Alloys

Detwinned Martensite

Austenite

Str

ess,

σ

Strain, ε

MfσMsσ

Afσ

Asσ

Detwinned Martensite

Austenite

Str

ess,

σ

Strain, ε

MfσMsσ

Afσ

Asσ

Fig. 1.8. Schematic of a pseudoelastic stress-strain diagram.

Temperature, T

Detwinned Martensite

Austenite

A to Md

M to Ad

M to Mdt

Twinned Martensite

Str

ess,

σ

f s s fM M A A

sσfσ

Temperature, T

Detwinned Martensite

Austenite

A to Md

A to Md

M to Ad

M to Ad

M to Mdt

M to Mdt

Twinned Martensite

Str

ess,

σ

f s s fM M A A

sσfσ

Fig. 1.9. Schematic of a stress-temperature phase diagram for an SMA.

phase diagram involves the interpretation of the SMA material response sub-jected to various thermomechanical loading paths resulting in shape memorythermal actuation under load and pseudoelastic behavior. In the following sec-tions, the two important characteristics of SMAs, namely the shape memoryeffect and pseudoelasticity, will be discussed in more detail.

1.4 Shape Memory Effect 11

1.4 Shape Memory Effect

An SMA exhibits the shape memory effect (SME) when it is deformed whilein the twinned martensitic phase and then unloaded while at a temperaturebelow As. When it is subsequently heated above Af , the SMA will regainits original shape by transforming back into the parent austenitic phase. Thenature of the SME can be better understood by following the thermomechan-ical loading path in a combined stress-strain-temperature space as shown inFig. 1.10. Figure 1.10 represents experimental data for a typical NiTi speci-men tested under uniaxial loading. The stress σ is the uniaxial stress on thespecimen due to an applied load. The corresponding strain ε is the change inthe length of the specimen along the direction of applied load, normalized bythe original length.

Starting from the parent phase (point A in Fig. 1.10), the stress-free cool-ing of austenite below the forward transformation temperatures (Ms and Mf )results in the formation of twinned martensite (point B). When the twinnedmartensite is subjected to an applied stress that exceeds the start stress level(σs), the reorientation process is initiated, resulting in the growth of cer-tain favorably oriented martensitic variants that grow at the expense of otherless favorable variants. The stress level for reorientation of the variants is farlower than the permanent plastic yield stress of martensite. The detwinningprocess is completed at a stress level, σf , that is characterized by the end of

2% 4% 6%

50

100

T

200

400

600

800

cooling

Detwinning

A

B

C

D

E

FfA

sA

Twinned Martensite

Austenite

Detwinned Martensite

Detwinned Martensite

fσsσ

(MPa)

(°C)

σ

ε2% 4% 6%

50

100

T

200

400

600

800

cooling

Detwinning

A

B

C

D

E

FfA

sA

Twinned Martensite

Austenite

Detwinned Martensite

Detwinned Martensite

fσsσ

(MPa)

(°C)

σ

ε

Fig. 1.10. Stress-strain-temperature data exhibiting the shape memory effect for atypical NiTi SMA.

12 1 Introduction to Shape Memory Alloys

the plateau in the σ-ε diagram in Fig. 1.10. The material is then elasticallyunloaded from C to D and the detwinned martensitic state is retained. Uponheating in the absence of stress, the reverse transformation initiates as thetemperature reaches As, (at E) and is completed at temperature Af (pointF), above which only the parent austenitic phase exists. In the absence ofpermanent plastic strain generated during detwinning, the original shape ofthe SMA is regained (indicated by A). The strain recovered due to the phasetransformation from detwinned martensite to austenite is termed as the trans-formation strain (εt). Subsequent cooling to martensite will again result in theformation of self-accommodated twinned martensitic variants with no asso-ciated shape change, and the whole cycle of the SME can be repeated. Theabove described phenomenon is called one-way shape memory effect, or sim-ply SME, because the shape recovery is achieved only during heating afterthe material has been detwinned by an applied mechanical load.

Example 1.1. In order to review the SME, let us consider an SMAwire whose behavioral characteristics are represented by the stress-strain-temperature diagram shown in Fig. 1.10. The SME of the wire is used fora one time actuation application. The wire, held at a temperature below theMf (twinned martensitic state), is stretched along the axial direction. Underthe applied loading, the material exhibits an elastic behavior and continuesto elastically deform as the stress is increased. When the stress due to theapplied loading reaches approximately 150MPa, the SMA wire begins to elon-gate significantly with a small increment in the stress level. This point marksthe beginning of the martensitic detwinning in the wire. The detwinning con-tinues until the total strain reaches approximately 4% and the entire wirehas detwinned. At this point, the wire begins to stiffen again as the stress isincreased. The end of the detwinning process is marked by the change in theslope during loading. The detwinned wire elastically unloads as the stress isreleased and the strain induced due to the detwinning is not recovered. Thisdetwinned wire is then attached on the structure for the actuation application.During the actuation process, the wire is heated using a thermal source suchas resistive heating. As the temperature of the wire increases, the wire ini-tially undergoes thermal expansion. However, as the temperature reaches theaustenitic start temperature of approximately 30 C, the detwinned marten-site in the material begins transformation into austenite. This results in thecontraction (i.e., actuation) of the SMA. As the temperature reaches a valueabove 70 C, the transformation (actuation) is complete and the wire is in theaustenitic state. The exact austenitic finish temperature will depend on thestress of the SMA wire during the reverse transformation. Subsequent cool-ing returns the wire to the twinned state in the absence of a recovery stressapplied by the structure on which the SMA is attached. The wire would thenhave to be detwinned for the next actuation cycle unless the structure canprovide sufficient stress for detwinning upon cooling.

1.5 Pseudoelasticity 13

1.5 Pseudoelasticity

The pseudoelastic behavior of SMAs is associated with stress-induced trans-formation, which leads to strain generation during loading and subsequentstrain recovery upon unloading at temperatures above Af . A pseudoelasticthermomechanical loading path generally starts at a sufficiently high temper-ature where stable austenite exists, then develops under an applied load toa state at which detwinned martensite is stable, and finally returns to theaustenitic phase when returned to zero stress state. An example of this path(a → b → c → d → e → a) is shown in Fig. 1.11 as path 1. Most commonly,a pseudoelastic test is performed at a nominally constant temperature aboveAf . The loading path for such a test is shown as path 2 in Fig. 1.11.

To illustrate the pseudoelastic behavior in greater detail, let us considerthe thermomechanical loading path (A → B → C → D → E → F → A)in Fig. 1.11, which starts at zero stress at a temperature above Af . Thecorresponding σ-ε experimental data for the loading path is shown in Fig. 1.12.When a mechanical load is applied, the parent phase (austenite) undergoeselastic loading (A → B). At a specific load level, the loading path intersects thesurface for initiation of martensitic transformation on the phase diagram. Thismarks the stress level (σMs) for the onset of transformation into martensite.Note that the stress-induced transformation from austenite to martensite isaccompanied by the generation of large inelastic strains as shown in the stress-strain diagram of Fig. 1.12. The transformation proceeds (B → C), to thestress level (σMf ) where the loading path intersects the Mf transformationsurface, indicating the end of the transformation.

Temperature, T

Austenite

Str

ess,

σ

f s s fM M A A

Detwinned Martensite

Path 2

A

B

C

D

E

F

Path 1 bc

d

e

Mfσ

Msσ

Afσ

Asσ

a

Temperature, T

Austenite

Str

ess,

σ

f s s fM M A A

Detwinned Martensite

Path 2

A

B

C

D

E

F

Path 1 bc

d

e

Mfσ

Msσ

Afσ

Asσ

a

Fig. 1.11. Phase diagram and two possible pseudoelastic loading paths.

14 1 Introduction to Shape Memory Alloys

Fig. 1.12. A typical SMA pseudoelastic loading cycle.

The completion of martensitic transformation is indicated by a distinctchange in slope on the σ-ε curve, which is associated with the elastic load-ing of the martensitic phase. A subsequent increase in the stress causes nofurther transformation and only the elastic deformation of detwinned marten-site occurs (C → D). When the stress is released gradually by unloading,the martensite elastically unloads along the path (D → E). At point E, theunloading path intersects the austenitic start surface (at σAs), which causesthe martensite to revert to austenite. The process is accompanied by therecovery of the strain due to phase transformation at the end of unloading.The end of the transformation back into austenite is denoted by the point atwhich the σ-ε unloading curve rejoins the elastic region of austenite (pointF corresponding to stress σAf ). The material then elastically unloads to A.The forward and reverse phase transformation during a complete pseudoelas-tic cycle results in a hysteresis, which, in the σ-ε space, represents the energydissipated in the transformation cycle. The transformation stress levels andthe size of the hysteresis vary depending on the SMA material and testingconditions.

The detwinned martensite that forms from austenite as a result of theapplied stress during Path 1 or 2 in Fig. 1.11 is one form of stress-inducedmartensite (SIM). SIM, in general, is martensite that forms from austenite inthe presence of stress. There are many thermomechanical loading paths thatcan result in the formation of SIM.

1.6 Cyclic Behavior of SMAs 15

Generally, the term pseudoelasticity describes both superelastic behaviorand so-called rubber-like behavior [5]. The reversible phase transformation(described in the previous paragraph) caused by a thermomechanical load-ing path is strictly called the superelastic behavior. The rubber-like effect isan exclusive behavior of the martensite phase only and occurs due to thereversible reorientation of martensite. In some cases, aging the martensiticphase can enable the reversal of the martensitic detwinning process uponunloading at temperatures below Mf . The resulting σ-ε curve is similar tothe superelastic curve, and this phenomenon is called the rubber-like effect toemphasize the similarities with the nonlinear elastic behavior of rubber. InSMAs exhibiting the rubber-like effect, the stress required to detwin marten-site is very small compared to σMs. We will not consider the rubber-like effectany further, and the term pseudoelasticity will refer to the superelastic behav-ior of SMAs only.

1.6 Cyclic Behavior of SMAs

We have studied the one-way SME behavior in SMAs. Sometimes an SMAcan exhibit repeatable shape changes under no applied mechanical load whensubjected to a cyclic thermal load. This behavior is termed two-way shapememory effect (TWSME). The TWSME can be observed in a SMA mate-rial which has undergone repeated thermomechanical cycling along a specificloading path (training). Repetition along a loading path for a large number ofcycles can induce changes in the microstructure, which causes macroscopicallyobservable permanent changes in the material behavior.

Training an SMA refers to a process of repeatedly loading the materialfollowing a cyclic thermomechanical loading path until the hysteretic responseof the material stabilizes and the inelastic strain saturates. Let us consider thecase of cyclic thermal loading of an SMA specimen under a constant appliedstress (Fig. 1.13). During the first thermal cycle, only a partial recovery ofthe strain generated during cooling is observed upon heating with some per-manent (irrecoverable or plastic) strain generated during the cycle. A small,permanent strain remains after each thermal cycle is completed. The addi-tional permanent strain associated with each consecutive cycle begins to grad-ually decrease until it practically ceases to further accumulate (Fig. 1.13). Asimilar behavior can be noticed in the case of mechanically cycling an SMArepeatedly in its pseudoelastic regime, until saturation takes place (Fig. 1.14).The TWSME behavior can also be achieved by adopting different trainingsequences [17, 18]. A more recent technique that leads to TWSME deals withaging the material under stress in the martensitic state [19].

TWSME is a result of defects introduced during training. These perma-nent defects create a residual internal stress state, thereby facilitating theformation of preferred martensitic variants when the SMA is cooled in the

16 1 Introduction to Shape Memory Alloys

0%

2%

4%

6%

8%

10%

-10 0 10 20 30 40 50 60

Temperature (°.C)

Str

ain

σ = 150 MPa

Final cycle

Initial cycle

Fig. 1.13. Thermal cyclic loading (50 cycles) of a NiTi shape memory alloy wireunder constant load of 150 MPa [18].

Fig. 1.14. Pseudoelastic response of an as-received NiTi wire with Af =65 C, testedat a temperature of 70 C. Also shown is the stabilized pseudoelastic hysteresis loopafter 20 cycles.

Shape Memory Alloys (SMA) Marek Novotny

Email: novotny@ac.tut.fi

Juha Kilpi

Abstract

This report introduces Shape Memory Alloys, describes properties of SMA as an actuator and introduces some available commercial SMA actuator products.

Keywords: Shape Memory Alloy, active materials, actuator, microsystem technology

1. Introduction This section presents brief history of SMA actuators. Next in Section 1.2, the basic operation principle of SMA is given. Shape setting in NiTi alloys is discussed. The section ends with an introduction of a two-way Shape memory effect and superelasticity.

1.1 Brief history of SMA [1]

A Swedish physicist Arne Olander discovered “the Shape Memory Effect” (SME) in gold-cadmium (AuCd) alloy in 1932. The alloy could be deformed when cool and then heated to return to original “remembered” shape. The metal alloys with SME are called “Shape Memory Alloys” (SMA). In 1958, SME was demonstrated at the Brussels World’s Fair, where the SME was used to cyclically lift a load mass. Researchers of U.S. Naval Ordnance Laboratory found SME in nickel-titanium (NiTi) alloy in 1961 by accident, while studying the heat and corrosion resistance of NiTi. Today, the NiTi alloys are commonly referred to as “Nitinol”, for NiTi Naval Ordnance Laboratory.

The benefits of NiTi alloys, such as lower costs, smaller dangers (from health standpoint) and easier manufacturing and machining methods refreshed the interest in SME and its applications. In 1970’s, commercial products began to emerge. First devices were static, taking advantage of a single dimensional change, for example fasteners, couplings and electrical connectors. Then, SMA devices started to perform dynamic tasks as actuators. Ambient temperature-controlled valves and clutches were the first applications, later actuators with resistive heating and thus electrical control were proposed to be used in micro-robotics, for example. More sophisticated devices are studied continuously, for example [2, 3, 4].

1.2 Principle of operation [1]

Shape Memory Alloys, for example Ag-Cd, Au-Cd, Cu-Al-Ni, Cu-Sn, Cu-Zn-(X), In-Ti, Ni-Al, Ni-Ti, Fe-Pt, Mn-Cu and Fe-Mn-Si alloys, are a group of metallic materials having ability to return to a previously defined shape when subjected to appropriate thermal procedure.

Shape Memory Alloys, Introduction

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The SME occurs due to a temperature and stress dependent shift in the material’s crystalline structure between two different phases, martensite (low temperature phase) and austenite (high temperature phase). The temperature, where the phase transformation occurs, is called the transformation temperature. Figure 1 is a simplified representation of material’s crystalline arrangement during different phases.

Figure 1: Crystalline arrangement of SMA in different phases.

In austenite phase, the structure of the material is symmetrical; each “grain” of material is a cube with right angles (a). When the alloy cools, it forms the martensite phase and collapses to a structure with different shape (b). If an external stress is applied, the alloy will yield and deform to an alternate state (c). Now, if the alloy is heated again above the transformation temperature, the austenite phase will be formed and the structure of the material returns to the original “cubic” form (a), generating force/stress.

An example of an SMA wire is represented in Figure 2. If the wire is below the transformation temperature (and therefore in the martensite form), it can be stretched with an external stress. Now, if the wire is heated to austenite phase, it will generate force/stress and recover the original, shorter, shape.

Also, hysteresis and non-linear behaviour are seen from Figure 2. The change in the SMA crystalline structure is not thermodynamically reversible process due to internal frictions and creation of structural defects. When heated, SMA follows the upper curve, As is the temperature, where austenite phase starts to form and in Af the material is 100 % austenite. When the alloy cools, it follows the lower curve: Ms is the temperature, where martensite starts to form and in Mf the alloy is 100 % martensite.

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Figure 2: Contraction of an SMA wire as a function of temperature.

1.3 Shape setting in NiTi alloys [5]

The Shape Memory Effect must be “programmed” into the SMA alloys with an appropriate thermal procedure. Basically the procedure is simple; the alloy is formed into desired austenite form and heated into a specific temperature. The temperature and the duration of the heating depend on the alloy and the required properties.

For a NiTi alloy, a temperature of 400 °C and heating duration of 1…2 minutes can be sufficient, but generally 500 °C and over 5 minutes are used. Higher heat treatment times and temperatures will increase the actuation temperature of the element and often give a sharper thermal response, but may reduce the maximum output force.

Although straightforward procedure, the parameters for the heat treatment are critical and often require experimental determination before the requirements can be met.

1.4 Two-way Shape Memory Effect [6]

The ability of SMA to recover a specific shape upon heating and then return to an alternate shape when cooled (below the transformation temperature) is known as two-way shape memory. However, there are limitations that reduce the usability of the two-way effect, such as smaller strains (2 %), extremely low cooling transformation forces and unknown long-term fatigue and stability. Even slight overheating removes the SME in two-way devices.

Setting shapes in two-way SMAs is a more complex procedure than the one used with one-way SMAs.

1.5 Superelasticity [7]

SMA also shows a superelastic behaviour if deformed at a temperature which is slightly above their transformation temperatures. This effect is caused by the stress-induced formation of some martensite above its normal temperature. Because it has been formed

Shape Memory Alloys, Introduction

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above its normal temperature, the martensite reverts immediately to undeformed austenite as soon as the stress is removed. This process provides a very springy, "rubberlike" elasticity in these alloys.

Because the superelastic behaviour is not usable in actuators, it is not described in details. As an example, the superelastic alloys are used in eyeglass frames. Figure 3 presents DuraFLEX eyeglasses.

Figure 3: DuraFLEX eyeglasses.

2. SMA as an actuator The properties of SMA as an actuator can be divided into advantages and disadvantages rather clearly. On the other hand some properties must be categorized according to a specific application. Also the properties vary between different alloy compositions. The properties are discussed in the following Sections, from 3.1 to 3.8. The focus is on the NiTi alloy, because this alloy is the most widely used and considered as the most suitable alloy in engineering applications [1].

2.1 Force and Deformations

The greatest advantage of the SMA material is the availability of a large force from very small element dimensions and weight. Table 1 shows some properties of commercially available “Flexinol” NiTi alloy SMA wires, manufactured by DYNALLOY, Inc. [9]. It can be seen that a ≈0.38 mm (0.015”) diameter wire can generate a pull force of ≈2000 g (≈19.5 N), for example. This gives about 170 N/mm2 stress (force per cross-sectional area).

Table 1: Properties of Flexinol wire (NiTi alloy).

Diameter Size (Inches)

Resistance (Ohms/Inch)

MaximumPull

Force (gms.)

Approximate*Current at

Room Temperature

(mA)

Contraction*Time

(seconds)

Off Time 70° C

Wire** (seconds)

Off Time 90° C

Wire** (seconds)

0.0015 21.0 17 30 1 0.25 0.09 0.002 12.0 35 50 1 0.3 0.1 0.003 5.0 80 100 1 0.5 0.2 0.004 3.0 150 180 1 0.8 0.4 0.005 1.8 230 250 1 1.6 0.9 0.006 1.3 330 400 1 2.0 1.2

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0.008 0.8 590 610 1 3.5 2.2 0.010 0.5 930 1000 1 5.5 3.5 0.012 0.33 1250 1750 1 8.0 6.0 0.015 0.2 2000 2750 1 13.0 10.0

Theoretically, a force generated by any shape/size SMA element can be calculated from maximum stress generated by the SMA material.

SMA alloys provide a large deformation, compared to other active materials. Maximum deformation is approximately 7…8 % for NiTi element. The effects of cycling (repeated use) to maximum deformation are described is Section 2.5. Table 2 shows some properties of different alloys, manufactured by Advanced Materials and Technologies (AMT). It can be seen that the normal recommended deformation is from 3.2 % (NiTi) to only 0.8 % (Cu-Zn-Al).

Table 2: Properties of different SMA alloys (by AMT).

ITEM Ni-Ti Cu-Cu-Zn-Al Cu-Al-Ni

Melting point (°C) Density (Kg/m³) Electrical Resistivity (Ω *m*10E-6) Thermal Conductivity, RT (W/m*K) Thermal Expansion Coeff. (10E-6/K) Specific Heat (J/Kg*K) Transformation Enthalpy (J/Kg) E-modulus (GPa) UTS, mart. MPa) Elongation at Fracture, mart. (%) Fatigue Strength N=10E+6 (MPa) Grain size (m*10E-6) Transformation Temp. Range (°C.) Hysteresis (K) Max one-way memory (%) Normal two-way memory (%) Normal working Stress (MPa) Normal number of thermal cycles Max. Overheating Temp. (°C) Damping capacity (SDC %) Corrosion Resistance Biological Compatibility

1250 6450 0.5-1.1 10-18 6.6-10 490 28,000 95 800-1000 30-50 350 20-100 -100 to +11030 7 3.2 100-130 +100 000 400 20 Excellent Excellent

1020 7900 0.07-0.12 120 17 390 7,000 70-100 800-900 15 270 50-150 -200 to +110 15 4 .8 40 +10 000 150 85 Fair Bad

1050 7150 0.1-0.14 75 17 440 9,000 80-100 1000 8-10 350 30-100 -150 to +200 20 6 1 70 +5 000 300 20 Good Bad

2.2 One-way force

As an actuator, the SMA element can only provide force/displacement in one direction. For example, a wire that compresses when heated does not expand without external force, when the alloy cools down. This is one disadvantage of the SMA actuators. A bias (return)

Shape Memory Alloys, Introduction

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mechanism must be used, if actuator has to be returned to the original (cold) shape after the heating phase. Figure 4 shows possibilities for generating the bias force.

Figure 4: Bias mechanisms in SMA actuators.

The bias mechanism is usually implemented with a conventional spring, for example with a standard steel coil spring. The bias mechanism requires space, increases the weight of the actuator and the mechanical design becomes more complex. It must also be noted that the net output force decreases, because the force of the bias mechanism opposes the force of the SMA element.

If possible, a load force can be used as bias force. In Figure 4, gravity is used as an example of a load force as a bias force. The load force has to be large enough at all times, otherwise the actuator remains in the austenite position, even if heating is deactivated.

Another method to generate the bias force is to use an actuator that has SMA elements operating in both directions of movement. This is referred to as “an antagonistic SMA”. This provides output force to both directions, but the heating and cooling of opposing elements must be arranged properly. For example, if one element has been heated and then immediately after this an opposing element is heated, the first element resists the movement of the second, before the first element cools down enough. Also, if the elements are very close to each other, the heat transfer between elements can generate undesired forces.

There have been studies of “two-way” Shape Memory Effect that could provide force in both heating and cooling phases. This would remove the need for a bias mechanism. Due to restrictions of two-way memory (Section 1.4), it is recommended that one-way devices with return (bias) mechanism are preferred instead of two-way devices [7].

2.3 Cycling effects

Cycling (repeated use) affects the properties of the SMA. This must be considered when actuators are designed for a repeated/continuous use. Cycling causes the maximum available deformation, force and hysteresis to decrease, while the transformation temperatures increase gradually.

The reduction in the maximum strain and output force must be taken into account when actuators are designed. For NiTi alloys, only 2…3 % strain and stress level of 100...150 MPa are available after 100 000 cycles.

2.4 Hysteresis and non-linearity

SMA materials have a non-linear behaviour with a large hysteresis, as can be seen in Figure 2. This is a major setback when actuators are designed. If the movement of the

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actuator has to be controlled, for example the displacement of an actuator generating linear movement, hysteresis and non-linearity cause difficulties. Therefore, many SMA actuators are “on/off” controlled, having only two positions of movement. This is easily obtained with continuous heating to maintain totally austenite phase or continuous cooling to obtain totally martensite phase.

Amount of hysteresis depends on the alloy composition, as can be seen in Table 2. Typical values for hysteresis in NiTi alloys are 25…50 °C [10].

In some applications hysteresis can be beneficial, as in a temperature control thermostat. When temperature raises enough, the SMA deactivates heating or activates cooling. Hysteresis prevents immediate “on/off” toggling of heaters/coolers and creates a proper thermostat function.

2.5 Temperature control of SMA element

Because the SMA effect is based on the temperature changes of the SMA material, the SMA actuators must have a method for controlling the temperature of the SMA element. Heating and cooling solutions and their properties are described in following Sections, 2.6.1 to 2.6.3.

2.5.1 Heating of SMA element The heating of the SMA element can be accomplished with several methods by an electric current fed through the alloy, a separate heater element or heating with ambient material. These provide convenient and flexible possibilities for controlling the temperature of the alloy.

The heating with current (“Joule heating”) gives effective control over the temperature and therefore force and displacement. Although the concept is simple, it has two disadvantages. First, the resistance of the SMA is small (metal alloy). This causes the requirement for a large heating current, Table 1 shows some currents for different “Flexinol” wire sizes, for example 2.75 A is needed for a 0.38 mm wire. A current supply able to provide enough current increases the overall size and costs of the actuator system. Secondly, the heating current must flow through the SMA element, not through other conductive parts near or in contact with the SMA element. Therefore, the SMA must be electrically isolated from the surrounding environment. This causes special requirements for the components of the actuators.

Both DC and AC current can be used in heating. If AC is used, the frequency must be high enough to prevent oscillation in the SMA element temperature, which would cause oscillation of the actuator displacement and force. With AC, the heating effect depends on the root-mean-square (RMS) value of the current.

A separate heater element can overcome the difficulties of large currents used with the current heating method. A resistive heater element can provide enough power with smaller currents due to possibility to use larger voltage. On the other hand, a separate heater requires more components and additional space around the SMA element, also the total weight of the actuator increases. A heater element increases the cooling cycle time (Section 2.6.2) due to additional heated mass.

If the ambient material is used for heating (without any active elements), the SMA element operates according to the ambient temperature. This gives a possibility to use SMA as an ambient temperature controlled actuator, for example a heating thermostat controlling the

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heating or cooling of ambient material. This is a very effective method, because in this case the SMA operates as an integrated actuator and a sensor, without any electric connectors.

2.5.2 Cooling of SMA element The cooling of SMA element can be done with ambient material, requiring that the ambient temperature is lower than the transformation temperature range of the SMA element.

This method is useful, if the speed/band-width requirements are not critical. When the ambient temperature is close to the transformation temperatures, the cooling is slow. On the other hand, smaller heating current is needed to increase temperature to achieve the austenite phase. If the ambient temperature is much lower than the transformation temperatures, the cooling is quicker, but larger heating currents are needed.

Active cooling elements are needed if it is necessary to lower the temperature quickly or the ambient temperature is too high to achieve temperatures low enough to achieve martensite phase.

Forced convection cooling (with a fan, for example) is a relatively easy method for active cooling. Also cooling with moving liquid can be used in some applications. However, it must be noted that more powerful cooling system increases the required heating current, if the cooling is active continuously.

2.5.3 Peltier elements, integrated heating and cooling One method for achieving active heating and cooling capacity is to use Peltier elements. These elements can heat or cool the SMA element, depending on the polarity of the voltage fed into the Peltier element. This method is useful, if both heating and cooling cycles must be quick. On the other hand also Peltier elements require space and create additional weight to the actuator entity.

2.6 Raw material

The raw material for SMA elements is inexpensive, especially NiTi alloy having only two component metals. It must be noted that the actual price for a complete SMA actuator depends on the other components and devices needed to create a proper actuator. Current supplies, Peltier elements, required measurements/sensors and other components that must be used set the total price, not the SMA material/element.

The corrosion resistance of NiTi alloys is excellent (comparable to stainless steels), providing a possibility to use SMA in environment with high humidity or even water. Also the biological compatibility of NiTi is excellent.

3. Shape Memory Alloy device examples There are quite a few devices utilizing SMA commercially available. Some of these are described in Sections 3.1 to 3.6 to give a brief overview of possibilities.

Raw material for SMA elements is available from several companies, as well as ready-to-use (heat treated) SMA wires, expanding and contracting springs, and superelastic tubes. A list of manufacturers supplying SMA materials, elements or actuators is given in Section 3.7.

2235 Polvorosa Ave, San Leandro, CA 94577 Tel: (510) 483-2564 Fax: (510) 483-2032 E-mail: marketing@tiniaerospace.com Web: www.tiniaerospace.com

Shape Memory Alloys

Shape Memory Alloys (SMAs) refer to a group of materials which have the ability to return to a predetermined shape when heated. The shape memory effect is caused by a temperature dependent crystal structure. When an SMA is below its phase transformation temperature, it possesses a low yield strength crystallography referred to as Martensite (see Stress-Strain figure). While in this state, the material can be deformed into other shapes with relatively little force. The new shape is retained provided the material is kept below its transformation temperature. When heated above this temperature, the material reverts to its parent structure known as Austenite causing it to return to its original shape (see Phase Transformation figure). This phenomenon can be harnessed to provide a unique and powerful actuator. The most widely used shape memory material is an alloy of Nickel and Titanium called Nitinol. This particular alloy has excellent electrical and mechanical properties, long fatigue life, and high corrosion resistance. As an actuator, it is capable of up to 5% strain and 50,000 psi recovery stress, resulting in ~1 Joule/gm of work output. Nitinol is readily available in the form of wire, rod, and bar stock with transformation temperature in the range of -100º to +100º Celsius. More recently applications in Micro-Electro-Mechanical-Systems (MEMS) have led to the development of Nitinol in the form of sputter deposited thin film. For more information about Shape Memory Alloy and its applications, contact TiNi Aerospace at the address below.

STRESS-STRAIN CHARACTERISTICS

PHASE TRANSFORMATION

Properties of Nitinol Density 6.45 gm/cm3 0.23 lb/in3

Thermal Conductivity 10 W/moK 5.78 Btu/hr ftoF

Specific Heat 322 j/kgoK 0.08 Btu/lboF

Latent Heat 24,200 J/kg 10.4 Btu/lb

Ultimate Tensile Strength 750-960 Mpa 110-140 ksi

Elongation to Failure 15.5% 15.5 %

Yield Strength (Austenite) 560 Mpa 80 ksi

Young's Modulus (Austenite) 75 Gpa 11 Mpsi

Yield Strength (Martensite) 100 Mpa 15 ksi